RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-03-27_08:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.86 20.9316 0.770634 2 to 25 15.60 21.2220 0.783482 3 to 26 15.73 11.5507 0.173451 4 to 27 15.71 21.5701 0.798179 5 to 28 15.59 15.6590 0.451876 6 to 29 15.68 19.7623 0.713433 7 to 30 15.80 16.1501 0.486781 8 to 31 15.68 24.1934 0.885726 9 to 32 15.70 18.8956 0.665445 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.182967 Tough bday spacings test for dh-ranFile-2018-03-27_08:31: 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 8 42 74 78 96 78 56 42 14 9 3 (O-E)^2/E 0.1 0.8 0.0 4.0 0.0 0.0 0.3 5.0 0.1 0.9 0.3 Birthday Spacings: Sum(O-E)^2/E= 11.444, p= 0.676 RESULTS OF GCD FOR dh-ranFile-2018-03-27_08:31 Euclid's algorithm: p-value, steps to gcd: 0.100422 p-value, dist. of gcd's: 0.248822 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-03-27_08:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.819 0.322 0.849 0.343 0.046 0.305 0.494 0.483 Bits 8 to 15---> 0.325 0.398 0.188 0.555 0.222 0.788 0.036 0.243 Bits 16 to 23---> 0.772 0.885 0.612 0.283 0.975 0.580 0.586 0.223 Bits 24 to 31---> 0.764 0.555 0.821 0.135 0.904 0.935 0.510 0.553 KS test for the above 32 p values: 0.084 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-03-27_08:31, p-values for 5 runs: 0.6645, 0.9443, 0.4411, 0.6808, 0.9113 Rank test for binary matrices (31x31) for dh-ranFile-2018-03-27_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 216 211.4 0.099 0.099 r= 29 5140 5134.0 0.007 0.106 r= 30 23064 23103.0 0.066 0.172 r= 31 11580 11551.5 0.070 0.242 chi-square = 0.242 with df = 3; p-value = 0.030 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-03-27_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 187 211.4 2.820 2.820 r= 30 5125 5134.0 0.016 2.836 r= 31 23038 23103.0 0.183 3.019 r= 32 11650 11551.5 0.840 3.859 chi-square = 3.859 with df = 3; p-value = 0.723 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-03-27_08:31 b-rank test for bits 1 to 8, p=0.83850 b-rank test for bits 2 to 9, p=0.77377 b-rank test for bits 3 to 10, p=0.36199 b-rank test for bits 4 to 11, p=0.04777 b-rank test for bits 5 to 12, p=0.09999 b-rank test for bits 6 to 13, p=0.35768 b-rank test for bits 7 to 14, p=0.50209 b-rank test for bits 8 to 15, p=0.73505 b-rank test for bits 9 to 16, p=0.52613 b-rank test for bits 10 to 17, p=0.04003 b-rank test for bits 11 to 18, p=0.00665 b-rank test for bits 12 to 19, p=0.65804 b-rank test for bits 13 to 20, p=0.79834 b-rank test for bits 14 to 21, p=0.97398 b-rank test for bits 15 to 22, p=0.13373 b-rank test for bits 16 to 23, p=0.94327 b-rank test for bits 17 to 24, p=0.84292 b-rank test for bits 18 to 25, p=0.65514 b-rank test for bits 19 to 26, p=0.15679 b-rank test for bits 20 to 27, p=0.19002 b-rank test for bits 21 to 28, p=0.14528 b-rank test for bits 22 to 29, p=0.32137 b-rank test for bits 23 to 30, p=0.46353 b-rank test for bits 24 to 31, p=0.49669 b-rank test for bits 25 to 32, p=0.54690 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 = 0.825011 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-03-27_08:31 (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 141922 0.03 0.511808 2 142221 0.73 0.766755 3 141539 -0.87 0.193449 4 142357 1.05 0.852210 5 141390 -1.21 0.112491 6 141978 0.16 0.563734 7 141671 -0.56 0.288816 8 141325 -1.37 0.086086 9 141358 -1.29 0.098846 10 141226 -1.60 0.055181 11 142330 0.98 0.837165 12 142198 0.67 0.749991 13 142372 1.08 0.860153 14 141907 -0.01 0.497828 15 141435 -1.11 0.133877 16 142333 0.99 0.838884 17 142394 1.13 0.871268 18 142760 1.99 0.976569 19 141995 0.20 0.579324 20 142779 2.03 0.978920 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-03-27_08:31 Bits used No. missing words z-score p-value 23 to 32 141554 -1.2253 0.110236 22 to 31 142171 0.9023 0.816554 21 to 30 141826 -0.2873 0.386924 20 to 29 141587 -1.1115 0.133180 19 to 28 142182 0.9402 0.826453 18 to 27 142239 1.1368 0.872188 17 to 26 141791 -0.4080 0.341624 16 to 25 142078 0.5816 0.719589 15 to 24 141834 -0.2598 0.397525 14 to 23 141618 -1.0046 0.157548 13 to 22 141280 -2.1701 0.015000 12 to 21 141609 -1.0356 0.150190 11 to 20 142017 0.3713 0.644784 10 to 19 142051 0.4885 0.687408 9 to 18 142397 1.6816 0.953679 8 to 17 141704 -0.7080 0.239462 7 to 16 141899 -0.0356 0.485792 6 to 15 141669 -0.8287 0.203630 5 to 14 141939 0.1023 0.540745 4 to 13 142154 0.8437 0.800579 3 to 12 142104 0.6713 0.748978 2 to 11 141810 -0.3425 0.365981 1 to 10 142255 1.1920 0.883363 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-03-27_08:31 Bits used No. missing words z-score p-value 28 to 32 142141 0.7853 0.783868 27 to 31 141394 -1.7469 0.040329 26 to 30 142065 0.5277 0.701145 25 to 29 141556 -1.1977 0.115511 24 to 28 142210 1.0192 0.845951 23 to 27 141817 -0.3130 0.377147 22 to 26 141387 -1.7706 0.038313 21 to 25 142038 0.4362 0.668643 20 to 24 141853 -0.1909 0.424283 19 to 23 141678 -0.7842 0.216470 18 to 22 141878 -0.1062 0.457711 17 to 21 141779 -0.4418 0.329318 16 to 20 141906 -0.0113 0.495497 15 to 19 142521 2.0735 0.980935 14 to 18 141854 -0.1876 0.425611 13 to 17 141797 -0.3808 0.351683 12 to 16 142037 0.4328 0.667413 11 to 15 142100 0.6463 0.740970 10 to 14 142269 1.2192 0.888620 9 to 13 141769 -0.4757 0.317146 8 to 12 142127 0.7379 0.769702 7 to 11 141817 -0.3130 0.377147 6 to 10 141714 -0.6621 0.253942 5 to 9 142179 0.9141 0.819677 4 to 8 142391 1.6328 0.948742 3 to 7 141866 -0.1469 0.441613 2 to 6 141787 -0.4147 0.339189 1 to 5 141222 -2.3299 0.009905 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-03-27_08:31 Bits used No. missing words z-score p-value 31 to 32 141456 -1.3373 0.090569 30 to 31 142208 0.8810 0.810850 29 to 30 141965 0.1642 0.565220 28 to 29 142058 0.4386 0.669508 27 to 28 142309 1.1790 0.880794 26 to 27 142590 2.0079 0.977672 25 to 26 141886 -0.0688 0.472566 24 to 25 141906 -0.0098 0.496081 23 to 24 141620 -0.8535 0.196696 22 to 23 142024 0.3383 0.632416 21 to 22 141955 0.1347 0.553583 20 to 21 142178 0.7925 0.785976 19 to 20 141541 -1.0865 0.138625 18 to 19 141636 -0.8063 0.210040 17 to 18 142429 1.5329 0.937356 16 to 17 142113 0.6008 0.726012 15 to 16 142170 0.7689 0.779035 14 to 15 141998 0.2616 0.603171 13 to 14 142378 1.3825 0.916592 12 to 13 141568 -1.0069 0.156998 11 to 12 142398 1.4415 0.925279 10 to 11 142144 0.6922 0.755607 9 to 10 141779 -0.3845 0.350321 8 to 9 141693 -0.6381 0.261691 7 to 8 141624 -0.8417 0.199983 6 to 7 141781 -0.3786 0.352509 5 to 6 141914 0.0138 0.505496 4 to 5 142055 0.4297 0.666295 3 to 4 141705 -0.6027 0.273340 2 to 3 142128 0.6450 0.740551 1 to 2 141424 -1.4317 0.076122 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-03-27_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2445.44 -0.772 0.220174 Test results for specific bytes for dh-ranFile-2018-03-27_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2546.33 0.655 0.743844 2 to 9 2592.58 1.309 0.904785 3 to 10 2357.41 -2.017 0.021872 4 to 11 2496.82 -0.045 0.482041 5 to 12 2581.44 1.152 0.875273 6 to 13 2641.41 2.000 0.977239 7 to 14 2470.45 -0.418 0.337998 8 to 15 2394.07 -1.498 0.067049 9 to 16 2520.43 0.289 0.613683 10 to 17 2621.58 1.719 0.957231 11 to 18 2497.59 -0.034 0.486392 12 to 19 2570.51 0.997 0.840659 13 to 20 2540.93 0.579 0.718634 14 to 21 2562.44 0.883 0.811406 15 to 22 2575.01 1.061 0.855611 16 to 23 2419.68 -1.136 0.127998 17 to 24 2326.37 -2.456 0.007034 18 to 25 2476.18 -0.337 0.368130 19 to 26 2443.19 -0.803 0.210888 20 to 27 2299.59 -2.834 0.002297 21 to 28 2542.41 0.600 0.725646 22 to 29 2548.42 0.685 0.753244 23 to 30 2615.79 1.637 0.949236 24 to 31 2506.90 0.098 0.538887 25 to 32 2410.37 -1.268 0.102486 CDPARK for dh-ranFile-2018-03-27_08:31: 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 3511 -0.5479 0.291865 3464 -2.6941 0.003529 3512 -0.5023 0.307734 3501 -1.0046 0.157553 3505 -0.8219 0.205562 3534 0.5023 0.692266 3545 1.0046 0.842447 3512 -0.5023 0.307734 3531 0.3653 0.642555 3495 -1.2785 0.100530 Square side=100, avg. no. parked=3511.00 sample std.=21.65 p-value of the KSTEST for those 10 p-values: 0.154071 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-03-27_08:31 0.1700,0.5692,0.2365,0.5754,0.3138,0.7260,0.4977,0.1292,0.6295,0.8213, The KS test for those 10 p-values: 0.753573 The 3DSPHERES test for dh-ranFile-2018-03-27_08:31 sample no r^3 equiv. uni. 1 33.238 0.669756 2 41.278 0.747395 3 6.946 0.206684 4 33.230 0.669668 5 1.279 0.041725 6 12.697 0.345069 7 6.396 0.192006 8 44.051 0.769699 9 1.735 0.056200 10 8.516 0.247138 11 8.817 0.254652 12 32.616 0.662843 13 7.841 0.230004 14 39.404 0.731118 15 85.470 0.942099 16 6.903 0.205552 17 7.172 0.212627 18 32.797 0.664870 19 4.904 0.150794 20 11.202 0.311599 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.181597 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-03-27_08:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 2.2 1.5 -0.8 -0.8 -1.0 1.7 -0.7 0.1 -0.1 0.6 -0.7 0.0 -0.9 -0.1 -0.6 -0.4 0.8 -2.0 -0.7 -0.3 0.8 1.3 0.2 0.0 1.9 2.0 -0.5 1.2 1.3 -0.2 -0.6 0.8 0.2 0.5 -2.5 -1.4 1.5 0.5 0.4 -0.6 -1.0 -1.1 Chi-square with 42 degrees of freedom:48.561190 z-score=0.715884, p-value=0.774454 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-03-27_08:31 Test no p-value 1 0.025848 2 0.363233 3 0.221756 4 0.021904 5 0.995062 6 0.222265 7 0.115848 8 0.301878 9 0.009457 10 0.930731 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.011788 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-03-27_08:31: (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 66679 0.00 66755 0.12 3 25000.00 25006 0.00 24980 0.02 4 6666.67 6611 0.46 6604 0.59 5 1388.89 1445 2.27 1393 0.01 6 238.10 224 0.83 229 0.35 7 34.72 29 0.94 34 0.01 8 4.96 5 0.00 4 0.19 p=0.39233 p=0.02739 Number of rngs required: 688042, p-value: 0.339 RESULTS OF CRAPS TEST for dh-ranFile-2018-03-27_08:31 No. of wins: Observed Expected 98151 98585.9 z-score=-1.945, pvalue=0.02589 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66723 66666.7 0.048 0.048 2 37668 37654.3 0.005 0.053 3 27350 26954.7 5.796 5.849 4 19204 19313.5 0.620 6.469 5 13554 13851.4 6.386 12.855 6 9949 9943.5 0.003 12.858 7 7069 7145.0 0.809 13.667 8 5082 5139.1 0.634 14.301 9 3746 3699.9 0.575 14.876 10 2647 2666.3 0.140 15.016 11 1955 1923.3 0.522 15.538 12 1375 1388.7 0.136 15.674 13 1023 1003.7 0.371 16.044 14 682 726.1 2.683 18.727 15 513 525.8 0.313 19.041 16 399 381.2 0.836 19.877 17 295 276.5 1.232 21.109 18 198 200.8 0.040 21.149 19 160 146.0 1.346 22.494 20 118 106.2 1.308 23.802 21 290 287.1 0.029 23.831 Chisq= 23.83 for 20 degrees of freedom, p= 0.75015 SUMMARY of craptest p-value for no. of wins: 0.025891 p-value for throws/game: 0.750146 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-03-27_08:31 No. of wins: Observed Expected 98352 98585.9 z-score=-1.046, pvalue=0.14779 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66563 66666.7 0.161 0.161 2 37472 37654.3 0.883 1.044 3 27056 26954.7 0.380 1.424 4 19384 19313.5 0.258 1.682 5 13979 13851.4 1.175 2.857 6 9835 9943.5 1.185 4.042 7 7241 7145.0 1.289 5.331 8 5101 5139.1 0.282 5.613 9 3652 3699.9 0.619 6.232 10 2653 2666.3 0.066 6.299 11 1968 1923.3 1.038 7.336 12 1452 1388.7 2.882 10.218 13 959 1003.7 1.992 12.210 14 736 726.1 0.134 12.344 15 520 525.8 0.065 12.409 16 387 381.2 0.090 12.498 17 320 276.5 6.830 19.329 18 192 200.8 0.388 19.717 19 146 146.0 0.000 19.717 20 89 106.2 2.790 22.507 21 295 287.1 0.217 22.724 Chisq= 22.72 for 20 degrees of freedom, p= 0.69743 SUMMARY of craptest p-value for no. of wins: 0.147792 p-value for throws/game: 0.697429 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0023,0.0035,0.0066,0.0070,0.0095,0.0099,0.0118,0.0150,0.0219,0.0219, 0.0258,0.0259,0.0274,0.0295,0.0356,0.0383,0.0400,0.0403,0.0417,0.0464, 0.0478,0.0552,0.0562,0.0670,0.0761,0.0837,0.0861,0.0906,0.0988,0.1000, 0.1004,0.1005,0.1025,0.1102,0.1125,0.1155,0.1158,0.1280,0.1292,0.1332, 0.1337,0.1339,0.1345,0.1386,0.1453,0.1478,0.1502,0.1508,0.1541,0.1568, 0.1570,0.1575,0.1576,0.1700,0.1735,0.1816,0.1830,0.1879,0.1900,0.1920, 0.1934,0.1967,0.2000,0.2036,0.2056,0.2056,0.2067,0.2100,0.2109,0.2126, 0.2165,0.2202,0.2218,0.2219,0.2223,0.2232,0.2300,0.2365,0.2395,0.2428, 0.2471,0.2488,0.2539,0.2547,0.2617,0.2733,0.2830,0.2888,0.2919,0.3019, 0.3049,0.3077,0.3077,0.3116,0.3138,0.3171,0.3214,0.3217,0.3254,0.3293, 0.3380,0.3388,0.3392,0.3416,0.3431,0.3451,0.3503,0.3517,0.3525,0.3577, 0.3620,0.3632,0.3660,0.3681,0.3771,0.3771,0.3869,0.3923,0.3975,0.3979, 0.4243,0.4256,0.4411,0.4416,0.4519,0.4577,0.4635,0.4726,0.4820,0.4831, 0.4858,0.4864,0.4868,0.4942,0.4955,0.4961,0.4967,0.4977,0.4978,0.5021, 0.5055,0.5103,0.5118,0.5261,0.5389,0.5407,0.5469,0.5529,0.5536,0.5547, 0.5551,0.5637,0.5652,0.5692,0.5754,0.5793,0.5803,0.5860,0.6032,0.6120, 0.6137,0.6295,0.6324,0.6426,0.6448,0.6551,0.6580,0.6628,0.6645,0.6649, 0.6654,0.6663,0.6674,0.6686,0.6695,0.6697,0.6698,0.6760,0.6808,0.6874, 0.6923,0.6974,0.7011,0.7134,0.7186,0.7196,0.7229,0.7256,0.7260,0.7260, 0.7311,0.7351,0.7406,0.7410,0.7438,0.7474,0.7490,0.7500,0.7501,0.7532, 0.7536,0.7556,0.7644,0.7668,0.7697,0.7697,0.7706,0.7722,0.7738,0.7745, 0.7790,0.7835,0.7839,0.7860,0.7884,0.7982,0.7983,0.8006,0.8108,0.8114, 0.8166,0.8193,0.8197,0.8212,0.8213,0.8250,0.8265,0.8372,0.8385,0.8389, 0.8407,0.8424,0.8429,0.8460,0.8486,0.8522,0.8556,0.8602,0.8713,0.8722, 0.8753,0.8808,0.8834,0.8848,0.8857,0.8886,0.9042,0.9048,0.9113,0.9166, 0.9253,0.9307,0.9355,0.9374,0.9421,0.9433,0.9443,0.9487,0.9492,0.9537, 0.9572,0.9740,0.9749,0.9766,0.9772,0.9777,0.9789,0.9809,0.9951, Overall p-value after applying KStest on 269 p-values = 0.268490 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.