RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-11-05_14:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 16.01 11.8506 0.190901 2 to 25 15.85 16.9240 0.540474 3 to 26 15.59 18.5335 0.644041 4 to 27 15.83 17.5843 0.584490 5 to 28 15.74 22.1201 0.819854 6 to 29 15.82 14.4213 0.362910 7 to 30 15.54 23.3669 0.862319 8 to 31 15.76 12.3644 0.222416 9 to 32 15.76 25.6347 0.918621 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.756821 Tough bday spacings test for dh-ranFile-2015-11-05_14:31: 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 48 86 100 86 74 42 30 14 8 3 (O-E)^2/E 0.0 3.5 2.2 0.1 1.4 0.2 2.0 0.0 0.1 0.3 0.3 Birthday Spacings: Sum(O-E)^2/E= 9.999, p= 0.559 RESULTS OF GCD FOR dh-ranFile-2015-11-05_14:31 Euclid's algorithm: p-value, steps to gcd: 0.845746 p-value, dist. of gcd's: 0.306814 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-11-05_14:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.743 0.653 0.962 0.091 0.807 0.979 0.808 0.615 Bits 8 to 15---> 0.576 0.285 0.359 0.606 0.726 0.921 0.793 0.618 Bits 16 to 23---> 0.249 0.042 0.666 0.273 0.130 0.583 0.656 0.093 Bits 24 to 31---> 0.343 0.334 0.711 0.098 0.977 0.425 0.677 0.182 KS test for the above 32 p values: 0.290 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-11-05_14:31, p-values for 5 runs: 0.5315, 0.5462, 0.3758, 0.4811, 0.4886 Rank test for binary matrices (31x31) for dh-ranFile-2015-11-05_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 194 211.4 1.435 1.435 r= 29 5181 5134.0 0.430 1.865 r= 30 22919 23103.0 1.466 3.331 r= 31 11706 11551.5 2.066 5.397 chi-square = 5.397 with df = 3; p-value = 0.855 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-11-05_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 203 211.4 0.335 0.335 r= 30 5097 5134.0 0.267 0.602 r= 31 23029 23103.0 0.237 0.839 r= 32 11671 11551.5 1.236 2.075 chi-square = 2.075 with df = 3; p-value = 0.443 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-11-05_14:31 b-rank test for bits 1 to 8, p=0.13706 b-rank test for bits 2 to 9, p=0.36576 b-rank test for bits 3 to 10, p=0.82025 b-rank test for bits 4 to 11, p=0.24215 b-rank test for bits 5 to 12, p=0.80229 b-rank test for bits 6 to 13, p=0.91187 b-rank test for bits 7 to 14, p=0.49962 b-rank test for bits 8 to 15, p=0.64161 b-rank test for bits 9 to 16, p=0.59909 b-rank test for bits 10 to 17, p=0.15552 b-rank test for bits 11 to 18, p=0.94317 b-rank test for bits 12 to 19, p=0.08780 b-rank test for bits 13 to 20, p=0.19653 b-rank test for bits 14 to 21, p=0.69555 b-rank test for bits 15 to 22, p=0.42100 b-rank test for bits 16 to 23, p=0.14749 b-rank test for bits 17 to 24, p=0.72293 b-rank test for bits 18 to 25, p=0.30450 b-rank test for bits 19 to 26, p=0.36663 b-rank test for bits 20 to 27, p=0.65772 b-rank test for bits 21 to 28, p=0.40814 b-rank test for bits 22 to 29, p=0.16551 b-rank test for bits 23 to 30, p=0.45708 b-rank test for bits 24 to 31, p=0.86279 b-rank test for bits 25 to 32, p=0.00484 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 = 0.878111 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-11-05_14:31 (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 142555 1.51 0.934296 2 141484 -0.99 0.160169 3 141599 -0.73 0.234205 4 141619 -0.68 0.248778 5 142243 0.78 0.782188 6 141806 -0.24 0.404613 7 142163 0.59 0.723305 8 142067 0.37 0.643708 9 141651 -0.60 0.273063 10 142454 1.27 0.898419 11 142049 0.33 0.627913 12 141395 -1.20 0.114739 13 141396 -1.20 0.115192 14 141742 -0.39 0.347914 15 141511 -0.93 0.176010 16 141338 -1.33 0.090957 17 142734 1.93 0.972998 18 141566 -0.80 0.211227 19 142753 1.97 0.975649 20 142698 1.84 0.967313 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-11-05_14:31 Bits used No. missing words z-score p-value 23 to 32 142106 0.6782 0.751169 22 to 31 141960 0.1747 0.569352 21 to 30 141845 -0.2218 0.412224 20 to 29 141598 -1.0736 0.141512 19 to 28 141721 -0.6494 0.258036 18 to 27 141759 -0.5184 0.302097 17 to 26 142037 0.4402 0.670119 16 to 25 142253 1.1851 0.882005 15 to 24 142308 1.3747 0.915392 14 to 23 141382 -1.8184 0.034503 13 to 22 142266 1.2299 0.890632 12 to 21 141577 -1.1460 0.125905 11 to 20 141595 -1.0839 0.139205 10 to 19 141812 -0.3356 0.368579 9 to 18 142424 1.7747 0.962028 8 to 17 141940 0.1058 0.542113 7 to 16 142486 1.9885 0.976623 6 to 15 142083 0.5989 0.725368 5 to 14 141796 -0.3908 0.347975 4 to 13 141570 -1.1701 0.120980 3 to 12 141812 -0.3356 0.368579 2 to 11 141986 0.2644 0.604256 1 to 10 141810 -0.3425 0.365981 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-11-05_14:31 Bits used No. missing words z-score p-value 28 to 32 142141 0.7853 0.783868 27 to 31 141774 -0.4587 0.323208 26 to 30 141254 -2.2215 0.013160 25 to 29 142099 0.6429 0.739872 24 to 28 141864 -0.1537 0.438939 23 to 27 142063 0.5209 0.698787 22 to 26 142193 0.9616 0.831873 21 to 25 141877 -0.1096 0.456366 20 to 24 141905 -0.0147 0.494145 19 to 23 141911 0.0057 0.502258 18 to 22 141475 -1.4723 0.070469 17 to 21 141650 -0.8791 0.189678 16 to 20 142006 0.3277 0.628429 15 to 19 142537 2.1277 0.983319 14 to 18 142015 0.3582 0.639905 13 to 17 141593 -1.0723 0.141792 12 to 16 141578 -1.1232 0.130686 11 to 15 142111 0.6836 0.752895 10 to 14 142112 0.6870 0.753964 9 to 13 141621 -0.9774 0.164188 8 to 12 141980 0.2396 0.594664 7 to 11 142117 0.7040 0.759273 6 to 10 141554 -1.2045 0.114197 5 to 9 141960 0.1718 0.568188 4 to 8 142013 0.3514 0.637365 3 to 7 141659 -0.8486 0.198059 2 to 6 142087 0.6023 0.726503 1 to 5 141233 -2.2926 0.010934 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-11-05_14:31 Bits used No. missing words z-score p-value 31 to 32 142089 0.5300 0.701944 30 to 31 142426 1.5241 0.936258 29 to 30 142443 1.5742 0.942285 28 to 29 142280 1.0934 0.862896 27 to 28 141085 -2.4317 0.007515 26 to 27 141182 -2.1455 0.015956 25 to 26 141641 -0.7915 0.214316 24 to 25 142182 0.8043 0.789399 23 to 24 142070 0.4740 0.682233 22 to 23 142042 0.3914 0.652233 21 to 22 141968 0.1731 0.568701 20 to 21 141364 -1.6086 0.053847 19 to 20 141569 -1.0039 0.157708 18 to 19 141858 -0.1514 0.439824 17 to 18 141519 -1.1514 0.124781 16 to 17 141381 -1.5585 0.059558 15 to 16 142221 0.9194 0.821052 14 to 15 142069 0.4710 0.681181 13 to 14 141806 -0.3048 0.380256 12 to 13 142080 0.5035 0.692677 11 to 12 141584 -0.9597 0.168609 10 to 11 142660 2.2144 0.986598 9 to 10 141809 -0.2960 0.383631 8 to 9 141666 -0.7178 0.236444 7 to 8 142249 1.0020 0.841823 6 to 7 142816 2.6745 0.996258 5 to 6 142282 1.0993 0.864186 4 to 5 142073 0.4828 0.685382 3 to 4 141471 -1.2930 0.098004 2 to 3 141898 -0.0334 0.486669 1 to 2 142122 0.6273 0.734784 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-11-05_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2575.17 1.063 0.856110 Test results for specific bytes for dh-ranFile-2015-11-05_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2554.95 0.777 0.781470 2 to 9 2539.57 0.560 0.712117 3 to 10 2525.08 0.355 0.638574 4 to 11 2491.83 -0.115 0.454031 5 to 12 2519.71 0.279 0.609760 6 to 13 2325.40 -2.469 0.006770 7 to 14 2460.35 -0.561 0.287512 8 to 15 2584.71 1.198 0.884534 9 to 16 2521.61 0.306 0.620050 10 to 17 2498.02 -0.028 0.488829 11 to 18 2540.27 0.570 0.715515 12 to 19 2521.14 0.299 0.617501 13 to 20 2604.56 1.479 0.930391 14 to 21 2609.14 1.544 0.938649 15 to 22 2405.48 -1.337 0.090647 16 to 23 2409.28 -1.283 0.099747 17 to 24 2576.08 1.076 0.859037 18 to 25 2392.33 -1.523 0.063924 19 to 26 2537.85 0.535 0.703778 20 to 27 2565.27 0.923 0.822002 21 to 28 2453.22 -0.662 0.254111 22 to 29 2522.99 0.325 0.627475 23 to 30 2471.72 -0.400 0.344608 24 to 31 2444.99 -0.778 0.218317 25 to 32 2407.42 -1.309 0.095231 CDPARK for dh-ranFile-2015-11-05_14:31: 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 3533 0.4566 0.676028 3534 0.5023 0.692266 3494 -1.3242 0.092718 3516 -0.3196 0.374623 3562 1.7808 0.962529 3530 0.3196 0.625377 3539 0.7306 0.767486 3492 -1.4155 0.078457 3521 -0.0913 0.463617 Square side=100, avg. no. parked=3524.80 sample std.=19.71 p-value of the KSTEST for those 10 p-values: 0.853058 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-11-05_14:31 0.6442,0.0670,0.1981,0.6981,0.4547,0.2194,0.6563,0.0282,0.0378,0.6106, The KS test for those 10 p-values: 0.134628 The 3DSPHERES test for dh-ranFile-2015-11-05_14:31 sample no r^3 equiv. uni. 1 52.598 0.826795 2 8.298 0.241635 3 1.371 0.044686 4 8.940 0.257701 5 29.089 0.620773 6 6.860 0.204414 7 28.921 0.618649 8 66.950 0.892650 9 14.738 0.388147 10 12.388 0.338299 11 0.994 0.032581 12 34.605 0.684468 13 16.431 0.421720 14 22.504 0.527695 15 3.191 0.100894 16 29.061 0.620426 17 3.988 0.124481 18 3.336 0.105234 19 18.715 0.464105 20 26.639 0.588513 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.236937 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-11-05_14:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -0.3 0.1 0.5 0.5 1.1 0.8 0.3 -0.6 1.3 -0.6 -0.3 -0.6 1.4 -1.1 -0.4 0.4 -1.5 -0.7 1.1 -0.2 -0.0 2.7 1.2 -0.6 -0.9 -0.5 0.0 -0.8 -0.6 -0.3 0.9 -1.2 -0.9 -1.2 -1.7 1.7 1.5 0.9 2.1 -1.3 1.0 -1.1 Chi-square with 42 degrees of freedom:45.813470 z-score=0.416084, p-value=0.683108 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-11-05_14:31 Test no p-value 1 0.678578 2 0.049272 3 0.581247 4 0.419912 5 0.302252 6 0.834186 7 0.217649 8 0.497394 9 0.004019 10 0.497980 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.405990 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-11-05_14:31: (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 66339 1.61 66955 1.25 3 25000.00 25357 5.10 24672 4.30 4 6666.67 6637 0.13 6724 0.49 5 1388.89 1346 1.32 1378 0.09 6 238.10 275 5.72 232 0.16 7 34.72 43 1.97 32 0.21 8 4.96 2 1.77 6 0.22 p=0.99276 p=0.65208 Number of rngs required: 687710, p-value: 0.212 RESULTS OF CRAPS TEST for dh-ranFile-2015-11-05_14:31 No. of wins: Observed Expected 98658 98585.9 z-score= 0.323, pvalue=0.62652 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66840 66666.7 0.451 0.451 2 37529 37654.3 0.417 0.868 3 26958 26954.7 0.000 0.868 4 19203 19313.5 0.632 1.500 5 13999 13851.4 1.572 3.072 6 9865 9943.5 0.620 3.693 7 7205 7145.0 0.503 4.196 8 5129 5139.1 0.020 4.216 9 3718 3699.9 0.089 4.305 10 2671 2666.3 0.008 4.313 11 1894 1923.3 0.447 4.760 12 1279 1388.7 8.672 13.432 13 1010 1003.7 0.039 13.472 14 711 726.1 0.316 13.787 15 538 525.8 0.281 14.069 16 365 381.2 0.684 14.753 17 317 276.5 5.920 20.673 18 214 200.8 0.864 21.536 19 166 146.0 2.744 24.281 20 105 106.2 0.014 24.295 21 284 287.1 0.034 24.328 Chisq= 24.33 for 20 degrees of freedom, p= 0.77166 SUMMARY of craptest p-value for no. of wins: 0.626523 p-value for throws/game: 0.771658 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-11-05_14:31 No. of wins: Observed Expected 98436 98585.9 z-score=-0.670, pvalue=0.25135 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66612 66666.7 0.045 0.045 2 37359 37654.3 2.316 2.361 3 27071 26954.7 0.502 2.863 4 19544 19313.5 2.752 5.614 5 13981 13851.4 1.212 6.827 6 9818 9943.5 1.585 8.412 7 7143 7145.0 0.001 8.412 8 5214 5139.1 1.092 9.505 9 3673 3699.9 0.195 9.700 10 2677 2666.3 0.043 9.743 11 1902 1923.3 0.237 9.979 12 1361 1388.7 0.554 10.533 13 1067 1003.7 3.990 14.524 14 681 726.1 2.806 17.330 15 514 525.8 0.266 17.596 16 351 381.2 2.385 19.981 17 291 276.5 0.756 20.737 18 186 200.8 1.095 21.832 19 146 146.0 0.000 21.832 20 108 106.2 0.030 21.862 21 301 287.1 0.672 22.534 Chisq= 22.53 for 20 degrees of freedom, p= 0.68775 SUMMARY of craptest p-value for no. of wins: 0.251348 p-value for throws/game: 0.687746 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0040,0.0048,0.0068,0.0075,0.0109,0.0132,0.0160,0.0282,0.0326,0.0345, 0.0378,0.0420,0.0447,0.0493,0.0538,0.0596,0.0639,0.0670,0.0705,0.0785, 0.0878,0.0906,0.0908,0.0910,0.0927,0.0933,0.0952,0.0977,0.0980,0.0997, 0.1009,0.1052,0.1142,0.1147,0.1152,0.1210,0.1245,0.1248,0.1259,0.1301, 0.1307,0.1346,0.1371,0.1392,0.1415,0.1418,0.1475,0.1555,0.1577,0.1602, 0.1642,0.1655,0.1686,0.1760,0.1820,0.1897,0.1909,0.1965,0.1981,0.1981, 0.2044,0.2112,0.2116,0.2143,0.2176,0.2183,0.2194,0.2224,0.2342,0.2364, 0.2369,0.2416,0.2421,0.2486,0.2488,0.2513,0.2541,0.2577,0.2580,0.2728, 0.2731,0.2848,0.2875,0.2896,0.3021,0.3023,0.3045,0.3068,0.3232,0.3335, 0.3383,0.3426,0.3446,0.3479,0.3480,0.3586,0.3629,0.3658,0.3660,0.3666, 0.3686,0.3686,0.3746,0.3758,0.3803,0.3836,0.3881,0.4046,0.4060,0.4081, 0.4122,0.4199,0.4210,0.4217,0.4253,0.4389,0.4398,0.4430,0.4540,0.4547, 0.4564,0.4571,0.4636,0.4641,0.4811,0.4867,0.4886,0.4888,0.4941,0.4974, 0.4980,0.4996,0.5023,0.5277,0.5315,0.5405,0.5421,0.5462,0.5594,0.5682, 0.5687,0.5694,0.5725,0.5756,0.5812,0.5829,0.5845,0.5885,0.5947,0.5991, 0.6043,0.6062,0.6098,0.6106,0.6153,0.6175,0.6179,0.6186,0.6200,0.6204, 0.6208,0.6254,0.6265,0.6275,0.6279,0.6284,0.6374,0.6386,0.6399,0.6416, 0.6437,0.6440,0.6442,0.6521,0.6522,0.6533,0.6563,0.6565,0.6577,0.6661, 0.6701,0.6760,0.6773,0.6786,0.6812,0.6822,0.6831,0.6845,0.6854,0.6877, 0.6923,0.6927,0.6955,0.6981,0.6988,0.7019,0.7038,0.7106,0.7121,0.7155, 0.7229,0.7233,0.7254,0.7261,0.7265,0.7348,0.7399,0.7426,0.7512,0.7529, 0.7540,0.7568,0.7593,0.7675,0.7717,0.7815,0.7822,0.7839,0.7894,0.7929, 0.8023,0.8066,0.8078,0.8199,0.8203,0.8211,0.8220,0.8268,0.8319,0.8342, 0.8418,0.8457,0.8531,0.8551,0.8561,0.8590,0.8623,0.8628,0.8629,0.8642, 0.8781,0.8820,0.8845,0.8906,0.8927,0.8984,0.9119,0.9154,0.9186,0.9213, 0.9304,0.9343,0.9363,0.9386,0.9423,0.9432,0.9618,0.9620,0.9625,0.9673, 0.9730,0.9756,0.9766,0.9774,0.9794,0.9833,0.9866,0.9928,0.9963, Overall p-value after applying KStest on 269 p-values = 0.659178 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.