TestU01 results
The Alphabit, Rabbit,
and SmallCrush tests are described below.
The Crush and
BigCrush tests are
described on separate pages.
All of these tests were run on the same set of samples which were
read directly from the
BitBabbler White devices
during this test run with Dieharder.
By capturing the stream of bits as it was read for that test we can
subject exactly the same 230GB of data to other testing to see if might
identify anything suspicious which Dieharder had missed.
Testing the
tests is just as important as testing the data if we are to have any
confidence in the results that they report to us, which is part of what
we'd like to demonstrate here too.
Alphabit battery test
The Alphabit battery was designed primarily for testing hardware random
number generators. It can be very quick to run on relatively small blocks
of data. On a 500MB sample, this test completes in well under 2 minutes.
On the same amount of data that Dieharder consumes though, it took just
under 13 hours to run - which is about 2 hours longer than it took to
extract these bits from the BitBabbler devices in real time and
analyse it with Dieharder in the runs that we did without folding.
To be fair, this battery does run nine separate tests over the entire
dataset, rewinding it to the beginning for the start of each of them, so
really it has processed more like 2TB of data (but to be picky, the
machine it ran on has more than one CPU, so it could have heavily
parallelised that too and saved a bunch of I/O waiting time if nothing
else). From those nine tests it produces 17 statistics. None of which
it flagged as being outside of its significance thresholds on this data,
though a couple are in the neighbourhood of them. A random stream of
bits is expected to have results that go right out to the very edges of
probability, but as always, more testing is warranted to determine if
that was just a pure chance result, or if it is a sign of some systemic
bias in the output.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Starting Alphabit: nb = 1971905953792
Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
***********************************************************
HOST = itb1, Linux
ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits
smultin_MultinomialBitsOver test:
-----------------------------------------------
N = 1972, n = 999952288, r = 0, s = 32, L = 2,
Sparse = FALSE
Number of bits = n = 999952288
Number of cells = 2^L = 4
Expected number per cell = 2.4998807e+08
Hashing = FALSE
For Delta > -1, we use the ChiSquare approximation
Correction factor of the ChiSquare:
Delta = 1, Mu = 5.0002391e-10, Sigma = 1
-----------------------------------------------
Test Results for Delta = 1.0000
Kolmogorov-Smirnov+ statistic = D+ : 7.27e-3
p-value of test : 0.81
Kolmogorov-Smirnov- statistic = D- : 0.020
p-value of test : 0.21
Anderson-Darling statistic = A2 : 0.83
p-value of test : 0.46
For the sum of the N observations, we use
the Normal approximation:
Standardized empirical mean : 0.19
p-value of test : 0.42
Standardized empirical correlation : -0.42
p-value of test : 0.66
-----------------------------------------------
CPU time used : 00:45:06.88
Generator state:
1971905911936 bits have been read.
***********************************************************
HOST = itb1, Linux
ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits
smultin_MultinomialBitsOver test:
-----------------------------------------------
N = 1972, n = 999952288, r = 0, s = 32, L = 4,
Sparse = FALSE
Number of bits = n = 999952288
Number of cells = 2^L = 16
Expected number per cell = 62497018
Hashing = FALSE
For Delta > -1, we use the ChiSquare approximation
Correction factor of the ChiSquare:
Delta = 1, Mu = 3.5001674e-09, Sigma = 1
-----------------------------------------------
Test Results for Delta = 1.0000
Kolmogorov-Smirnov+ statistic = D+ : 0.021
p-value of test : 0.16
Kolmogorov-Smirnov- statistic = D- : 2.69e-3
p-value of test : 0.97
Anderson-Darling statistic = A2 : 2.01
p-value of test : 0.09
For the sum of the N observations, we use
the Normal approximation:
Standardized empirical mean : -2.07
p-value of test : 0.98
Standardized empirical correlation : 0.70
p-value of test : 0.24
-----------------------------------------------
CPU time used : 00:44:01.22
Generator state:
1971905911936 bits have been read.
***********************************************************
HOST = itb1, Linux
ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits
smultin_MultinomialBitsOver test:
-----------------------------------------------
N = 1972, n = 999952288, r = 0, s = 32, L = 8,
Sparse = FALSE
Number of bits = n = 999952288
Number of cells = 2^L = 256
Expected number per cell = 3906063.6
Hashing = FALSE
For Delta > -1, we use the ChiSquare approximation
Correction factor of the ChiSquare:
Delta = 1, Mu = 6.3503037e-08, Sigma = 1
-----------------------------------------------
Test Results for Delta = 1.0000
Kolmogorov-Smirnov+ statistic = D+ : 0.022
p-value of test : 0.15
Kolmogorov-Smirnov- statistic = D- : 5.91e-3
p-value of test : 0.87
Anderson-Darling statistic = A2 : 1.26
p-value of test : 0.25
For the sum of the N observations, we use
the Normal approximation:
Standardized empirical mean : -1.23
p-value of test : 0.89
Standardized empirical correlation : -0.66
p-value of test : 0.75
-----------------------------------------------
CPU time used : 00:43:19.65
Generator state:
1971905911936 bits have been read.
***********************************************************
HOST = itb1, Linux
ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits
smultin_MultinomialBitsOver test:
-----------------------------------------------
N = 1972, n = 999952288, r = 0, s = 32, L = 16,
Sparse = FALSE
Number of bits = n = 999952288
Number of cells = 2^L = 65536
Expected number per cell = 15258.061
Hashing = FALSE
For Delta > -1, we use the ChiSquare approximation
Correction factor of the ChiSquare:
Delta = 1, Mu = 1.6384283e-05, Sigma = 1
-----------------------------------------------
Test Results for Delta = 1.0000
Kolmogorov-Smirnov+ statistic = D+ : 0.013
p-value of test : 0.52
Kolmogorov-Smirnov- statistic = D- : 9.92e-3
p-value of test : 0.67
Anderson-Darling statistic = A2 : 0.37
p-value of test : 0.87
For the sum of the N observations, we use
the Normal approximation:
Standardized empirical mean : 0.53
p-value of test : 0.30
Standardized empirical correlation : -0.74
p-value of test : 0.77
-----------------------------------------------
CPU time used : 02:21:17.22
Generator state:
1971905911936 bits have been read.
***********************************************************
HOST = itb1, Linux
ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits
sstring_HammingIndep test:
-----------------------------------------------
N = 62, n = 993904210, r = 0, s = 32, L = 16, d = 0
Counters with expected numbers >= 10
-----------------------------------------------
Kolmogorov-Smirnov+ statistic = D+ : 0.085
p-value of test : 0.38
Kolmogorov-Smirnov- statistic = D- : 0.17
p-value of test : 0.02
Anderson-Darling statistic = A2 : 1.74
p-value of test : 0.13
Test on the sum of all N observations
Number of degrees of freedom : 17174
Chi-square statistic :17387.63
p-value of test : 0.12
-----------------------------------------------
CPU time used : 00:29:09.68
Generator state:
1971905952640 bits have been read.
***********************************************************
HOST = itb1, Linux
ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits
sstring_HammingIndep test:
-----------------------------------------------
N = 62, n = 496952105, r = 0, s = 32, L = 32, d = 0
Counters with expected numbers >= 10
-----------------------------------------------
Kolmogorov-Smirnov+ statistic = D+ : 0.13
p-value of test : 0.13
Kolmogorov-Smirnov- statistic = D- : 0.050
p-value of test : 0.71
Anderson-Darling statistic = A2 : 0.89
p-value of test : 0.42
Test on the sum of all N observations
Number of degrees of freedom : 38998
Chi-square statistic :38762.64
p-value of test : 0.80
-----------------------------------------------
CPU time used : 00:24:24.45
Generator state:
1971905952640 bits have been read.
***********************************************************
HOST = itb1, Linux
ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits
sstring_HammingCorr test:
-----------------------------------------------
N = 62, n = 993904210, r = 0, s = 32, L = 32
-----------------------------------------------
Kolmogorov-Smirnov+ statistic = D+ : 0.017
p-value of test : 0.95
Kolmogorov-Smirnov- statistic = D- : 0.13
p-value of test : 0.12
Anderson-Darling statistic = A2 : 1.55
p-value of test : 0.17
Tests on the sum of all N observations
Standardized normal statistic : 1.56
p-value of test : 0.06
Sample variance : 0.98
p-value of test : 0.52
-----------------------------------------------
CPU time used : 00:24:17.36
Generator state:
1971905952640 bits have been read.
***********************************************************
HOST = itb1, Linux
ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits
swalk_RandomWalk1 test:
-----------------------------------------------
N = 31, n = 993904210, r = 0, s = 32, L0 = 64, L1 = 64
-----------------------------------------------
Test on the values of the Statistic H
Kolmogorov-Smirnov+ statistic = D+ : 0.042
p-value of test : 0.87
Kolmogorov-Smirnov- statistic = D- : 0.096
p-value of test : 0.53
Anderson-Darling statistic = A2 : 0.35
p-value of test : 0.90
Test on the sum of all N observations
Number of degrees of freedom : 1302
Chi-square statistic : 1328.85
p-value of test : 0.30
-----------------------------------------------
Test on the values of the Statistic M
Kolmogorov-Smirnov+ statistic = D+ : 0.073
p-value of test : 0.69
Kolmogorov-Smirnov- statistic = D- : 0.099
p-value of test : 0.51
Anderson-Darling statistic = A2 : 0.40
p-value of test : 0.85
Test on the sum of all N observations
Number of degrees of freedom : 1333
Chi-square statistic : 1345.20
p-value of test : 0.40
-----------------------------------------------
Test on the values of the Statistic J
Kolmogorov-Smirnov+ statistic = D+ : 0.12
p-value of test : 0.40
Kolmogorov-Smirnov- statistic = D- : 0.12
p-value of test : 0.39
Anderson-Darling statistic = A2 : 0.65
p-value of test : 0.60
Test on the sum of all N observations
Number of degrees of freedom : 992
Chi-square statistic : 967.02
p-value of test : 0.71
-----------------------------------------------
Test on the values of the Statistic R
Kolmogorov-Smirnov+ statistic = D+ : 0.079
p-value of test : 0.64
Kolmogorov-Smirnov- statistic = D- : 0.091
p-value of test : 0.56
Anderson-Darling statistic = A2 : 0.28
p-value of test : 0.95
Test on the sum of all N observations
Number of degrees of freedom : 930
Chi-square statistic : 933.63
p-value of test : 0.46
-----------------------------------------------
Test on the values of the Statistic C
Kolmogorov-Smirnov+ statistic = D+ : 0.14
p-value of test : 0.25
Kolmogorov-Smirnov- statistic = D- : 0.073
p-value of test : 0.69
Anderson-Darling statistic = A2 : 0.53
p-value of test : 0.72
Test on the sum of all N observations
Number of degrees of freedom : 651
Chi-square statistic : 632.65
p-value of test : 0.69
-----------------------------------------------
CPU time used : 03:39:58.87
Generator state:
1971905952640 bits have been read.
***********************************************************
HOST = itb1, Linux
ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits
swalk_RandomWalk1 test:
-----------------------------------------------
N = 7, n = 880315157, r = 0, s = 32, L0 = 320, L1 = 320
-----------------------------------------------
Test on the values of the Statistic H
Kolmogorov-Smirnov+ statistic = D+ : 1.18e-3
p-value of test : 0.9988
Kolmogorov-Smirnov- statistic = D- : 0.44
p-value of test : 0.05
Anderson-Darling statistic = A2 : 2.22
p-value of test : 0.07
Test on the sum of all N observations
Number of degrees of freedom : 686
Chi-square statistic : 769.09
p-value of test : 0.01
-----------------------------------------------
Test on the values of the Statistic M
Kolmogorov-Smirnov+ statistic = D+ : 0.22
p-value of test : 0.44
Kolmogorov-Smirnov- statistic = D- : 0.070
p-value of test : 0.90
Anderson-Darling statistic = A2 : 0.33
p-value of test : 0.91
Test on the sum of all N observations
Number of degrees of freedom : 693
Chi-square statistic : 675.13
p-value of test : 0.68
-----------------------------------------------
Test on the values of the Statistic J
Kolmogorov-Smirnov+ statistic = D+ : 0.078
p-value of test : 0.88
Kolmogorov-Smirnov- statistic = D- : 0.22
p-value of test : 0.43
Anderson-Darling statistic = A2 : 0.48
p-value of test : 0.76
Test on the sum of all N observations
Number of degrees of freedom : 1120
Chi-square statistic : 1150.30
p-value of test : 0.26
-----------------------------------------------
Test on the values of the Statistic R
Kolmogorov-Smirnov+ statistic = D+ : 0.33
p-value of test : 0.17
Kolmogorov-Smirnov- statistic = D- : 4.43e-3
p-value of test : 0.9954
Anderson-Darling statistic = A2 : 1.83
p-value of test : 0.12
Test on the sum of all N observations
Number of degrees of freedom : 595
Chi-square statistic : 531.47
p-value of test : 0.97
-----------------------------------------------
Test on the values of the Statistic C
Kolmogorov-Smirnov+ statistic = D+ : 0.15
p-value of test : 0.65
Kolmogorov-Smirnov- statistic = D- : 0.26
p-value of test : 0.34
Anderson-Darling statistic = A2 : 1.01
p-value of test : 0.35
Test on the sum of all N observations
Number of degrees of freedom : 350
Chi-square statistic : 379.05
p-value of test : 0.14
-----------------------------------------------
CPU time used : 03:28:03.08
Generator state:
1971905951680 bits have been read.
========= Summary results of Alphabit =========
Version: TestU01 1.2.3
File: dieharder-bbwhite-f1-20150505.bits
Number of bits: 1971905953792
Number of statistics: 17
Total CPU time: 12:59:38.48
All tests were passed
Rabbit battery test
The Rabbit battery is also largely focussed on testing binary data,
but some of its tests run with fixed parameters (including the number
of bits analysed) regardless of the number of bits we make available to
it. In practice we've had to cap the size of the data fed to it at 64MB
since in the TestU01-1.2.3 release a larger number of bits triggers a
numerical error in the svaria_AppearanceSpacings test which
then tries to consume all of the system RAM and doesn't end very well.
It runs 26 separate tests to produce 40 statistics on the data.
There is some overlap with the Alphabit battery
for the type of tests that are run, but most of them are run with
different parameters (though some of them do have less statistical power
when a large number of bits are available, because of it limiting the
maximum number of them that it will test in this battery).
In our testing so far, it has not been often that this battery will
flag an unusual result that no other test also caught, but in this
particular run, it did return one test statistic for which there was a
1 in 1818 chance that a random stream would have been more uniformly
distributed than the bits it analysed here – which was in fact the
only flagged result across all of the TestU01 batteries run on this set
of bits. Even BigCrush
didn't blink on this run. That gives us some confidence that this is
just a chance result, but like all weak results, the only way to resolve
that uncertainty is by conducting more and stronger testing.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Starting Rabbit: nb = 549755813888
Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
***********************************************************
HOST = itb1, Linux
ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits
smultin_MultinomialBitsOver test:
-----------------------------------------------
N = 30, n = 9999904, r = 0, s = 32, L = 38,
Sparse = TRUE
Number of bits = n = 9999904
Number of cells = 2^L = 274877906944
Expected number per cell = 1 / 27488.055
EColl = n^2 / (2k) = 181.8954479
Hashing = TRUE
Collision test
CollisionOver: density = n / k = 1 / 27488.05
Expected number of collisions = Mu = 181.89
-----------------------------------------------
Results of CollisionOver test:
POISSON approximation :
Expected number of collisions = N*Mu : 5456.76
Observed number of collisions : 5218
p-value of test : 0.9994 *****
-----------------------------
Total number of cells containing j balls
j = 0 : 8246037216418
j = 1 : 299986684
j = 2 : 5218
j = 3 : 0
j = 4 : 0
j = 5 : 0
-----------------------------------------------
CPU time used : 00:01:46.37
Generator state:
299997120 bits have been read.
***********************************************************
HOST = itb1, Linux
ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits
snpair_ClosePairsBitMatch test:
-----------------------------------------------
N = 25, n = 1999984, r = 0, t = 2
-----------------------------------------------
Max of all bit distances : 22.00
p-value of test : 0.51
-----------------------------------------------
CPU time used : 00:00:19.56
Generator state:
3199974400 bits have been read.
***********************************************************
HOST = itb1, Linux
ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits
snpair_ClosePairsBitMatch test:
-----------------------------------------------
N = 25, n = 999992, r = 0, t = 4
-----------------------------------------------
Max of all bit distances : 10.00
p-value of test : 0.51
-----------------------------------------------
CPU time used : 00:00:16.00
Generator state:
3199974400 bits have been read.
***********************************************************
HOST = itb1, Linux
ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits
svaria_AppearanceSpacings test:
-----------------------------------------------
N = 1, Q = 1908874353, K = 1908874353, r = 0, s = 30, L = 15
Sequences of n = (K + Q)L = 57266230590 bits
Q = 1908874353 initialization blocks
K = 1908874353 blocks for the test
the blocks have L = 15 bits
-----------------------------------------------
Normal statistic : -0.70
p-value of test : 0.76
-----------------------------------------------
CPU time used : 00:02:07.19
Generator state:
61083979264 bits have been read.
***********************************************************
HOST = itb1, Linux
ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits
scomp_LinearComp test:
-----------------------------------------------
N = 1, n = 300000, r = 0, s = 32
-----------------------------------------------
Number of degrees of freedom : 11
Chi2 statistic for size of jumps : 6.28
p-value of test : 0.85
-----------------------------------------------
Normal statistic for number of jumps : -0.23
p-value of test : 0.59
-----------------------------------------------
CPU time used : 00:01:06.81
Generator state:
300000 bits have been read.
***********************************************************
HOST = itb1, Linux
ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits
scomp_LempelZiv test:
-----------------------------------------------
N = 1, n = 268435456, r = 0, s = 32, k = 28
-----------------------------------------------
Normal statistic : -1.39
p-value of test : 0.92
-----------------------------------------------
CPU time used : 00:00:08.38
Generator state:
268435456 bits have been read.
***********************************************************
HOST = itb1, Linux
ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits
sspectral_Fourier1 test:
-----------------------------------------------
N = 1, n = 1048576, r = 0, s = 32, k = 20
-----------------------------------------------
Normal statistic : 0.98
p-value of test : 0.16
-----------------------------------------------
CPU time used : 00:00:02.45
Generator state:
1048576 bits have been read.
***********************************************************
HOST = itb1, Linux
ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits
sspectral_Fourier3 test:
-----------------------------------------------
N = 300000, n = 16384, r = 0, s = 32, k = 14
-----------------------------------------------
Kolmogorov-Smirnov+ statistic = D+ : 0.010
p-value of test : 0.40
Kolmogorov-Smirnov- statistic = D- : 3.11e-3
p-value of test : 0.92
Anderson-Darling statistic = A2 : 0.67
p-value of test : 0.58
-----------------------------------------------
CPU time used : 00:01:35.18
Generator state:
4924800000 bits have been read.
***********************************************************
HOST = itb1, Linux
ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits
sstring_LongestHeadRun test:
-----------------------------------------------
N = 1, n = 600, r = 0, s = 32, L = 166666656
-----------------------------------------------
Number of degrees of freedom : 8
Chi-square statistic : 6.54
p-value of test : 0.59
-----------------------------------------------
Global longest run of 1 : 36.00
p-value of test : 0.52
-----------------------------------------------
CPU time used : 00:07:42.75
Generator state:
99999993600 bits have been read.
***********************************************************
HOST = itb1, Linux
ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits
sstring_PeriodsInStrings test:
-----------------------------------------------
N = 5, n = 800000000, r = 0, s = 31
-----------------------------------------------
Kolmogorov-Smirnov+ statistic = D+ : 0.64
p-value of test : 7.7e-3
Kolmogorov-Smirnov- statistic = D- : 0.043
p-value of test : 0.95
Anderson-Darling statistic = A2 : 3.13
p-value of test : 0.03
Test on the sum of all N observations
Number of degrees of freedom : 1710
Chi-square statistic : 1587.01
p-value of test : 0.98
-----------------------------------------------
CPU time used : 00:02:41.10
Generator state:
128000000000 bits have been read.
***********************************************************
HOST = itb1, Linux
ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits
sstring_HammingWeight test:
-----------------------------------------------
N = 10, n = 954437176, r = 0, s = 32, L = 32
-----------------------------------------------
Kolmogorov-Smirnov+ statistic = D+ : 0.17
p-value of test : 0.50
Kolmogorov-Smirnov- statistic = D- : 0.22
p-value of test : 0.32
Anderson-Darling statistic = A2 : 0.94
p-value of test : 0.39
Test on the sum of all N observations
Number of degrees of freedom : 280
Chi-square statistic : 308.61
p-value of test : 0.12
-----------------------------------------------
CPU time used : 00:03:43.69
Generator state:
305419896320 bits have been read.
***********************************************************
HOST = itb1, Linux
ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits
sstring_HammingCorr test:
-----------------------------------------------
N = 10, n = 954437176, r = 0, s = 32, L = 32
-----------------------------------------------
Kolmogorov-Smirnov+ statistic = D+ : 0.091
p-value of test : 0.80
Kolmogorov-Smirnov- statistic = D- : 0.14
p-value of test : 0.62
Anderson-Darling statistic = A2 : 0.34
p-value of test : 0.90
Tests on the sum of all N observations
Standardized normal statistic : 0.17
p-value of test : 0.43
Sample variance : 1.52
p-value of test : 0.13
-----------------------------------------------
CPU time used : 00:03:50.78
Generator state:
305419896320 bits have been read.
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HOST = itb1, Linux
ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits
sstring_HammingCorr test:
-----------------------------------------------
N = 1, n = 954437176, r = 0, s = 32, L = 64
-----------------------------------------------
Normal statistic : -0.46
p-value of test : 0.68
-----------------------------------------------
CPU time used : 00:00:43.46
Generator state:
61083979264 bits have been read.
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HOST = itb1, Linux
ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits
sstring_HammingCorr test:
-----------------------------------------------
N = 1, n = 238609294, r = 0, s = 32, L = 128
-----------------------------------------------
Normal statistic : -0.80
p-value of test : 0.79
-----------------------------------------------
CPU time used : 00:00:22.15
Generator state:
30541989632 bits have been read.
***********************************************************
HOST = itb1, Linux
ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits
sstring_HammingIndep test:
-----------------------------------------------
N = 5, n = 954437176, r = 0, s = 32, L = 16, d = 0
Counters with expected numbers >= 10
-----------------------------------------------
Kolmogorov-Smirnov+ statistic = D+ : 0.091
p-value of test : 0.87
Kolmogorov-Smirnov- statistic = D- : 0.42
p-value of test : 0.13
Anderson-Darling statistic = A2 : 1.11
p-value of test : 0.30
Test on the sum of all N observations
Number of degrees of freedom : 1385
Chi-square statistic : 1450.18
p-value of test : 0.11
-----------------------------------------------
CPU time used : 00:02:16.19
Generator state:
152709948160 bits have been read.
***********************************************************
HOST = itb1, Linux
ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits
sstring_HammingIndep test:
-----------------------------------------------
N = 1, n = 477218588, r = 0, s = 32, L = 32, d = 0
Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom : 621
Chi-square statistic : 613.96
p-value of test : 0.57
-----------------------------------------------
CPU time used : 00:00:22.86
Generator state:
30541989632 bits have been read.
***********************************************************
HOST = itb1, Linux
ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits
sstring_HammingIndep test:
-----------------------------------------------
N = 1, n = 99882960, r = 0, s = 32, L = 64, d = 0
Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom : 1117
Chi-square statistic : 1174.87
p-value of test : 0.11
-----------------------------------------------
CPU time used : 00:00:09.50
Generator state:
12785018880 bits have been read.
***********************************************************
HOST = itb1, Linux
ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits
sstring_AutoCor test:
-----------------------------------------------
N = 100, n = 999555969, r = 0, s = 32, d = 1
-----------------------------------------------
Kolmogorov-Smirnov+ statistic = D+ : 0.055
p-value of test : 0.52
Kolmogorov-Smirnov- statistic = D- : 0.062
p-value of test : 0.45
Anderson-Darling statistic = A2 : 0.38
p-value of test : 0.87
Tests on the sum of all N observations
Standardized normal statistic : -0.096
p-value of test : 0.54
Sample variance : 1.01
p-value of test : 0.45
-----------------------------------------------
CPU time used : 00:02:35.27
Generator state:
99955600000 bits have been read.
***********************************************************
HOST = itb1, Linux
ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits
sstring_AutoCor test:
-----------------------------------------------
N = 100, n = 999555970, r = 0, s = 32, d = 2
-----------------------------------------------
Kolmogorov-Smirnov+ statistic = D+ : 0.071
p-value of test : 0.34
Kolmogorov-Smirnov- statistic = D- : 0.043
p-value of test : 0.67
Anderson-Darling statistic = A2 : 0.61
p-value of test : 0.64
Tests on the sum of all N observations
Standardized normal statistic : -0.35
p-value of test : 0.64
Sample variance : 1.15
p-value of test : 0.15
-----------------------------------------------
CPU time used : 00:02:35.36
Generator state:
99955600000 bits have been read.
***********************************************************
HOST = itb1, Linux
ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits
sstring_Run test:
-----------------------------------------------
N = 20, n = 999556025, r = 0, s = 32
-----------------------------------------------
Test results for the number of runs:
Kolmogorov-Smirnov+ statistic = D+ : 0.015
p-value of test : 0.98
Kolmogorov-Smirnov- statistic = D- : 0.18
p-value of test : 0.26
Anderson-Darling statistic = A2 : 1.12
p-value of test : 0.30
Test on the sum of all N observations
Number of degrees of freedom : 1040
Chi-square statistic : 1104.73
p-value of test : 0.08
-----------------------------------------------
Test results for the number of bits:
Kolmogorov-Smirnov+ statistic = D+ : 0.14
p-value of test : 0.40
Kolmogorov-Smirnov- statistic = D- : 0.11
p-value of test : 0.58
Anderson-Darling statistic = A2 : 0.46
p-value of test : 0.79
Tests on the sum of all N observations
Standardized normal statistic : -0.27
p-value of test : 0.61
Sample variance : 0.66
p-value of test : 0.86
-----------------------------------------------
CPU time used : 00:05:16.75
Generator state:
79964375392 bits have been read.
***********************************************************
HOST = itb1, Linux
ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits
smarsa_MatrixRank test:
-----------------------------------------------
N = 1, n = 50000000, r = 0, s = 32, L = 32, k = 32
-----------------------------------------------
Number of degrees of freedom : 4
Chi-square statistic : 2.68
p-value of test : 0.61
-----------------------------------------------
CPU time used : 00:04:08.36
Generator state:
51200000000 bits have been read.
***********************************************************
HOST = itb1, Linux
ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits
smarsa_MatrixRank test:
-----------------------------------------------
N = 1, n = 300000, r = 0, s = 32, L = 320, k = 320
-----------------------------------------------
Number of degrees of freedom : 4
Chi-square statistic : 5.06
p-value of test : 0.28
-----------------------------------------------
CPU time used : 00:03:28.96
Generator state:
30720000000 bits have been read.
***********************************************************
HOST = itb1, Linux
ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits
smarsa_MatrixRank test:
-----------------------------------------------
N = 1, n = 20000, r = 0, s = 32, L = 1024, k = 1024
-----------------------------------------------
Number of degrees of freedom : 3
Chi-square statistic : 1.83
p-value of test : 0.61
-----------------------------------------------
CPU time used : 00:04:12.55
Generator state:
20971520000 bits have been read.
***********************************************************
HOST = itb1, Linux
ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits
swalk_RandomWalk1 test:
-----------------------------------------------
N = 1, n = 500000000, r = 0, s = 32, L0 = 128, L1 = 128
-----------------------------------------------
Test on the values of the Statistic H
Number of degrees of freedom : 60
ChiSquare statistic : 61.89
p-value of test : 0.41
-----------------------------------------------
Test on the values of the Statistic M
Number of degrees of freedom : 61
ChiSquare statistic : 49.24
p-value of test : 0.86
-----------------------------------------------
Test on the values of the Statistic J
Number of degrees of freedom : 64
ChiSquare statistic : 87.50
p-value of test : 0.03
-----------------------------------------------
Test on the values of the Statistic R
Number of degrees of freedom : 48
ChiSquare statistic : 44.63
p-value of test : 0.61
-----------------------------------------------
Test on the values of the Statistic C
Number of degrees of freedom : 30
ChiSquare statistic : 21.91
p-value of test : 0.86
-----------------------------------------------
CPU time used : 00:06:52.71
Generator state:
64000000000 bits have been read.
***********************************************************
HOST = itb1, Linux
ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits
swalk_RandomWalk1 test:
-----------------------------------------------
N = 1, n = 50000000, r = 0, s = 32, L0 = 1024, L1 = 1024
-----------------------------------------------
Test on the values of the Statistic H
Number of degrees of freedom : 158
ChiSquare statistic : 127.78
p-value of test : 0.96
-----------------------------------------------
Test on the values of the Statistic M
Number of degrees of freedom : 158
ChiSquare statistic : 150.97
p-value of test : 0.64
-----------------------------------------------
Test on the values of the Statistic J
Number of degrees of freedom : 512
ChiSquare statistic : 537.38
p-value of test : 0.21
-----------------------------------------------
Test on the values of the Statistic R
Number of degrees of freedom : 147
ChiSquare statistic : 124.98
p-value of test : 0.91
-----------------------------------------------
Test on the values of the Statistic C
Number of degrees of freedom : 81
ChiSquare statistic : 55.23
p-value of test : 0.99
-----------------------------------------------
CPU time used : 00:05:22.17
Generator state:
51200000000 bits have been read.
***********************************************************
HOST = itb1, Linux
ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits
swalk_RandomWalk1 test:
-----------------------------------------------
N = 1, n = 5000000, r = 0, s = 32, L0 = 10016, L1 = 10016
-----------------------------------------------
Test on the values of the Statistic H
Number of degrees of freedom : 424
ChiSquare statistic : 413.94
p-value of test : 0.63
-----------------------------------------------
Test on the values of the Statistic M
Number of degrees of freedom : 424
ChiSquare statistic : 419.49
p-value of test : 0.55
-----------------------------------------------
Test on the values of the Statistic J
Number of degrees of freedom : 5008
ChiSquare statistic : 5165.83
p-value of test : 0.06
-----------------------------------------------
Test on the values of the Statistic R
Number of degrees of freedom : 416
ChiSquare statistic : 394.34
p-value of test : 0.77
-----------------------------------------------
Test on the values of the Statistic C
Number of degrees of freedom : 219
ChiSquare statistic : 198.03
p-value of test : 0.84
-----------------------------------------------
CPU time used : 00:05:11.69
Generator state:
50080000000 bits have been read.
========= Summary results of Rabbit =========
Version: TestU01 1.2.3
File: dieharder-bbwhite-f1-20150505.bits
Number of bits: 549755813888
Number of statistics: 40
Total CPU time: 01:08:58.65
The following tests gave p-values outside [0.001, 0.9990]:
(eps means a value < 1.0e-300):
(eps1 means a value < 1.0e-15):
Test p-value
----------------------------------------------
1 MultinomialBitsOver 0.9994
----------------------------------------------
All other tests were passed
SmallCrush battery test
The Crush series of tests are mostly designed to destroy PRNGs and
largely focus on random numbers in the interval [0,1)
rather than on bits, though they do include bit string tests too.
Random numbers in that interval are created from our raw bitstream by
taking non-overlapping blocks of 32 bits as an unsigned integer and
dividing them by 232 to return a double precision floating
point value.
The SmallCrush battery is a very quick test, most commonly used to
gauge if it is even worth running the heavier tests. It does however
run some of the tests with slightly different parameters and due to the
ordering of the tests will also run them on a different part of the
bitstream too. Since it also completes almost instantly we do include
it in the TestU01 runs that we do. In this run, it unsurprisingly fails
to tell us anything that we didn't already know from the previous tests
on this set of bits – that if they are not actually random, we
still don't yet have a test that can prove it to us.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Starting SmallCrush
Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
***********************************************************
HOST = itb1, Linux
ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits
smarsa_BirthdaySpacings test:
-----------------------------------------------
N = 1, n = 5000000, r = 0, d = 1073741824, t = 2, p = 1
Number of cells = d^t = 1152921504606846976
Lambda = Poisson mean = 27.1051
----------------------------------------------------
Total expected number = N*Lambda : 27.11
Total observed number : 24
p-value of test : 0.68
-----------------------------------------------
CPU time used : 00:00:01.03
Generator state:
320000000 bits have been read.
***********************************************************
Test sknuth_Collision calling smultin_Multinomial
***********************************************************
HOST = itb1, Linux
ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits
smultin_Multinomial test:
-----------------------------------------------
N = 1, n = 5000000, r = 0, d = 65536, t = 2,
Sparse = TRUE
GenerCell = smultin_GenerCellSerial
Number of cells = d^t = 4294967296
Expected number per cell = 1 / 858.99346
EColl = n^2 / (2k) = 2910.383046
Hashing = TRUE
Collision test, Mu = 2909.2534, Sigma = 53.8957
-----------------------------------------------
Test Results for Collisions
Expected number of collisions = Mu : 2909.25
Observed number of collisions : 2873
p-value of test : 0.75
-----------------------------
Total number of cells containing j balls
j = 0 : 4289970169
j = 1 : 4994255
j = 2 : 2871
j = 3 : 1
j = 4 : 0
j = 5 : 0
-----------------------------------------------
CPU time used : 00:00:00.91
Generator state:
640000000 bits have been read.
***********************************************************
HOST = itb1, Linux
ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits
sknuth_Gap test:
-----------------------------------------------
N = 1, n = 200000, r = 22, Alpha = 0, Beta = 0.00390625
-----------------------------------------------
Number of degrees of freedom : 1114
Chi-square statistic : 1074.84
p-value of test : 0.80
-----------------------------------------------
CPU time used : 00:00:00.67
Generator state:
2276755360 bits have been read.
***********************************************************
HOST = itb1, Linux
ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits
sknuth_SimpPoker test:
-----------------------------------------------
N = 1, n = 400000, r = 24, d = 64, k = 64
-----------------------------------------------
Number of degrees of freedom : 19
Chi-square statistic : 25.52
p-value of test : 0.14
-----------------------------------------------
CPU time used : 00:00:00.71
Generator state:
3095955360 bits have been read.
***********************************************************
HOST = itb1, Linux
ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits
sknuth_CouponCollector test:
-----------------------------------------------
N = 1, n = 500000, r = 26, d = 16
-----------------------------------------------
Number of degrees of freedom : 44
Chi-square statistic : 31.12
p-value of test : 0.93
-----------------------------------------------
CPU time used : 00:00:00.46
Generator state:
3886034112 bits have been read.
***********************************************************
HOST = itb1, Linux
ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits
sknuth_MaxOft test:
-----------------------------------------------
N = 1, n = 2000000, r = 0, d = 100000, t = 6
Number of categories = 100000
Expected number per category = 20.00
-----------------------------------------------
Number of degrees of freedom : 99999
Chi-square statistic :99415.90
p-value of test : 0.90
-----------------------------------------------
Anderson-Darling statistic : 0.20
p-value of test : 0.80
-----------------------------------------------
CPU time used : 00:00:00.71
Generator state:
4270034112 bits have been read.
***********************************************************
HOST = itb1, Linux
ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits
svaria_WeightDistrib test:
-----------------------------------------------
N = 1, n = 200000, r = 27, k = 256, Alpha = 0, Beta = 0.125
-----------------------------------------------
Number of degrees of freedom : 41
Chi-square statistic : 40.71
p-value of test : 0.48
-----------------------------------------------
CPU time used : 00:00:00.71
Generator state:
5908434112 bits have been read.
***********************************************************
HOST = itb1, Linux
ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits
smarsa_MatrixRank test:
-----------------------------------------------
N = 1, n = 20000, r = 20, s = 10, L = 60, k = 60
-----------------------------------------------
Number of degrees of freedom : 3
Chi-square statistic : 2.99
p-value of test : 0.39
-----------------------------------------------
CPU time used : 00:00:00.42
Generator state:
6138834112 bits have been read.
***********************************************************
HOST = itb1, Linux
ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits
sstring_HammingIndep test:
-----------------------------------------------
N = 1, n = 500000, r = 20, s = 10, L = 300, d = 0
Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom : 2209
Chi-square statistic : 2254.09
p-value of test : 0.25
-----------------------------------------------
CPU time used : 00:00:00.62
Generator state:
7098834112 bits have been read.
***********************************************************
HOST = itb1, Linux
ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits
swalk_RandomWalk1 test:
-----------------------------------------------
N = 1, n = 1000000, r = 0, s = 30, L0 = 150, L1 = 150
-----------------------------------------------
Test on the values of the Statistic H
Number of degrees of freedom : 52
ChiSquare statistic : 41.68
p-value of test : 0.85
-----------------------------------------------
Test on the values of the Statistic M
Number of degrees of freedom : 52
ChiSquare statistic : 50.11
p-value of test : 0.55
-----------------------------------------------
Test on the values of the Statistic J
Number of degrees of freedom : 75
ChiSquare statistic : 80.99
p-value of test : 0.30
-----------------------------------------------
Test on the values of the Statistic R
Number of degrees of freedom : 44
ChiSquare statistic : 56.81
p-value of test : 0.09
-----------------------------------------------
Test on the values of the Statistic C
Number of degrees of freedom : 26
ChiSquare statistic : 22.13
p-value of test : 0.68
-----------------------------------------------
CPU time used : 00:00:01.00
Generator state:
7258834112 bits have been read.
========= Summary results of SmallCrush =========
Version: TestU01 1.2.3
Generator: ufile_CreateReadBin
Number of statistics: 15
Total CPU time: 00:00:07.29
All tests were passed