RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-04-10_09:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.70 10.7517 0.130824 2 to 25 15.70 12.7866 0.249650 3 to 26 15.72 13.6150 0.305856 4 to 27 15.80 8.9049 0.056802 5 to 28 15.80 14.8235 0.391806 6 to 29 15.92 20.0192 0.726749 7 to 30 16.15 25.6562 0.919043 8 to 31 15.80 24.2331 0.886762 9 to 32 16.12 26.7498 0.938160 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.726631 Tough bday spacings test for dh-ranFile-2016-04-10_09:31: 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 4 37 59 106 86 84 64 32 16 7 5 (O-E)^2/E 2.9 0.0 2.8 0.7 1.4 0.4 2.7 0.2 0.1 0.0 0.2 Birthday Spacings: Sum(O-E)^2/E= 11.436, p= 0.675 RESULTS OF GCD FOR dh-ranFile-2016-04-10_09:31 Euclid's algorithm: p-value, steps to gcd: 0.587264 p-value, dist. of gcd's: 0.938438 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-04-10_09:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.744 0.948 0.244 0.585 0.791 0.611 0.400 0.594 Bits 8 to 15---> 0.879 0.860 0.599 0.823 0.503 0.947 0.856 0.764 Bits 16 to 23---> 0.383 0.116 0.729 0.790 0.250 0.232 0.627 0.083 Bits 24 to 31---> 0.076 0.716 0.942 0.601 0.193 0.274 0.141 0.305 KS test for the above 32 p values: 0.508 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-04-10_09:31, p-values for 5 runs: 0.5141, 0.8452, 0.2711, 0.6476, 0.4877 Rank test for binary matrices (31x31) for dh-ranFile-2016-04-10_09:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 196 211.4 1.124 1.124 r= 29 5098 5134.0 0.253 1.377 r= 30 23239 23103.0 0.800 2.177 r= 31 11467 11551.5 0.618 2.795 chi-square = 2.795 with df = 3; p-value = 0.576 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-04-10_09:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 208 211.4 0.055 0.055 r= 30 5064 5134.0 0.955 1.010 r= 31 23041 23103.0 0.167 1.177 r= 32 11687 11551.5 1.589 2.765 chi-square = 2.765 with df = 3; p-value = 0.571 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-04-10_09:31 b-rank test for bits 1 to 8, p=0.18785 b-rank test for bits 2 to 9, p=0.61947 b-rank test for bits 3 to 10, p=0.05753 b-rank test for bits 4 to 11, p=0.58804 b-rank test for bits 5 to 12, p=0.68019 b-rank test for bits 6 to 13, p=0.39787 b-rank test for bits 7 to 14, p=0.38492 b-rank test for bits 8 to 15, p=0.47883 b-rank test for bits 9 to 16, p=0.72960 b-rank test for bits 10 to 17, p=0.79237 b-rank test for bits 11 to 18, p=0.16070 b-rank test for bits 12 to 19, p=0.72792 b-rank test for bits 13 to 20, p=0.91783 b-rank test for bits 14 to 21, p=0.42632 b-rank test for bits 15 to 22, p=0.87328 b-rank test for bits 16 to 23, p=0.94936 b-rank test for bits 17 to 24, p=0.87737 b-rank test for bits 18 to 25, p=0.76992 b-rank test for bits 19 to 26, p=0.48202 b-rank test for bits 20 to 27, p=0.73206 b-rank test for bits 21 to 28, p=0.81209 b-rank test for bits 22 to 29, p=0.83444 b-rank test for bits 23 to 30, p=0.92752 b-rank test for bits 24 to 31, p=0.94906 b-rank test for bits 25 to 32, p=0.29264 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 = 0.044892 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-04-10_09:31 (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 142205 0.69 0.755160 2 141798 -0.26 0.397387 3 142680 1.80 0.964119 4 143095 2.77 0.997199 5 142008 0.23 0.591163 6 142016 0.25 0.598408 7 142183 0.64 0.738724 8 142034 0.29 0.614583 9 141964 0.13 0.550820 10 142271 0.85 0.800951 11 142082 0.40 0.656686 12 142339 1.00 0.842287 13 141657 -0.59 0.277744 14 141558 -0.82 0.205862 15 141985 0.18 0.570167 16 142111 0.47 0.681248 17 142035 0.29 0.615476 18 141702 -0.48 0.314045 19 142732 1.92 0.972705 20 141573 -0.79 0.215987 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-04-10_09:31 Bits used No. missing words z-score p-value 23 to 32 141139 -2.6563 0.003950 22 to 31 142180 0.9333 0.824679 21 to 30 141676 -0.8046 0.210529 20 to 29 141791 -0.4080 0.341624 19 to 28 141981 0.2471 0.597599 18 to 27 141931 0.0747 0.529783 17 to 26 142192 0.9747 0.835151 16 to 25 141777 -0.4563 0.324083 15 to 24 142072 0.5609 0.712578 14 to 23 142375 1.6058 0.945837 13 to 22 142471 1.9368 0.973615 12 to 21 142262 1.2161 0.888027 11 to 20 141559 -1.2080 0.113517 10 to 19 142445 1.8471 0.967636 9 to 18 141923 0.0471 0.518798 8 to 17 141902 -0.0253 0.489918 7 to 16 141965 0.1920 0.576115 6 to 15 141721 -0.6494 0.258036 5 to 14 142123 0.7368 0.769376 4 to 13 141869 -0.1391 0.444698 3 to 12 141625 -0.9804 0.163432 2 to 11 141768 -0.4873 0.313007 1 to 10 142205 1.0196 0.846029 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-04-10_09:31 Bits used No. missing words z-score p-value 28 to 32 141721 -0.6384 0.261605 27 to 31 141585 -1.0994 0.135792 26 to 30 141746 -0.5537 0.289905 25 to 29 141540 -1.2520 0.105291 24 to 28 141682 -0.7706 0.220469 23 to 27 141993 0.2836 0.611652 22 to 26 141846 -0.2147 0.415009 21 to 25 141673 -0.8011 0.211532 20 to 24 141994 0.2870 0.612950 19 to 23 141695 -0.7265 0.233753 18 to 22 141643 -0.9028 0.183312 17 to 21 141683 -0.7672 0.221475 16 to 20 141983 0.2497 0.598602 15 to 19 141878 -0.1062 0.457711 14 to 18 142302 1.3311 0.908419 13 to 17 141456 -1.5367 0.062182 12 to 16 141834 -0.2554 0.399224 11 to 15 141435 -1.6079 0.053929 10 to 14 141841 -0.2316 0.408414 9 to 13 142093 0.6226 0.733230 8 to 12 141913 0.0124 0.504963 7 to 11 141798 -0.3774 0.352942 6 to 10 141876 -0.1130 0.455022 5 to 9 142469 1.8972 0.971098 4 to 8 142030 0.4091 0.658749 3 to 7 142021 0.3785 0.647486 2 to 6 141543 -1.2418 0.107156 1 to 5 142284 1.2701 0.897970 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-04-10_09:31 Bits used No. missing words z-score p-value 31 to 32 141875 -0.1013 0.459669 30 to 31 142141 0.6834 0.752821 29 to 30 141615 -0.8682 0.192634 28 to 29 141911 0.0049 0.501965 27 to 28 141915 0.0167 0.506672 26 to 27 142254 1.0167 0.845358 25 to 26 141618 -0.8594 0.195065 24 to 25 141473 -1.2871 0.099028 23 to 24 141554 -1.0482 0.147280 22 to 23 141283 -1.8476 0.032331 21 to 22 141844 -0.1927 0.423592 20 to 21 141582 -0.9656 0.167128 19 to 20 141762 -0.4346 0.331926 18 to 19 141766 -0.4228 0.336220 17 to 18 142124 0.6332 0.736713 16 to 17 142365 1.3442 0.910552 15 to 16 141610 -0.8830 0.188624 14 to 15 141840 -0.2045 0.418976 13 to 14 142211 0.8899 0.813235 12 to 13 141752 -0.4641 0.321288 11 to 12 142440 1.5654 0.941255 10 to 11 141869 -0.1190 0.452651 9 to 10 142205 0.8722 0.808446 8 to 9 142125 0.6362 0.737675 7 to 8 141591 -0.9390 0.173859 6 to 7 141864 -0.1337 0.446813 5 to 6 141905 -0.0128 0.494905 4 to 5 141965 0.1642 0.565220 3 to 4 141324 -1.7266 0.042116 2 to 3 142121 0.6244 0.733816 1 to 2 141795 -0.3373 0.367962 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-04-10_09:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2428.35 -1.013 0.155458 Test results for specific bytes for dh-ranFile-2016-04-10_09:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2477.56 -0.317 0.375480 2 to 9 2458.25 -0.590 0.277463 3 to 10 2547.38 0.670 0.748609 4 to 11 2531.57 0.446 0.672379 5 to 12 2468.69 -0.443 0.328967 6 to 13 2672.98 2.446 0.992783 7 to 14 2486.33 -0.193 0.423355 8 to 15 2480.65 -0.274 0.392179 9 to 16 2516.99 0.240 0.594918 10 to 17 2476.57 -0.331 0.370179 11 to 18 2421.90 -1.105 0.134684 12 to 19 2503.89 0.055 0.521942 13 to 20 2453.53 -0.657 0.255533 14 to 21 2572.61 1.027 0.847753 15 to 22 2486.86 -0.186 0.426302 16 to 23 2435.80 -0.908 0.181965 17 to 24 2611.79 1.581 0.943055 18 to 25 2546.81 0.662 0.746031 19 to 26 2333.42 -2.356 0.009243 20 to 27 2435.35 -0.914 0.180285 21 to 28 2383.17 -1.652 0.049248 22 to 29 2549.32 0.697 0.757238 23 to 30 2469.56 -0.430 0.333440 24 to 31 2461.83 -0.540 0.294650 25 to 32 2506.96 0.098 0.539186 CDPARK for dh-ranFile-2016-04-10_09:31: 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 3536 0.5936 0.723613 3531 0.3653 0.642555 3515 -0.3653 0.357445 3512 -0.5023 0.307734 3519 -0.1826 0.427537 3501 -1.0046 0.157553 3542 0.8676 0.807188 3519 -0.1826 0.427537 3515 -0.3653 0.357445 3531 0.3653 0.642555 Square side=100, avg. no. parked=3522.10 sample std.=11.89 p-value of the KSTEST for those 10 p-values: 0.512513 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-04-10_09:31 0.5246,0.7532,0.8333,0.0908,0.9932,0.0725,0.0409,0.4137,0.5461,0.1187, The KS test for those 10 p-values: 0.416181 The 3DSPHERES test for dh-ranFile-2016-04-10_09:31 sample no r^3 equiv. uni. 1 0.222 0.007386 2 98.055 0.961937 3 17.425 0.440573 4 109.598 0.974094 5 21.724 0.515263 6 6.875 0.204801 7 0.453 0.014999 8 82.851 0.936816 9 1.864 0.060236 10 20.727 0.498878 11 42.971 0.761256 12 50.464 0.814020 13 1.089 0.035639 14 5.797 0.175699 15 7.986 0.233717 16 3.766 0.117968 17 1.892 0.061125 18 101.446 0.966004 19 31.112 0.645508 20 11.647 0.321744 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.095457 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-04-10_09:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 2.0 0.1 -0.6 -3.0 0.0 0.1 0.3 -1.0 -1.1 -0.8 0.6 -1.4 0.4 -0.1 0.5 -0.1 0.3 0.6 1.4 0.2 0.4 -0.4 -1.6 -0.5 -0.3 0.5 0.9 -1.0 -0.2 0.6 0.2 1.4 -0.5 0.0 0.6 -1.6 1.9 -1.0 0.1 -0.7 -0.6 -1.0 -1.1 Chi-square with 42 degrees of freedom:39.766307 z-score=-0.243716, p-value=0.430529 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-04-10_09:31 Test no p-value 1 0.154154 2 0.134760 3 0.403209 4 0.525397 5 0.576584 6 0.011367 7 0.082355 8 0.049947 9 0.190611 10 0.544108 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.013907 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-04-10_09:31: (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 66583 0.11 66801 0.27 3 25000.00 24990 0.00 24920 0.26 4 6666.67 6730 0.60 6638 0.12 5 1388.89 1406 0.21 1354 0.88 6 238.10 244 0.15 250 0.60 7 34.72 39 0.53 25 2.72 8 4.96 7 0.84 11 7.36 p=0.12427 p=0.94230 Number of rngs required: 688040, p-value: 0.338 RESULTS OF CRAPS TEST for dh-ranFile-2016-04-10_09:31 No. of wins: Observed Expected 98836 98585.9 z-score= 1.119, pvalue=0.86838 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66832 66666.7 0.410 0.410 2 37882 37654.3 1.377 1.787 3 26879 26954.7 0.213 1.999 4 19299 19313.5 0.011 2.010 5 13918 13851.4 0.320 2.330 6 9864 9943.5 0.636 2.967 7 7060 7145.0 1.012 3.978 8 5113 5139.1 0.132 4.111 9 3610 3699.9 2.183 6.293 10 2626 2666.3 0.609 6.902 11 1888 1923.3 0.649 7.551 12 1322 1388.7 3.207 10.759 13 1020 1003.7 0.264 11.023 14 719 726.1 0.070 11.093 15 542 525.8 0.497 11.590 16 400 381.2 0.932 12.522 17 286 276.5 0.324 12.846 18 202 200.8 0.007 12.853 19 140 146.0 0.245 13.098 20 97 106.2 0.800 13.898 21 301 287.1 0.672 14.569 Chisq= 14.57 for 20 degrees of freedom, p= 0.19950 SUMMARY of craptest p-value for no. of wins: 0.868383 p-value for throws/game: 0.199495 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-04-10_09:31 No. of wins: Observed Expected 98777 98585.9 z-score= 0.855, pvalue=0.80370 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66835 66666.7 0.425 0.425 2 37570 37654.3 0.189 0.614 3 26982 26954.7 0.028 0.641 4 19243 19313.5 0.257 0.899 5 13807 13851.4 0.142 1.041 6 9984 9943.5 0.165 1.206 7 7210 7145.0 0.591 1.796 8 5029 5139.1 2.358 4.154 9 3626 3699.9 1.475 5.629 10 2623 2666.3 0.703 6.332 11 1974 1923.3 1.335 7.667 12 1413 1388.7 0.424 8.091 13 1015 1003.7 0.127 8.217 14 737 726.1 0.162 8.380 15 527 525.8 0.003 8.382 16 403 381.2 1.253 9.635 17 268 276.5 0.264 9.899 18 220 200.8 1.830 11.728 19 156 146.0 0.687 12.416 20 101 106.2 0.256 12.672 21 277 287.1 0.356 13.028 Chisq= 13.03 for 20 degrees of freedom, p= 0.12382 SUMMARY of craptest p-value for no. of wins: 0.803696 p-value for throws/game: 0.123818 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0040,0.0074,0.0092,0.0114,0.0139,0.0150,0.0323,0.0356,0.0409,0.0421, 0.0449,0.0492,0.0499,0.0539,0.0568,0.0575,0.0602,0.0611,0.0622,0.0725, 0.0758,0.0824,0.0832,0.0908,0.0955,0.0990,0.1053,0.1072,0.1135,0.1162, 0.1180,0.1187,0.1238,0.1243,0.1308,0.1347,0.1348,0.1358,0.1408,0.1473, 0.1542,0.1555,0.1576,0.1607,0.1634,0.1671,0.1739,0.1757,0.1803,0.1820, 0.1833,0.1878,0.1886,0.1906,0.1926,0.1928,0.1951,0.1995,0.2048,0.2059, 0.2105,0.2115,0.2160,0.2205,0.2215,0.2319,0.2337,0.2338,0.2440,0.2497, 0.2501,0.2555,0.2580,0.2616,0.2711,0.2738,0.2775,0.2777,0.2899,0.2926, 0.2946,0.3052,0.3059,0.3077,0.3130,0.3140,0.3213,0.3217,0.3241,0.3290, 0.3319,0.3334,0.3362,0.3379,0.3416,0.3529,0.3574,0.3574,0.3680,0.3702, 0.3755,0.3826,0.3849,0.3918,0.3922,0.3974,0.3979,0.3992,0.4004,0.4032, 0.4084,0.4137,0.4150,0.4162,0.4190,0.4234,0.4236,0.4263,0.4263,0.4275, 0.4275,0.4305,0.4406,0.4447,0.4468,0.4527,0.4550,0.4577,0.4597,0.4788, 0.4820,0.4877,0.4899,0.4949,0.4989,0.5020,0.5030,0.5050,0.5067,0.5083, 0.5125,0.5141,0.5153,0.5188,0.5219,0.5246,0.5254,0.5298,0.5392,0.5441, 0.5461,0.5508,0.5652,0.5702,0.5708,0.5758,0.5761,0.5766,0.5850,0.5873, 0.5880,0.5912,0.5940,0.5949,0.5976,0.5984,0.5986,0.5990,0.6009,0.6115, 0.6117,0.6130,0.6146,0.6155,0.6195,0.6270,0.6426,0.6426,0.6455,0.6475, 0.6476,0.6567,0.6587,0.6724,0.6754,0.6802,0.6812,0.7126,0.7163,0.7236, 0.7266,0.7267,0.7279,0.7288,0.7296,0.7321,0.7332,0.7338,0.7367,0.7377, 0.7387,0.7437,0.7460,0.7486,0.7528,0.7532,0.7552,0.7572,0.7613,0.7642, 0.7694,0.7699,0.7897,0.7911,0.7924,0.8010,0.8037,0.8072,0.8084,0.8121, 0.8132,0.8140,0.8228,0.8247,0.8333,0.8344,0.8352,0.8423,0.8452,0.8454, 0.8460,0.8478,0.8564,0.8597,0.8684,0.8733,0.8774,0.8786,0.8868,0.8880, 0.8980,0.9084,0.9106,0.9178,0.9190,0.9275,0.9368,0.9382,0.9384,0.9413, 0.9421,0.9423,0.9431,0.9458,0.9466,0.9479,0.9491,0.9494,0.9619,0.9641, 0.9660,0.9676,0.9711,0.9727,0.9736,0.9741,0.9928,0.9932,0.9972, Overall p-value after applying KStest on 269 p-values = 0.992347 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.