TestU01 results

BigCrush battery test

The BigCrush battery of tests is a thing of modern legend. When it first appeared as a test for PRNG algorithms it left almost nothing still standing. Even algorithms which were long thought to be good, by respected authorities on the subject, crumbled under the pressure that it brought to bear on them. It consumes an enormous number of bits (about 5 times more than a default Dieharder run does), but on a reasonably modest modern machine can still get through them in under 4 hours.

Somewhat curiously though, in our testing we've mostly found that any stream of bits which does not already fail at least one test in the Crush battery, will also usually get past this one without failure too. Which isn't a totally surprising result, and in no way diminishes the extra power which this test has for finding statistical anomalies. It seems to be more a function of the particular foibles of hardware generated random numbers. Since their weakness, if it exists, does not usually depend on the long periods or other fine pattern details of a deterministic algorithm, it would seem that (for the designs which we have tested at least), either they do have some real and fatal flaw in their operation, and that is sufficient for a smaller test suite like Crush (or for some of our continuous tests over the long term) to detect it – or the samples from them really are independent and identically distributed to within a margin of error that is still not statistically significant even in tests of this size and power. We might be able to contrive a device that deliberately falls between what Crush and BigCrush can detect, but we haven't seen the same sort of gap between them as we saw between what would pass lesser tests seemingly easily, yet have reality come crashing down brutally hard on it when analysed by Crush.

When the output of a device failed the Crush battery, it would then usually also fail this battery much more severely and in many more tests, but since it only takes just one convincingly certain failure to prove that a RNG is bad, also running this test on such a device mostly became a demonstration of shooting fish in a barrel. If we already knew that it was bad, even in only one test, this battery would just run amok with bracketing the litany of other ways in which that failure was also clearly observable.

Failing to fail

Not failing BigCrush though is still no guarantee that some test, which was able to better model the source, would not be able to detect a real weakness – but there is a limit, beyond which simply increasing the statistical power of existing tests starts to have less value in real terms. If an adversary is able to determine that there is a small statistical anomaly of one part in some huge number of samples (say for example, the number that it would take a full year to completely analyse), does that really give them any practical advantage beyond chance at predicting the output? Even if we (and they) can detect that quickly, the risk of it being exploitable does diminish unless it leads to the discovery of some much more powerful mechanism for prediction. None of which means that you can safely handwave away a genuine failure of any of the currently existing test suites, but the question of how much more statistically powerful they can usefully be made without creating some entirely new test statistic is a real constraint, since at some point numeric precision will itself become the limiting error.

In the run shown here, TestU01 again does not flag any result as being outside of its significance thresholds, but detailed inspection of the results shows that two of them are just beyond the limit of what Dieharder would classify as uncertain (with around a 1 in 240 chance that a random sample would exceed it). Once again we've failed to prove that this source is bad, but only more testing can improve the confidence that a future test with this battery would not do so.

For this particular test run, it is also important to note that not all of the tests are strictly independent. Since we wanted to run this demonstration of BigCrush over exactly the same bitstream that we had already analysed earlier with Dieharder to give something of an apples to apples comparison of what they detected in it, that means we didn't have enough bits for the full run of BigCrush. We dealt with that here by treating the 230GB of samples from Dieharder as a circular buffer, 'transparently' reading from the beginning again after we get to the end. No single test in BigCrush uses so many bits that it will have seen the same sequence of them twice, but some tests have been run over the same set of bits as others were. In one respect that is a Good Thing here, it means each non-overlapping subset of bits was subjected to more than one of the BigCrush tests – but it does mean that the p-values from all tests cannot themselves be considered IID for the sake of doing further analysis of their distribution. Since BigCrush does not itself test that, it has no influence on any of the outcomes that it reports. The log below is marked with the five places where the bitstream was 'rewound' to start again at the beginning. The results of tests entirely between any of those points are still independent though (except where BigCrush itself runs more than one statistic on a single block of samples making them not so).

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx Starting BigCrush 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 = 1000000000, r = 0, d = 256, t = 3, Sparse = FALSE GenerCell = smultin_GenerCellSerial Number of cells = d^t = 16777216 Expected number per cell = 59.604645 Hashing = FALSE For Delta > -1, we use the ChiSquare approximation Correction factor of the ChiSquare: Delta = 1, Mu = 0.0083558402, Sigma = 1 ----------------------------------------------- Test Results for Delta = 1.0000 Number of degrees of freedom : 16711680 Value of the statistic : 1.67e+7 p-value of test : 0.41 ----------------------------------------------- CPU time used : 00:01:25.70 Generator state: 32000000000 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 = 1000000000, r = 22, d = 256, t = 3, Sparse = FALSE GenerCell = smultin_GenerCellSerial Number of cells = d^t = 16777216 Expected number per cell = 59.604645 Hashing = FALSE For Delta > -1, we use the ChiSquare approximation Correction factor of the ChiSquare: Delta = 1, Mu = 0.0083558402, Sigma = 1 ----------------------------------------------- Test Results for Delta = 1.0000 Number of degrees of freedom : 16711680 Value of the statistic : 1.67e+7 p-value of test : 0.02 ----------------------------------------------- CPU time used : 00:01:31.15 Generator state: 64000000000 bits have been read. *********************************************************** Test smarsa_CollisionOver calling smultin_MultinomialOver *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smultin_MultinomialOver test: ----------------------------------------------- N = 30, n = 20000000, r = 0, d = 2097152, t = 2, Sparse = TRUE GenerCell = smultin_GenerCellSerial Number of cells = d^t = 4398046511104 Expected number per cell = 1 / 219902.33 EColl = n^2 / (2k) = 45.47473509 Hashing = TRUE Collision test CollisionOver: density = n / k = 1 / 219902.33 Expected number of collisions = Mu = 45.47 ----------------------------------------------- Results of CollisionOver test: POISSON approximation : Expected number of collisions = N*Mu : 1364.24 Observed number of collisions : 1381 p-value of test : 0.33 ----------------------------- Total number of cells containing j balls j = 0 : 131940795334501 j = 1 : 599997238 j = 2 : 1381 j = 3 : 0 j = 4 : 0 j = 5 : 0 ----------------------------------------------- CPU time used : 00:02:58.69 Generator state: 83200000000 bits have been read. *********************************************************** Test smarsa_CollisionOver calling smultin_MultinomialOver *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smultin_MultinomialOver test: ----------------------------------------------- N = 30, n = 20000000, r = 9, d = 2097152, t = 2, Sparse = TRUE GenerCell = smultin_GenerCellSerial Number of cells = d^t = 4398046511104 Expected number per cell = 1 / 219902.33 EColl = n^2 / (2k) = 45.47473509 Hashing = TRUE Collision test CollisionOver: density = n / k = 1 / 219902.33 Expected number of collisions = Mu = 45.47 ----------------------------------------------- Results of CollisionOver test: POISSON approximation : Expected number of collisions = N*Mu : 1364.24 Observed number of collisions : 1345 p-value of test : 0.69 ----------------------------- Total number of cells containing j balls j = 0 : 131940795334465 j = 1 : 599997310 j = 2 : 1345 j = 3 : 0 j = 4 : 0 j = 5 : 0 ----------------------------------------------- CPU time used : 00:02:54.57 Generator state: 102400000000 bits have been read. *********************************************************** Test smarsa_CollisionOver calling smultin_MultinomialOver *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smultin_MultinomialOver test: ----------------------------------------------- N = 30, n = 20000000, r = 0, d = 16384, t = 3, Sparse = TRUE GenerCell = smultin_GenerCellSerial Number of cells = d^t = 4398046511104 Expected number per cell = 1 / 219902.33 EColl = n^2 / (2k) = 45.47473509 Hashing = TRUE Collision test CollisionOver: density = n / k = 1 / 219902.33 Expected number of collisions = Mu = 45.47 ----------------------------------------------- Results of CollisionOver test: POISSON approximation : Expected number of collisions = N*Mu : 1364.24 Observed number of collisions : 1413 p-value of test : 0.10 ----------------------------- Total number of cells containing j balls j = 0 : 131940795334533 j = 1 : 599997174 j = 2 : 1413 j = 3 : 0 j = 4 : 0 j = 5 : 0 ----------------------------------------------- CPU time used : 00:03:53.30 Generator state: 121600000000 bits have been read. *********************************************************** Test smarsa_CollisionOver calling smultin_MultinomialOver *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smultin_MultinomialOver test: ----------------------------------------------- N = 30, n = 20000000, r = 16, d = 16384, t = 3, Sparse = TRUE GenerCell = smultin_GenerCellSerial Number of cells = d^t = 4398046511104 Expected number per cell = 1 / 219902.33 EColl = n^2 / (2k) = 45.47473509 Hashing = TRUE Collision test CollisionOver: density = n / k = 1 / 219902.33 Expected number of collisions = Mu = 45.47 ----------------------------------------------- Results of CollisionOver test: POISSON approximation : Expected number of collisions = N*Mu : 1364.24 Observed number of collisions : 1400 p-value of test : 0.17 ----------------------------- Total number of cells containing j balls j = 0 : 131940795334520 j = 1 : 599997200 j = 2 : 1400 j = 3 : 0 j = 4 : 0 j = 5 : 0 ----------------------------------------------- CPU time used : 00:03:49.63 Generator state: 140800000000 bits have been read. *********************************************************** Test smarsa_CollisionOver calling smultin_MultinomialOver *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smultin_MultinomialOver test: ----------------------------------------------- N = 30, n = 20000000, r = 0, d = 64, t = 7, Sparse = TRUE GenerCell = smultin_GenerCellSerial Number of cells = d^t = 4398046511104 Expected number per cell = 1 / 219902.33 EColl = n^2 / (2k) = 45.47473509 Hashing = TRUE Collision test CollisionOver: density = n / k = 1 / 219902.33 Expected number of collisions = Mu = 45.47 ----------------------------------------------- Results of CollisionOver test: POISSON approximation : Expected number of collisions = N*Mu : 1364.24 Observed number of collisions : 1267 p-value of test : 0.9959 ----------------------------- Total number of cells containing j balls j = 0 : 131940795334387 j = 1 : 599997466 j = 2 : 1267 j = 3 : 0 j = 4 : 0 j = 5 : 0 ----------------------------------------------- CPU time used : 00:03:50.36 Generator state: 160000000000 bits have been read. *********************************************************** Test smarsa_CollisionOver calling smultin_MultinomialOver *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smultin_MultinomialOver test: ----------------------------------------------- N = 30, n = 20000000, r = 24, d = 64, t = 7, Sparse = TRUE GenerCell = smultin_GenerCellSerial Number of cells = d^t = 4398046511104 Expected number per cell = 1 / 219902.33 EColl = n^2 / (2k) = 45.47473509 Hashing = TRUE Collision test CollisionOver: density = n / k = 1 / 219902.33 Expected number of collisions = Mu = 45.47 ----------------------------------------------- Results of CollisionOver test: POISSON approximation : Expected number of collisions = N*Mu : 1364.24 Observed number of collisions : 1304 p-value of test : 0.95 ----------------------------- Total number of cells containing j balls j = 0 : 131940795334424 j = 1 : 599997392 j = 2 : 1304 j = 3 : 0 j = 4 : 0 j = 5 : 0 ----------------------------------------------- CPU time used : 00:03:59.25 Generator state: 179200000000 bits have been read. *********************************************************** Test smarsa_CollisionOver calling smultin_MultinomialOver *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smultin_MultinomialOver test: ----------------------------------------------- N = 30, n = 20000000, r = 0, d = 8, t = 14, Sparse = TRUE GenerCell = smultin_GenerCellSerial Number of cells = d^t = 4398046511104 Expected number per cell = 1 / 219902.33 EColl = n^2 / (2k) = 45.47473509 Hashing = TRUE Collision test CollisionOver: density = n / k = 1 / 219902.33 Expected number of collisions = Mu = 45.47 ----------------------------------------------- Results of CollisionOver test: POISSON approximation : Expected number of collisions = N*Mu : 1364.24 Observed number of collisions : 1409 p-value of test : 0.12 ----------------------------- Total number of cells containing j balls j = 0 : 131940795334529 j = 1 : 599997182 j = 2 : 1409 j = 3 : 0 j = 4 : 0 j = 5 : 0 ----------------------------------------------- CPU time used : 00:03:53.13 Generator state: 198400000000 bits have been read. *********************************************************** Test smarsa_CollisionOver calling smultin_MultinomialOver *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smultin_MultinomialOver test: ----------------------------------------------- N = 30, n = 20000000, r = 27, d = 8, t = 14, Sparse = TRUE GenerCell = smultin_GenerCellSerial Number of cells = d^t = 4398046511104 Expected number per cell = 1 / 219902.33 EColl = n^2 / (2k) = 45.47473509 Hashing = TRUE Collision test CollisionOver: density = n / k = 1 / 219902.33 Expected number of collisions = Mu = 45.47 ----------------------------------------------- Results of CollisionOver test: POISSON approximation : Expected number of collisions = N*Mu : 1364.24 Observed number of collisions : 1323 p-value of test : 0.87 ----------------------------- Total number of cells containing j balls j = 0 : 131940795334443 j = 1 : 599997354 j = 2 : 1323 j = 3 : 0 j = 4 : 0 j = 5 : 0 ----------------------------------------------- CPU time used : 00:03:52.98 Generator state: 217600000000 bits have been read. *********************************************************** Test smarsa_CollisionOver calling smultin_MultinomialOver *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smultin_MultinomialOver test: ----------------------------------------------- N = 30, n = 20000000, r = 0, d = 4, t = 21, Sparse = TRUE GenerCell = smultin_GenerCellSerial Number of cells = d^t = 4398046511104 Expected number per cell = 1 / 219902.33 EColl = n^2 / (2k) = 45.47473509 Hashing = TRUE Collision test CollisionOver: density = n / k = 1 / 219902.33 Expected number of collisions = Mu = 45.47 ----------------------------------------------- Results of CollisionOver test: POISSON approximation : Expected number of collisions = N*Mu : 1364.24 Observed number of collisions : 1365 p-value of test : 0.50 ----------------------------- Total number of cells containing j balls j = 0 : 131940795334485 j = 1 : 599997270 j = 2 : 1365 j = 3 : 0 j = 4 : 0 j = 5 : 0 ----------------------------------------------- CPU time used : 00:03:56.94 Generator state: 236800000000 bits have been read. *********************************************************** Test smarsa_CollisionOver calling smultin_MultinomialOver *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smultin_MultinomialOver test: ----------------------------------------------- N = 30, n = 20000000, r = 28, d = 4, t = 21, Sparse = TRUE GenerCell = smultin_GenerCellSerial Number of cells = d^t = 4398046511104 Expected number per cell = 1 / 219902.33 EColl = n^2 / (2k) = 45.47473509 Hashing = TRUE Collision test CollisionOver: density = n / k = 1 / 219902.33 Expected number of collisions = Mu = 45.47 ----------------------------------------------- Results of CollisionOver test: POISSON approximation : Expected number of collisions = N*Mu : 1364.24 Observed number of collisions : 1380 p-value of test : 0.34 ----------------------------- Total number of cells containing j balls j = 0 : 131940795334500 j = 1 : 599997240 j = 2 : 1380 j = 3 : 0 j = 4 : 0 j = 5 : 0 ----------------------------------------------- CPU time used : 00:03:52.27 Generator state: 256000000000 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smarsa_BirthdaySpacings test: ----------------------------------------------- N = 100, n = 10000000, r = 0, d = 2147483648, t = 2, p = 1 Number of cells = d^t = 4611686018427387904 Lambda = Poisson mean = 54.2101 ---------------------------------------------------- Total expected number = N*Lambda : 5421.01 Total observed number : 5366 p-value of test : 0.77 ----------------------------------------------- CPU time used : 00:03:30.97 Generator state: 320000000000 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smarsa_BirthdaySpacings test: ----------------------------------------------- N = 20, 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 : 4336.81 Total observed number : 4336 p-value of test : 0.50 ----------------------------------------------- CPU time used : 00:01:32.30 Generator state: 358400000000 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smarsa_BirthdaySpacings test: ----------------------------------------------- N = 20, n = 30000000, r = 14, d = 65536, t = 4, p = 1 Number of cells = d^t = 18446744073709551616 Lambda = Poisson mean = 365.9182 ---------------------------------------------------- Total expected number = N*Lambda : 7318.36 Total observed number : 7239 p-value of test : 0.82 ----------------------------------------------- CPU time used : 00:02:32.72 Generator state: 435200000000 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smarsa_BirthdaySpacings test: ----------------------------------------------- N = 20, 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 : 4336.81 Total observed number : 4392 p-value of test : 0.20 ----------------------------------------------- CPU time used : 00:01:52.81 Generator state: 524800000000 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smarsa_BirthdaySpacings test: ----------------------------------------------- N = 20, 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 : 4336.81 Total observed number : 4265 p-value of test : 0.86 ----------------------------------------------- CPU time used : 00:01:56.85 Generator state: 614400000000 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smarsa_BirthdaySpacings test: ----------------------------------------------- N = 20, n = 30000000, r = 14, d = 256, t = 8, p = 1 Number of cells = d^t = 18446744073709551616 Lambda = Poisson mean = 365.9182 ---------------------------------------------------- Total expected number = N*Lambda : 7318.36 Total observed number : 7418 p-value of test : 0.12 ----------------------------------------------- CPU time used : 00:03:06.68 Generator state: 768000000000 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smarsa_BirthdaySpacings test: ----------------------------------------------- N = 20, n = 30000000, r = 22, d = 256, t = 8, p = 1 Number of cells = d^t = 18446744073709551616 Lambda = Poisson mean = 365.9182 ---------------------------------------------------- Total expected number = N*Lambda : 7318.36 Total observed number : 7455 p-value of test : 0.06 ----------------------------------------------- CPU time used : 00:03:06.63 Generator state: 921600000000 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smarsa_BirthdaySpacings test: ----------------------------------------------- N = 20, n = 30000000, r = 0, d = 16, t = 16, p = 1 Number of cells = d^t = 18446744073709551616 Lambda = Poisson mean = 365.9182 ---------------------------------------------------- Total expected number = N*Lambda : 7318.36 Total observed number : 7424 p-value of test : 0.11 ----------------------------------------------- CPU time used : 00:04:02.10 Generator state: 1228800000000 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smarsa_BirthdaySpacings test: ----------------------------------------------- N = 20, n = 30000000, r = 26, d = 16, t = 16, p = 1 Number of cells = d^t = 18446744073709551616 Lambda = Poisson mean = 365.9182 ---------------------------------------------------- Total expected number = N*Lambda : 7318.36 Total observed number : 7385 p-value of test : 0.22 ----------------------------------------------- CPU time used : 00:04:16.09 Generator state: 1536000000000 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits snpair_ClosePairs test: ----------------------------------------------- N = 30, n = 6000000, 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) : 1.36 p-value of test : 0.21 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) : 0.57 p-value of test : 0.68 Test on the Nm values of W_{n,i}(mNP1): 0.80 p-value of test : 0.48 Test on the jump times of Y (superposition of Yn): Expected number of jumps of Y = mN : 900 Number of jumps of Y : 865 p-value of test : 0.88 Stat. AD (mNP2) : 0.55 p-value of test : 0.70 Stat. AD after spacings (mNP2-S) : 1.07 p-value of test : 0.32 ----------------------------------------------- CPU time used : 00:02:14.02 Generator state: 1553280000000 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits snpair_ClosePairs test: ----------------------------------------------- N = 20, n = 4000000, r = 0, t = 5, p = 0, m = 30, Torus = TRUE --------------------------------------- Test based on the 2 nearest points (NP): Stat. AD on the N values (NP) : 1.01 p-value of test : 0.35 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) : 1.24 p-value of test : 0.25 Test on the Nm values of W_{n,i}(mNP1): 0.62 p-value of test : 0.63 Test on the jump times of Y (superposition of Yn): Expected number of jumps of Y = mN : 600 Number of jumps of Y : 600 p-value of test : 0.51 Stat. AD (mNP2) : 1.55 p-value of test : 0.16 Stat. AD after spacings (mNP2-S) : 0.52 p-value of test : 0.73 ----------------------------------------------- CPU time used : 00:01:28.36 Generator state: 1566080000000 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits snpair_ClosePairs test: ----------------------------------------------- N = 10, n = 3000000, r = 0, t = 9, p = 0, m = 30, Torus = TRUE --------------------------------------- Test based on the 2 nearest points (NP): Stat. AD on the N values (NP) : 0.77 p-value of test : 0.50 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) : 0.79 p-value of test : 0.48 Test on the Nm values of W_{n,i}(mNP1): 1.29 p-value of test : 0.23 Test on the jump times of Y (superposition of Yn): Expected number of jumps of Y = mN : 300 Number of jumps of Y : 313 p-value of test : 0.23 Stat. AD (mNP2) : 1.66 p-value of test : 0.14 Stat. AD after spacings (mNP2-S) : 0.91 p-value of test : 0.41 ----------------------------------------------- CPU time used : 00:02:18.22 Generator state: 1574720000000 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits snpair_ClosePairs test: ----------------------------------------------- N = 5, n = 2000000, r = 0, t = 16, p = 0, m = 30, Torus = TRUE --------------------------------------- Test based on the 2 nearest points (NP): Stat. AD on the N values (NP) : 0.28 p-value of test : 0.95 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) : 0.40 p-value of test : 0.84 Test on the Nm values of W_{n,i}(mNP1): 1.58 p-value of test : 0.16 Test on the jump times of Y (superposition of Yn): Expected number of jumps of Y = mN : 150 Number of jumps of Y : 132 p-value of test : 0.93 Stat. AD (mNP2) : 0.28 p-value of test : 0.95 Stat. AD after spacings (mNP2-S) : 1.81 p-value of test : 0.12 ----------------------------------------------- CPU time used : 00:02:37.25 Generator state: 1579840000000 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sknuth_SimpPoker test: ----------------------------------------------- N = 1, n = 400000000, r = 0, d = 8, k = 8 ----------------------------------------------- Number of degrees of freedom : 7 Chi-square statistic : 9.93 p-value of test : 0.19 ----------------------------------------------- CPU time used : 00:01:12.67 Generator state: 1682240000000 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sknuth_SimpPoker test: ----------------------------------------------- N = 1, n = 400000000, r = 27, d = 8, k = 8 ----------------------------------------------- Number of degrees of freedom : 7 Chi-square statistic : 7.58 p-value of test : 0.37 ----------------------------------------------- CPU time used : 00:01:28.27 Generator state: 1784640000000 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sknuth_SimpPoker test: ----------------------------------------------- N = 1, n = 100000000, r = 0, d = 32, k = 32 ----------------------------------------------- Number of degrees of freedom : 18 Chi-square statistic : 29.50 p-value of test : 0.04 ----------------------------------------------- CPU time used : 00:01:15.60 Generator state: 1887040000000 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sknuth_SimpPoker test: ----------------------------------------------- N = 1, n = 100000000, r = 25, d = 32, k = 32 1971905953792 bits have been read. EOF, rewinding dieharder-bbwhite-f1-20150505.bits ----------------------------------------------- Number of degrees of freedom : 18 Chi-square statistic : 19.67 p-value of test : 0.35 ----------------------------------------------- CPU time used : 00:01:31.00 Generator state: 1989440000000 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sknuth_CouponCollector test: ----------------------------------------------- N = 1, n = 200000000, r = 0, d = 8 ----------------------------------------------- Number of degrees of freedom : 54 Chi-square statistic : 45.80 p-value of test : 0.78 ----------------------------------------------- CPU time used : 00:01:17.78 Generator state: 2128479702368 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sknuth_CouponCollector test: ----------------------------------------------- N = 1, n = 200000000, r = 10, d = 8 ----------------------------------------------- Number of degrees of freedom : 54 Chi-square statistic : 77.07 p-value of test : 0.02 ----------------------------------------------- CPU time used : 00:01:27.38 Generator state: 2267504900896 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sknuth_CouponCollector test: ----------------------------------------------- N = 1, n = 200000000, r = 20, d = 8 ----------------------------------------------- Number of degrees of freedom : 54 Chi-square statistic : 69.40 p-value of test : 0.08 ----------------------------------------------- CPU time used : 00:01:27.52 Generator state: 2406540395360 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sknuth_CouponCollector test: ----------------------------------------------- N = 1, n = 200000000, r = 27, d = 8 ----------------------------------------------- Number of degrees of freedom : 54 Chi-square statistic : 56.04 p-value of test : 0.40 ----------------------------------------------- CPU time used : 00:01:27.51 Generator state: 2545577215968 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sknuth_Gap test: ----------------------------------------------- N = 1, n = 500000000, r = 0, Alpha = 0, Beta = 0.0625 ----------------------------------------------- Number of degrees of freedom : 232 Chi-square statistic : 228.06 p-value of test : 0.56 ----------------------------------------------- CPU time used : 00:01:40.85 Generator state: 2801586866784 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sknuth_Gap test: ----------------------------------------------- N = 1, n = 300000000, r = 25, Alpha = 0, Beta = 0.03125 ----------------------------------------------- Number of degrees of freedom : 434 Chi-square statistic : 441.16 p-value of test : 0.40 ----------------------------------------------- CPU time used : 00:02:16.76 Generator state: 3108761501792 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 = 0.0078125 ----------------------------------------------- Number of degrees of freedom : 1437 Chi-square statistic : 1493.21 p-value of test : 0.15 ----------------------------------------------- CPU time used : 00:02:31.22 Generator state: 3518365384032 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sknuth_Gap test: ----------------------------------------------- N = 1, n = 10000000, r = 20, Alpha = 0, Beta = 0.000976562 ----------------------------------------------- Number of degrees of freedom : 7046 Chi-square statistic : 7093.31 p-value of test : 0.34 ----------------------------------------------- CPU time used : 00:02:19.68 Generator state: 3845879525760 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sknuth_Run test: ----------------------------------------------- N = 5, n = 1000000000, r = 0, Up = FALSE 3943811907584 bits have been read. EOF, rewinding dieharder-bbwhite-f1-20150505.bits ----------------------------------------------- Kolmogorov-Smirnov+ statistic = D+ : 0.49 p-value of test : 0.06 Kolmogorov-Smirnov- statistic = D- : 0.22 p-value of test : 0.53 Anderson-Darling statistic = A2 : 2.15 p-value of test : 0.08 Test on the sum of all N observations Number of degrees of freedom : 30 Chi-square statistic : 23.43 p-value of test : 0.80 ----------------------------------------------- CPU time used : 00:01:22.85 Generator state: 4005879525760 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sknuth_Run test: ----------------------------------------------- N = 10, n = 1000000000, r = 15, Up = TRUE ----------------------------------------------- Kolmogorov-Smirnov+ statistic = D+ : 0.33 p-value of test : 0.09 Kolmogorov-Smirnov- statistic = D- : 0.18 p-value of test : 0.47 Anderson-Darling statistic = A2 : 1.32 p-value of test : 0.23 Test on the sum of all N observations Number of degrees of freedom : 60 Chi-square statistic : 62.28 p-value of test : 0.40 ----------------------------------------------- CPU time used : 00:03:17.81 Generator state: 4325879525760 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 = 1000000000, r = 5, t = 3, Sparse = FALSE GenerCell = smultin_GenerCellPermut Number of cells = t! = 6 Expected number per cell = 1.6666667e+08 Hashing = FALSE For Delta > -1, we use the ChiSquare approximation Correction factor of the ChiSquare: Delta = 1, Mu = 2.5000002e-09, Sigma = 1 ----------------------------------------------- Test Results for Delta = 1.0000 Number of degrees of freedom : 5 Value of the statistic : 7.70 p-value of test : 0.17 ----------------------------------------------- CPU time used : 00:00:58.19 Generator state: 4421879525760 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 = 1000000000, r = 5, t = 5, Sparse = FALSE GenerCell = smultin_GenerCellPermut Number of cells = t! = 120 Expected number per cell = 8333333.3 Hashing = FALSE For Delta > -1, we use the ChiSquare approximation Correction factor of the ChiSquare: Delta = 1, Mu = 5.9500005e-08, Sigma = 1 ----------------------------------------------- Test Results for Delta = 1.0000 Number of degrees of freedom : 119 Value of the statistic : 122.15 p-value of test : 0.40 ----------------------------------------------- CPU time used : 00:01:40.78 Generator state: 4581879525760 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 = 500000000, r = 5, t = 7, Sparse = FALSE GenerCell = smultin_GenerCellPermut Number of cells = t! = 5040 Expected number per cell = 99206.349 Hashing = FALSE For Delta > -1, we use the ChiSquare approximation Correction factor of the ChiSquare: Delta = 1, Mu = 5.0390004e-06, Sigma = 1 ----------------------------------------------- Test Results for Delta = 1.0000 Number of degrees of freedom : 5039 Value of the statistic : 5054.11 p-value of test : 0.44 ----------------------------------------------- CPU time used : 00:01:17.34 Generator state: 4693879525760 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 = 500000000, r = 10, t = 10, Sparse = FALSE GenerCell = smultin_GenerCellPermut Number of cells = t! = 3628800 Expected number per cell = 137.7866 Hashing = FALSE For Delta > -1, we use the ChiSquare approximation Correction factor of the ChiSquare: Delta = 1, Mu = 0.0036287993, 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 : 0.27 ----------------------------------------------- CPU time used : 00:02:43.92 Generator state: 4853879525760 bits have been read. *********************************************************** Test sknuth_CollisionPermut calling smultin_Multinomial *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smultin_Multinomial test: ----------------------------------------------- N = 20, n = 20000000, r = 0, t = 14, Sparse = TRUE GenerCell = smultin_GenerCellPermut Number of cells = t! = 87178291200 Expected number per cell = 1 / 4358.9146 EColl = n^2 / (2k) = 2294.14912 Hashing = TRUE Collision test, Mu = 2293.9736, Sigma = 47.8841 ----------------------------------------------- Test Results for Collisions For the total number of collisions, we use the Poisson approximation: Expected number of collisions = N*Mu : 45879.47 Observed number of collisions : 45896 p-value of test : 0.47 ----------------------------- Total number of cells containing j balls j = 0 : 1743165869896 j = 1 : 399908211 j = 2 : 45890 j = 3 : 3 j = 4 : 0 j = 5 : 0 ----------------------------------------------- CPU time used : 00:04:01.95 Generator state: 5033079525760 bits have been read. *********************************************************** Test sknuth_CollisionPermut calling smultin_Multinomial *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smultin_Multinomial test: ----------------------------------------------- N = 20, n = 20000000, r = 10, t = 14, Sparse = TRUE GenerCell = smultin_GenerCellPermut Number of cells = t! = 87178291200 Expected number per cell = 1 / 4358.9146 EColl = n^2 / (2k) = 2294.14912 Hashing = TRUE Collision test, Mu = 2293.9736, Sigma = 47.8841 ----------------------------------------------- Test Results for Collisions For the total number of collisions, we use the Poisson approximation: Expected number of collisions = N*Mu : 45879.47 Observed number of collisions : 46033 p-value of test : 0.24 ----------------------------- Total number of cells containing j balls j = 0 : 1743165870033 j = 1 : 399907936 j = 2 : 46029 j = 3 : 2 j = 4 : 0 j = 5 : 0 ----------------------------------------------- CPU time used : 00:04:11.97 Generator state: 5212279525760 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sknuth_MaxOft test: ----------------------------------------------- N = 40, n = 10000000, r = 0, d = 100000, t = 8 Number of categories = 100000 Expected number per category = 100.00 ----------------------------------------------- Test results for chi2 with 99999 degrees of freedom: Kolmogorov-Smirnov+ statistic = D+ : 0.073 p-value of test : 0.63 Kolmogorov-Smirnov- statistic = D- : 0.14 p-value of test : 0.20 Anderson-Darling statistic = A2 : 0.85 p-value of test : 0.45 Test on the sum of all N observations Number of degrees of freedom : 3999960 Chi-square statistic : 4.00e+6 p-value of test : 0.20 ----------------------------------------------- Test results for Anderson-Darling: Kolmogorov-Smirnov+ statistic = D+ : 0.13 p-value of test : 0.26 Kolmogorov-Smirnov- statistic = D- : 0.040 p-value of test : 0.86 Anderson-Darling statistic = A2 : 0.54 p-value of test : 0.70 ----------------------------------------------- CPU time used : 00:02:36.62 Generator state: 5314679525760 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sknuth_MaxOft test: ----------------------------------------------- N = 30, n = 10000000, r = 0, d = 100000, t = 16 Number of categories = 100000 Expected number per category = 100.00 ----------------------------------------------- Test results for chi2 with 99999 degrees of freedom: Kolmogorov-Smirnov+ statistic = D+ : 0.074 p-value of test : 0.69 Kolmogorov-Smirnov- statistic = D- : 0.12 p-value of test : 0.39 Anderson-Darling statistic = A2 : 0.52 p-value of test : 0.73 Test on the sum of all N observations Number of degrees of freedom : 2999970 Chi-square statistic : 3.00e+6 p-value of test : 0.41 ----------------------------------------------- Test results for Anderson-Darling: Kolmogorov-Smirnov+ statistic = D+ : 0.027 p-value of test : 0.94 Kolmogorov-Smirnov- statistic = D- : 0.17 p-value of test : 0.17 Anderson-Darling statistic = A2 : 0.72 p-value of test : 0.54 ----------------------------------------------- CPU time used : 00:02:26.47 Generator state: 5468279525760 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sknuth_MaxOft test: ----------------------------------------------- N = 20, n = 10000000, r = 0, d = 100000, t = 24 Number of categories = 100000 Expected number per category = 100.00 ----------------------------------------------- Test results for chi2 with 99999 degrees of freedom: Kolmogorov-Smirnov+ statistic = D+ : 0.14 p-value of test : 0.43 Kolmogorov-Smirnov- statistic = D- : 0.070 p-value of test : 0.79 Anderson-Darling statistic = A2 : 0.27 p-value of test : 0.96 Test on the sum of all N observations Number of degrees of freedom : 1999980 Chi-square statistic : 2.00e+6 p-value of test : 0.66 ----------------------------------------------- Test results for Anderson-Darling: Kolmogorov-Smirnov+ statistic = D+ : 0.081 p-value of test : 0.73 Kolmogorov-Smirnov- statistic = D- : 0.14 p-value of test : 0.41 Anderson-Darling statistic = A2 : 0.55 p-value of test : 0.69 ----------------------------------------------- CPU time used : 00:01:55.96 Generator state: 5621879525760 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sknuth_MaxOft test: ----------------------------------------------- N = 20, n = 10000000, r = 0, d = 100000, t = 32 Number of categories = 100000 Expected number per category = 100.00 ----------------------------------------------- Test results for chi2 with 99999 degrees of freedom: Kolmogorov-Smirnov+ statistic = D+ : 0.24 p-value of test : 0.08 Kolmogorov-Smirnov- statistic = D- : 0.040 p-value of test : 0.92 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 : 1999980 Chi-square statistic : 2.00e+6 p-value of test : 0.87 ----------------------------------------------- Test results for Anderson-Darling: Kolmogorov-Smirnov+ statistic = D+ : 0.11 p-value of test : 0.56 Kolmogorov-Smirnov- statistic = D- : 0.15 p-value of test : 0.37 Anderson-Darling statistic = A2 : 0.52 p-value of test : 0.72 ----------------------------------------------- CPU time used : 00:02:13.84 Generator state: 5826679525760 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits svaria_SampleProd test: ----------------------------------------------- N = 40, n = 10000000, r = 0, t = 8 5915717861376 bits have been read. EOF, rewinding dieharder-bbwhite-f1-20150505.bits ----------------------------------------------- Kolmogorov-Smirnov+ statistic = D+ : 0.077 p-value of test : 0.59 Kolmogorov-Smirnov- statistic = D- : 0.10 p-value of test : 0.41 Anderson-Darling statistic = A2 : 0.31 p-value of test : 0.93 ----------------------------------------------- CPU time used : 00:01:58.03 Generator state: 5929079525760 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits svaria_SampleProd test: ----------------------------------------------- N = 20, n = 10000000, r = 0, t = 16 ----------------------------------------------- Kolmogorov-Smirnov+ statistic = D+ : 0.13 p-value of test : 0.45 Kolmogorov-Smirnov- statistic = D- : 0.25 p-value of test : 0.07 Anderson-Darling statistic = A2 : 1.46 p-value of test : 0.19 ----------------------------------------------- CPU time used : 00:01:27.20 Generator state: 6031479525760 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits svaria_SampleProd test: ----------------------------------------------- N = 20, n = 10000000, r = 0, t = 24 ----------------------------------------------- Kolmogorov-Smirnov+ statistic = D+ : 0.14 p-value of test : 0.40 Kolmogorov-Smirnov- statistic = D- : 0.12 p-value of test : 0.52 Anderson-Darling statistic = A2 : 0.82 p-value of test : 0.47 ----------------------------------------------- CPU time used : 00:01:54.48 Generator state: 6185079525760 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits svaria_SampleMean test: ----------------------------------------------- N = 20000000, n = 30, r = 0 ----------------------------------------------- Kolmogorov-Smirnov+ statistic = D+ : 1.09e-4 p-value of test : 0.62 Kolmogorov-Smirnov- statistic = D- : 2.47e-4 p-value of test : 0.09 Anderson-Darling statistic = A2 : 1.44 p-value of test : 0.19 ----------------------------------------------- CPU time used : 00:00:28.18 Generator state: 6204279525760 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits svaria_SampleMean test: ----------------------------------------------- N = 20000000, n = 30, r = 10 ----------------------------------------------- Kolmogorov-Smirnov+ statistic = D+ : 1.96e-4 p-value of test : 0.21 Kolmogorov-Smirnov- statistic = D- : 1.80e-4 p-value of test : 0.27 Anderson-Darling statistic = A2 : 1.17 p-value of test : 0.28 ----------------------------------------------- CPU time used : 00:00:29.00 Generator state: 6223479525760 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits svaria_SampleCorr test: ----------------------------------------------- N = 1, n = 2000000000, r = 0, k = 1 ----------------------------------------------- Normal statistic : -1.43 p-value of test : 0.92 ----------------------------------------------- CPU time used : 00:00:26.42 Generator state: 6287479525760 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits svaria_SampleCorr test: ----------------------------------------------- N = 1, n = 2000000000, r = 0, k = 2 ----------------------------------------------- Normal statistic : 0.67 p-value of test : 0.25 ----------------------------------------------- CPU time used : 00:00:26.54 Generator state: 6351479525760 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits svaria_AppearanceSpacings test: ----------------------------------------------- N = 1, Q = 10000000, K = 1000000000, r = 0, s = 3, L = 15 Sequences of n = (K + Q)L = 15150000000 bits Q = 10000000 initialization blocks K = 1000000000 blocks for the test the blocks have L = 15 bits ----------------------------------------------- Normal statistic : 0.25 p-value of test : 0.40 ----------------------------------------------- CPU time used : 00:01:37.61 Generator state: 6513079525760 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits svaria_AppearanceSpacings test: ----------------------------------------------- N = 1, Q = 10000000, K = 1000000000, r = 27, s = 3, L = 15 Sequences of n = (K + Q)L = 15150000000 bits Q = 10000000 initialization blocks K = 1000000000 blocks for the test the blocks have L = 15 bits ----------------------------------------------- Normal statistic : -0.032 p-value of test : 0.51 ----------------------------------------------- CPU time used : 00:01:39.60 Generator state: 6674679525760 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits svaria_WeightDistrib test: ----------------------------------------------- N = 1, n = 20000000, r = 0, k = 256, Alpha = 0, Beta = 0.25 ----------------------------------------------- Number of degrees of freedom : 67 Chi-square statistic : 68.91 p-value of test : 0.41 ----------------------------------------------- CPU time used : 00:01:02.56 Generator state: 6838519525760 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits svaria_WeightDistrib test: ----------------------------------------------- N = 1, n = 20000000, r = 20, k = 256, Alpha = 0, Beta = 0.25 ----------------------------------------------- Number of degrees of freedom : 67 Chi-square statistic : 68.89 p-value of test : 0.41 ----------------------------------------------- CPU time used : 00:01:13.85 Generator state: 7002359525760 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits svaria_WeightDistrib test: ----------------------------------------------- N = 1, n = 20000000, r = 28, k = 256, Alpha = 0, Beta = 0.25 ----------------------------------------------- Number of degrees of freedom : 67 Chi-square statistic : 81.61 p-value of test : 0.11 ----------------------------------------------- CPU time used : 00:01:13.93 Generator state: 7166199525760 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits svaria_WeightDistrib test: ----------------------------------------------- N = 1, n = 20000000, r = 0, k = 256, Alpha = 0, Beta = 0.0625 ----------------------------------------------- Number of degrees of freedom : 37 Chi-square statistic : 46.07 p-value of test : 0.15 ----------------------------------------------- CPU time used : 00:01:02.53 Generator state: 7330039525760 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits svaria_WeightDistrib test: ----------------------------------------------- N = 1, n = 20000000, r = 10, k = 256, Alpha = 0, Beta = 0.0625 ----------------------------------------------- Number of degrees of freedom : 37 Chi-square statistic : 33.78 p-value of test : 0.62 ----------------------------------------------- CPU time used : 00:01:13.89 Generator state: 7493879525760 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits svaria_WeightDistrib test: ----------------------------------------------- N = 1, n = 20000000, r = 26, k = 256, Alpha = 0, Beta = 0.0625 ----------------------------------------------- Number of degrees of freedom : 37 Chi-square statistic : 33.64 p-value of test : 0.63 ----------------------------------------------- CPU time used : 00:01:14.00 Generator state: 7657719525760 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits svaria_SumCollector test: ----------------------------------------------- N = 1, n = 500000000, r = 0, g = 10 7887623815168 bits have been read. EOF, rewinding dieharder-bbwhite-f1-20150505.bits ----------------------------------------------- Number of degrees of freedom : 29 Chi-square statistic : 14.29 p-value of test : 0.99 ----------------------------------------------- CPU time used : 00:02:06.07 Generator state: 7988385125792 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smarsa_MatrixRank test: ----------------------------------------------- N = 10, n = 1000000, r = 0, s = 5, L = 30, k = 30 ----------------------------------------------- Kolmogorov-Smirnov+ statistic = D+ : 0.085 p-value of test : 0.82 Kolmogorov-Smirnov- statistic = D- : 0.19 p-value of test : 0.45 Anderson-Darling statistic = A2 : 0.29 p-value of test : 0.95 Test on the sum of all N observations Number of degrees of freedom : 40 Chi-square statistic : 43.47 p-value of test : 0.33 ----------------------------------------------- CPU time used : 00:01:02.40 Generator state: 8045985125792 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smarsa_MatrixRank test: ----------------------------------------------- N = 10, n = 1000000, r = 25, s = 5, L = 30, k = 30 ----------------------------------------------- Kolmogorov-Smirnov+ statistic = D+ : 0.17 p-value of test : 0.51 Kolmogorov-Smirnov- statistic = D- : 0.18 p-value of test : 0.48 Anderson-Darling statistic = A2 : 0.56 p-value of test : 0.68 Test on the sum of all N observations Number of degrees of freedom : 40 Chi-square statistic : 44.20 p-value of test : 0.30 ----------------------------------------------- CPU time used : 00:01:02.26 Generator state: 8103585125792 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smarsa_MatrixRank test: ----------------------------------------------- N = 1, n = 5000, r = 0, s = 4, L = 1000, k = 1000 ----------------------------------------------- Number of degrees of freedom : 3 Chi-square statistic : 2.19 p-value of test : 0.53 ----------------------------------------------- CPU time used : 00:02:43.87 Generator state: 8143585125792 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smarsa_MatrixRank test: ----------------------------------------------- N = 1, n = 5000, r = 26, s = 4, L = 1000, k = 1000 ----------------------------------------------- Number of degrees of freedom : 3 Chi-square statistic : 0.78 p-value of test : 0.85 ----------------------------------------------- CPU time used : 00:02:43.87 Generator state: 8183585125792 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smarsa_MatrixRank test: ----------------------------------------------- N = 1, n = 80, r = 15, s = 15, L = 5000, k = 5000 ----------------------------------------------- Number of degrees of freedom : 2 Chi-square statistic : 1.63 p-value of test : 0.44 ----------------------------------------------- CPU time used : 00:01:59.34 Generator state: 8187860325792 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smarsa_MatrixRank test: ----------------------------------------------- N = 1, n = 80, r = 0, s = 30, L = 5000, k = 5000 ----------------------------------------------- Number of degrees of freedom : 2 Chi-square statistic : 5.55 p-value of test : 0.06 ----------------------------------------------- CPU time used : 00:01:32.79 Generator state: 8189997925792 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smarsa_Savir2 test: ----------------------------------------------- N = 10, n = 10000000, r = 10, m = 1048576, t = 30 ----------------------------------------------- Kolmogorov-Smirnov+ statistic = D+ : 0.16 p-value of test : 0.56 Kolmogorov-Smirnov- statistic = D- : 0.17 p-value of test : 0.52 Anderson-Darling statistic = A2 : 0.43 p-value of test : 0.82 Test on the sum of all N observations Number of degrees of freedom : 130 Chi-square statistic : 132.41 p-value of test : 0.42 ----------------------------------------------- CPU time used : 00:00:41.62 Generator state: 8285997925792 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits smarsa_GCD test: ----------------------------------------------- N = 10, n = 50000000, r = 0, s = 30 ----------------------------------------------- Test results for GCD values: Kolmogorov-Smirnov+ statistic = D+ : 0.21 p-value of test : 0.36 Kolmogorov-Smirnov- statistic = D- : 0.10 p-value of test : 0.75 Anderson-Darling statistic = A2 : 0.66 p-value of test : 0.59 Test on the sum of all N observations Number of degrees of freedom : 17430 Chi-square statistic :17318.76 p-value of test : 0.72 ----------------------------------------------- CPU time used : 00:01:37.47 Generator state: 8317997925856 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits swalk_RandomWalk1 test: ----------------------------------------------- N = 1, n = 100000000, r = 0, s = 5, L0 = 50, L1 = 50 ----------------------------------------------- Test on the values of the Statistic H Number of degrees of freedom : 36 ChiSquare statistic : 47.72 p-value of test : 0.09 ----------------------------------------------- Test on the values of the Statistic M Number of degrees of freedom : 35 ChiSquare statistic : 41.85 p-value of test : 0.20 ----------------------------------------------- Test on the values of the Statistic J Number of degrees of freedom : 25 ChiSquare statistic : 28.77 p-value of test : 0.27 ----------------------------------------------- Test on the values of the Statistic R Number of degrees of freedom : 24 ChiSquare statistic : 22.33 p-value of test : 0.56 ----------------------------------------------- Test on the values of the Statistic C Number of degrees of freedom : 17 ChiSquare statistic : 16.69 p-value of test : 0.48 ----------------------------------------------- CPU time used : 00:00:49.72 Generator state: 8349997925856 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits swalk_RandomWalk1 test: ----------------------------------------------- N = 1, n = 100000000, r = 25, s = 5, L0 = 50, L1 = 50 ----------------------------------------------- Test on the values of the Statistic H Number of degrees of freedom : 36 ChiSquare statistic : 17.61 p-value of test : 0.9957 ----------------------------------------------- Test on the values of the Statistic M Number of degrees of freedom : 35 ChiSquare statistic : 24.77 p-value of test : 0.90 ----------------------------------------------- Test on the values of the Statistic J Number of degrees of freedom : 25 ChiSquare statistic : 21.43 p-value of test : 0.67 ----------------------------------------------- Test on the values of the Statistic R Number of degrees of freedom : 24 ChiSquare statistic : 31.03 p-value of test : 0.15 ----------------------------------------------- Test on the values of the Statistic C Number of degrees of freedom : 17 ChiSquare statistic : 20.91 p-value of test : 0.23 ----------------------------------------------- CPU time used : 00:00:50.61 Generator state: 8381997925856 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits swalk_RandomWalk1 test: ----------------------------------------------- N = 1, n = 10000000, r = 0, s = 10, L0 = 1000, L1 = 1000 ----------------------------------------------- Test on the values of the Statistic H Number of degrees of freedom : 146 ChiSquare statistic : 150.02 p-value of test : 0.39 ----------------------------------------------- Test on the values of the Statistic M Number of degrees of freedom : 146 ChiSquare statistic : 131.48 p-value of test : 0.80 ----------------------------------------------- Test on the values of the Statistic J Number of degrees of freedom : 500 ChiSquare statistic : 502.09 p-value of test : 0.47 ----------------------------------------------- Test on the values of the Statistic R Number of degrees of freedom : 136 ChiSquare statistic : 139.38 p-value of test : 0.40 ----------------------------------------------- Test on the values of the Statistic C Number of degrees of freedom : 74 ChiSquare statistic : 83.28 p-value of test : 0.22 ----------------------------------------------- CPU time used : 00:01:18.35 Generator state: 8413997925856 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 = 1000, L1 = 1000 ----------------------------------------------- Test on the values of the Statistic H Number of degrees of freedom : 146 ChiSquare statistic : 147.38 p-value of test : 0.45 ----------------------------------------------- Test on the values of the Statistic M Number of degrees of freedom : 146 ChiSquare statistic : 151.53 p-value of test : 0.36 ----------------------------------------------- Test on the values of the Statistic J Number of degrees of freedom : 500 ChiSquare statistic : 506.29 p-value of test : 0.41 ----------------------------------------------- Test on the values of the Statistic R Number of degrees of freedom : 136 ChiSquare statistic : 125.91 p-value of test : 0.72 ----------------------------------------------- Test on the values of the Statistic C Number of degrees of freedom : 74 ChiSquare statistic : 75.17 p-value of test : 0.44 ----------------------------------------------- CPU time used : 00:01:19.10 Generator state: 8445997925856 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits swalk_RandomWalk1 test: ----------------------------------------------- N = 1, n = 1000000, r = 0, s = 15, L0 = 10000, L1 = 10000 ----------------------------------------------- Test on the values of the Statistic H Number of degrees of freedom : 384 ChiSquare statistic : 371.28 p-value of test : 0.67 ----------------------------------------------- Test on the values of the Statistic M Number of degrees of freedom : 384 ChiSquare statistic : 352.53 p-value of test : 0.87 ----------------------------------------------- Test on the values of the Statistic J Number of degrees of freedom : 5000 ChiSquare statistic : 5070.24 p-value of test : 0.24 ----------------------------------------------- Test on the values of the Statistic R Number of degrees of freedom : 378 ChiSquare statistic : 333.33 p-value of test : 0.95 ----------------------------------------------- Test on the values of the Statistic C Number of degrees of freedom : 200 ChiSquare statistic : 207.51 p-value of test : 0.34 ----------------------------------------------- CPU time used : 00:01:10.73 Generator state: 8467341925856 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits swalk_RandomWalk1 test: ----------------------------------------------- N = 1, n = 1000000, r = 15, s = 15, L0 = 10000, L1 = 10000 ----------------------------------------------- Test on the values of the Statistic H Number of degrees of freedom : 384 ChiSquare statistic : 418.90 p-value of test : 0.11 ----------------------------------------------- Test on the values of the Statistic M Number of degrees of freedom : 384 ChiSquare statistic : 373.10 p-value of test : 0.65 ----------------------------------------------- Test on the values of the Statistic J Number of degrees of freedom : 5000 ChiSquare statistic : 4964.15 p-value of test : 0.64 ----------------------------------------------- Test on the values of the Statistic R Number of degrees of freedom : 378 ChiSquare statistic : 380.81 p-value of test : 0.45 ----------------------------------------------- Test on the values of the Statistic C Number of degrees of freedom : 200 ChiSquare statistic : 185.92 p-value of test : 0.75 ----------------------------------------------- CPU time used : 00:01:11.05 Generator state: 8488685925856 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits scomp_LinearComp test: ----------------------------------------------- N = 1, n = 400020, r = 0, s = 1 ----------------------------------------------- Number of degrees of freedom : 12 Chi2 statistic for size of jumps : 3.75 p-value of test : 0.99 ----------------------------------------------- Normal statistic for number of jumps : 0.097 p-value of test : 0.46 ----------------------------------------------- CPU time used : 00:01:58.09 Generator state: 8488698726496 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits scomp_LinearComp test: ----------------------------------------------- N = 1, n = 400020, r = 29, s = 1 ----------------------------------------------- Number of degrees of freedom : 12 Chi2 statistic for size of jumps : 5.68 p-value of test : 0.93 ----------------------------------------------- Normal statistic for number of jumps : 0.96 p-value of test : 0.17 ----------------------------------------------- CPU time used : 00:01:59.09 Generator state: 8488711527136 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits scomp_LempelZiv test: ----------------------------------------------- N = 10, n = 134217728, r = 0, s = 30, k = 27 ----------------------------------------------- Kolmogorov-Smirnov+ statistic = D+ : 0.15 p-value of test : 0.57 Kolmogorov-Smirnov- statistic = D- : 0.17 p-value of test : 0.50 Anderson-Darling statistic = A2 : 0.33 p-value of test : 0.91 Tests on the sum of all N observations Standardized normal statistic : 0.36 p-value of test : 0.36 Sample variance : 0.75 p-value of test : 0.67 ----------------------------------------------- CPU time used : 00:00:50.12 Generator state: 8490143183136 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits scomp_LempelZiv test: ----------------------------------------------- N = 10, n = 134217728, r = 15, s = 15, k = 27 ----------------------------------------------- Kolmogorov-Smirnov+ statistic = D+ : 0.097 p-value of test : 0.77 Kolmogorov-Smirnov- statistic = D- : 0.26 p-value of test : 0.22 Anderson-Darling statistic = A2 : 0.72 p-value of test : 0.54 Tests on the sum of all N observations Standardized normal statistic : 0.12 p-value of test : 0.45 Sample variance : 1.38 p-value of test : 0.19 ----------------------------------------------- CPU time used : 00:00:52.12 Generator state: 8493006494816 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sspectral_Fourier3 test: ----------------------------------------------- N = 100000, n = 16384, r = 0, s = 3, k = 14 ----------------------------------------------- Kolmogorov-Smirnov+ statistic = D+ : 0.018 p-value of test : 0.06 Kolmogorov-Smirnov- statistic = D- : 0.014 p-value of test : 0.20 Anderson-Darling statistic = A2 : 2.46 p-value of test : 0.05 ----------------------------------------------- CPU time used : 00:00:41.20 Generator state: 8510484894816 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sspectral_Fourier3 test: ----------------------------------------------- N = 100000, n = 16384, r = 27, s = 3, k = 14 ----------------------------------------------- Kolmogorov-Smirnov+ statistic = D+ : 8.69e-3 p-value of test : 0.54 Kolmogorov-Smirnov- statistic = D- : 7.39e-3 p-value of test : 0.64 Anderson-Darling statistic = A2 : 0.21 p-value of test : 0.99 ----------------------------------------------- CPU time used : 00:00:40.04 Generator state: 8527963294816 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sstring_LongestHeadRun test: ----------------------------------------------- N = 1, n = 1000, r = 0, s = 3, L = 10000020 ----------------------------------------------- Number of degrees of freedom : 8 Chi-square statistic : 7.40 p-value of test : 0.49 ----------------------------------------------- Global longest run of 1 : 32.00 p-value of test : 0.50 ----------------------------------------------- CPU time used : 00:01:27.45 Generator state: 8634630174816 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sstring_LongestHeadRun test: ----------------------------------------------- N = 1, n = 1000, r = 27, s = 3, L = 10000020 ----------------------------------------------- Number of degrees of freedom : 8 Chi-square statistic : 5.91 p-value of test : 0.66 ----------------------------------------------- Global longest run of 1 : 36.00 p-value of test : 0.07 ----------------------------------------------- CPU time used : 00:01:28.12 Generator state: 8741297054816 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sstring_PeriodsInStrings test: ----------------------------------------------- N = 10, n = 500000000, r = 0, s = 10 ----------------------------------------------- Kolmogorov-Smirnov+ statistic = D+ : 0.091 p-value of test : 0.80 Kolmogorov-Smirnov- statistic = D- : 0.15 p-value of test : 0.59 Anderson-Darling statistic = A2 : 0.36 p-value of test : 0.88 Test on the sum of all N observations Number of degrees of freedom : 200 Chi-square statistic : 204.53 p-value of test : 0.40 ----------------------------------------------- CPU time used : 00:02:12.31 Generator state: 8901297054816 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sstring_PeriodsInStrings test: ----------------------------------------------- N = 10, n = 500000000, r = 20, s = 10 ----------------------------------------------- Kolmogorov-Smirnov+ statistic = D+ : 0.092 p-value of test : 0.80 Kolmogorov-Smirnov- statistic = D- : 0.22 p-value of test : 0.33 Anderson-Darling statistic = A2 : 0.47 p-value of test : 0.77 Test on the sum of all N observations Number of degrees of freedom : 200 Chi-square statistic : 207.74 p-value of test : 0.34 ----------------------------------------------- CPU time used : 00:02:15.64 Generator state: 9061297054816 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sstring_HammingWeight2 test: ----------------------------------------------- N = 10, n = 1000000000, r = 0, s = 3, L = 1000000 ----------------------------------------------- Kolmogorov-Smirnov+ statistic = D+ : 0.098 p-value of test : 0.77 Kolmogorov-Smirnov- statistic = D- : 0.25 p-value of test : 0.23 Anderson-Darling statistic = A2 : 0.52 p-value of test : 0.72 Test on the sum of all N observations Number of degrees of freedom : 10000 Chi-square statistic :10069.33 p-value of test : 0.31 ----------------------------------------------- CPU time used : 00:00:57.59 Generator state: 9167963934816 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sstring_HammingWeight2 test: ----------------------------------------------- N = 10, n = 1000000000, r = 27, s = 3, L = 1000000 ----------------------------------------------- Kolmogorov-Smirnov+ statistic = D+ : 0.15 p-value of test : 0.58 Kolmogorov-Smirnov- statistic = D- : 0.13 p-value of test : 0.65 Anderson-Darling statistic = A2 : 0.54 p-value of test : 0.70 Test on the sum of all N observations Number of degrees of freedom : 10000 Chi-square statistic : 9963.61 p-value of test : 0.60 ----------------------------------------------- CPU time used : 00:00:58.78 Generator state: 9274630814816 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sstring_HammingCorr test: ----------------------------------------------- N = 1, n = 1000000000, r = 10, s = 10, L = 30 ----------------------------------------------- Normal statistic : -0.94 p-value of test : 0.83 ----------------------------------------------- CPU time used : 00:01:06.62 Generator state: 9370630814816 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sstring_HammingCorr test: ----------------------------------------------- N = 1, n = 100000000, r = 10, s = 10, L = 300 ----------------------------------------------- Normal statistic : 0.055 p-value of test : 0.48 ----------------------------------------------- CPU time used : 00:01:04.12 Generator state: 9466630814816 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sstring_HammingCorr test: ----------------------------------------------- N = 1, n = 100000000, r = 10, s = 10, L = 1200 ----------------------------------------------- Normal statistic : 1.69 p-value of test : 0.05 ----------------------------------------------- CPU time used : 00:04:14.79 Generator state: 9850630814816 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sstring_HammingIndep test: ----------------------------------------------- N = 10, n = 30000000, r = 0, s = 3, L = 30, d = 0 9859529768960 bits have been read. EOF, rewinding dieharder-bbwhite-f1-20150505.bits Counters with expected numbers >= 10 ----------------------------------------------- Kolmogorov-Smirnov+ statistic = D+ : 0.093 p-value of test : 0.79 Kolmogorov-Smirnov- statistic = D- : 0.29 p-value of test : 0.15 Anderson-Darling statistic = A2 : 0.84 p-value of test : 0.45 Test on the sum of all N observations Number of degrees of freedom : 4890 Chi-square statistic : 4959.99 p-value of test : 0.24 ----------------------------------------------- CPU time used : 00:01:50.54 Generator state: 10042630814816 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sstring_HammingIndep test: ----------------------------------------------- N = 10, n = 30000000, r = 27, s = 3, L = 30, d = 0 Counters with expected numbers >= 10 ----------------------------------------------- Kolmogorov-Smirnov+ statistic = D+ : 0.35 p-value of test : 0.06 Kolmogorov-Smirnov- statistic = D- : 0.16 p-value of test : 0.53 Anderson-Darling statistic = A2 : 1.28 p-value of test : 0.24 Test on the sum of all N observations Number of degrees of freedom : 4890 Chi-square statistic : 4853.54 p-value of test : 0.64 ----------------------------------------------- CPU time used : 00:01:52.02 Generator state: 10234630814816 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sstring_HammingIndep test: ----------------------------------------------- N = 1, n = 30000000, r = 0, s = 4, L = 300, d = 0 Counters with expected numbers >= 10 ----------------------------------------------- Number of degrees of freedom : 4117 Chi-square statistic : 4146.96 p-value of test : 0.37 ----------------------------------------------- CPU time used : 00:01:22.38 Generator state: 10378630814816 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sstring_HammingIndep test: ----------------------------------------------- N = 1, n = 30000000, r = 26, s = 4, L = 300, d = 0 Counters with expected numbers >= 10 ----------------------------------------------- Number of degrees of freedom : 4117 Chi-square statistic : 4266.12 p-value of test : 0.05 ----------------------------------------------- CPU time used : 00:01:23.29 Generator state: 10522630814816 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sstring_HammingIndep test: ----------------------------------------------- N = 1, n = 10000000, r = 0, s = 5, L = 1200, d = 0 Counters with expected numbers >= 10 ----------------------------------------------- Number of degrees of freedom : 11825 Chi-square statistic :11614.51 p-value of test : 0.92 ----------------------------------------------- CPU time used : 00:01:30.30 Generator state: 10676230814816 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sstring_HammingIndep test: ----------------------------------------------- N = 1, n = 10000000, r = 25, s = 5, L = 1200, d = 0 Counters with expected numbers >= 10 ----------------------------------------------- Number of degrees of freedom : 11825 Chi-square statistic :11751.23 p-value of test : 0.68 ----------------------------------------------- CPU time used : 00:01:32.62 Generator state: 10829830814816 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sstring_Run test: ----------------------------------------------- N = 1, n = 2000000000, r = 0, s = 3 ----------------------------------------------- Total number of 1 runs: 2000000000 Number of degrees of freedom : 54 Chi2 statistic for number of runs : 57.93 p-value of test : 0.33 ----------------------------------------------- Total number of bits: 7999893693 Normal statistic for number of bits : -0.84 p-value of test : 0.80 ----------------------------------------------- CPU time used : 00:01:05.87 Generator state: 10915163014208 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sstring_Run test: ----------------------------------------------- N = 1, n = 2000000000, r = 27, s = 3 ----------------------------------------------- Total number of 1 runs: 2000000000 Number of degrees of freedom : 54 Chi2 statistic for number of runs : 48.02 p-value of test : 0.70 ----------------------------------------------- Total number of bits: 7999992681 Normal statistic for number of bits : -0.058 p-value of test : 0.52 ----------------------------------------------- CPU time used : 00:01:07.78 Generator state: 11000496269472 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sstring_AutoCor test: ----------------------------------------------- N = 10, n = 1000000030, r = 0, s = 3, d = 1 ----------------------------------------------- Kolmogorov-Smirnov+ statistic = D+ : 6.28e-3 p-value of test : 0.9934 Kolmogorov-Smirnov- statistic = D- : 0.27 p-value of test : 0.19 Anderson-Darling statistic = A2 : 1.61 p-value of test : 0.15 Tests on the sum of all N observations Standardized normal statistic : 1.76 p-value of test : 0.04 Sample variance : 1.40 p-value of test : 0.18 ----------------------------------------------- CPU time used : 00:02:17.10 Generator state: 11107162939552 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sstring_AutoCor test: ----------------------------------------------- N = 10, n = 1000000029, r = 0, s = 3, d = 3 ----------------------------------------------- Kolmogorov-Smirnov+ statistic = D+ : 0.16 p-value of test : 0.54 Kolmogorov-Smirnov- statistic = D- : 0.18 p-value of test : 0.47 Anderson-Darling statistic = A2 : 0.52 p-value of test : 0.73 Tests on the sum of all N observations Standardized normal statistic : 0.34 p-value of test : 0.37 Sample variance : 0.44 p-value of test : 0.91 ----------------------------------------------- CPU time used : 00:02:02.07 Generator state: 11213829609632 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sstring_AutoCor test: ----------------------------------------------- N = 10, n = 1000000030, r = 27, s = 3, d = 1 ----------------------------------------------- Kolmogorov-Smirnov+ statistic = D+ : 0.26 p-value of test : 0.22 Kolmogorov-Smirnov- statistic = D- : 0.035 p-value of test : 0.95 Anderson-Darling statistic = A2 : 1.62 p-value of test : 0.15 Tests on the sum of all N observations Standardized normal statistic : -1.61 p-value of test : 0.95 Sample variance : 1.01 p-value of test : 0.43 ----------------------------------------------- CPU time used : 00:02:19.52 Generator state: 11320496279712 bits have been read. *********************************************************** HOST = itb1, Linux ufile_CreateReadBin: dieharder-bbwhite-f1-20150505.bits sstring_AutoCor test: ----------------------------------------------- N = 10, n = 1000000029, r = 27, s = 3, d = 3 ----------------------------------------------- Kolmogorov-Smirnov+ statistic = D+ : 0.32 p-value of test : 0.10 Kolmogorov-Smirnov- statistic = D- : 0.12 p-value of test : 0.69 Anderson-Darling statistic = A2 : 1.23 p-value of test : 0.26 Tests on the sum of all N observations Standardized normal statistic : -0.70 p-value of test : 0.76 Sample variance : 1.20 p-value of test : 0.29 ----------------------------------------------- CPU time used : 00:02:04.44 Generator state: 11427162949792 bits have been read. ========= Summary results of BigCrush ========= Version: TestU01 1.2.3 Generator: ufile_CreateReadBin Number of statistics: 160 Total CPU time: 03:26:09.39 All tests were passed

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