RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-08-14_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 15.81 17.1957 0.558817 2 to 25 15.73 10.4355 0.115637 3 to 26 15.96 19.8306 0.717013 4 to 27 15.71 18.7514 0.657013 5 to 28 15.68 14.7021 0.383073 6 to 29 15.84 21.4412 0.792824 7 to 30 15.73 11.0499 0.146041 8 to 31 15.80 12.1547 0.209320 9 to 32 15.93 16.7351 0.527552 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.800272 Tough bday spacings test for dh-ranFile-2016-08-14_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 8 49 64 120 88 79 39 33 10 7 3 (O-E)^2/E 0.1 4.2 1.2 5.1 1.0 0.0 3.3 0.4 1.6 0.0 0.3 Birthday Spacings: Sum(O-E)^2/E= 17.110, p= 0.928 RESULTS OF GCD FOR dh-ranFile-2016-08-14_09:31 Euclid's algorithm: p-value, steps to gcd: 0.349306 p-value, dist. of gcd's: 0.433760 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-08-14_09:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.760 0.518 0.076 0.629 0.672 0.919 0.474 0.531 Bits 8 to 15---> 0.107 0.472 0.369 0.546 0.166 0.042 0.043 0.884 Bits 16 to 23---> 0.966 0.265 0.676 0.033 0.382 0.203 0.262 0.974 Bits 24 to 31---> 0.884 0.466 0.450 0.402 0.996 0.580 0.426 0.419 KS test for the above 32 p values: 0.250 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-08-14_09:31, p-values for 5 runs: 0.5434, 0.3844, 0.2573, 0.1458, 0.0803 Rank test for binary matrices (31x31) for dh-ranFile-2016-08-14_09:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 213 211.4 0.012 0.012 r= 29 5182 5134.0 0.449 0.460 r= 30 23106 23103.0 0.000 0.461 r= 31 11499 11551.5 0.239 0.700 chi-square = 0.700 with df = 3; p-value = 0.127 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-08-14_09:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 213 211.4 0.012 0.012 r= 30 5052 5134.0 1.310 1.322 r= 31 23301 23103.0 1.696 3.018 r= 32 11434 11551.5 1.196 4.214 chi-square = 4.214 with df = 3; p-value = 0.761 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-08-14_09:31 b-rank test for bits 1 to 8, p=0.80297 b-rank test for bits 2 to 9, p=0.76465 b-rank test for bits 3 to 10, p=0.26975 b-rank test for bits 4 to 11, p=0.96863 b-rank test for bits 5 to 12, p=0.78310 b-rank test for bits 6 to 13, p=0.49155 b-rank test for bits 7 to 14, p=0.31922 b-rank test for bits 8 to 15, p=0.12285 b-rank test for bits 9 to 16, p=0.60541 b-rank test for bits 10 to 17, p=0.06139 b-rank test for bits 11 to 18, p=0.76070 b-rank test for bits 12 to 19, p=0.78203 b-rank test for bits 13 to 20, p=0.07472 b-rank test for bits 14 to 21, p=0.12492 b-rank test for bits 15 to 22, p=0.27106 b-rank test for bits 16 to 23, p=0.02970 b-rank test for bits 17 to 24, p=0.54466 b-rank test for bits 18 to 25, p=0.39616 b-rank test for bits 19 to 26, p=0.84477 b-rank test for bits 20 to 27, p=0.74067 b-rank test for bits 21 to 28, p=0.06930 b-rank test for bits 22 to 29, p=0.68612 b-rank test for bits 23 to 30, p=0.39444 b-rank test for bits 24 to 31, p=0.41933 b-rank test for bits 25 to 32, p=0.82096 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 = 0.782601 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-08-14_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 141953 0.10 0.540635 2 141868 -0.10 0.461536 3 141630 -0.65 0.256994 4 142244 0.78 0.782875 5 141516 -0.92 0.179049 6 141680 -0.54 0.296042 7 142467 1.30 0.903707 8 141906 -0.01 0.496896 9 141911 0.00 0.501557 10 141370 -1.26 0.103814 11 142494 1.37 0.914039 12 141711 -0.46 0.321543 13 142233 0.76 0.775247 14 141860 -0.12 0.454121 15 142127 0.51 0.694475 16 141494 -0.97 0.165924 17 141610 -0.70 0.242161 18 142005 0.22 0.588438 19 141499 -0.96 0.168851 20 141203 -1.65 0.049440 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-08-14_09:31 Bits used No. missing words z-score p-value 23 to 32 141743 -0.5736 0.283136 22 to 31 142260 1.2092 0.886708 21 to 30 142280 1.2782 0.899406 20 to 29 142183 0.9437 0.827336 19 to 28 142069 0.5506 0.709041 18 to 27 141989 0.2747 0.608236 17 to 26 142408 1.7196 0.957243 16 to 25 141922 0.0437 0.517424 15 to 24 141664 -0.8460 0.198786 14 to 23 142217 1.0609 0.855639 13 to 22 141900 -0.0322 0.487167 12 to 21 141455 -1.5667 0.058598 11 to 20 141966 0.1954 0.577466 10 to 19 142375 1.6058 0.945837 9 to 18 141969 0.2058 0.581510 8 to 17 142226 1.0920 0.862576 7 to 16 142310 1.3816 0.916456 6 to 15 141726 -0.6322 0.263637 5 to 14 142235 1.1230 0.869281 4 to 13 141923 0.0471 0.518798 3 to 12 141941 0.1092 0.543481 2 to 11 141715 -0.6701 0.251396 1 to 10 141998 0.3058 0.620106 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-08-14_09:31 Bits used No. missing words z-score p-value 28 to 32 141438 -1.5977 0.055052 27 to 31 142378 1.5887 0.943937 26 to 30 141966 0.1921 0.576169 25 to 29 141930 0.0701 0.527930 24 to 28 142037 0.4328 0.667413 23 to 27 142084 0.5921 0.723109 22 to 26 142021 0.3785 0.647486 21 to 25 142280 1.2565 0.895534 20 to 24 141705 -0.6926 0.244267 19 to 23 142048 0.4701 0.680847 18 to 22 141543 -1.2418 0.107156 17 to 21 141770 -0.4723 0.318355 16 to 20 141593 -1.0723 0.141792 15 to 19 142097 0.6362 0.737667 14 to 18 142101 0.6497 0.742066 13 to 17 142151 0.8192 0.793670 12 to 16 142252 1.1616 0.877300 11 to 15 142043 0.4531 0.674768 10 to 14 142061 0.5141 0.696421 9 to 13 141858 -0.1740 0.430933 8 to 12 141905 -0.0147 0.494145 7 to 11 141807 -0.3469 0.364340 6 to 10 141291 -2.0960 0.018040 5 to 9 142232 1.0938 0.862978 4 to 8 142240 1.1209 0.868838 3 to 7 141552 -1.2113 0.112893 2 to 6 141641 -0.9096 0.181519 1 to 5 141602 -1.0418 0.148753 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-08-14_09:31 Bits used No. missing words z-score p-value 31 to 32 142035 0.3707 0.644573 30 to 31 142274 1.0757 0.858974 29 to 30 142245 0.9902 0.838956 28 to 29 142127 0.6421 0.739594 27 to 28 141906 -0.0098 0.496081 26 to 27 141502 -1.2016 0.114766 25 to 26 141844 -0.1927 0.423592 24 to 25 141668 -0.7119 0.238267 23 to 24 142137 0.6716 0.749079 22 to 23 141669 -0.7089 0.239182 21 to 22 141334 -1.6971 0.044835 20 to 21 142125 0.6362 0.737675 19 to 20 141694 -0.6352 0.262652 18 to 19 141701 -0.6145 0.269428 17 to 18 142018 0.3206 0.625728 16 to 17 141688 -0.6529 0.256913 15 to 16 141985 0.2232 0.588316 14 to 15 141563 -1.0216 0.153480 13 to 14 141292 -1.8210 0.034301 12 to 13 141879 -0.0895 0.464355 11 to 12 141816 -0.2753 0.391539 10 to 11 141765 -0.4258 0.335144 9 to 10 141859 -0.1485 0.440988 8 to 9 142009 0.2940 0.615626 7 to 8 141597 -0.9213 0.178440 6 to 7 142134 0.6627 0.746253 5 to 6 141901 -0.0246 0.490198 4 to 5 141793 -0.3432 0.365740 3 to 4 142054 0.4268 0.665221 2 to 3 141860 -0.1455 0.442152 1 to 2 141037 -2.5732 0.005037 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-08-14_09:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2457.38 -0.603 0.273336 Test results for specific bytes for dh-ranFile-2016-08-14_09:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2494.59 -0.077 0.469505 2 to 9 2487.66 -0.175 0.430706 3 to 10 2515.54 0.220 0.586967 4 to 11 2625.91 1.781 0.962519 5 to 12 2529.95 0.424 0.664040 6 to 13 2459.90 -0.567 0.285318 7 to 14 2458.41 -0.588 0.278221 8 to 15 2448.48 -0.729 0.233128 9 to 16 2533.34 0.472 0.681375 10 to 17 2389.46 -1.563 0.058997 11 to 18 2401.13 -1.398 0.081020 12 to 19 2498.65 -0.019 0.492371 13 to 20 2478.97 -0.297 0.383076 14 to 21 2628.68 1.820 0.965609 15 to 22 2465.18 -0.492 0.311214 16 to 23 2446.46 -0.757 0.224464 17 to 24 2500.05 0.001 0.500257 18 to 25 2540.47 0.572 0.716447 19 to 26 2534.48 0.488 0.687074 20 to 27 2455.41 -0.631 0.264138 21 to 28 2481.05 -0.268 0.394355 22 to 29 2555.50 0.785 0.783732 23 to 30 2451.48 -0.686 0.246295 24 to 31 2560.79 0.860 0.805027 25 to 32 2510.70 0.151 0.560158 CDPARK for dh-ranFile-2016-08-14_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 3517 -0.2740 0.392053 3537 0.6393 0.738676 3482 -1.8721 0.030593 3572 2.2374 0.987371 3540 0.7763 0.781201 3533 0.4566 0.676028 3527 0.1826 0.572463 3498 -1.1416 0.126820 3540 0.7763 0.781201 3533 0.4566 0.676028 Square side=100, avg. no. parked=3527.90 sample std.=23.44 p-value of the KSTEST for those 10 p-values: 0.477286 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-08-14_09:31 0.2555,0.8127,0.9686,0.2698,0.6536,0.1494,0.8462,0.7099,0.8627,0.1734, The KS test for those 10 p-values: 0.542843 The 3DSPHERES test for dh-ranFile-2016-08-14_09:31 sample no r^3 equiv. uni. 1 26.692 0.589241 2 8.706 0.251886 3 41.950 0.752993 4 0.947 0.031066 5 121.662 0.982671 6 40.574 0.741395 7 0.616 0.020335 8 1.519 0.049382 9 61.908 0.873005 10 8.422 0.244772 11 69.463 0.901276 12 16.485 0.422760 13 42.774 0.759685 14 26.336 0.584326 15 109.737 0.974213 16 61.615 0.871758 17 38.253 0.720601 18 10.539 0.296234 19 35.338 0.692089 20 3.832 0.119904 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.437626 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-08-14_09:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 0.5 0.6 1.6 1.0 0.3 0.5 0.6 0.4 -0.2 0.7 -0.3 0.4 0.5 -0.6 -0.6 -0.4 0.9 0.6 -0.2 -1.5 1.8 0.7 -1.7 -1.1 -0.7 -0.3 -0.5 0.3 1.1 1.2 -0.7 -0.5 0.5 -0.6 -0.5 -0.2 -0.4 -0.4 -0.7 -1.3 0.0 -0.1 Chi-square with 42 degrees of freedom:27.976570 z-score=-1.530082, p-value=0.047574 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-08-14_09:31 Test no p-value 1 0.740322 2 0.572203 3 0.338888 4 0.725665 5 0.008683 6 0.030751 7 0.506272 8 0.010846 9 0.002686 10 0.184412 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.005698 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-08-14_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 66631 0.02 66809 0.30 3 25000.00 25019 0.01 24730 2.92 4 6666.67 6664 0.00 6728 0.56 5 1388.89 1378 0.09 1440 1.88 6 238.10 259 1.84 244 0.15 7 34.72 37 0.15 45 3.04 8 4.96 11 7.36 3 0.77 p=0.85070 p=0.85886 Number of rngs required: 689048, p-value: 0.772 RESULTS OF CRAPS TEST for dh-ranFile-2016-08-14_09:31 No. of wins: Observed Expected 98898 98585.9 z-score= 1.396, pvalue=0.91865 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66790 66666.7 0.228 0.228 2 37658 37654.3 0.000 0.229 3 26796 26954.7 0.935 1.163 4 19464 19313.5 1.173 2.337 5 13720 13851.4 1.247 3.584 6 10013 9943.5 0.485 4.069 7 7137 7145.0 0.009 4.078 8 5142 5139.1 0.002 4.079 9 3745 3699.9 0.551 4.630 10 2667 2666.3 0.000 4.630 11 1934 1923.3 0.059 4.689 12 1387 1388.7 0.002 4.692 13 951 1003.7 2.769 7.460 14 698 726.1 1.091 8.551 15 499 525.8 1.370 9.920 16 359 381.2 1.287 11.208 17 306 276.5 3.139 14.346 18 210 200.8 0.419 14.765 19 143 146.0 0.061 14.826 20 100 106.2 0.364 15.189 21 281 287.1 0.130 15.320 Chisq= 15.32 for 20 degrees of freedom, p= 0.24217 SUMMARY of craptest p-value for no. of wins: 0.918655 p-value for throws/game: 0.242167 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-08-14_09:31 No. of wins: Observed Expected 98841 98585.9 z-score= 1.141, pvalue=0.87309 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66846 66666.7 0.482 0.482 2 37740 37654.3 0.195 0.677 3 26779 26954.7 1.146 1.823 4 19135 19313.5 1.649 3.472 5 13906 13851.4 0.215 3.687 6 9896 9943.5 0.227 3.914 7 7170 7145.0 0.087 4.002 8 5144 5139.1 0.005 4.007 9 3802 3699.9 2.819 6.826 10 2650 2666.3 0.100 6.926 11 1907 1923.3 0.139 7.064 12 1379 1388.7 0.068 7.133 13 960 1003.7 1.904 9.036 14 722 726.1 0.024 9.060 15 527 525.8 0.003 9.063 16 406 381.2 1.620 10.683 17 260 276.5 0.989 11.672 18 224 200.8 2.673 14.345 19 143 146.0 0.061 14.406 20 102 106.2 0.167 14.573 21 302 287.1 0.772 15.345 Chisq= 15.35 for 20 degrees of freedom, p= 0.24367 SUMMARY of craptest p-value for no. of wins: 0.873094 p-value for throws/game: 0.243673 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0027,0.0050,0.0057,0.0087,0.0108,0.0180,0.0203,0.0297,0.0306,0.0308, 0.0311,0.0325,0.0343,0.0418,0.0435,0.0448,0.0476,0.0494,0.0494,0.0551, 0.0586,0.0590,0.0614,0.0693,0.0747,0.0758,0.0803,0.0810,0.1038,0.1071, 0.1072,0.1129,0.1148,0.1156,0.1199,0.1228,0.1249,0.1267,0.1268,0.1418, 0.1458,0.1460,0.1488,0.1494,0.1535,0.1659,0.1662,0.1689,0.1734,0.1784, 0.1790,0.1815,0.1844,0.1988,0.2028,0.2093,0.2245,0.2331,0.2383,0.2392, 0.2422,0.2422,0.2437,0.2443,0.2448,0.2463,0.2499,0.2514,0.2519,0.2555, 0.2569,0.2570,0.2573,0.2615,0.2627,0.2636,0.2641,0.2648,0.2694,0.2698, 0.2698,0.2711,0.2733,0.2782,0.2831,0.2853,0.2960,0.2962,0.3112,0.3184, 0.3192,0.3215,0.3351,0.3389,0.3493,0.3643,0.3657,0.3694,0.3821,0.3831, 0.3831,0.3844,0.3915,0.3921,0.3944,0.3944,0.3962,0.4015,0.4192,0.4193, 0.4228,0.4236,0.4255,0.4307,0.4309,0.4338,0.4376,0.4410,0.4422,0.4500, 0.4541,0.4615,0.4644,0.4664,0.4695,0.4715,0.4741,0.4773,0.4872,0.4902, 0.4915,0.4924,0.4941,0.4961,0.4969,0.5003,0.5016,0.5063,0.5174,0.5184, 0.5188,0.5276,0.5279,0.5308,0.5406,0.5428,0.5434,0.5435,0.5447,0.5457, 0.5588,0.5602,0.5722,0.5725,0.5762,0.5775,0.5797,0.5815,0.5843,0.5870, 0.5883,0.5884,0.5892,0.6054,0.6082,0.6156,0.6201,0.6257,0.6288,0.6446, 0.6475,0.6536,0.6570,0.6640,0.6652,0.6674,0.6715,0.6748,0.6760,0.6760, 0.6760,0.6808,0.6814,0.6861,0.6871,0.6921,0.6945,0.6964,0.7090,0.7099, 0.7164,0.7170,0.7206,0.7231,0.7257,0.7377,0.7377,0.7387,0.7396,0.7403, 0.7407,0.7414,0.7421,0.7463,0.7491,0.7530,0.7597,0.7603,0.7607,0.7607, 0.7646,0.7719,0.7752,0.7812,0.7812,0.7820,0.7826,0.7829,0.7831,0.7837, 0.7928,0.7937,0.8003,0.8030,0.8050,0.8127,0.8210,0.8273,0.8390,0.8448, 0.8462,0.8507,0.8556,0.8589,0.8590,0.8626,0.8627,0.8630,0.8688,0.8693, 0.8718,0.8730,0.8731,0.8773,0.8836,0.8838,0.8867,0.8955,0.8994,0.9013, 0.9037,0.9140,0.9165,0.9187,0.9187,0.9280,0.9439,0.9458,0.9572,0.9625, 0.9656,0.9663,0.9686,0.9686,0.9735,0.9742,0.9827,0.9874,0.9965, Overall p-value after applying KStest on 269 p-values = 0.792404 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.