TestU01 results

Crush battery test

The Crush battery of tests is a fairly formidable gauntlet to run. It chews up about half as many bits as Dieharder, and only takes about half an hour to run on even a moderately fast modern machine, but we've seen it catch things that seemed to get past Dieharder, at least at its default test power settings. We confirmed those were real because they also didn't get past some of our other tests once enough bits were accumulated by them to make the very small biases which were present become statistically significant, but it emphasised the value of regularly using this test to assess the output of the BitBabbler devices, despite it ostensibly being more oriented to finding the flaws in algorithmic PRNGs.

In this particular run, TestU01 does not flag any result as being outside of its significance thresholds, but a careful examination of the detailed results shows there is one test statistic which is beyond the normal Dieharder threshold for being considered an uncertain result (with a 1 in 454 chance that a random sample would exceed it), and a couple more which are fairly close to, but still inside that limit.

As always, not much can be concluded from the results of just a single test run (unless that test conclusively shows failure), but the more uncertain results should be singled out for special attention in subsequent runs to confirm they really are a chance result as expected and not a genuinely systemic weakness in the RNG.

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx Starting Crush Version: TestU01 1.2.3 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx *********************************************************** Test smarsa_SerialOver calling smultin_MultinomialOver *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smultin_MultinomialOver test: ----------------------------------------------- N = 1, n = 500000000, r = 0, d = 4096, t = 2, Sparse = FALSE GenerCell = smultin_GenerCellSerial Number of cells = d^t = 16777216 Expected number per cell = 29.802322 Hashing = FALSE For Delta > -1, we use the ChiSquare approximation Correction factor of the ChiSquare: Delta = 1, Mu = 0.01677312, Sigma = 1 ----------------------------------------------- Test Results for Delta = 1.0000 Number of degrees of freedom : 16773120 Value of the statistic : 1.68e+7 p-value of test : 0.05 ----------------------------------------------- CPU time used : 00:00:41.99 Generator state: 16000000000 bits have been read. *********************************************************** Test smarsa_SerialOver calling smultin_MultinomialOver *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smultin_MultinomialOver test: ----------------------------------------------- N = 1, n = 300000000, r = 0, d = 64, t = 4, Sparse = FALSE GenerCell = smultin_GenerCellSerial Number of cells = d^t = 16777216 Expected number per cell = 17.881393 Hashing = FALSE For Delta > -1, we use the ChiSquare approximation Correction factor of the ChiSquare: Delta = 1, Mu = 0.027525119, Sigma = 1 ----------------------------------------------- Test Results for Delta = 1.0000 Number of degrees of freedom : 16515072 Value of the statistic : 1.65e+7 p-value of test : 0.82 ----------------------------------------------- CPU time used : 00:00:26.04 Generator state: 25600000000 bits have been read. *********************************************************** Test smarsa_CollisionOver calling smultin_MultinomialOver *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smultin_MultinomialOver test: ----------------------------------------------- N = 10, n = 10000000, r = 0, d = 1048576, t = 2, Sparse = TRUE GenerCell = smultin_GenerCellSerial Number of cells = d^t = 1099511627776 Expected number per cell = 1 / 109951.16 EColl = n^2 / (2k) = 45.47473509 Hashing = TRUE Collision test CollisionOver: density = n / k = 1 / 109951.16 Expected number of collisions = Mu = 45.47 ----------------------------------------------- Results of CollisionOver test: POISSON approximation : Expected number of collisions = N*Mu : 454.75 Observed number of collisions : 443 p-value of test : 0.70 ----------------------------- Total number of cells containing j balls j = 0 : 10995016278203 j = 1 : 99999114 j = 2 : 443 j = 3 : 0 j = 4 : 0 j = 5 : 0 ----------------------------------------------- CPU time used : 00:00:28.23 Generator state: 28800000000 bits have been read. *********************************************************** Test smarsa_CollisionOver calling smultin_MultinomialOver *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smultin_MultinomialOver test: ----------------------------------------------- N = 10, n = 10000000, r = 10, d = 1048576, t = 2, Sparse = TRUE GenerCell = smultin_GenerCellSerial Number of cells = d^t = 1099511627776 Expected number per cell = 1 / 109951.16 EColl = n^2 / (2k) = 45.47473509 Hashing = TRUE Collision test CollisionOver: density = n / k = 1 / 109951.16 Expected number of collisions = Mu = 45.47 ----------------------------------------------- Results of CollisionOver test: POISSON approximation : Expected number of collisions = N*Mu : 454.75 Observed number of collisions : 469 p-value of test : 0.26 ----------------------------- Total number of cells containing j balls j = 0 : 10995016278229 j = 1 : 99999062 j = 2 : 469 j = 3 : 0 j = 4 : 0 j = 5 : 0 ----------------------------------------------- CPU time used : 00:00:28.03 Generator state: 32000000000 bits have been read. *********************************************************** Test smarsa_CollisionOver calling smultin_MultinomialOver *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smultin_MultinomialOver test: ----------------------------------------------- N = 10, n = 10000000, r = 0, d = 1024, t = 4, Sparse = TRUE GenerCell = smultin_GenerCellSerial Number of cells = d^t = 1099511627776 Expected number per cell = 1 / 109951.16 EColl = n^2 / (2k) = 45.47473509 Hashing = TRUE Collision test CollisionOver: density = n / k = 1 / 109951.16 Expected number of collisions = Mu = 45.47 ----------------------------------------------- Results of CollisionOver test: POISSON approximation : Expected number of collisions = N*Mu : 454.75 Observed number of collisions : 448 p-value of test : 0.61 ----------------------------- Total number of cells containing j balls j = 0 : 10995016278208 j = 1 : 99999104 j = 2 : 448 j = 3 : 0 j = 4 : 0 j = 5 : 0 ----------------------------------------------- CPU time used : 00:00:36.28 Generator state: 35200000000 bits have been read. *********************************************************** Test smarsa_CollisionOver calling smultin_MultinomialOver *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smultin_MultinomialOver test: ----------------------------------------------- N = 10, n = 10000000, r = 20, d = 1024, t = 4, Sparse = TRUE GenerCell = smultin_GenerCellSerial Number of cells = d^t = 1099511627776 Expected number per cell = 1 / 109951.16 EColl = n^2 / (2k) = 45.47473509 Hashing = TRUE Collision test CollisionOver: density = n / k = 1 / 109951.16 Expected number of collisions = Mu = 45.47 ----------------------------------------------- Results of CollisionOver test: POISSON approximation : Expected number of collisions = N*Mu : 454.75 Observed number of collisions : 434 p-value of test : 0.83 ----------------------------- Total number of cells containing j balls j = 0 : 10995016278194 j = 1 : 99999132 j = 2 : 434 j = 3 : 0 j = 4 : 0 j = 5 : 0 ----------------------------------------------- CPU time used : 00:00:36.34 Generator state: 38400000000 bits have been read. *********************************************************** Test smarsa_CollisionOver calling smultin_MultinomialOver *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smultin_MultinomialOver test: ----------------------------------------------- N = 10, n = 10000000, r = 0, d = 32, t = 8, Sparse = TRUE GenerCell = smultin_GenerCellSerial Number of cells = d^t = 1099511627776 Expected number per cell = 1 / 109951.16 EColl = n^2 / (2k) = 45.47473509 Hashing = TRUE Collision test CollisionOver: density = n / k = 1 / 109951.16 Expected number of collisions = Mu = 45.47 ----------------------------------------------- Results of CollisionOver test: POISSON approximation : Expected number of collisions = N*Mu : 454.75 Observed number of collisions : 442 p-value of test : 0.72 ----------------------------- Total number of cells containing j balls j = 0 : 10995016278202 j = 1 : 99999116 j = 2 : 442 j = 3 : 0 j = 4 : 0 j = 5 : 0 ----------------------------------------------- CPU time used : 00:00:37.12 Generator state: 41600000000 bits have been read. *********************************************************** Test smarsa_CollisionOver calling smultin_MultinomialOver *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smultin_MultinomialOver test: ----------------------------------------------- N = 10, n = 10000000, r = 25, d = 32, t = 8, Sparse = TRUE GenerCell = smultin_GenerCellSerial Number of cells = d^t = 1099511627776 Expected number per cell = 1 / 109951.16 EColl = n^2 / (2k) = 45.47473509 Hashing = TRUE Collision test CollisionOver: density = n / k = 1 / 109951.16 Expected number of collisions = Mu = 45.47 ----------------------------------------------- Results of CollisionOver test: POISSON approximation : Expected number of collisions = N*Mu : 454.75 Observed number of collisions : 442 p-value of test : 0.72 ----------------------------- Total number of cells containing j balls j = 0 : 10995016278202 j = 1 : 99999116 j = 2 : 442 j = 3 : 0 j = 4 : 0 j = 5 : 0 ----------------------------------------------- CPU time used : 00:00:37.64 Generator state: 44800000000 bits have been read. *********************************************************** Test smarsa_CollisionOver calling smultin_MultinomialOver *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smultin_MultinomialOver test: ----------------------------------------------- N = 10, n = 10000000, r = 0, d = 4, t = 20, Sparse = TRUE GenerCell = smultin_GenerCellSerial Number of cells = d^t = 1099511627776 Expected number per cell = 1 / 109951.16 EColl = n^2 / (2k) = 45.47473509 Hashing = TRUE Collision test CollisionOver: density = n / k = 1 / 109951.16 Expected number of collisions = Mu = 45.47 ----------------------------------------------- Results of CollisionOver test: POISSON approximation : Expected number of collisions = N*Mu : 454.74 Observed number of collisions : 459 p-value of test : 0.43 ----------------------------- Total number of cells containing j balls j = 0 : 10995016278219 j = 1 : 99999082 j = 2 : 459 j = 3 : 0 j = 4 : 0 j = 5 : 0 ----------------------------------------------- CPU time used : 00:00:36.00 Generator state: 48000000000 bits have been read. *********************************************************** Test smarsa_CollisionOver calling smultin_MultinomialOver *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smultin_MultinomialOver test: ----------------------------------------------- N = 10, n = 10000000, r = 28, d = 4, t = 20, Sparse = TRUE GenerCell = smultin_GenerCellSerial Number of cells = d^t = 1099511627776 Expected number per cell = 1 / 109951.16 EColl = n^2 / (2k) = 45.47473509 Hashing = TRUE Collision test CollisionOver: density = n / k = 1 / 109951.16 Expected number of collisions = Mu = 45.47 ----------------------------------------------- Results of CollisionOver test: POISSON approximation : Expected number of collisions = N*Mu : 454.74 Observed number of collisions : 497 p-value of test : 0.03 ----------------------------- Total number of cells containing j balls j = 0 : 10995016278257 j = 1 : 99999006 j = 2 : 497 j = 3 : 0 j = 4 : 0 j = 5 : 0 ----------------------------------------------- CPU time used : 00:00:36.35 Generator state: 51200000000 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smarsa_BirthdaySpacings test: ----------------------------------------------- N = 5, n = 20000000, r = 0, d = 2147483648, t = 2, p = 1 Number of cells = d^t = 4611686018427387904 Lambda = Poisson mean = 433.6809 ---------------------------------------------------- Total expected number = N*Lambda : 2168.40 Total observed number : 2253 p-value of test : 0.04 ----------------------------------------------- CPU time used : 00:00:21.85 Generator state: 57600000000 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smarsa_BirthdaySpacings test: ----------------------------------------------- N = 5, n = 20000000, r = 0, d = 2097152, t = 3, p = 1 Number of cells = d^t = 9223372036854775808 Lambda = Poisson mean = 216.8404 ---------------------------------------------------- Total expected number = N*Lambda : 1084.20 Total observed number : 1061 p-value of test : 0.75 ----------------------------------------------- CPU time used : 00:00:23.11 Generator state: 67200000000 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smarsa_BirthdaySpacings test: ----------------------------------------------- N = 5, n = 20000000, r = 0, d = 65536, t = 4, p = 1 Number of cells = d^t = 18446744073709551616 Lambda = Poisson mean = 108.4202 ---------------------------------------------------- Total expected number = N*Lambda : 542.10 Total observed number : 566 p-value of test : 0.16 ----------------------------------------------- CPU time used : 00:00:24.38 Generator state: 80000000000 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smarsa_BirthdaySpacings test: ----------------------------------------------- N = 3, n = 20000000, r = 0, d = 512, t = 7, p = 1 Number of cells = d^t = 9223372036854775808 Lambda = Poisson mean = 216.8404 ---------------------------------------------------- Total expected number = N*Lambda : 650.52 Total observed number : 636 p-value of test : 0.71 ----------------------------------------------- CPU time used : 00:00:16.94 Generator state: 93440000000 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smarsa_BirthdaySpacings test: ----------------------------------------------- N = 3, n = 20000000, r = 7, d = 512, t = 7, p = 1 Number of cells = d^t = 9223372036854775808 Lambda = Poisson mean = 216.8404 ---------------------------------------------------- Total expected number = N*Lambda : 650.52 Total observed number : 645 p-value of test : 0.58 ----------------------------------------------- CPU time used : 00:00:17.56 Generator state: 106880000000 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smarsa_BirthdaySpacings test: ----------------------------------------------- N = 3, n = 20000000, r = 14, d = 256, t = 8, p = 1 Number of cells = d^t = 18446744073709551616 Lambda = Poisson mean = 108.4202 ---------------------------------------------------- Total expected number = N*Lambda : 325.26 Total observed number : 316 p-value of test : 0.68 ----------------------------------------------- CPU time used : 00:00:18.39 Generator state: 122240000000 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smarsa_BirthdaySpacings test: ----------------------------------------------- N = 3, n = 20000000, r = 22, d = 256, t = 8, p = 1 Number of cells = d^t = 18446744073709551616 Lambda = Poisson mean = 108.4202 ---------------------------------------------------- Total expected number = N*Lambda : 325.26 Total observed number : 328 p-value of test : 0.45 ----------------------------------------------- CPU time used : 00:00:18.43 Generator state: 137600000000 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits snpair_ClosePairs test: ----------------------------------------------- N = 10, n = 2000000, r = 0, t = 2, p = 0, m = 30, Torus = TRUE --------------------------------------- Test based on the 2 nearest points (NP): Stat. AD on the N values (NP) : 0.87 p-value of test : 0.43 A2 test based on the spacings between the successive jump times of process Y_n(t): A2 test on the values of A2 (m-NP) : 0.99 p-value of test : 0.36 Test on the Nm values of W_{n,i}(mNP1): 1.13 p-value of test : 0.30 Test on the jump times of Y (superposition of Yn): Expected number of jumps of Y = mN : 300 Number of jumps of Y : 312 p-value of test : 0.25 Stat. AD (mNP2) : 0.65 p-value of test : 0.61 ----------------------------------------------- CPU time used : 00:00:07.91 Generator state: 138880000000 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits snpair_ClosePairs test: ----------------------------------------------- N = 10, n = 2000000, r = 0, t = 3, p = 0, m = 30, Torus = TRUE --------------------------------------- Test based on the 2 nearest points (NP): Stat. AD on the N values (NP) : 0.59 p-value of test : 0.66 A2 test based on the spacings between the successive jump times of process Y_n(t): A2 test on the values of A2 (m-NP) : 1.48 p-value of test : 0.18 Test on the Nm values of W_{n,i}(mNP1): 0.88 p-value of test : 0.43 Test on the jump times of Y (superposition of Yn): Expected number of jumps of Y = mN : 300 Number of jumps of Y : 317 p-value of test : 0.17 Stat. AD (mNP2) : 1.14 p-value of test : 0.29 Stat. AD after spacings (mNP2-S) : 1.27 p-value of test : 0.24 ----------------------------------------------- CPU time used : 00:00:11.68 Generator state: 140800000000 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits snpair_ClosePairs test: ----------------------------------------------- N = 5, n = 2000000, r = 0, t = 7, p = 0, m = 30, Torus = TRUE --------------------------------------- Test based on the 2 nearest points (NP): Stat. AD on the N values (NP) : 0.31 p-value of test : 0.93 A2 test based on the spacings between the successive jump times of process Y_n(t): A2 test on the values of A2 (m-NP) : 0.55 p-value of test : 0.68 Test on the Nm values of W_{n,i}(mNP1): 0.68 p-value of test : 0.57 Test on the jump times of Y (superposition of Yn): Expected number of jumps of Y = mN : 150 Number of jumps of Y : 157 p-value of test : 0.29 Stat. AD (mNP2) : 0.53 p-value of test : 0.71 Stat. AD after spacings (mNP2-S) : 0.48 p-value of test : 0.76 ----------------------------------------------- CPU time used : 00:00:20.87 Generator state: 143040000000 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits snpair_ClosePairsBitMatch test: ----------------------------------------------- N = 4, n = 4000000, r = 0, t = 2 ----------------------------------------------- Max of all bit distances : 21.00 p-value of test : 0.84 ----------------------------------------------- CPU time used : 00:00:08.37 Generator state: 144064000000 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits snpair_ClosePairsBitMatch test: ----------------------------------------------- N = 2, n = 4000000, r = 0, t = 4 ----------------------------------------------- Max of all bit distances : 11.00 p-value of test : 0.06 ----------------------------------------------- CPU time used : 00:00:07.64 Generator state: 145088000000 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sknuth_SimpPoker test: ----------------------------------------------- N = 1, n = 40000000, r = 0, d = 16, k = 16 ----------------------------------------------- Number of degrees of freedom : 12 Chi-square statistic : 9.92 p-value of test : 0.62 ----------------------------------------------- CPU time used : 00:00:14.92 Generator state: 165568000000 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sknuth_SimpPoker test: ----------------------------------------------- N = 1, n = 40000000, r = 26, d = 16, k = 16 ----------------------------------------------- Number of degrees of freedom : 12 Chi-square statistic : 12.75 p-value of test : 0.39 ----------------------------------------------- CPU time used : 00:00:17.91 Generator state: 186048000000 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sknuth_SimpPoker test: ----------------------------------------------- N = 1, n = 10000000, r = 0, d = 64, k = 64 ----------------------------------------------- Number of degrees of freedom : 23 Chi-square statistic : 38.77 p-value of test : 0.02 ----------------------------------------------- CPU time used : 00:00:15.04 Generator state: 206528000000 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sknuth_SimpPoker test: ----------------------------------------------- N = 1, n = 10000000, r = 24, d = 64, k = 64 ----------------------------------------------- Number of degrees of freedom : 23 Chi-square statistic : 27.52 p-value of test : 0.23 ----------------------------------------------- CPU time used : 00:00:18.26 Generator state: 227008000000 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sknuth_CouponCollector test: ----------------------------------------------- N = 1, n = 40000000, r = 0, d = 4 ----------------------------------------------- Number of degrees of freedom : 51 Chi-square statistic : 53.05 p-value of test : 0.39 ----------------------------------------------- CPU time used : 00:00:06.12 Generator state: 237673711296 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sknuth_CouponCollector test: ----------------------------------------------- N = 1, n = 40000000, r = 28, d = 4 ----------------------------------------------- Number of degrees of freedom : 51 Chi-square statistic : 68.27 p-value of test : 0.05 ----------------------------------------------- CPU time used : 00:00:07.08 Generator state: 248340156928 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sknuth_CouponCollector test: ----------------------------------------------- N = 1, n = 10000000, r = 0, d = 16 ----------------------------------------------- Number of degrees of freedom : 46 Chi-square statistic : 41.60 p-value of test : 0.66 ----------------------------------------------- CPU time used : 00:00:08.54 Generator state: 264136889248 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sknuth_CouponCollector test: ----------------------------------------------- N = 1, n = 10000000, r = 26, d = 16 ----------------------------------------------- Number of degrees of freedom : 46 Chi-square statistic : 56.21 p-value of test : 0.14 ----------------------------------------------- CPU time used : 00:00:09.75 Generator state: 279934758208 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sknuth_Gap test: ----------------------------------------------- N = 1, n = 100000000, r = 0, Alpha = 0, Beta = 0.125 ----------------------------------------------- Number of degrees of freedom : 106 Chi-square statistic : 92.97 p-value of test : 0.81 ----------------------------------------------- CPU time used : 00:00:10.74 Generator state: 305535568576 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sknuth_Gap test: ----------------------------------------------- N = 1, n = 100000000, r = 27, Alpha = 0, Beta = 0.125 ----------------------------------------------- Number of degrees of freedom : 106 Chi-square statistic : 105.36 p-value of test : 0.50 ----------------------------------------------- CPU time used : 00:00:12.52 Generator state: 331134249376 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sknuth_Gap test: ----------------------------------------------- N = 1, n = 5000000, r = 0, Alpha = 0, Beta = 0.00390625 ----------------------------------------------- Number of degrees of freedom : 1936 Chi-square statistic : 1848.57 p-value of test : 0.92 ----------------------------------------------- CPU time used : 00:00:15.02 Generator state: 372094615392 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sknuth_Gap test: ----------------------------------------------- N = 1, n = 5000000, r = 22, Alpha = 0, Beta = 0.00390625 ----------------------------------------------- Number of degrees of freedom : 1936 Chi-square statistic : 1990.42 p-value of test : 0.19 ----------------------------------------------- CPU time used : 00:00:17.45 Generator state: 413025456640 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sknuth_Run test: ----------------------------------------------- N = 1, n = 500000000, r = 0, Up = TRUE ----------------------------------------------- Number of degrees of freedom : 6 Chi-square statistic : 2.91 p-value of test : 0.82 ----------------------------------------------- CPU time used : 00:00:08.60 Generator state: 429025456640 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sknuth_Run test: ----------------------------------------------- N = 1, n = 500000000, r = 15, Up = FALSE ----------------------------------------------- Number of degrees of freedom : 6 Chi-square statistic : 3.78 p-value of test : 0.71 ----------------------------------------------- CPU time used : 00:00:09.52 Generator state: 445025456640 bits have been read. *********************************************************** Test sknuth_Permutation calling smultin_Multinomial *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smultin_Multinomial test: ----------------------------------------------- N = 1, n = 50000000, r = 0, t = 10, Sparse = FALSE GenerCell = smultin_GenerCellPermut Number of cells = t! = 3628800 Expected number per cell = 13.77866 Hashing = FALSE For Delta > -1, we use the ChiSquare approximation Correction factor of the ChiSquare: Delta = 1, Mu = 0.03628799, Sigma = 1 ----------------------------------------------- Test Results for Delta = 1.0000 Number of degrees of freedom : 3628799 Value of the statistic : 3.63e+6 p-value of test : 0.15 ----------------------------------------------- CPU time used : 00:00:15.38 Generator state: 461025456640 bits have been read. *********************************************************** Test sknuth_Permutation calling smultin_Multinomial *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smultin_Multinomial test: ----------------------------------------------- N = 1, n = 50000000, r = 15, t = 10, Sparse = FALSE GenerCell = smultin_GenerCellPermut Number of cells = t! = 3628800 Expected number per cell = 13.77866 Hashing = FALSE For Delta > -1, we use the ChiSquare approximation Correction factor of the ChiSquare: Delta = 1, Mu = 0.03628799, Sigma = 1 ----------------------------------------------- Test Results for Delta = 1.0000 Number of degrees of freedom : 3628799 Value of the statistic : 3.63e+6 p-value of test : 0.38 ----------------------------------------------- CPU time used : 00:00:16.47 Generator state: 477025456640 bits have been read. *********************************************************** Test sknuth_CollisionPermut calling smultin_Multinomial *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smultin_Multinomial test: ----------------------------------------------- N = 5, n = 10000000, r = 0, t = 13, Sparse = TRUE GenerCell = smultin_GenerCellPermut Number of cells = t! = 6227020800 Expected number per cell = 1 / 622.70208 EColl = n^2 / (2k) = 8029.521918 Hashing = TRUE Collision test, Mu = 8025.2245, Sigma = 89.5098 ----------------------------------------------- Test Results for Collisions For the total number of collisions, we use the Poisson approximation: Expected number of collisions = N*Mu : 40126.12 Observed number of collisions : 40424 p-value of test : 0.07 ----------------------------- Total number of cells containing j balls j = 0 : 31085144424 j = 1 : 49919173 j = 2 : 40382 j = 3 : 21 j = 4 : 0 j = 5 : 0 ----------------------------------------------- CPU time used : 00:00:27.58 Generator state: 497825456640 bits have been read. *********************************************************** Test sknuth_CollisionPermut calling smultin_Multinomial *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smultin_Multinomial test: ----------------------------------------------- N = 5, n = 10000000, r = 15, t = 13, Sparse = TRUE GenerCell = smultin_GenerCellPermut Number of cells = t! = 6227020800 Expected number per cell = 1 / 622.70208 EColl = n^2 / (2k) = 8029.521918 Hashing = TRUE Collision test, Mu = 8025.2245, Sigma = 89.5098 ----------------------------------------------- Test Results for Collisions For the total number of collisions, we use the Poisson approximation: Expected number of collisions = N*Mu : 40126.12 Observed number of collisions : 40234 p-value of test : 0.30 ----------------------------- Total number of cells containing j balls j = 0 : 31085144234 j = 1 : 49919551 j = 2 : 40196 j = 3 : 19 j = 4 : 0 j = 5 : 0 ----------------------------------------------- CPU time used : 00:00:28.82 Generator state: 518625456640 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sknuth_MaxOft test: ----------------------------------------------- N = 10, n = 10000000, r = 0, d = 100000, t = 5 Number of categories = 100000 Expected number per category = 100.00 ----------------------------------------------- Test results for chi2 with 99999 degrees of freedom: Kolmogorov-Smirnov+ statistic = D+ : 0.061 p-value of test : 0.90 Kolmogorov-Smirnov- statistic = D- : 0.41 p-value of test : 0.03 Anderson-Darling statistic = A2 : 2.21 p-value of test : 0.07 Test on the sum of all N observations Number of degrees of freedom : 999990 Chi-square statistic : 1.00e+6 p-value of test : 0.04 ----------------------------------------------- Test results for Anderson-Darling: Kolmogorov-Smirnov+ statistic = D+ : 0.14 p-value of test : 0.62 Kolmogorov-Smirnov- statistic = D- : 0.22 p-value of test : 0.33 Anderson-Darling statistic = A2 : 0.56 p-value of test : 0.68 ----------------------------------------------- CPU time used : 00:00:35.74 Generator state: 534625456640 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sknuth_MaxOft test: ----------------------------------------------- N = 5, n = 10000000, r = 0, d = 100000, t = 10 Number of categories = 100000 Expected number per category = 100.00 ----------------------------------------------- Test results for chi2 with 99999 degrees of freedom: Kolmogorov-Smirnov+ statistic = D+ : 0.43 p-value of test : 0.12 Kolmogorov-Smirnov- statistic = D- : 0.092 p-value of test : 0.87 Anderson-Darling statistic = A2 : 1.19 p-value of test : 0.27 Test on the sum of all N observations Number of degrees of freedom : 499995 Chi-square statistic : 4.99e+5 p-value of test : 0.90 ----------------------------------------------- Test results for Anderson-Darling: Kolmogorov-Smirnov+ statistic = D+ : 0.45 p-value of test : 0.09 Kolmogorov-Smirnov- statistic = D- : 2.17e-3 p-value of test : 0.9978 Anderson-Darling statistic = A2 : 2.72 p-value of test : 0.04 ----------------------------------------------- CPU time used : 00:00:20.66 Generator state: 550625456640 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sknuth_MaxOft test: ----------------------------------------------- N = 1, n = 10000000, r = 0, d = 100000, t = 20 Number of categories = 100000 Expected number per category = 100.00 ----------------------------------------------- Number of degrees of freedom : 99999 Chi-square statistic : 1.00e+5 p-value of test : 0.25 ----------------------------------------------- Anderson-Darling statistic : 0.34 p-value of test : 0.66 ----------------------------------------------- CPU time used : 00:00:05.33 Generator state: 557025456640 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sknuth_MaxOft test: ----------------------------------------------- N = 1, n = 10000000, r = 0, d = 100000, t = 30 Number of categories = 100000 Expected number per category = 100.00 ----------------------------------------------- Number of degrees of freedom : 99999 Chi-square statistic : 1.00e+5 p-value of test : 0.21 ----------------------------------------------- Anderson-Darling statistic : 0.67 p-value of test : 0.33 ----------------------------------------------- CPU time used : 00:00:06.49 Generator state: 566625456640 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits svaria_SampleProd test: ----------------------------------------------- N = 1, n = 10000000, r = 0, t = 10 ----------------------------------------------- Anderson-Darling statistic : 0.29 p-value of test : 0.71 ----------------------------------------------- CPU time used : 00:00:03.28 Generator state: 569825456640 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits svaria_SampleProd test: ----------------------------------------------- N = 1, n = 10000000, r = 0, t = 30 ----------------------------------------------- Anderson-Darling statistic : 0.81 p-value of test : 0.19 ----------------------------------------------- CPU time used : 00:00:06.76 Generator state: 579425456640 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits svaria_SampleMean test: ----------------------------------------------- N = 10000000, n = 20, r = 0 ----------------------------------------------- Kolmogorov-Smirnov+ statistic = D+ : 1.26e-4 p-value of test : 0.73 Kolmogorov-Smirnov- statistic = D- : 1.69e-4 p-value of test : 0.56 Anderson-Darling statistic = A2 : 0.52 p-value of test : 0.72 ----------------------------------------------- CPU time used : 00:00:09.87 Generator state: 585825456640 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits svaria_SampleCorr test: ----------------------------------------------- N = 1, n = 500000000, r = 0, k = 1 ----------------------------------------------- Normal statistic : 0.14 p-value of test : 0.44 ----------------------------------------------- CPU time used : 00:00:06.62 Generator state: 601825456640 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits svaria_AppearanceSpacings test: ----------------------------------------------- N = 1, Q = 10000000, K = 400000000, r = 0, s = 30, L = 15 Sequences of n = (K + Q)L = 6150000000 bits Q = 10000000 initialization blocks K = 400000000 blocks for the test the blocks have L = 15 bits ----------------------------------------------- Normal statistic : 0.30 p-value of test : 0.38 ----------------------------------------------- CPU time used : 00:00:22.99 Generator state: 608385456640 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits svaria_AppearanceSpacings test: ----------------------------------------------- N = 1, Q = 10000000, K = 100000000, r = 20, s = 10, L = 15 Sequences of n = (K + Q)L = 1650000000 bits Q = 10000000 initialization blocks K = 100000000 blocks for the test the blocks have L = 15 bits ----------------------------------------------- Normal statistic : -0.40 p-value of test : 0.65 ----------------------------------------------- CPU time used : 00:00:06.82 Generator state: 615425456640 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits svaria_WeightDistrib test: ----------------------------------------------- N = 1, n = 2000000, r = 0, k = 256, Alpha = 0, Beta = 0.125 ----------------------------------------------- Number of degrees of freedom : 46 Chi-square statistic : 32.39 p-value of test : 0.94 ----------------------------------------------- CPU time used : 00:00:06.28 Generator state: 631809456640 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits svaria_WeightDistrib test: ----------------------------------------------- N = 1, n = 2000000, r = 8, k = 256, Alpha = 0, Beta = 0.125 ----------------------------------------------- Number of degrees of freedom : 46 Chi-square statistic : 56.70 p-value of test : 0.13 ----------------------------------------------- CPU time used : 00:00:07.37 Generator state: 648193456640 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits svaria_WeightDistrib test: ----------------------------------------------- N = 1, n = 2000000, r = 16, k = 256, Alpha = 0, Beta = 0.125 ----------------------------------------------- Number of degrees of freedom : 46 Chi-square statistic : 44.28 p-value of test : 0.54 ----------------------------------------------- CPU time used : 00:00:07.37 Generator state: 664577456640 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits svaria_WeightDistrib test: ----------------------------------------------- N = 1, n = 2000000, r = 24, k = 256, Alpha = 0, Beta = 0.125 ----------------------------------------------- Number of degrees of freedom : 46 Chi-square statistic : 42.98 p-value of test : 0.60 ----------------------------------------------- CPU time used : 00:00:07.40 Generator state: 680961456640 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits svaria_SumCollector test: ----------------------------------------------- N = 1, n = 20000000, r = 0, g = 10 ----------------------------------------------- Number of degrees of freedom : 25 Chi-square statistic : 29.23 p-value of test : 0.25 ----------------------------------------------- CPU time used : 00:00:05.03 Generator state: 694187284128 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smarsa_MatrixRank test: ----------------------------------------------- N = 1, n = 1000000, r = 0, s = 30, L = 60, k = 60 ----------------------------------------------- Number of degrees of freedom : 4 Chi-square statistic : 3.48 p-value of test : 0.48 ----------------------------------------------- CPU time used : 00:00:17.98 Generator state: 698027284128 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smarsa_MatrixRank test: ----------------------------------------------- N = 1, n = 1000000, r = 20, s = 10, L = 60, k = 60 ----------------------------------------------- Number of degrees of freedom : 4 Chi-square statistic : 1.97 p-value of test : 0.74 ----------------------------------------------- CPU time used : 00:00:21.14 Generator state: 709547284128 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smarsa_MatrixRank test: ----------------------------------------------- N = 1, n = 50000, r = 0, s = 30, L = 300, k = 300 ----------------------------------------------- Number of degrees of freedom : 3 Chi-square statistic : 6.97 p-value of test : 0.07 ----------------------------------------------- CPU time used : 00:00:33.47 Generator state: 714347284128 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smarsa_MatrixRank test: ----------------------------------------------- N = 1, n = 50000, r = 20, s = 10, L = 300, k = 300 ----------------------------------------------- Number of degrees of freedom : 3 Chi-square statistic : 1.27 p-value of test : 0.74 ----------------------------------------------- CPU time used : 00:00:43.17 Generator state: 728747284128 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smarsa_MatrixRank test: ----------------------------------------------- N = 1, n = 2000, r = 0, s = 30, L = 1200, k = 1200 ----------------------------------------------- Number of degrees of freedom : 3 Chi-square statistic : 1.96 p-value of test : 0.58 ----------------------------------------------- CPU time used : 00:00:48.85 Generator state: 731819284128 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smarsa_MatrixRank test: ----------------------------------------------- N = 1, n = 2000, r = 20, s = 10, L = 1200, k = 1200 ----------------------------------------------- Number of degrees of freedom : 3 Chi-square statistic : 4.42 p-value of test : 0.22 ----------------------------------------------- CPU time used : 00:01:08.43 Generator state: 741035284128 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smarsa_Savir2 test: ----------------------------------------------- N = 1, n = 20000000, r = 0, m = 1048576, t = 30 ----------------------------------------------- Number of degrees of freedom : 17 Chi-square statistic : 18.37 p-value of test : 0.37 ----------------------------------------------- CPU time used : 00:00:07.23 Generator state: 760235284128 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smarsa_GCD test: ----------------------------------------------- N = 1, n = 100000000, r = 0, s = 30 ----------------------------------------------- Number of degrees of freedom : 2465 Chi2 statistic for GCD values : 2437.40 p-value of test : 0.65 ----------------------------------------------- CPU time used : 00:00:19.49 Generator state: 766635284128 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smarsa_GCD test: ----------------------------------------------- N = 1, n = 40000000, r = 10, s = 20 ----------------------------------------------- Number of degrees of freedom : 1559 Chi2 statistic for GCD values : 1527.39 p-value of test : 0.71 ----------------------------------------------- CPU time used : 00:00:05.68 Generator state: 769195288928 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits swalk_RandomWalk1 test: ----------------------------------------------- N = 1, n = 50000000, r = 0, s = 30, L0 = 90, L1 = 90 ----------------------------------------------- Test on the values of the Statistic H Number of degrees of freedom : 46 ChiSquare statistic : 41.42 p-value of test : 0.66 ----------------------------------------------- Test on the values of the Statistic M Number of degrees of freedom : 47 ChiSquare statistic : 48.88 p-value of test : 0.40 ----------------------------------------------- Test on the values of the Statistic J Number of degrees of freedom : 45 ChiSquare statistic : 39.15 p-value of test : 0.72 ----------------------------------------------- Test on the values of the Statistic R Number of degrees of freedom : 36 ChiSquare statistic : 38.63 p-value of test : 0.35 ----------------------------------------------- Test on the values of the Statistic C Number of degrees of freedom : 23 ChiSquare statistic : 19.30 p-value of test : 0.68 ----------------------------------------------- CPU time used : 00:00:30.29 Generator state: 773995288928 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits swalk_RandomWalk1 test: ----------------------------------------------- N = 1, n = 10000000, r = 20, s = 10, L0 = 90, L1 = 90 ----------------------------------------------- Test on the values of the Statistic H Number of degrees of freedom : 44 ChiSquare statistic : 48.07 p-value of test : 0.31 ----------------------------------------------- Test on the values of the Statistic M Number of degrees of freedom : 45 ChiSquare statistic : 40.08 p-value of test : 0.68 ----------------------------------------------- Test on the values of the Statistic J Number of degrees of freedom : 45 ChiSquare statistic : 45.13 p-value of test : 0.47 ----------------------------------------------- Test on the values of the Statistic R Number of degrees of freedom : 35 ChiSquare statistic : 38.53 p-value of test : 0.31 ----------------------------------------------- Test on the values of the Statistic C Number of degrees of freedom : 22 ChiSquare statistic : 26.42 p-value of test : 0.23 ----------------------------------------------- CPU time used : 00:00:07.39 Generator state: 776875288928 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits swalk_RandomWalk1 test: ----------------------------------------------- N = 1, n = 5000000, r = 0, s = 30, L0 = 1000, L1 = 1000 ----------------------------------------------- Test on the values of the Statistic H Number of degrees of freedom : 140 ChiSquare statistic : 131.62 p-value of test : 0.68 ----------------------------------------------- Test on the values of the Statistic M Number of degrees of freedom : 141 ChiSquare statistic : 144.91 p-value of test : 0.39 ----------------------------------------------- Test on the values of the Statistic J Number of degrees of freedom : 500 ChiSquare statistic : 500.08 p-value of test : 0.49 ----------------------------------------------- Test on the values of the Statistic R Number of degrees of freedom : 132 ChiSquare statistic : 146.96 p-value of test : 0.18 ----------------------------------------------- Test on the values of the Statistic C Number of degrees of freedom : 72 ChiSquare statistic : 86.95 p-value of test : 0.11 ----------------------------------------------- CPU time used : 00:00:32.45 Generator state: 782315288928 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits swalk_RandomWalk1 test: ----------------------------------------------- N = 1, n = 1000000, r = 20, s = 10, L0 = 1000, L1 = 1000 ----------------------------------------------- Test on the values of the Statistic H Number of degrees of freedom : 128 ChiSquare statistic : 119.99 p-value of test : 0.68 ----------------------------------------------- Test on the values of the Statistic M Number of degrees of freedom : 130 ChiSquare statistic : 138.04 p-value of test : 0.30 ----------------------------------------------- Test on the values of the Statistic J Number of degrees of freedom : 500 ChiSquare statistic : 476.01 p-value of test : 0.77 ----------------------------------------------- Test on the values of the Statistic R Number of degrees of freedom : 122 ChiSquare statistic : 98.55 p-value of test : 0.94 ----------------------------------------------- Test on the values of the Statistic C Number of degrees of freedom : 66 ChiSquare statistic : 73.51 p-value of test : 0.25 ----------------------------------------------- CPU time used : 00:00:07.90 Generator state: 785515288928 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits swalk_RandomWalk1 test: ----------------------------------------------- N = 1, n = 500000, r = 0, s = 30, L0 = 10000, L1 = 10000 ----------------------------------------------- Test on the values of the Statistic H Number of degrees of freedom : 366 ChiSquare statistic : 400.47 p-value of test : 0.10 ----------------------------------------------- Test on the values of the Statistic M Number of degrees of freedom : 366 ChiSquare statistic : 359.60 p-value of test : 0.58 ----------------------------------------------- Test on the values of the Statistic J Number of degrees of freedom : 5000 ChiSquare statistic : 4947.20 p-value of test : 0.70 ----------------------------------------------- Test on the values of the Statistic R Number of degrees of freedom : 360 ChiSquare statistic : 370.06 p-value of test : 0.35 ----------------------------------------------- Test on the values of the Statistic C Number of degrees of freedom : 192 ChiSquare statistic : 204.56 p-value of test : 0.25 ----------------------------------------------- CPU time used : 00:00:31.96 Generator state: 790859288928 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits swalk_RandomWalk1 test: ----------------------------------------------- N = 1, n = 100000, r = 20, s = 10, L0 = 10000, L1 = 10000 ----------------------------------------------- Test on the values of the Statistic H Number of degrees of freedom : 318 ChiSquare statistic : 297.50 p-value of test : 0.79 ----------------------------------------------- Test on the values of the Statistic M Number of degrees of freedom : 318 ChiSquare statistic : 315.07 p-value of test : 0.54 ----------------------------------------------- Test on the values of the Statistic J Number of degrees of freedom : 5000 ChiSquare statistic : 5117.91 p-value of test : 0.12 ----------------------------------------------- Test on the values of the Statistic R Number of degrees of freedom : 315 ChiSquare statistic : 305.00 p-value of test : 0.65 ----------------------------------------------- Test on the values of the Statistic C Number of degrees of freedom : 169 ChiSquare statistic : 147.96 p-value of test : 0.88 ----------------------------------------------- CPU time used : 00:00:07.79 Generator state: 794059288928 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits scomp_LinearComp test: ----------------------------------------------- N = 1, n = 120000, r = 0, s = 1 ----------------------------------------------- Number of degrees of freedom : 10 Chi2 statistic for size of jumps : 7.58 p-value of test : 0.67 ----------------------------------------------- Normal statistic for number of jumps : -0.50 p-value of test : 0.69 ----------------------------------------------- CPU time used : 00:00:10.57 Generator state: 794063128928 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits scomp_LinearComp test: ----------------------------------------------- N = 1, n = 120000, r = 29, s = 1 ----------------------------------------------- Number of degrees of freedom : 10 Chi2 statistic for size of jumps : 11.67 p-value of test : 0.31 ----------------------------------------------- Normal statistic for number of jumps : -1.73 p-value of test : 0.96 ----------------------------------------------- CPU time used : 00:00:10.59 Generator state: 794066968928 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits scomp_LempelZiv test: ----------------------------------------------- N = 10, n = 33554432, r = 0, s = 30, k = 25 ----------------------------------------------- Kolmogorov-Smirnov+ statistic = D+ : 5.92e-3 p-value of test : 0.9938 Kolmogorov-Smirnov- statistic = D- : 0.18 p-value of test : 0.48 Anderson-Darling statistic = A2 : 0.81 p-value of test : 0.47 Tests on the sum of all N observations Standardized normal statistic : 1.24 p-value of test : 0.11 Sample variance : 1.50 p-value of test : 0.14 ----------------------------------------------- CPU time used : 00:00:09.54 Generator state: 794424883168 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sspectral_Fourier3 test: ----------------------------------------------- N = 50000, n = 16384, r = 0, s = 30, k = 14 ----------------------------------------------- Kolmogorov-Smirnov+ statistic = D+ : 3.66e-3 p-value of test : 0.89 Kolmogorov-Smirnov- statistic = D- : 0.012 p-value of test : 0.32 Anderson-Darling statistic = A2 : 0.68 p-value of test : 0.57 ----------------------------------------------- CPU time used : 00:00:16.44 Generator state: 795300083168 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sspectral_Fourier3 test: ----------------------------------------------- N = 50000, n = 16384, r = 20, s = 10, k = 14 ----------------------------------------------- Kolmogorov-Smirnov+ statistic = D+ : 9.99e-3 p-value of test : 0.44 Kolmogorov-Smirnov- statistic = D- : 7.10e-3 p-value of test : 0.66 Anderson-Darling statistic = A2 : 0.70 p-value of test : 0.56 ----------------------------------------------- CPU time used : 00:00:17.20 Generator state: 797922483168 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sstring_LongestHeadRun test: ----------------------------------------------- N = 1, n = 1000, r = 0, s = 30, L = 10000020 ----------------------------------------------- Number of degrees of freedom : 8 Chi-square statistic : 8.11 p-value of test : 0.42 ----------------------------------------------- Global longest run of 1 : 34.00 p-value of test : 0.25 ----------------------------------------------- CPU time used : 00:00:48.48 Generator state: 808589171168 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sstring_LongestHeadRun test: ----------------------------------------------- N = 1, n = 300, r = 20, s = 10, L = 10000020 ----------------------------------------------- Number of degrees of freedom : 7 Chi-square statistic : 3.51 p-value of test : 0.83 ----------------------------------------------- Global longest run of 1 : 32.00 p-value of test : 0.29 ----------------------------------------------- CPU time used : 00:00:17.57 Generator state: 818189190368 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sstring_PeriodsInStrings test: ----------------------------------------------- N = 1, n = 300000000, r = 0, s = 30 ----------------------------------------------- Number of degrees of freedom : 302 Chi-square statistic : 299.80 p-value of test : 0.52 ----------------------------------------------- CPU time used : 00:00:12.60 Generator state: 827789190368 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sstring_PeriodsInStrings test: ----------------------------------------------- N = 1, n = 300000000, r = 15, s = 15 ----------------------------------------------- Number of degrees of freedom : 56 Chi-square statistic : 67.84 p-value of test : 0.13 ----------------------------------------------- CPU time used : 00:00:09.52 Generator state: 837389190368 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sstring_HammingWeight2 test: ----------------------------------------------- N = 100, n = 100000000, r = 0, s = 30, L = 1000000 ----------------------------------------------- Kolmogorov-Smirnov+ statistic = D+ : 0.11 p-value of test : 0.09 Kolmogorov-Smirnov- statistic = D- : 0.014 p-value of test : 0.95 Anderson-Darling statistic = A2 : 2.96 p-value of test : 0.03 Test on the sum of all N observations Number of degrees of freedom : 10000 Chi-square statistic : 9663.76 p-value of test : 0.9918 ----------------------------------------------- CPU time used : 00:00:09.43 Generator state: 848056070368 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sstring_HammingWeight2 test: ----------------------------------------------- N = 30, n = 100000000, r = 20, s = 10, L = 1000000 ----------------------------------------------- Kolmogorov-Smirnov+ statistic = D+ : 0.059 p-value of test : 0.78 Kolmogorov-Smirnov- statistic = D- : 0.14 p-value of test : 0.30 Anderson-Darling statistic = A2 : 0.39 p-value of test : 0.86 Test on the sum of all N observations Number of degrees of freedom : 3000 Chi-square statistic : 3020.14 p-value of test : 0.39 ----------------------------------------------- CPU time used : 00:00:06.42 Generator state: 857656070368 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sstring_HammingCorr test: ----------------------------------------------- N = 1, n = 500000000, r = 0, s = 30, L = 30 ----------------------------------------------- Normal statistic : 0.23 p-value of test : 0.41 ----------------------------------------------- CPU time used : 00:00:15.14 Generator state: 873656070368 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sstring_HammingCorr test: ----------------------------------------------- N = 1, n = 50000000, r = 0, s = 30, L = 300 ----------------------------------------------- Normal statistic : 1.26 p-value of test : 0.10 ----------------------------------------------- CPU time used : 00:00:14.38 Generator state: 889656070368 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sstring_HammingCorr test: ----------------------------------------------- N = 1, n = 10000000, r = 0, s = 30, L = 1200 ----------------------------------------------- Normal statistic : 0.64 p-value of test : 0.26 ----------------------------------------------- CPU time used : 00:00:11.39 Generator state: 902456070368 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sstring_HammingIndep test: ----------------------------------------------- N = 1, n = 300000000, r = 0, s = 30, L = 30, d = 0 Counters with expected numbers >= 10 ----------------------------------------------- Number of degrees of freedom : 577 Chi-square statistic : 534.89 p-value of test : 0.89 ----------------------------------------------- CPU time used : 00:00:18.06 Generator state: 921656070368 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sstring_HammingIndep test: ----------------------------------------------- N = 1, n = 100000000, r = 20, s = 10, L = 30, d = 0 Counters with expected numbers >= 10 ----------------------------------------------- Number of degrees of freedom : 533 Chi-square statistic : 528.55 p-value of test : 0.55 ----------------------------------------------- CPU time used : 00:00:14.00 Generator state: 940856070368 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sstring_HammingIndep test: ----------------------------------------------- N = 1, n = 30000000, r = 0, s = 30, L = 300, d = 0 Counters with expected numbers >= 10 ----------------------------------------------- Number of degrees of freedom : 4117 Chi-square statistic : 4068.50 p-value of test : 0.70 ----------------------------------------------- CPU time used : 00:00:17.80 Generator state: 960056070368 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sstring_HammingIndep test: ----------------------------------------------- N = 1, n = 10000000, r = 20, s = 10, L = 300, d = 0 Counters with expected numbers >= 10 ----------------------------------------------- Number of degrees of freedom : 3585 Chi-square statistic : 3575.19 p-value of test : 0.54 ----------------------------------------------- CPU time used : 00:00:13.25 Generator state: 979256070368 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sstring_HammingIndep test: ----------------------------------------------- N = 1, n = 10000000, r = 0, s = 30, L = 1200, d = 0 Counters with expected numbers >= 10 ----------------------------------------------- Number of degrees of freedom : 11825 Chi-square statistic :11759.98 p-value of test : 0.66 ----------------------------------------------- CPU time used : 00:00:23.27 Generator state: 1004856070368 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sstring_HammingIndep test: ----------------------------------------------- N = 1, n = 1000000, r = 20, s = 10, L = 1200, d = 0 Counters with expected numbers >= 10 ----------------------------------------------- Number of degrees of freedom : 7473 Chi-square statistic : 7526.74 p-value of test : 0.33 ----------------------------------------------- CPU time used : 00:00:05.24 Generator state: 1012536070368 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sstring_Run test: ----------------------------------------------- N = 1, n = 1000000000, r = 0, s = 30 ----------------------------------------------- Total number of 1 runs: 1000000002 Number of degrees of freedom : 52 Chi2 statistic for number of runs : 47.47 p-value of test : 0.65 ----------------------------------------------- Total number of bits: 3999906060 Normal statistic for number of bits : -1.05 p-value of test : 0.85 ----------------------------------------------- CPU time used : 00:00:16.64 Generator state: 1016802636832 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sstring_Run test: ----------------------------------------------- N = 1, n = 1000000000, r = 20, s = 10 ----------------------------------------------- Total number of 1 runs: 1000000000 Number of degrees of freedom : 52 Chi2 statistic for number of runs : 55.24 p-value of test : 0.35 ----------------------------------------------- Total number of bits: 3999926000 Normal statistic for number of bits : -0.83 p-value of test : 0.80 ----------------------------------------------- CPU time used : 00:00:22.03 Generator state: 1029602400032 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sstring_AutoCor test: ----------------------------------------------- N = 10, n = 1000000021, r = 0, s = 30, d = 1 ----------------------------------------------- Kolmogorov-Smirnov+ statistic = D+ : 0.27 p-value of test : 0.19 Kolmogorov-Smirnov- statistic = D- : 4.86e-3 p-value of test : 0.9949 Anderson-Darling statistic = A2 : 2.13 p-value of test : 0.08 Tests on the sum of all N observations Standardized normal statistic : -1.93 p-value of test : 0.97 Sample variance : 1.73 p-value of test : 0.08 ----------------------------------------------- CPU time used : 00:00:17.51 Generator state: 1040269067232 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sstring_AutoCor test: ----------------------------------------------- N = 5, n = 1000000001, r = 20, s = 10, d = 1 ----------------------------------------------- Kolmogorov-Smirnov+ statistic = D+ : 0.11 p-value of test : 0.83 Kolmogorov-Smirnov- statistic = D- : 0.27 p-value of test : 0.41 Anderson-Darling statistic = A2 : 0.39 p-value of test : 0.85 Tests on the sum of all N observations Standardized normal statistic : 0.62 p-value of test : 0.27 Sample variance : 0.81 p-value of test : 0.52 ----------------------------------------------- CPU time used : 00:00:23.43 Generator state: 1056269067392 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sstring_AutoCor test: ----------------------------------------------- N = 10, n = 1000000020, r = 0, s = 30, d = 30 ----------------------------------------------- Kolmogorov-Smirnov+ statistic = D+ : 0.35 p-value of test : 0.06 Kolmogorov-Smirnov- statistic = D- : 0.052 p-value of test : 0.92 Anderson-Darling statistic = A2 : 1.74 p-value of test : 0.13 Tests on the sum of all N observations Standardized normal statistic : -1.53 p-value of test : 0.94 Sample variance : 0.68 p-value of test : 0.73 ----------------------------------------------- CPU time used : 00:00:15.94 Generator state: 1066935734592 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sstring_AutoCor test: ----------------------------------------------- N = 5, n = 1000000010, r = 20, s = 10, d = 10 ----------------------------------------------- Kolmogorov-Smirnov+ statistic = D+ : 0.32 p-value of test : 0.29 Kolmogorov-Smirnov- statistic = D- : 0.20 p-value of test : 0.58 Anderson-Darling statistic = A2 : 0.51 p-value of test : 0.73 Tests on the sum of all N observations Standardized normal statistic : -0.21 p-value of test : 0.58 Sample variance : 0.35 p-value of test : 0.84 ----------------------------------------------- CPU time used : 00:00:20.82 Generator state: 1082935734912 bits have been read. ========= Summary results of Crush ========= Version: TestU01 1.2.3 Generator: ufile_CreateReadBin Number of statistics: 144 Total CPU time: 00:29:21.38 All tests were passed

There are separate pages for the Alphabit, Rabbit, SmallCrush, and BigCrush batteries.