RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-03-29_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 15.81 17.7963 0.598200 2 to 25 15.92 21.4363 0.792619 3 to 26 15.90 19.9589 0.723661 4 to 27 15.96 15.0499 0.408114 5 to 28 15.88 13.4705 0.295834 6 to 29 15.57 14.2599 0.351371 7 to 30 15.48 20.0381 0.727716 8 to 31 15.95 16.2964 0.497070 9 to 32 15.84 18.9421 0.668132 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.335677 Tough bday spacings test for dh-ranFile-2016-03-29_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 6 36 78 99 106 67 57 27 20 2 2 (O-E)^2/E 1.1 0.0 0.3 0.0 0.7 1.6 0.5 0.3 1.8 3.2 1.0 Birthday Spacings: Sum(O-E)^2/E= 10.469, p= 0.600 RESULTS OF GCD FOR dh-ranFile-2016-03-29_08:31 Euclid's algorithm: p-value, steps to gcd: 0.169648 p-value, dist. of gcd's: 0.885781 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-03-29_08:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.201 0.293 0.574 0.842 0.040 0.045 0.255 0.367 Bits 8 to 15---> 0.134 0.014 0.809 0.227 0.637 0.284 0.004 0.251 Bits 16 to 23---> 0.143 0.465 0.555 0.803 0.255 0.522 0.758 0.956 Bits 24 to 31---> 0.100 0.448 0.838 0.806 0.123 0.240 0.822 0.868 KS test for the above 32 p values: 0.824 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-03-29_08:31, p-values for 5 runs: 0.5084, 0.0750, 0.0972, 0.4066, 0.1255 Rank test for binary matrices (31x31) for dh-ranFile-2016-03-29_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 177 211.4 5.603 5.603 r= 29 5086 5134.0 0.449 6.052 r= 30 23141 23103.0 0.062 6.114 r= 31 11596 11551.5 0.171 6.286 chi-square = 6.286 with df = 3; p-value = 0.901 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-03-29_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 206 211.4 0.139 0.139 r= 30 5117 5134.0 0.056 0.195 r= 31 23094 23103.0 0.004 0.199 r= 32 11583 11551.5 0.086 0.285 chi-square = 0.285 with df = 3; p-value = 0.037 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-03-29_08:31 b-rank test for bits 1 to 8, p=0.34894 b-rank test for bits 2 to 9, p=0.55039 b-rank test for bits 3 to 10, p=0.76474 b-rank test for bits 4 to 11, p=0.53481 b-rank test for bits 5 to 12, p=0.86730 b-rank test for bits 6 to 13, p=0.25329 b-rank test for bits 7 to 14, p=0.97378 b-rank test for bits 8 to 15, p=0.98393 b-rank test for bits 9 to 16, p=0.93647 b-rank test for bits 10 to 17, p=0.07672 b-rank test for bits 11 to 18, p=0.26703 b-rank test for bits 12 to 19, p=0.47175 b-rank test for bits 13 to 20, p=0.89835 b-rank test for bits 14 to 21, p=0.34976 b-rank test for bits 15 to 22, p=0.87305 b-rank test for bits 16 to 23, p=0.31444 b-rank test for bits 17 to 24, p=0.67277 b-rank test for bits 18 to 25, p=0.14682 b-rank test for bits 19 to 26, p=0.17942 b-rank test for bits 20 to 27, p=0.57041 b-rank test for bits 21 to 28, p=0.29748 b-rank test for bits 22 to 29, p=0.15433 b-rank test for bits 23 to 30, p=0.23010 b-rank test for bits 24 to 31, p=0.12280 b-rank test for bits 25 to 32, p=0.12822 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 = 0.583579 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-03-29_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 141657 -0.59 0.277744 2 142015 0.25 0.597504 3 141554 -0.83 0.203210 4 142650 1.73 0.958233 5 143000 2.55 0.994587 6 141936 0.06 0.524843 7 141527 -0.89 0.185850 8 141553 -0.83 0.202550 9 141994 0.20 0.578410 10 142390 1.12 0.869294 11 141673 -0.55 0.290415 12 142440 1.24 0.892491 13 141794 -0.27 0.393787 14 141854 -0.13 0.448570 15 142183 0.64 0.738724 16 141743 -0.39 0.348778 17 141733 -0.41 0.340175 18 142087 0.42 0.660972 19 141592 -0.74 0.229218 20 142333 0.99 0.838884 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-03-29_08:31 Bits used No. missing words z-score p-value 23 to 32 141722 -0.6460 0.259151 22 to 31 141932 0.0782 0.531155 21 to 30 142084 0.6023 0.726516 20 to 29 142060 0.5196 0.698312 19 to 28 142375 1.6058 0.945837 18 to 27 141721 -0.6494 0.258036 17 to 26 142037 0.4402 0.670119 16 to 25 141979 0.2402 0.594928 15 to 24 141741 -0.5804 0.280806 14 to 23 142005 0.3299 0.629261 13 to 22 142162 0.8713 0.808198 12 to 21 142241 1.1437 0.873624 11 to 20 142101 0.6609 0.745672 10 to 19 141902 -0.0253 0.489918 9 to 18 142098 0.6506 0.742343 8 to 17 141549 -1.2425 0.107023 7 to 16 142136 0.7816 0.782781 6 to 15 142420 1.7609 0.960875 5 to 14 141933 0.0816 0.532526 4 to 13 141867 -0.1460 0.441974 3 to 12 141820 -0.3080 0.379028 2 to 11 141548 -1.2460 0.106389 1 to 10 142205 1.0196 0.846029 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-03-29_08:31 Bits used No. missing words z-score p-value 28 to 32 141717 -0.6520 0.257212 27 to 31 141735 -0.5909 0.277277 26 to 30 142258 1.1819 0.881384 25 to 29 141801 -0.3672 0.356727 24 to 28 141997 0.2972 0.616838 23 to 27 141599 -1.0520 0.146408 22 to 26 142384 1.6091 0.946197 21 to 25 142192 0.9582 0.831020 20 to 24 142313 1.3684 0.914402 19 to 23 142172 0.8904 0.813376 18 to 22 142194 0.9650 0.832723 17 to 21 142048 0.4701 0.680847 16 to 20 142043 0.4531 0.674768 15 to 19 142223 1.0633 0.856174 14 to 18 141608 -1.0215 0.153519 13 to 17 141992 0.2802 0.610352 12 to 16 142474 1.9141 0.972199 11 to 15 141838 -0.2418 0.404469 10 to 14 141994 0.2870 0.612950 9 to 13 141545 -1.2350 0.108412 8 to 12 141816 -0.3164 0.375860 7 to 11 141850 -0.2011 0.420303 6 to 10 142130 0.7480 0.772780 5 to 9 141930 0.0701 0.527930 4 to 8 141629 -0.9503 0.170987 3 to 7 141808 -0.3435 0.365614 2 to 6 141778 -0.4452 0.328093 1 to 5 141846 -0.2147 0.415009 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-03-29_08:31 Bits used No. missing words z-score p-value 31 to 32 141986 0.2262 0.589464 30 to 31 141684 -0.6647 0.253124 29 to 30 141566 -1.0128 0.155584 28 to 29 142578 1.9725 0.975722 27 to 28 141938 0.0846 0.533699 26 to 27 141945 0.1052 0.541900 25 to 26 141615 -0.8682 0.192634 24 to 25 142107 0.5831 0.720086 23 to 24 141961 0.1524 0.560572 22 to 23 141685 -0.6617 0.254069 21 to 22 142305 1.1672 0.878429 20 to 21 142588 2.0020 0.977356 19 to 20 142125 0.6362 0.737675 18 to 19 141409 -1.4759 0.069985 17 to 18 141791 -0.3491 0.363524 16 to 17 141840 -0.2045 0.418976 15 to 16 141729 -0.5319 0.297381 14 to 15 141807 -0.3019 0.381380 13 to 14 142002 0.2734 0.607713 12 to 13 142576 1.9666 0.975384 11 to 12 141983 0.2173 0.586019 10 to 11 142077 0.4946 0.689559 9 to 10 141595 -0.9272 0.176904 8 to 9 141753 -0.4612 0.322345 7 to 8 142283 1.1023 0.864828 6 to 7 142252 1.0108 0.843950 5 to 6 141920 0.0315 0.512555 4 to 5 141852 -0.1691 0.432853 3 to 4 141573 -0.9921 0.160569 2 to 3 142261 1.0374 0.850219 1 to 2 141465 -1.3107 0.094978 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-03-29_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2615.59 1.635 0.948942 Test results for specific bytes for dh-ranFile-2016-03-29_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2545.54 0.644 0.740238 2 to 9 2495.65 -0.062 0.475461 3 to 10 2507.24 0.102 0.540796 4 to 11 2492.31 -0.109 0.456703 5 to 12 2519.40 0.274 0.608116 6 to 13 2559.70 0.844 0.800761 7 to 14 2495.84 -0.059 0.476563 8 to 15 2441.67 -0.825 0.204700 9 to 16 2472.07 -0.395 0.346403 10 to 17 2478.80 -0.300 0.382180 11 to 18 2478.34 -0.306 0.379681 12 to 19 2472.96 -0.382 0.351096 13 to 20 2453.63 -0.656 0.255971 14 to 21 2511.48 0.162 0.564494 15 to 22 2576.57 1.083 0.860579 16 to 23 2573.87 1.045 0.851908 17 to 24 2434.12 -0.932 0.175765 18 to 25 2491.00 -0.127 0.449379 19 to 26 2447.87 -0.737 0.230489 20 to 27 2471.81 -0.399 0.345081 21 to 28 2596.52 1.365 0.913880 22 to 29 2576.67 1.084 0.860870 23 to 30 2458.14 -0.592 0.276952 24 to 31 2419.65 -1.136 0.127917 25 to 32 2477.70 -0.315 0.376252 CDPARK for dh-ranFile-2016-03-29_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 3515 -0.3653 0.357445 3552 1.3242 0.907282 3558 1.5982 0.944998 3516 -0.3196 0.374623 3518 -0.2283 0.409702 3503 -0.9132 0.180558 3544 0.9589 0.831196 3512 -0.5023 0.307734 3519 -0.1826 0.427537 3537 0.6393 0.738676 Square side=100, avg. no. parked=3527.40 sample std.=17.84 p-value of the KSTEST for those 10 p-values: 0.648218 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-03-29_08:31 0.1632,0.8051,0.8541,0.3251,0.5303,0.1702,0.6908,0.8012,0.5175,0.3590, The KS test for those 10 p-values: 0.867058 The 3DSPHERES test for dh-ranFile-2016-03-29_08:31 sample no r^3 equiv. uni. 1 90.928 0.951730 2 14.361 0.380418 3 20.180 0.489655 4 16.613 0.425226 5 106.218 0.971004 6 50.144 0.812030 7 2.370 0.075954 8 40.495 0.740718 9 15.034 0.394149 10 37.851 0.716824 11 0.555 0.018333 12 7.371 0.217856 13 16.142 0.416121 14 13.016 0.351995 15 49.653 0.808929 16 137.071 0.989632 17 111.175 0.975420 18 14.335 0.379880 19 52.089 0.823831 20 29.422 0.624966 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.236811 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-03-29_08:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 0.1 1.5 0.6 -0.9 -0.6 -1.7 -0.9 0.5 1.1 -0.9 1.1 -0.0 -0.3 0.5 0.7 0.3 1.2 0.5 -0.4 -1.1 -0.4 -0.4 -0.2 -0.7 1.4 -2.0 -1.5 -1.6 0.8 0.1 1.1 0.2 0.2 1.2 -1.0 0.5 0.2 2.1 0.4 -0.6 0.0 -1.1 Chi-square with 42 degrees of freedom:37.804238 z-score=-0.457795, p-value=0.344375 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-03-29_08:31 Test no p-value 1 0.097562 2 0.076298 3 0.970191 4 0.000658 5 0.137158 6 0.112146 7 0.448158 8 0.280138 9 0.034757 10 0.588399 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.005894 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-03-29_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 66695 0.01 66420 0.91 3 25000.00 25093 0.35 25191 1.46 4 6666.67 6546 2.18 6825 3.76 5 1388.89 1357 0.73 1291 6.90 6 238.10 258 1.66 231 0.21 7 34.72 46 3.66 39 0.53 8 4.96 4 0.19 2 1.77 p=0.81420 p=0.98353 Number of rngs required: 690994, p-value: 0.999 RESULTS OF CRAPS TEST for dh-ranFile-2016-03-29_08:31 No. of wins: Observed Expected 98562 98585.9 z-score=-0.107, pvalue=0.45751 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66710 66666.7 0.028 0.028 2 37626 37654.3 0.021 0.049 3 26761 26954.7 1.392 1.442 4 19294 19313.5 0.020 1.461 5 13798 13851.4 0.206 1.668 6 9935 9943.5 0.007 1.675 7 7156 7145.0 0.017 1.692 8 5254 5139.1 2.570 4.262 9 3774 3699.9 1.485 5.747 10 2700 2666.3 0.426 6.173 11 1916 1923.3 0.028 6.201 12 1357 1388.7 0.725 6.927 13 990 1003.7 0.187 7.114 14 750 726.1 0.784 7.898 15 543 525.8 0.560 8.458 16 393 381.2 0.368 8.827 17 286 276.5 0.324 9.150 18 222 200.8 2.232 11.382 19 128 146.0 2.216 13.598 20 122 106.2 2.346 15.943 21 285 287.1 0.016 15.959 Chisq= 15.96 for 20 degrees of freedom, p= 0.28083 SUMMARY of craptest p-value for no. of wins: 0.457510 p-value for throws/game: 0.280832 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-03-29_08:31 No. of wins: Observed Expected 98789 98585.9 z-score= 0.909, pvalue=0.81821 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66599 66666.7 0.069 0.069 2 37587 37654.3 0.120 0.189 3 27112 26954.7 0.918 1.107 4 19310 19313.5 0.001 1.107 5 13809 13851.4 0.130 1.237 6 9927 9943.5 0.028 1.265 7 7161 7145.0 0.036 1.300 8 5246 5139.1 2.225 3.525 9 3663 3699.9 0.367 3.893 10 2718 2666.3 1.003 4.895 11 1863 1923.3 1.892 6.787 12 1334 1388.7 2.158 8.945 13 1037 1003.7 1.104 10.049 14 733 726.1 0.065 10.114 15 503 525.8 0.992 11.105 16 328 381.2 7.412 18.517 17 288 276.5 0.475 18.992 18 204 200.8 0.050 19.042 19 164 146.0 2.223 21.265 20 105 106.2 0.014 21.279 21 309 287.1 1.668 22.948 Chisq= 22.95 for 20 degrees of freedom, p= 0.70863 SUMMARY of craptest p-value for no. of wins: 0.818211 p-value for throws/game: 0.708629 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0007,0.0040,0.0059,0.0139,0.0183,0.0348,0.0371,0.0398,0.0446,0.0700, 0.0750,0.0760,0.0763,0.0767,0.0950,0.0972,0.0976,0.0998,0.1064,0.1070, 0.1084,0.1121,0.1228,0.1233,0.1255,0.1279,0.1282,0.1341,0.1372,0.1435, 0.1464,0.1468,0.1535,0.1543,0.1556,0.1606,0.1632,0.1696,0.1702,0.1710, 0.1758,0.1769,0.1794,0.1806,0.1858,0.1926,0.2010,0.2026,0.2032,0.2047, 0.2179,0.2274,0.2292,0.2301,0.2305,0.2368,0.2403,0.2510,0.2531,0.2533, 0.2541,0.2550,0.2554,0.2560,0.2572,0.2580,0.2592,0.2670,0.2770,0.2773, 0.2777,0.2801,0.2808,0.2808,0.2838,0.2904,0.2929,0.2958,0.2974,0.2975, 0.3077,0.3144,0.3223,0.3251,0.3281,0.3357,0.3402,0.3444,0.3451,0.3464, 0.3488,0.3489,0.3498,0.3511,0.3514,0.3520,0.3567,0.3574,0.3590,0.3635, 0.3656,0.3674,0.3746,0.3759,0.3763,0.3790,0.3797,0.3799,0.3804,0.3814, 0.3822,0.3938,0.3941,0.4045,0.4066,0.4081,0.4097,0.4150,0.4161,0.4190, 0.4203,0.4252,0.4275,0.4329,0.4420,0.4481,0.4482,0.4486,0.4494,0.4567, 0.4575,0.4655,0.4718,0.4755,0.4766,0.4897,0.4899,0.4971,0.5084,0.5126, 0.5175,0.5220,0.5248,0.5279,0.5303,0.5312,0.5325,0.5337,0.5348,0.5408, 0.5419,0.5504,0.5552,0.5606,0.5645,0.5704,0.5740,0.5784,0.5836,0.5860, 0.5884,0.5895,0.5949,0.5975,0.5982,0.5996,0.6077,0.6081,0.6104,0.6130, 0.6168,0.6250,0.6293,0.6370,0.6482,0.6610,0.6681,0.6701,0.6728,0.6748, 0.6808,0.6896,0.6908,0.6983,0.7086,0.7168,0.7201,0.7237,0.7265,0.7277, 0.7377,0.7387,0.7387,0.7402,0.7407,0.7423,0.7457,0.7577,0.7647,0.7728, 0.7828,0.7926,0.8008,0.8012,0.8034,0.8051,0.8063,0.8082,0.8089,0.8090, 0.8120,0.8134,0.8142,0.8182,0.8224,0.8237,0.8238,0.8310,0.8312,0.8327, 0.8381,0.8389,0.8420,0.8440,0.8460,0.8502,0.8519,0.8541,0.8562,0.8606, 0.8609,0.8648,0.8671,0.8673,0.8680,0.8693,0.8731,0.8736,0.8784,0.8814, 0.8858,0.8925,0.8984,0.9015,0.9073,0.9139,0.9144,0.9365,0.9450,0.9458, 0.9462,0.9489,0.9517,0.9563,0.9582,0.9609,0.9702,0.9710,0.9722,0.9738, 0.9754,0.9754,0.9757,0.9774,0.9835,0.9839,0.9896,0.9946,0.9991, Overall p-value after applying KStest on 269 p-values = 0.416043 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.