RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-05-16_17:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.82 14.1715 0.345074 2 to 25 15.84 16.6148 0.519259 3 to 26 15.74 17.2725 0.563942 4 to 27 15.32 34.6867 0.993162 5 to 28 15.51 12.8908 0.256535 6 to 29 15.79 10.7233 0.129421 7 to 30 16.00 8.4645 0.044419 8 to 31 15.75 20.6688 0.758542 9 to 32 16.03 19.7124 0.710799 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.945368 Tough bday spacings test for dh-ranFile-2016-05-16_17:31: 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 16 35 85 90 113 79 42 17 13 5 5 (O-E)^2/E 5.1 0.1 1.9 0.6 2.4 0.0 2.0 5.5 0.2 0.4 0.2 Birthday Spacings: Sum(O-E)^2/E= 18.363, p= 0.951 RESULTS OF GCD FOR dh-ranFile-2016-05-16_17:31 Euclid's algorithm: p-value, steps to gcd: 0.348811 p-value, dist. of gcd's: 0.960656 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-05-16_17:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.783 0.191 0.776 0.210 0.294 0.204 0.972 0.204 Bits 8 to 15---> 0.630 0.630 0.163 0.124 0.018 0.985 0.580 0.993 Bits 16 to 23---> 0.153 0.167 0.586 0.721 0.066 0.353 0.494 0.209 Bits 24 to 31---> 0.413 0.565 0.905 0.932 0.670 0.867 0.364 0.681 KS test for the above 32 p values: 0.221 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-05-16_17:31, p-values for 5 runs: 0.1752, 0.1497, 0.7747, 0.0840, 0.4079 Rank test for binary matrices (31x31) for dh-ranFile-2016-05-16_17:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 205 211.4 0.195 0.195 r= 29 5179 5134.0 0.394 0.589 r= 30 23200 23103.0 0.407 0.996 r= 31 11416 11551.5 1.590 2.586 chi-square = 2.586 with df = 3; p-value = 0.540 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-05-16_17:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 193 211.4 1.605 1.605 r= 30 5088 5134.0 0.412 2.017 r= 31 23103 23103.0 0.000 2.017 r= 32 11616 11551.5 0.360 2.377 chi-square = 2.377 with df = 3; p-value = 0.502 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-05-16_17:31 b-rank test for bits 1 to 8, p=0.02686 b-rank test for bits 2 to 9, p=0.54092 b-rank test for bits 3 to 10, p=0.56631 b-rank test for bits 4 to 11, p=0.99332 b-rank test for bits 5 to 12, p=0.78202 b-rank test for bits 6 to 13, p=0.88101 b-rank test for bits 7 to 14, p=0.92018 b-rank test for bits 8 to 15, p=0.49866 b-rank test for bits 9 to 16, p=0.83578 b-rank test for bits 10 to 17, p=0.98069 b-rank test for bits 11 to 18, p=0.07428 b-rank test for bits 12 to 19, p=0.10353 b-rank test for bits 13 to 20, p=0.77743 b-rank test for bits 14 to 21, p=0.20038 b-rank test for bits 15 to 22, p=0.04533 b-rank test for bits 16 to 23, p=0.35808 b-rank test for bits 17 to 24, p=0.52102 b-rank test for bits 18 to 25, p=0.54167 b-rank test for bits 19 to 26, p=0.70204 b-rank test for bits 20 to 27, p=0.86977 b-rank test for bits 21 to 28, p=0.86268 b-rank test for bits 22 to 29, p=0.77929 b-rank test for bits 23 to 30, p=0.49419 b-rank test for bits 24 to 31, p=0.96154 b-rank test for bits 25 to 32, p=0.38824 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 = 0.137475 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-05-16_17:31 (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 141494 -0.97 0.165924 2 141887 -0.05 0.479196 3 142007 0.23 0.590255 4 141985 0.18 0.570167 5 141734 -0.41 0.341032 6 142178 0.63 0.734911 7 141452 -1.07 0.142641 8 141711 -0.46 0.321543 9 142687 1.82 0.965390 10 141854 -0.13 0.448570 11 141738 -0.40 0.344466 12 142242 0.78 0.781499 13 142249 0.79 0.786292 14 141198 -1.66 0.048258 15 141457 -1.06 0.145291 16 142675 1.79 0.963188 17 141581 -0.77 0.221503 18 141935 0.06 0.523913 19 141962 0.12 0.548971 20 142508 1.40 0.919058 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-05-16_17:31 Bits used No. missing words z-score p-value 23 to 32 142165 0.8816 0.811009 22 to 31 142142 0.8023 0.788813 21 to 30 141867 -0.1460 0.441974 20 to 29 141903 -0.0218 0.491293 19 to 28 141926 0.0575 0.522920 18 to 27 141929 0.0678 0.527039 17 to 26 142132 0.7678 0.778705 16 to 25 141679 -0.7942 0.213528 15 to 24 141416 -1.7011 0.044459 14 to 23 141758 -0.5218 0.300895 13 to 22 141834 -0.2598 0.397525 12 to 21 141404 -1.7425 0.040709 11 to 20 141564 -1.1908 0.116867 10 to 19 141822 -0.3011 0.381655 9 to 18 141533 -1.2977 0.097197 8 to 17 141641 -0.9253 0.177411 7 to 16 142142 0.8023 0.788813 6 to 15 141651 -0.8908 0.186520 5 to 14 142210 1.0368 0.850084 4 to 13 142315 1.3989 0.919073 3 to 12 141682 -0.7839 0.216550 2 to 11 141844 -0.2253 0.410882 1 to 10 141783 -0.4356 0.331556 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-05-16_17:31 Bits used No. missing words z-score p-value 28 to 32 142051 0.4802 0.684471 27 to 31 142113 0.6904 0.755031 26 to 30 142242 1.1277 0.870276 25 to 29 141349 -1.8994 0.028754 24 to 28 142358 1.5209 0.935859 23 to 27 142078 0.5718 0.716259 22 to 26 141950 0.1379 0.554826 21 to 25 141892 -0.0587 0.476577 20 to 24 142482 1.9413 0.973886 19 to 23 141592 -1.0757 0.141032 18 to 22 142710 2.7141 0.996678 17 to 21 142153 0.8260 0.795598 16 to 20 141864 -0.1537 0.438939 15 to 19 141716 -0.6554 0.256119 14 to 18 141417 -1.6689 0.047567 13 to 17 141965 0.1887 0.574841 12 to 16 142271 1.2260 0.889901 11 to 15 141634 -0.9333 0.175327 10 to 14 141961 0.1752 0.569520 9 to 13 141929 0.0667 0.526581 8 to 12 142189 0.9480 0.828444 7 to 11 141794 -0.3909 0.347917 6 to 10 141786 -0.4181 0.337949 5 to 9 141628 -0.9537 0.170128 4 to 8 141701 -0.7062 0.240031 3 to 7 142483 1.9446 0.974091 2 to 6 142017 0.3650 0.642438 1 to 5 141543 -1.2418 0.107156 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-05-16_17:31 Bits used No. missing words z-score p-value 31 to 32 141742 -0.4936 0.310795 30 to 31 141668 -0.7119 0.238267 29 to 30 141827 -0.2429 0.404056 28 to 29 142058 0.4386 0.669508 27 to 28 141806 -0.3048 0.380256 26 to 27 141644 -0.7827 0.216906 25 to 26 142210 0.8869 0.812442 24 to 25 142215 0.9017 0.816387 23 to 24 141661 -0.7325 0.231921 22 to 23 142249 1.0020 0.841823 21 to 22 142288 1.1170 0.868007 20 to 21 142290 1.1229 0.869264 19 to 20 142142 0.6863 0.753751 18 to 19 143007 3.2380 0.999398 17 to 18 142270 1.0639 0.856318 16 to 17 142159 0.7365 0.769284 15 to 16 141493 -1.2281 0.109702 14 to 15 142099 0.5595 0.712089 13 to 14 141666 -0.7178 0.236444 12 to 13 142372 1.3648 0.913843 11 to 12 142398 1.4415 0.925279 10 to 11 141919 0.0285 0.511378 9 to 10 141946 0.1082 0.543070 8 to 9 141593 -0.9331 0.175377 7 to 8 141797 -0.3314 0.370187 6 to 7 141889 -0.0600 0.476090 5 to 6 141726 -0.5408 0.294324 4 to 5 142419 1.5035 0.933639 3 to 4 141816 -0.2753 0.391539 2 to 3 142068 0.4681 0.680127 1 to 2 141799 -0.3255 0.372418 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-05-16_17:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2413.36 -1.225 0.110246 Test results for specific bytes for dh-ranFile-2016-05-16_17:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2382.38 -1.663 0.048121 2 to 9 2601.35 1.433 0.924119 3 to 10 2498.53 -0.021 0.491685 4 to 11 2509.52 0.135 0.553532 5 to 12 2524.20 0.342 0.633894 6 to 13 2507.55 0.107 0.542507 7 to 14 2544.36 0.627 0.734775 8 to 15 2554.32 0.768 0.778823 9 to 16 2552.06 0.736 0.769213 10 to 17 2403.80 -1.360 0.086840 11 to 18 2473.89 -0.369 0.355995 12 to 19 2471.60 -0.402 0.343954 13 to 20 2544.99 0.636 0.737688 14 to 21 2570.43 0.996 0.840399 15 to 22 2487.91 -0.171 0.432121 16 to 23 2495.76 -0.060 0.476110 17 to 24 2433.71 -0.937 0.174270 18 to 25 2534.11 0.482 0.685254 19 to 26 2525.36 0.359 0.640084 20 to 27 2372.30 -1.806 0.035467 21 to 28 2613.79 1.609 0.946215 22 to 29 2528.40 0.402 0.656004 23 to 30 2614.98 1.626 0.948038 24 to 31 2601.07 1.429 0.923545 25 to 32 2499.11 -0.013 0.495006 CDPARK for dh-ranFile-2016-05-16_17:31: 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 3539 0.7306 0.767486 3512 -0.5023 0.307734 3503 -0.9132 0.180558 3519 -0.1826 0.427537 3531 0.3653 0.642555 3520 -0.1370 0.445521 3511 -0.5479 0.291865 3501 -1.0046 0.157553 3524 0.0457 0.518210 3541 0.8219 0.794438 Square side=100, avg. no. parked=3520.10 sample std.=13.17 p-value of the KSTEST for those 10 p-values: 0.625468 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-05-16_17:31 0.1836,0.3689,0.5341,0.7028,0.2666,0.6095,0.6035,0.6192,0.6869,0.9499, The KS test for those 10 p-values: 0.505907 The 3DSPHERES test for dh-ranFile-2016-05-16_17:31 sample no r^3 equiv. uni. 1 13.297 0.358041 2 16.308 0.419341 3 18.374 0.457988 4 16.566 0.424321 5 30.751 0.641215 6 39.236 0.729602 7 38.285 0.720895 8 47.071 0.791751 9 6.020 0.181819 10 31.196 0.646498 11 12.619 0.343376 12 11.702 0.322981 13 2.899 0.092126 14 2.213 0.071124 15 89.505 0.949385 16 61.616 0.871761 17 9.922 0.281597 18 33.726 0.675091 19 11.773 0.324599 20 23.476 0.542750 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.803348 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-05-16_17:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.1 -0.1 -0.4 1.4 -0.4 -0.6 1.0 2.3 -0.9 0.2 0.7 -0.9 -0.7 -1.8 -1.2 -0.3 -0.4 0.4 0.8 1.5 -1.7 -0.0 0.3 0.1 1.6 1.6 0.4 0.5 0.3 0.4 0.6 2.1 -1.5 -0.1 1.0 0.0 0.2 0.1 -0.7 -0.6 0.0 -1.1 Chi-square with 42 degrees of freedom:37.946513 z-score=-0.442272, p-value=0.350512 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-05-16_17:31 Test no p-value 1 0.041796 2 0.944537 3 0.194558 4 0.038598 5 0.177598 6 0.214428 7 0.532274 8 0.094125 9 0.058060 10 0.083162 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.001642 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-05-16_17:31: (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 66772 0.17 66552 0.20 3 25000.00 24945 0.12 25013 0.01 4 6666.67 6606 0.55 6733 0.66 5 1388.89 1378 0.09 1433 1.40 6 238.10 249 0.50 234 0.07 7 34.72 44 2.48 29 0.94 8 4.96 5 0.00 5 0.00 p=0.31048 p=0.22676 Number of rngs required: 688439, p-value: 0.517 RESULTS OF CRAPS TEST for dh-ranFile-2016-05-16_17:31 No. of wins: Observed Expected 98304 98585.9 z-score=-1.261, pvalue=0.10372 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66974 66666.7 1.417 1.417 2 37668 37654.3 0.005 1.422 3 27059 26954.7 0.403 1.825 4 19044 19313.5 3.760 5.585 5 13772 13851.4 0.455 6.040 6 9970 9943.5 0.070 6.110 7 7169 7145.0 0.080 6.191 8 5069 5139.1 0.955 7.146 9 3670 3699.9 0.241 7.387 10 2683 2666.3 0.105 7.492 11 1870 1923.3 1.479 8.971 12 1417 1388.7 0.575 9.546 13 1003 1003.7 0.001 9.546 14 687 726.1 2.110 11.656 15 546 525.8 0.773 12.429 16 355 381.2 1.794 14.223 17 306 276.5 3.139 17.362 18 205 200.8 0.087 17.449 19 154 146.0 0.440 17.889 20 94 106.2 1.405 19.293 21 285 287.1 0.016 19.309 Chisq= 19.31 for 20 degrees of freedom, p= 0.49817 SUMMARY of craptest p-value for no. of wins: 0.103720 p-value for throws/game: 0.498172 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-05-16_17:31 No. of wins: Observed Expected 98547 98585.9 z-score=-0.174, pvalue=0.43101 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66767 66666.7 0.151 0.151 2 37542 37654.3 0.335 0.486 3 27006 26954.7 0.098 0.584 4 19351 19313.5 0.073 0.657 5 13903 13851.4 0.192 0.849 6 9854 9943.5 0.806 1.655 7 7159 7145.0 0.027 1.682 8 5061 5139.1 1.186 2.868 9 3715 3699.9 0.062 2.930 10 2757 2666.3 3.086 6.016 11 1852 1923.3 2.645 8.661 12 1414 1388.7 0.459 9.121 13 1008 1003.7 0.018 9.139 14 718 726.1 0.091 9.230 15 508 525.8 0.605 9.835 16 352 381.2 2.229 12.065 17 268 276.5 0.264 12.328 18 232 200.8 4.838 17.166 19 144 146.0 0.027 17.193 20 98 106.2 0.635 17.828 21 291 287.1 0.053 17.881 Chisq= 17.88 for 20 degrees of freedom, p= 0.40475 SUMMARY of craptest p-value for no. of wins: 0.431012 p-value for throws/game: 0.404755 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0016,0.0180,0.0269,0.0288,0.0355,0.0386,0.0407,0.0418,0.0444,0.0445, 0.0453,0.0476,0.0481,0.0483,0.0581,0.0656,0.0711,0.0743,0.0832,0.0840, 0.0868,0.0921,0.0941,0.0972,0.1035,0.1037,0.1072,0.1097,0.1102,0.1169, 0.1244,0.1294,0.1375,0.1410,0.1426,0.1453,0.1497,0.1535,0.1576,0.1627, 0.1659,0.1666,0.1701,0.1743,0.1752,0.1753,0.1754,0.1774,0.1776,0.1806, 0.1818,0.1836,0.1865,0.1908,0.1946,0.2004,0.2035,0.2035,0.2092,0.2098, 0.2135,0.2144,0.2166,0.2169,0.2208,0.2215,0.2268,0.2319,0.2364,0.2383, 0.2400,0.2561,0.2565,0.2666,0.2816,0.2919,0.2943,0.2943,0.3009,0.3077, 0.3105,0.3108,0.3215,0.3230,0.3246,0.3316,0.3379,0.3410,0.3434,0.3440, 0.3445,0.3451,0.3479,0.3488,0.3505,0.3529,0.3560,0.3580,0.3581,0.3642, 0.3689,0.3702,0.3724,0.3803,0.3817,0.3882,0.3915,0.3975,0.4041,0.4048, 0.4079,0.4109,0.4125,0.4193,0.4243,0.4275,0.4310,0.4321,0.4389,0.4420, 0.4455,0.4486,0.4580,0.4761,0.4761,0.4766,0.4792,0.4913,0.4917,0.4939, 0.4942,0.4950,0.4982,0.4987,0.5020,0.5059,0.5114,0.5165,0.5182,0.5193, 0.5210,0.5229,0.5239,0.5266,0.5270,0.5323,0.5341,0.5400,0.5409,0.5417, 0.5425,0.5427,0.5431,0.5490,0.5535,0.5548,0.5639,0.5649,0.5663,0.5695, 0.5702,0.5748,0.5799,0.5861,0.5903,0.6035,0.6095,0.6192,0.6255,0.6296, 0.6299,0.6339,0.6401,0.6412,0.6424,0.6426,0.6465,0.6560,0.6695,0.6697, 0.6751,0.6801,0.6810,0.6845,0.6853,0.6869,0.7020,0.7028,0.7108,0.7121, 0.7163,0.7205,0.7209,0.7296,0.7348,0.7349,0.7377,0.7538,0.7550,0.7585, 0.7675,0.7692,0.7693,0.7747,0.7764,0.7774,0.7787,0.7788,0.7793,0.7815, 0.7820,0.7831,0.7863,0.7888,0.7888,0.7918,0.7944,0.7956,0.8033,0.8110, 0.8124,0.8164,0.8284,0.8358,0.8404,0.8418,0.8501,0.8563,0.8627,0.8674, 0.8680,0.8693,0.8698,0.8703,0.8718,0.8810,0.8899,0.9050,0.9138,0.9191, 0.9191,0.9202,0.9235,0.9241,0.9253,0.9322,0.9336,0.9359,0.9445,0.9454, 0.9462,0.9480,0.9494,0.9499,0.9509,0.9607,0.9615,0.9632,0.9654,0.9717, 0.9739,0.9741,0.9807,0.9853,0.9931,0.9932,0.9933,0.9967,0.9994, Overall p-value after applying KStest on 269 p-values = 0.879072 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.