RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-10-29_05:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.76 21.4524 0.793295 2 to 25 15.94 20.6185 0.756181 3 to 26 15.94 18.0365 0.613456 4 to 27 16.00 11.1718 0.152505 5 to 28 15.66 18.8174 0.660886 6 to 29 15.95 24.2899 0.888230 7 to 30 16.18 14.2861 0.353242 8 to 31 15.99 14.9962 0.404246 9 to 32 15.87 8.8877 0.056281 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.980016 Tough bday spacings test for dh-ranFile-2015-10-29_05:31: 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 42 67 107 100 67 51 33 18 3 5 (O-E)^2/E 0.5 0.8 0.5 0.9 0.1 1.6 0.0 0.4 0.7 2.0 0.2 Birthday Spacings: Sum(O-E)^2/E= 7.580, p= 0.330 RESULTS OF GCD FOR dh-ranFile-2015-10-29_05:31 Euclid's algorithm: p-value, steps to gcd: 0.853234 p-value, dist. of gcd's: 0.229382 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-10-29_05:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.943 0.217 0.214 0.398 0.557 0.914 0.306 0.317 Bits 8 to 15---> 0.169 0.754 0.089 0.851 0.646 0.662 0.115 0.107 Bits 16 to 23---> 0.374 0.221 0.174 0.662 0.908 0.640 0.236 0.751 Bits 24 to 31---> 0.241 0.648 0.768 0.118 0.082 0.996 0.021 0.723 KS test for the above 32 p values: 0.480 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-10-29_05:31, p-values for 5 runs: 0.0212, 0.0498, 0.6547, 0.8602, 0.2798 Rank test for binary matrices (31x31) for dh-ranFile-2015-10-29_05:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 208 211.4 0.055 0.055 r= 29 5155 5134.0 0.086 0.141 r= 30 23043 23103.0 0.156 0.297 r= 31 11594 11551.5 0.156 0.453 chi-square = 0.453 with df = 3; p-value = 0.071 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-10-29_05:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 226 211.4 1.006 1.006 r= 30 5177 5134.0 0.360 1.366 r= 31 23046 23103.0 0.141 1.507 r= 32 11551 11551.5 0.000 1.507 chi-square = 1.507 with df = 3; p-value = 0.319 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-10-29_05:31 b-rank test for bits 1 to 8, p=0.27083 b-rank test for bits 2 to 9, p=0.33195 b-rank test for bits 3 to 10, p=0.31828 b-rank test for bits 4 to 11, p=0.39984 b-rank test for bits 5 to 12, p=0.57060 b-rank test for bits 6 to 13, p=0.55722 b-rank test for bits 7 to 14, p=0.76054 b-rank test for bits 8 to 15, p=0.03279 b-rank test for bits 9 to 16, p=0.78341 b-rank test for bits 10 to 17, p=0.75783 b-rank test for bits 11 to 18, p=0.28363 b-rank test for bits 12 to 19, p=0.32711 b-rank test for bits 13 to 20, p=0.68298 b-rank test for bits 14 to 21, p=0.37425 b-rank test for bits 15 to 22, p=0.80859 b-rank test for bits 16 to 23, p=0.47621 b-rank test for bits 17 to 24, p=0.80220 b-rank test for bits 18 to 25, p=0.92710 b-rank test for bits 19 to 26, p=0.57579 b-rank test for bits 20 to 27, p=0.47736 b-rank test for bits 21 to 28, p=0.73519 b-rank test for bits 22 to 29, p=0.92109 b-rank test for bits 23 to 30, p=0.82127 b-rank test for bits 24 to 31, p=0.33075 b-rank test for bits 25 to 32, p=0.24373 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 = 0.359484 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-10-29_05:31 (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 141869 -0.09 0.462464 2 142012 0.24 0.594790 3 141827 -0.19 0.423730 4 142012 0.24 0.594790 5 141464 -1.04 0.149056 6 142111 0.47 0.681248 7 141885 -0.06 0.477334 8 142347 1.02 0.846750 9 140749 -2.71 0.003354 10 142145 0.55 0.709057 11 142523 1.43 0.924187 12 142121 0.49 0.689543 13 141345 -1.32 0.093663 14 141941 0.07 0.529493 15 141923 0.03 0.512740 16 141939 0.07 0.527634 17 142583 1.57 0.942256 18 142301 0.92 0.819935 19 141527 -0.89 0.185850 20 141533 -0.88 0.189626 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-10-29_05:31 Bits used No. missing words z-score p-value 23 to 32 141947 0.1299 0.551676 22 to 31 142265 1.2264 0.889985 21 to 30 141983 0.2540 0.600266 20 to 29 141737 -0.5942 0.276175 19 to 28 142336 1.4713 0.929392 18 to 27 141925 0.0540 0.521546 17 to 26 142459 1.8954 0.970981 16 to 25 142317 1.4058 0.920102 15 to 24 141693 -0.7460 0.227844 14 to 23 141699 -0.7253 0.234141 13 to 22 142036 0.4368 0.668869 12 to 21 141807 -0.3529 0.362096 11 to 20 141870 -0.1356 0.446061 10 to 19 141638 -0.9356 0.174734 9 to 18 141866 -0.1494 0.440614 8 to 17 141972 0.2161 0.585547 7 to 16 142056 0.5058 0.693487 6 to 15 141793 -0.4011 0.344159 5 to 14 141549 -1.2425 0.107023 4 to 13 142323 1.4264 0.923131 3 to 12 141312 -2.0598 0.019711 2 to 11 140962 -3.2667 0.000544 1 to 10 141396 -1.7701 0.038355 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-10-29_05:31 Bits used No. missing words z-score p-value 28 to 32 142499 1.9989 0.977189 27 to 31 141745 -0.5571 0.288746 26 to 30 141815 -0.3198 0.374574 25 to 29 142053 0.4870 0.686877 24 to 28 141815 -0.3198 0.374574 23 to 27 141625 -0.9638 0.167565 22 to 26 141850 -0.2011 0.420303 21 to 25 142011 0.3446 0.634819 20 to 24 141942 0.1107 0.544091 19 to 23 141612 -1.0079 0.156752 18 to 22 142917 3.4158 0.999682 17 to 21 141462 -1.5164 0.064713 16 to 20 142035 0.4260 0.664946 15 to 19 141648 -0.8859 0.187845 14 to 18 141948 0.1311 0.552146 13 to 17 141942 0.1107 0.544091 12 to 16 141814 -0.3232 0.373290 11 to 15 141900 -0.0316 0.487385 10 to 14 141846 -0.2147 0.415009 9 to 13 141684 -0.7638 0.222484 8 to 12 142075 0.5616 0.712803 7 to 11 141955 0.1548 0.561516 6 to 10 142017 0.3650 0.642438 5 to 9 142257 1.1785 0.880710 4 to 8 141105 -2.7265 0.003200 3 to 7 141872 -0.1265 0.449651 2 to 6 141865 -0.1503 0.440275 1 to 5 142011 0.3446 0.634819 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-10-29_05:31 Bits used No. missing words z-score p-value 31 to 32 141840 -0.2045 0.418976 30 to 31 141340 -1.6794 0.046533 29 to 30 142370 1.3589 0.912912 28 to 29 142189 0.8250 0.795310 27 to 28 141207 -2.0718 0.019143 26 to 27 142011 0.2999 0.617878 25 to 26 141647 -0.7738 0.219514 24 to 25 141903 -0.0187 0.492551 23 to 24 141676 -0.6883 0.245635 22 to 23 142195 0.8427 0.800298 21 to 22 141992 0.2439 0.596332 20 to 21 142646 2.1731 0.985112 19 to 20 141928 0.0551 0.521960 18 to 19 141893 -0.0482 0.480790 17 to 18 141197 -2.1013 0.017809 16 to 17 141846 -0.1868 0.425903 15 to 16 141826 -0.2458 0.402914 14 to 15 142273 1.0728 0.858314 13 to 14 142399 1.4445 0.925694 12 to 13 142003 0.2763 0.608846 11 to 12 141842 -0.1986 0.421283 10 to 11 141926 0.0492 0.519610 9 to 10 142064 0.4563 0.675896 8 to 9 142104 0.5742 0.717100 7 to 8 141611 -0.8800 0.189422 6 to 7 141709 -0.5909 0.277279 5 to 6 141950 0.1200 0.547747 4 to 5 141695 -0.6322 0.263614 3 to 4 142198 0.8515 0.802764 2 to 3 141359 -1.6234 0.052253 1 to 2 141680 -0.6765 0.249365 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-10-29_05:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2474.03 -0.367 0.356695 Test results for specific bytes for dh-ranFile-2015-10-29_05:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2492.71 -0.103 0.458970 2 to 9 2442.83 -0.808 0.209408 3 to 10 2473.50 -0.375 0.353913 4 to 11 2576.21 1.078 0.859442 5 to 12 2570.65 0.999 0.841121 6 to 13 2495.37 -0.065 0.473897 7 to 14 2404.64 -1.349 0.088726 8 to 15 2532.44 0.459 0.676808 9 to 16 2631.05 1.853 0.968086 10 to 17 2610.42 1.562 0.940804 11 to 18 2490.51 -0.134 0.446603 12 to 19 2684.44 2.608 0.995451 13 to 20 2454.47 -0.644 0.259839 14 to 21 2553.45 0.756 0.775125 15 to 22 2502.41 0.034 0.513604 16 to 23 2582.80 1.171 0.879184 17 to 24 2464.65 -0.500 0.308586 18 to 25 2359.95 -1.981 0.023820 19 to 26 2538.88 0.550 0.708797 20 to 27 2458.01 -0.594 0.276291 21 to 28 2398.12 -1.441 0.074824 22 to 29 2512.34 0.175 0.569286 23 to 30 2511.01 0.156 0.561894 24 to 31 2475.12 -0.352 0.362473 25 to 32 2470.74 -0.414 0.339495 CDPARK for dh-ranFile-2015-10-29_05:31: 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 3567 2.0091 0.977738 3475 -2.1918 0.014198 3519 -0.1826 0.427537 3524 0.0457 0.518210 3518 -0.2283 0.409702 3567 2.0091 0.977738 3488 -1.5982 0.055002 3553 1.3699 0.914635 3513 -0.4566 0.323972 3515 -0.3653 0.357445 Square side=100, avg. no. parked=3523.90 sample std.=29.15 p-value of the KSTEST for those 10 p-values: 0.348104 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-10-29_05:31 0.8045,0.8553,0.3076,0.5623,0.0019,0.4553,0.5382,0.9808,0.8315,0.4364, The KS test for those 10 p-values: 0.426634 The 3DSPHERES test for dh-ranFile-2015-10-29_05:31 sample no r^3 equiv. uni. 1 1.596 0.051808 2 22.284 0.524217 3 47.250 0.792992 4 1.584 0.051422 5 4.247 0.131990 6 8.781 0.253761 7 9.003 0.259253 8 12.273 0.335758 9 12.685 0.344812 10 9.282 0.266116 11 15.100 0.395481 12 44.238 0.771130 13 7.661 0.225365 14 29.871 0.630532 15 58.469 0.857581 16 122.142 0.982946 17 48.190 0.799375 18 22.589 0.529027 19 6.153 0.185442 20 23.332 0.540550 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.663623 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-10-29_05:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.5 1.1 -0.5 1.1 1.1 3.0 1.4 1.0 -0.9 -0.4 -0.6 -0.1 -0.2 -0.4 0.1 -1.1 1.0 0.5 0.7 -0.3 0.8 -0.3 -0.3 0.7 -0.3 -1.6 -0.5 -1.4 1.6 -0.6 -0.3 0.8 -0.8 -2.7 -0.8 -0.5 1.5 2.1 -0.1 0.1 1.0 -1.1 Chi-square with 42 degrees of freedom:48.334331 z-score=0.691132, p-value=0.767643 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-10-29_05:31 Test no p-value 1 0.125518 2 0.014472 3 0.330806 4 0.971263 5 0.730389 6 0.509128 7 0.006546 8 0.251072 9 0.000977 10 0.000552 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000528 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-10-29_05:31: (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 66587 0.10 66536 0.26 3 25000.00 25274 3.00 25134 0.72 4 6666.67 6529 2.84 6716 0.37 5 1388.89 1336 2.01 1371 0.23 6 238.10 231 0.21 213 2.65 7 34.72 38 0.31 26 2.19 8 4.96 4 0.19 3 0.77 p=0.80653 p=0.69543 Number of rngs required: 687829, p-value: 0.254 RESULTS OF CRAPS TEST for dh-ranFile-2015-10-29_05:31 No. of wins: Observed Expected 98667 98585.9 z-score= 0.363, pvalue=0.64166 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66610 66666.7 0.048 0.048 2 37597 37654.3 0.087 0.135 3 26776 26954.7 1.185 1.321 4 19387 19313.5 0.280 1.601 5 13766 13851.4 0.527 2.127 6 10162 9943.5 4.799 6.927 7 7172 7145.0 0.102 7.029 8 5152 5139.1 0.033 7.061 9 3685 3699.9 0.060 7.121 10 2698 2666.3 0.377 7.498 11 1964 1923.3 0.860 8.358 12 1402 1388.7 0.127 8.484 13 994 1003.7 0.094 8.578 14 724 726.1 0.006 8.585 15 523 525.8 0.015 8.600 16 388 381.2 0.123 8.723 17 280 276.5 0.043 8.766 18 190 200.8 0.584 9.350 19 148 146.0 0.028 9.378 20 106 106.2 0.000 9.379 21 276 287.1 0.430 9.809 Chisq= 9.81 for 20 degrees of freedom, p= 0.02850 SUMMARY of craptest p-value for no. of wins: 0.641665 p-value for throws/game: 0.028495 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-10-29_05:31 No. of wins: Observed Expected 98715 98585.9 z-score= 0.578, pvalue=0.71823 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66743 66666.7 0.087 0.087 2 37783 37654.3 0.440 0.527 3 26726 26954.7 1.941 2.468 4 19208 19313.5 0.576 3.044 5 13730 13851.4 1.064 4.108 6 10116 9943.5 2.991 7.099 7 7095 7145.0 0.350 7.450 8 5129 5139.1 0.020 7.469 9 3700 3699.9 0.000 7.469 10 2672 2666.3 0.012 7.482 11 1985 1923.3 1.977 9.459 12 1409 1388.7 0.296 9.755 13 1051 1003.7 2.228 11.982 14 721 726.1 0.036 12.019 15 493 525.8 2.050 14.069 16 414 381.2 2.831 16.900 17 308 276.5 3.579 20.479 18 197 200.8 0.073 20.552 19 144 146.0 0.027 20.579 20 96 106.2 0.982 21.562 21 280 287.1 0.176 21.738 Chisq= 21.74 for 20 degrees of freedom, p= 0.64510 SUMMARY of craptest p-value for no. of wins: 0.718231 p-value for throws/game: 0.645103 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0005,0.0005,0.0006,0.0010,0.0019,0.0032,0.0034,0.0065,0.0142,0.0145, 0.0178,0.0191,0.0197,0.0212,0.0213,0.0238,0.0285,0.0328,0.0384,0.0465, 0.0498,0.0514,0.0518,0.0523,0.0550,0.0563,0.0647,0.0710,0.0748,0.0824, 0.0887,0.0887,0.0937,0.1069,0.1070,0.1148,0.1183,0.1255,0.1320,0.1491, 0.1525,0.1568,0.1676,0.1687,0.1743,0.1747,0.1854,0.1858,0.1878,0.1894, 0.1896,0.2094,0.2139,0.2170,0.2195,0.2211,0.2225,0.2254,0.2278,0.2294, 0.2341,0.2356,0.2411,0.2437,0.2456,0.2494,0.2511,0.2538,0.2539,0.2593, 0.2598,0.2636,0.2661,0.2708,0.2762,0.2763,0.2773,0.2798,0.2836,0.2887, 0.3057,0.3076,0.3086,0.3167,0.3183,0.3193,0.3240,0.3271,0.3302,0.3308, 0.3308,0.3320,0.3358,0.3395,0.3442,0.3448,0.3481,0.3532,0.3539,0.3567, 0.3574,0.3595,0.3621,0.3625,0.3733,0.3742,0.3743,0.3746,0.3746,0.3955, 0.3982,0.3998,0.4029,0.4042,0.4097,0.4150,0.4190,0.4203,0.4213,0.4237, 0.4259,0.4266,0.4275,0.4364,0.4403,0.4406,0.4461,0.4466,0.4497,0.4553, 0.4590,0.4625,0.4739,0.4762,0.4773,0.4774,0.4804,0.4808,0.4874,0.4926, 0.5091,0.5127,0.5136,0.5182,0.5196,0.5215,0.5220,0.5242,0.5276,0.5290, 0.5295,0.5382,0.5405,0.5441,0.5441,0.5477,0.5517,0.5521,0.5569,0.5572, 0.5615,0.5619,0.5623,0.5693,0.5706,0.5758,0.5855,0.5948,0.5948,0.5963, 0.6003,0.6088,0.6135,0.6179,0.6305,0.6348,0.6348,0.6397,0.6417,0.6424, 0.6451,0.6459,0.6475,0.6547,0.6609,0.6622,0.6625,0.6636,0.6649,0.6689, 0.6759,0.6768,0.6812,0.6830,0.6869,0.6895,0.6935,0.6954,0.7088,0.7091, 0.7128,0.7171,0.7182,0.7233,0.7304,0.7352,0.7513,0.7543,0.7562,0.7578, 0.7605,0.7676,0.7682,0.7711,0.7751,0.7834,0.7930,0.7933,0.7953,0.7994, 0.8003,0.8022,0.8028,0.8045,0.8065,0.8086,0.8199,0.8213,0.8315,0.8411, 0.8467,0.8511,0.8532,0.8553,0.8576,0.8583,0.8594,0.8602,0.8792,0.8807, 0.8882,0.8900,0.9075,0.9129,0.9143,0.9146,0.9201,0.9211,0.9231,0.9242, 0.9257,0.9271,0.9294,0.9408,0.9423,0.9427,0.9681,0.9710,0.9713,0.9772, 0.9777,0.9777,0.9800,0.9808,0.9829,0.9851,0.9955,0.9956,0.9997, Overall p-value after applying KStest on 269 p-values = 0.242749 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.