RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-05-25_22:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.84 20.3261 0.742111 2 to 25 15.63 14.5890 0.374943 3 to 26 15.58 13.4476 0.294256 4 to 27 15.84 30.2282 0.975255 5 to 28 15.77 15.9063 0.469515 6 to 29 15.66 16.3473 0.500637 7 to 30 15.79 23.9921 0.880351 8 to 31 15.89 15.1212 0.413247 9 to 32 15.69 14.1500 0.343545 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.516489 Tough bday spacings test for dh-ranFile-2016-05-25_22:31: 4096 birthdays, year=2^32 days Table of Expected vs. Observed counts: Duplicates 0 1 2 3 4 5 6 7 8 9 >=10 Expected 9.2 36.6 73.3 97.7 97.7 78.1 52.1 29.8 14.9 6.6 4.1 Observed 7 34 75 97 96 77 66 31 11 3 3 (O-E)^2/E 0.5 0.2 0.0 0.0 0.0 0.0 3.7 0.1 1.0 2.0 0.3 Birthday Spacings: Sum(O-E)^2/E= 7.819, p= 0.354 RESULTS OF GCD FOR dh-ranFile-2016-05-25_22:31 Euclid's algorithm: p-value, steps to gcd: 0.134740 p-value, dist. of gcd's: 0.883955 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-05-25_22:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.869 0.872 0.037 0.773 0.997 0.468 0.771 0.315 Bits 8 to 15---> 0.459 0.106 0.640 0.510 0.352 0.575 0.969 0.849 Bits 16 to 23---> 0.538 0.388 0.849 0.486 0.937 0.331 0.840 0.575 Bits 24 to 31---> 0.196 0.748 0.760 0.169 0.508 0.763 0.122 0.957 KS test for the above 32 p values: 0.841 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-05-25_22:31, p-values for 5 runs: 0.2865, 0.6349, 0.2884, 0.2152, 0.8566 Rank test for binary matrices (31x31) for dh-ranFile-2016-05-25_22:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 204 211.4 0.260 0.260 r= 29 5143 5134.0 0.016 0.276 r= 30 23182 23103.0 0.270 0.546 r= 31 11471 11551.5 0.561 1.107 chi-square = 1.107 with df = 3; p-value = 0.225 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-05-25_22:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 199 211.4 0.729 0.729 r= 30 5201 5134.0 0.874 1.603 r= 31 22941 23103.0 1.137 2.740 r= 32 11659 11551.5 1.000 3.740 chi-square = 3.740 with df = 3; p-value = 0.709 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-05-25_22:31 b-rank test for bits 1 to 8, p=0.88573 b-rank test for bits 2 to 9, p=0.28649 b-rank test for bits 3 to 10, p=0.04036 b-rank test for bits 4 to 11, p=0.22642 b-rank test for bits 5 to 12, p=0.68692 b-rank test for bits 6 to 13, p=0.03784 b-rank test for bits 7 to 14, p=0.05877 b-rank test for bits 8 to 15, p=0.35022 b-rank test for bits 9 to 16, p=0.64436 b-rank test for bits 10 to 17, p=0.24461 b-rank test for bits 11 to 18, p=0.15485 b-rank test for bits 12 to 19, p=0.43359 b-rank test for bits 13 to 20, p=0.75048 b-rank test for bits 14 to 21, p=0.81539 b-rank test for bits 15 to 22, p=0.46894 b-rank test for bits 16 to 23, p=0.89738 b-rank test for bits 17 to 24, p=0.15044 b-rank test for bits 18 to 25, p=0.22741 b-rank test for bits 19 to 26, p=0.37493 b-rank test for bits 20 to 27, p=0.86031 b-rank test for bits 21 to 28, p=0.81640 b-rank test for bits 22 to 29, p=0.44346 b-rank test for bits 23 to 30, p=0.38129 b-rank test for bits 24 to 31, p=0.11203 b-rank test for bits 25 to 32, p=0.12533 TEST SUMMARY, 25 tests, each on 100,000 random 6x8 matrices The above should be 25 uniform [0,1] random variables: The KS test for those 25 supposed UNI's yields p = 0.243587 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-05-25_22:31 (20 bits/word, 2097152 words 20 bitstreams. No. missing words should average 141909.33 with sigma=428.00.) ---------------------------------------------------------------- BITSTREAM test results. Bitstream No. missing words z-score p-value 1 141496 -0.97 0.167091 2 141453 -1.07 0.143169 3 141389 -1.22 0.112045 4 142715 1.88 0.970110 5 141481 -1.00 0.158469 6 141729 -0.42 0.336756 7 141501 -0.95 0.170031 8 141300 -1.42 0.077271 9 141986 0.18 0.571084 10 141794 -0.27 0.393787 11 141556 -0.83 0.204533 12 141872 -0.09 0.465249 13 141841 -0.16 0.436579 14 141876 -0.08 0.468964 15 141712 -0.46 0.322381 16 142323 0.97 0.833108 17 141967 0.13 0.553593 18 142400 1.15 0.874190 19 141130 -1.82 0.034314 20 141556 -0.83 0.204533 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-05-25_22:31 Bits used No. missing words z-score p-value 23 to 32 142128 0.7540 0.774586 22 to 31 141433 -1.6425 0.050241 21 to 30 141633 -0.9529 0.170330 20 to 29 142022 0.3885 0.651183 19 to 28 141985 0.2609 0.602927 18 to 27 140906 -3.4598 0.000270 17 to 26 142009 0.3437 0.634460 16 to 25 142021 0.3851 0.649907 15 to 24 141627 -0.9736 0.165140 14 to 23 141713 -0.6770 0.249203 13 to 22 142334 1.4644 0.928455 12 to 21 142180 0.9333 0.824679 11 to 20 142135 0.7782 0.781766 10 to 19 141879 -0.1046 0.458352 9 to 18 141821 -0.3046 0.380341 8 to 17 141852 -0.1977 0.421644 7 to 16 141991 0.2816 0.610883 6 to 15 142036 0.4368 0.668869 5 to 14 141862 -0.1632 0.435178 4 to 13 141969 0.2058 0.581510 3 to 12 142104 0.6713 0.748978 2 to 11 141927 0.0609 0.524293 1 to 10 142695 2.7092 0.996628 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-05-25_22:31 Bits used No. missing words z-score p-value 28 to 32 141819 -0.3062 0.379725 27 to 31 141951 0.1413 0.556166 26 to 30 141901 -0.0282 0.488737 25 to 29 142244 1.1345 0.871702 24 to 28 141727 -0.6181 0.268265 23 to 27 141697 -0.7198 0.235836 22 to 26 141991 0.2768 0.609051 21 to 25 141680 -0.7774 0.218464 20 to 24 141972 0.2124 0.584118 19 to 23 141679 -0.7808 0.217466 18 to 22 141556 -1.1977 0.115511 17 to 21 141352 -1.8893 0.029429 16 to 20 141527 -1.2960 0.097482 15 to 19 141853 -0.1909 0.424283 14 to 18 141906 -0.0113 0.495497 13 to 17 141831 -0.2655 0.395302 12 to 16 142117 0.7040 0.759273 11 to 15 141440 -1.5909 0.055811 10 to 14 141972 0.2124 0.584118 9 to 13 141948 0.1311 0.552146 8 to 12 142207 1.0091 0.843525 7 to 11 142010 0.3413 0.633544 6 to 10 141475 -1.4723 0.070469 5 to 9 141546 -1.2316 0.109044 4 to 8 141902 -0.0248 0.490088 3 to 7 142226 1.0735 0.858467 2 to 6 141714 -0.6621 0.253942 1 to 5 142184 0.9311 0.824095 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-05-25_22:31 Bits used No. missing words z-score p-value 31 to 32 141993 0.2468 0.597474 30 to 31 141440 -1.3845 0.083110 29 to 30 142520 1.8014 0.964179 28 to 29 142447 1.5860 0.943636 27 to 28 142023 0.3353 0.631304 26 to 27 141621 -0.8505 0.197515 25 to 26 141247 -1.9538 0.025364 24 to 25 142226 0.9341 0.824882 23 to 24 141513 -1.1691 0.121179 22 to 23 142657 2.2055 0.986291 21 to 22 141886 -0.0688 0.472566 20 to 21 142085 0.5182 0.697841 19 to 20 141907 -0.0069 0.497258 18 to 19 142325 1.2262 0.889932 17 to 18 141939 0.0875 0.534872 16 to 17 142379 1.3855 0.917044 15 to 16 141995 0.2527 0.599755 14 to 15 142277 1.0846 0.860944 13 to 14 142123 0.6303 0.735749 12 to 13 142154 0.7217 0.764773 11 to 12 142476 1.6716 0.952698 10 to 11 141955 0.1347 0.553583 9 to 10 142515 1.7866 0.963002 8 to 9 141602 -0.9066 0.182315 7 to 8 141839 -0.2075 0.417824 6 to 7 142304 1.1642 0.877832 5 to 6 141803 -0.3137 0.376891 4 to 5 141727 -0.5378 0.295342 3 to 4 141861 -0.1426 0.443316 2 to 3 141511 -1.1750 0.119994 1 to 2 141837 -0.2134 0.415522 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-05-25_22:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2483.18 -0.238 0.406008 Test results for specific bytes for dh-ranFile-2016-05-25_22:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2548.19 0.682 0.752244 2 to 9 2427.07 -1.031 0.151188 3 to 10 2650.82 2.133 0.983535 4 to 11 2520.96 0.296 0.616530 5 to 12 2451.18 -0.690 0.244948 6 to 13 2455.24 -0.633 0.263378 7 to 14 2462.68 -0.528 0.298823 8 to 15 2499.15 -0.012 0.495218 9 to 16 2654.77 2.189 0.985693 10 to 17 2496.84 -0.045 0.482192 11 to 18 2441.27 -0.831 0.203089 12 to 19 2519.15 0.271 0.606740 13 to 20 2517.96 0.254 0.600276 14 to 21 2560.79 0.860 0.805020 15 to 22 2575.83 1.072 0.858215 16 to 23 2573.85 1.044 0.851843 17 to 24 2452.48 -0.672 0.250774 18 to 25 2461.63 -0.543 0.293673 19 to 26 2350.60 -2.113 0.017305 20 to 27 2606.98 1.513 0.934842 21 to 28 2473.58 -0.374 0.354317 22 to 29 2386.32 -1.608 0.053947 23 to 30 2366.36 -1.890 0.029386 24 to 31 2422.98 -1.089 0.138037 25 to 32 2422.33 -1.098 0.135997 CDPARK for dh-ranFile-2016-05-25_22:31: result of 10 tests (Of 12000 tries, the average no. of successes should be 3523.0 with sigma=21.9) No. succeses z-score p-value 3533 0.4566 0.676028 3499 -1.0959 0.136563 3518 -0.2283 0.409702 3536 0.5936 0.723613 3529 0.2740 0.607947 3530 0.3196 0.625377 3509 -0.6393 0.261324 3529 0.2740 0.607947 3536 0.5936 0.723613 3536 0.5936 0.723613 Square side=100, avg. no. parked=3525.50 sample std.=12.09 p-value of the KSTEST for those 10 p-values: 0.274745 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-05-25_22:31 0.3537,0.6626,0.2621,0.0226,0.9824,0.5298,0.9791,0.7920,0.2239,0.3550, The KS test for those 10 p-values: 0.667976 The 3DSPHERES test for dh-ranFile-2016-05-25_22:31 sample no r^3 equiv. uni. 1 53.172 0.830073 2 38.341 0.721413 3 13.190 0.355740 4 0.464 0.015349 5 14.369 0.380574 6 112.849 0.976754 7 11.869 0.326749 8 76.746 0.922556 9 43.233 0.763330 10 0.347 0.011513 11 53.140 0.829894 12 38.833 0.725946 13 55.163 0.840987 14 49.832 0.810064 15 15.261 0.398721 16 0.271 0.008997 17 21.488 0.511432 18 63.611 0.880014 19 14.559 0.384496 20 65.118 0.885889 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.102882 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-05-25_22:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 -0.3 1.5 0.2 -0.4 1.2 -0.2 1.7 -0.0 0.4 -0.4 -1.6 -0.6 -0.7 -0.3 -0.9 -0.2 -0.4 -0.4 1.8 -0.6 0.2 2.7 1.1 0.4 0.2 0.6 -0.6 -1.7 0.4 -0.1 -1.5 0.2 0.1 -0.9 0.2 0.5 -0.1 1.7 -0.7 0.1 0.0 -0.1 Chi-square with 42 degrees of freedom:37.103738 z-score=-0.534226, p-value=0.314558 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-05-25_22:31 Test no p-value 1 0.790363 2 0.031068 3 0.026242 4 0.740975 5 0.018751 6 0.590933 7 0.035242 8 0.057590 9 0.062132 10 0.073783 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000159 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-05-25_22:31: (for k>=2, the prob. of a run of length k is 2*k/(k+1)!) Length Expected UpRuns (O-E)^2/E DownRuns (O-E)^2/E 2 66666.67 66550 0.20 66778 0.19 3 25000.00 25106 0.45 24944 0.13 4 6666.67 6668 0.00 6654 0.02 5 1388.89 1388 0.00 1340 1.72 6 238.10 250 0.60 244 0.15 7 34.72 34 0.01 33 0.09 8 4.96 3 0.77 6 0.22 p=0.08394 p=0.13222 Number of rngs required: 687658, p-value: 0.194 RESULTS OF CRAPS TEST for dh-ranFile-2016-05-25_22:31 No. of wins: Observed Expected 99180 98585.9 z-score= 2.657, pvalue=0.99606 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66740 66666.7 0.081 0.081 2 37760 37654.3 0.297 0.377 3 26975 26954.7 0.015 0.393 4 19071 19313.5 3.044 3.436 5 13813 13851.4 0.107 3.543 6 10085 9943.5 2.012 5.555 7 7102 7145.0 0.259 5.814 8 5232 5139.1 1.680 7.495 9 3703 3699.9 0.003 7.497 10 2695 2666.3 0.309 7.806 11 1884 1923.3 0.804 8.611 12 1392 1388.7 0.008 8.618 13 1012 1003.7 0.068 8.687 14 722 726.1 0.024 8.710 15 497 525.8 1.581 10.292 16 362 381.2 0.962 11.254 17 282 276.5 0.108 11.362 18 162 200.8 7.508 18.869 19 149 146.0 0.062 18.932 20 94 106.2 1.405 20.336 21 268 287.1 1.272 21.609 Chisq= 21.61 for 20 degrees of freedom, p= 0.63789 SUMMARY of craptest p-value for no. of wins: 0.996062 p-value for throws/game: 0.637893 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-05-25_22:31 No. of wins: Observed Expected 98603 98585.9 z-score= 0.077, pvalue=0.53056 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66902 66666.7 0.831 0.831 2 37486 37654.3 0.752 1.583 3 27035 26954.7 0.239 1.822 4 19114 19313.5 2.060 3.882 5 13921 13851.4 0.350 4.232 6 9945 9943.5 0.000 4.232 7 7269 7145.0 2.151 6.383 8 5170 5139.1 0.186 6.569 9 3721 3699.9 0.121 6.690 10 2619 2666.3 0.839 7.529 11 1829 1923.3 4.626 12.155 12 1394 1388.7 0.020 12.175 13 1017 1003.7 0.176 12.351 14 702 726.1 0.803 13.153 15 492 525.8 2.177 15.331 16 427 381.2 5.515 20.846 17 257 276.5 1.381 22.227 18 189 200.8 0.697 22.923 19 123 146.0 3.619 26.542 20 101 106.2 0.256 26.798 21 287 287.1 0.000 26.798 Chisq= 26.80 for 20 degrees of freedom, p= 0.85897 SUMMARY of craptest p-value for no. of wins: 0.530556 p-value for throws/game: 0.858967 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0002,0.0003,0.0090,0.0115,0.0153,0.0173,0.0188,0.0226,0.0254,0.0262, 0.0294,0.0294,0.0311,0.0343,0.0352,0.0368,0.0378,0.0404,0.0502,0.0539, 0.0558,0.0576,0.0588,0.0621,0.0705,0.0738,0.0773,0.0831,0.0839,0.0975, 0.1029,0.1058,0.1090,0.1120,0.1120,0.1155,0.1200,0.1212,0.1223,0.1253, 0.1322,0.1347,0.1360,0.1366,0.1380,0.1432,0.1504,0.1512,0.1549,0.1585, 0.1651,0.1671,0.1693,0.1700,0.1703,0.1823,0.1944,0.1961,0.1975,0.2031, 0.2045,0.2045,0.2152,0.2175,0.2185,0.2239,0.2247,0.2264,0.2274,0.2358, 0.2436,0.2446,0.2449,0.2492,0.2508,0.2539,0.2613,0.2621,0.2634,0.2683, 0.2747,0.2865,0.2865,0.2884,0.2937,0.2943,0.2953,0.2988,0.3146,0.3152, 0.3224,0.3267,0.3313,0.3368,0.3435,0.3502,0.3516,0.3535,0.3537,0.3543, 0.3550,0.3557,0.3749,0.3749,0.3769,0.3797,0.3803,0.3806,0.3813,0.3845, 0.3883,0.3938,0.3953,0.3987,0.4060,0.4097,0.4132,0.4155,0.4178,0.4216, 0.4243,0.4336,0.4352,0.4366,0.4433,0.4435,0.4584,0.4588,0.4652,0.4684, 0.4689,0.4690,0.4695,0.4726,0.4822,0.4858,0.4887,0.4901,0.4952,0.4955, 0.4973,0.5006,0.5077,0.5099,0.5114,0.5165,0.5243,0.5298,0.5306,0.5349, 0.5376,0.5521,0.5536,0.5536,0.5562,0.5711,0.5748,0.5749,0.5815,0.5841, 0.5841,0.5909,0.5975,0.5998,0.6003,0.6029,0.6067,0.6079,0.6079,0.6091, 0.6109,0.6165,0.6254,0.6313,0.6335,0.6345,0.6349,0.6379,0.6400,0.6444, 0.6499,0.6512,0.6626,0.6680,0.6689,0.6760,0.6869,0.6978,0.7091,0.7214, 0.7236,0.7236,0.7236,0.7259,0.7357,0.7410,0.7421,0.7476,0.7490,0.7505, 0.7522,0.7593,0.7605,0.7630,0.7633,0.7648,0.7713,0.7728,0.7746,0.7818, 0.7904,0.7920,0.8050,0.8101,0.8154,0.8164,0.8241,0.8247,0.8249,0.8299, 0.8301,0.8331,0.8404,0.8409,0.8410,0.8435,0.8490,0.8495,0.8518,0.8566, 0.8582,0.8585,0.8590,0.8603,0.8609,0.8686,0.8717,0.8725,0.8742,0.8778, 0.8800,0.8804,0.8840,0.8857,0.8859,0.8899,0.8974,0.9170,0.9226,0.9285, 0.9348,0.9373,0.9436,0.9527,0.9575,0.9630,0.9642,0.9690,0.9701,0.9753, 0.9768,0.9791,0.9824,0.9835,0.9857,0.9863,0.9961,0.9966,0.9967, Overall p-value after applying KStest on 269 p-values = 0.644244 In response to requests, we have provided a list of all the p-values produced by the tests you have chosen for this run. The individual p-values are supposed to be uniform in [0,1), but they are not necessarily independent. So even though we have applied a KSTEST to the accumulated p-values, the result is not necessarily---even if your file contains truly random bits---uniform in [0,1). But it is probably pretty close, so take that last p-value with a grain of salt. In particular, there may be some values so close to 0 or 1 that the tests they came from should be applied several more times, or new, related tests should be undertaken.