RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-03-26_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 15.34 26.1983 0.929077 2 to 25 15.81 14.7356 0.385484 3 to 26 15.37 33.4884 0.990232 4 to 27 15.57 37.0962 0.996734 5 to 28 15.40 24.9920 0.905110 6 to 29 15.74 15.5316 0.442753 7 to 30 15.88 13.0196 0.265124 8 to 31 15.67 22.9939 0.850549 9 to 32 15.68 15.9586 0.473227 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.018983 Tough bday spacings test for dh-ranFile-2018-03-26_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 9 42 67 102 90 63 67 31 15 12 2 (O-E)^2/E 0.0 0.8 0.5 0.2 0.6 2.9 4.3 0.1 0.0 4.4 1.0 Birthday Spacings: Sum(O-E)^2/E= 14.802, p= 0.861 RESULTS OF GCD FOR dh-ranFile-2018-03-26_09:31 Euclid's algorithm: p-value, steps to gcd: 0.943883 p-value, dist. of gcd's: 0.867780 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-03-26_09:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.122 0.181 0.566 0.131 0.543 0.221 0.561 0.818 Bits 8 to 15---> 0.367 0.036 0.722 0.334 0.913 0.727 0.127 0.458 Bits 16 to 23---> 0.965 0.034 0.929 0.749 0.446 0.027 0.235 0.373 Bits 24 to 31---> 0.351 0.317 0.834 0.790 0.298 0.641 0.512 0.021 KS test for the above 32 p values: 0.441 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-03-26_09:31, p-values for 5 runs: 0.0946, 0.8924, 0.4720, 0.3538, 0.8869 Rank test for binary matrices (31x31) for dh-ranFile-2018-03-26_09:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 213 211.4 0.012 0.012 r= 29 5189 5134.0 0.589 0.601 r= 30 23046 23103.0 0.141 0.742 r= 31 11552 11551.5 0.000 0.742 chi-square = 0.742 with df = 3; p-value = 0.137 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-03-26_09:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 210 211.4 0.010 0.010 r= 30 5151 5134.0 0.056 0.066 r= 31 23181 23103.0 0.263 0.329 r= 32 11458 11551.5 0.757 1.086 chi-square = 1.086 with df = 3; p-value = 0.220 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-03-26_09:31 b-rank test for bits 1 to 8, p=0.56411 b-rank test for bits 2 to 9, p=0.21740 b-rank test for bits 3 to 10, p=0.05987 b-rank test for bits 4 to 11, p=0.92958 b-rank test for bits 5 to 12, p=0.73286 b-rank test for bits 6 to 13, p=0.53131 b-rank test for bits 7 to 14, p=0.55835 b-rank test for bits 8 to 15, p=0.26546 b-rank test for bits 9 to 16, p=0.31099 b-rank test for bits 10 to 17, p=0.24775 b-rank test for bits 11 to 18, p=0.32556 b-rank test for bits 12 to 19, p=0.63146 b-rank test for bits 13 to 20, p=0.20871 b-rank test for bits 14 to 21, p=0.54669 b-rank test for bits 15 to 22, p=0.81568 b-rank test for bits 16 to 23, p=0.91933 b-rank test for bits 17 to 24, p=0.63606 b-rank test for bits 18 to 25, p=0.18676 b-rank test for bits 19 to 26, p=0.37331 b-rank test for bits 20 to 27, p=0.63285 b-rank test for bits 21 to 28, p=0.94496 b-rank test for bits 22 to 29, p=0.99160 b-rank test for bits 23 to 30, p=0.83454 b-rank test for bits 24 to 31, p=0.72173 b-rank test for bits 25 to 32, p=0.85452 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 = 0.479057 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-03-26_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 142379 1.10 0.863758 2 141636 -0.64 0.261535 3 142528 1.45 0.925840 4 141946 0.09 0.534139 5 141950 0.10 0.537852 6 141964 0.13 0.550820 7 142247 0.79 0.784929 8 142484 1.34 0.910313 9 142176 0.62 0.733378 10 141950 0.10 0.537852 11 142047 0.32 0.626144 12 141690 -0.51 0.304167 13 142188 0.65 0.742508 14 141983 0.17 0.568331 15 142473 1.32 0.906078 16 142370 1.08 0.859111 17 141379 -1.24 0.107656 18 142146 0.55 0.709857 19 141118 -1.85 0.032236 20 141661 -0.58 0.280886 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-03-26_09:31 Bits used No. missing words z-score p-value 23 to 32 141871 -0.1322 0.447424 22 to 31 141432 -1.6460 0.049885 21 to 30 141150 -2.6184 0.004417 20 to 29 141811 -0.3391 0.367279 19 to 28 141365 -1.8770 0.030259 18 to 27 142007 0.3368 0.631864 17 to 26 142241 1.1437 0.873624 16 to 25 141851 -0.2011 0.420295 15 to 24 141938 0.0989 0.539376 14 to 23 141660 -0.8598 0.194961 13 to 22 142367 1.5782 0.942737 12 to 21 142710 2.7609 0.997118 11 to 20 141518 -1.3494 0.088602 10 to 19 142054 0.4989 0.691062 9 to 18 141444 -1.6046 0.054292 8 to 17 142188 0.9609 0.831707 7 to 16 142142 0.8023 0.788813 6 to 15 142218 1.0644 0.856422 5 to 14 142100 0.6575 0.744565 4 to 13 141923 0.0471 0.518798 3 to 12 142005 0.3299 0.629261 2 to 11 141263 -2.2287 0.012916 1 to 10 142018 0.3747 0.646067 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-03-26_09:31 Bits used No. missing words z-score p-value 28 to 32 141668 -0.8181 0.206659 27 to 31 141596 -1.0621 0.144087 26 to 30 141524 -1.3062 0.095742 25 to 29 142068 0.5379 0.704665 24 to 28 141799 -0.3740 0.354202 23 to 27 141367 -1.8384 0.033001 22 to 26 141790 -0.4045 0.342919 21 to 25 142036 0.4294 0.666180 20 to 24 141916 0.0226 0.509019 19 to 23 142032 0.4158 0.661233 18 to 22 141291 -2.0960 0.018040 17 to 21 141704 -0.6960 0.243204 16 to 20 141753 -0.5299 0.298080 15 to 19 142467 1.8904 0.970648 14 to 18 141917 0.0260 0.510371 13 to 17 141557 -1.1943 0.116173 12 to 16 141901 -0.0282 0.488737 11 to 15 141855 -0.1842 0.426940 10 to 14 142354 1.5074 0.934140 9 to 13 142106 0.6667 0.747511 8 to 12 140974 -3.1706 0.000761 7 to 11 142141 0.7853 0.783868 6 to 10 142050 0.4768 0.683265 5 to 9 142074 0.5582 0.711647 4 to 8 141576 -1.1299 0.129252 3 to 7 142211 1.0226 0.846754 2 to 6 142025 0.3921 0.652509 1 to 5 142138 0.7752 0.780875 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-03-26_09:31 Bits used No. missing words z-score p-value 31 to 32 142561 1.9223 0.972718 30 to 31 142003 0.2763 0.608846 29 to 30 142566 1.9371 0.973632 28 to 29 141294 -1.8151 0.034752 27 to 28 141878 -0.0924 0.463183 26 to 27 142231 0.9489 0.828659 25 to 26 142699 2.3294 0.990081 24 to 25 141741 -0.4965 0.309754 23 to 24 142090 0.5329 0.702966 22 to 23 142347 1.2911 0.901659 21 to 22 141547 -1.0688 0.142575 20 to 21 141912 0.0079 0.503142 19 to 20 142582 1.9843 0.976388 18 to 19 141903 -0.0187 0.492551 17 to 18 142094 0.5447 0.707037 16 to 17 141897 -0.0364 0.485493 15 to 16 141542 -1.0836 0.139278 14 to 15 141900 -0.0275 0.489022 13 to 14 142165 0.7542 0.774632 12 to 13 141717 -0.5673 0.285240 11 to 12 141919 0.0285 0.511378 10 to 11 142025 0.3412 0.633527 9 to 10 142011 0.2999 0.617878 8 to 9 141906 -0.0098 0.496081 7 to 8 141007 -2.6617 0.003887 6 to 7 141541 -1.0865 0.138625 5 to 6 141957 0.1406 0.555915 4 to 5 141314 -1.7561 0.039533 3 to 4 142240 0.9754 0.835326 2 to 3 142426 1.5241 0.936258 1 to 2 141930 0.0610 0.524310 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-03-26_09:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2522.90 0.324 0.626998 Test results for specific bytes for dh-ranFile-2018-03-26_09:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2462.20 -0.535 0.296469 2 to 9 2412.10 -1.243 0.106904 3 to 10 2400.67 -1.405 0.080041 4 to 11 2398.79 -1.431 0.076173 5 to 12 2481.55 -0.261 0.397083 6 to 13 2553.93 0.763 0.777168 7 to 14 2512.57 0.178 0.570560 8 to 15 2567.16 0.950 0.828886 9 to 16 2503.61 0.051 0.520340 10 to 17 2538.70 0.547 0.707926 11 to 18 2543.21 0.611 0.729437 12 to 19 2561.61 0.871 0.808186 13 to 20 2512.68 0.179 0.571174 14 to 21 2482.19 -0.252 0.400582 15 to 22 2522.38 0.317 0.624195 16 to 23 2515.33 0.217 0.585828 17 to 24 2369.82 -1.841 0.032804 18 to 25 2601.19 1.431 0.923798 19 to 26 2514.28 0.202 0.580005 20 to 27 2573.33 1.037 0.850137 21 to 28 2455.78 -0.625 0.265866 22 to 29 2432.28 -0.958 0.169098 23 to 30 2522.08 0.312 0.622588 24 to 31 2596.72 1.368 0.914320 25 to 32 2420.18 -1.129 0.129475 CDPARK for dh-ranFile-2018-03-26_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 3527 0.1826 0.572463 3517 -0.2740 0.392053 3483 -1.8265 0.033889 3520 -0.1370 0.445521 3490 -1.5068 0.065925 3519 -0.1826 0.427537 3501 -1.0046 0.157553 3524 0.0457 0.518210 3503 -0.9132 0.180558 3532 0.4110 0.659449 Square side=100, avg. no. parked=3511.60 sample std.=15.60 p-value of the KSTEST for those 10 p-values: 0.131883 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-03-26_09:31 0.2128,0.8036,0.2783,0.4047,0.9357,0.7156,0.9277,0.8890,0.6631,0.6269, The KS test for those 10 p-values: 0.184176 The 3DSPHERES test for dh-ranFile-2018-03-26_09:31 sample no r^3 equiv. uni. 1 13.334 0.358842 2 25.651 0.574727 3 5.166 0.158190 4 15.479 0.403079 5 9.035 0.260052 6 23.309 0.540199 7 9.200 0.264101 8 27.779 0.603852 9 18.377 0.458050 10 9.733 0.277063 11 13.949 0.371840 12 52.679 0.827259 13 8.536 0.247643 14 1.700 0.055076 15 9.310 0.266808 16 8.176 0.238553 17 38.442 0.722356 18 13.386 0.359944 19 41.413 0.748530 20 26.010 0.579793 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.110757 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-03-26_09:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 1.8 -0.1 -0.7 1.9 -1.5 1.1 -1.6 0.8 -1.5 -1.1 0.1 0.5 -0.8 1.6 -0.8 1.0 -0.5 -1.1 0.7 -0.6 0.1 0.0 -0.6 1.7 0.5 -0.9 -0.9 1.6 -0.5 1.8 1.6 0.2 0.0 -1.6 0.8 0.0 0.5 0.1 -0.7 0.1 0.0 0.8 Chi-square with 42 degrees of freedom:43.488641 z-score=0.162424, p-value=0.592179 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-03-26_09:31 Test no p-value 1 0.302727 2 0.146698 3 0.702748 4 0.037683 5 0.171280 6 0.758056 7 0.200536 8 0.257474 9 0.011341 10 0.101484 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.012054 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-03-26_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 66552 0.20 66889 0.74 3 25000.00 24995 0.00 24745 2.60 4 6666.67 6740 0.81 6730 0.60 5 1388.89 1461 3.74 1336 2.01 6 238.10 217 1.87 259 1.84 7 34.72 26 2.19 34 0.01 8 4.96 8 1.86 6 0.22 p=0.90091 p=0.76384 Number of rngs required: 688329, p-value: 0.466 RESULTS OF CRAPS TEST for dh-ranFile-2018-03-26_09:31 No. of wins: Observed Expected 98735 98585.9 z-score= 0.667, pvalue=0.74763 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66769 66666.7 0.157 0.157 2 37617 37654.3 0.037 0.194 3 26908 26954.7 0.081 0.275 4 19282 19313.5 0.051 0.326 5 13698 13851.4 1.699 2.026 6 10067 9943.5 1.533 3.558 7 7204 7145.0 0.487 4.045 8 5153 5139.1 0.038 4.083 9 3655 3699.9 0.544 4.627 10 2686 2666.3 0.146 4.773 11 1898 1923.3 0.334 5.106 12 1384 1388.7 0.016 5.122 13 968 1003.7 1.271 6.393 14 753 726.1 0.994 7.387 15 507 525.8 0.675 8.061 16 371 381.2 0.270 8.332 17 298 276.5 1.665 9.997 18 213 200.8 0.737 10.735 19 149 146.0 0.062 10.797 20 109 106.2 0.073 10.870 21 311 287.1 1.987 12.857 Chisq= 12.86 for 20 degrees of freedom, p= 0.11657 SUMMARY of craptest p-value for no. of wins: 0.747629 p-value for throws/game: 0.116571 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-03-26_09:31 No. of wins: Observed Expected 98499 98585.9 z-score=-0.388, pvalue=0.34883 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66098 66666.7 4.851 4.851 2 37971 37654.3 2.663 7.514 3 26907 26954.7 0.085 7.599 4 19410 19313.5 0.483 8.081 5 13844 13851.4 0.004 8.085 6 10014 9943.5 0.499 8.584 7 7199 7145.0 0.408 8.992 8 5163 5139.1 0.111 9.103 9 3702 3699.9 0.001 9.105 10 2701 2666.3 0.452 9.556 11 1924 1923.3 0.000 9.557 12 1406 1388.7 0.215 9.771 13 974 1003.7 0.880 10.651 14 740 726.1 0.265 10.915 15 538 525.8 0.281 11.197 16 381 381.2 0.000 11.197 17 256 276.5 1.526 12.722 18 186 200.8 1.095 13.817 19 170 146.0 3.951 17.768 20 108 106.2 0.030 17.798 21 308 287.1 1.519 19.318 Chisq= 19.32 for 20 degrees of freedom, p= 0.49872 SUMMARY of craptest p-value for no. of wins: 0.348830 p-value for throws/game: 0.498719 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0008,0.0039,0.0044,0.0113,0.0121,0.0129,0.0180,0.0190,0.0211,0.0271, 0.0303,0.0322,0.0328,0.0330,0.0339,0.0342,0.0348,0.0356,0.0377,0.0395, 0.0499,0.0543,0.0551,0.0599,0.0659,0.0762,0.0800,0.0886,0.0946,0.0957, 0.1015,0.1069,0.1077,0.1108,0.1162,0.1166,0.1224,0.1268,0.1293,0.1295, 0.1314,0.1319,0.1366,0.1386,0.1393,0.1426,0.1441,0.1467,0.1576,0.1582, 0.1691,0.1713,0.1806,0.1811,0.1842,0.1868,0.1950,0.2005,0.2067,0.2087, 0.2128,0.2174,0.2195,0.2212,0.2354,0.2386,0.2432,0.2476,0.2478,0.2575, 0.2601,0.2615,0.2641,0.2651,0.2655,0.2659,0.2668,0.2771,0.2783,0.2809, 0.2852,0.2965,0.2977,0.2981,0.3027,0.3042,0.3098,0.3110,0.3170,0.3256, 0.3341,0.3429,0.3488,0.3510,0.3538,0.3542,0.3588,0.3599,0.3673,0.3675, 0.3718,0.3728,0.3733,0.3855,0.3921,0.3971,0.4006,0.4031,0.4047,0.4203, 0.4269,0.4275,0.4415,0.4428,0.4455,0.4457,0.4474,0.4577,0.4581,0.4632, 0.4661,0.4720,0.4732,0.4791,0.4855,0.4887,0.4890,0.4926,0.4961,0.4987, 0.5031,0.5090,0.5104,0.5114,0.5121,0.5182,0.5188,0.5203,0.5243,0.5313, 0.5341,0.5379,0.5379,0.5394,0.5402,0.5435,0.5467,0.5508,0.5559,0.5584, 0.5609,0.5641,0.5665,0.5683,0.5706,0.5712,0.5725,0.5747,0.5798,0.5800, 0.5858,0.5922,0.6039,0.6088,0.6179,0.6226,0.6242,0.6261,0.6269,0.6270, 0.6293,0.6315,0.6319,0.6328,0.6335,0.6361,0.6413,0.6461,0.6525,0.6594, 0.6612,0.6631,0.6662,0.6833,0.6911,0.7027,0.7030,0.7047,0.7070,0.7079, 0.7099,0.7116,0.7156,0.7217,0.7224,0.7225,0.7268,0.7294,0.7329,0.7334, 0.7425,0.7446,0.7475,0.7476,0.7485,0.7490,0.7581,0.7638,0.7746,0.7772, 0.7809,0.7839,0.7849,0.7888,0.7904,0.8036,0.8082,0.8157,0.8175,0.8273, 0.8287,0.8289,0.8317,0.8344,0.8345,0.8353,0.8468,0.8501,0.8505,0.8545, 0.8564,0.8591,0.8606,0.8638,0.8678,0.8736,0.8869,0.8890,0.8924,0.9009, 0.9017,0.9051,0.9061,0.9103,0.9131,0.9143,0.9193,0.9238,0.9258,0.9277, 0.9291,0.9294,0.9296,0.9341,0.9357,0.9363,0.9427,0.9439,0.9450,0.9649, 0.9706,0.9727,0.9736,0.9764,0.9901,0.9902,0.9916,0.9967,0.9971, Overall p-value after applying KStest on 269 p-values = 0.826621 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.