RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-10-02_11:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.76 10.2958 0.109251 2 to 25 15.85 14.2645 0.351700 3 to 26 15.66 18.7158 0.654915 4 to 27 15.82 14.6003 0.375752 5 to 28 15.34 26.7897 0.938775 6 to 29 15.68 14.3297 0.356360 7 to 30 16.13 9.5023 0.076826 8 to 31 15.64 17.4804 0.577694 9 to 32 15.88 4.1236 0.000635 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.218422 Tough bday spacings test for dh-ranFile-2015-10-02_11:31: 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 42 73 92 88 69 67 34 16 8 3 (O-E)^2/E 0.1 0.8 0.0 0.3 1.0 1.1 4.3 0.6 0.1 0.3 0.3 Birthday Spacings: Sum(O-E)^2/E= 8.812, p= 0.450 RESULTS OF GCD FOR dh-ranFile-2015-10-02_11:31 Euclid's algorithm: p-value, steps to gcd: 0.306264 p-value, dist. of gcd's: 0.552441 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-10-02_11:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.176 0.088 0.389 0.405 0.785 0.748 0.725 0.578 Bits 8 to 15---> 0.991 0.911 0.854 0.422 0.129 0.935 0.463 0.892 Bits 16 to 23---> 0.005 0.288 0.192 0.940 0.932 0.109 0.559 0.567 Bits 24 to 31---> 0.452 0.415 0.169 0.162 0.940 0.276 0.667 0.077 KS test for the above 32 p values: 0.263 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-10-02_11:31, p-values for 5 runs: 0.9811, 0.2523, 0.3255, 0.1539, 0.6955 Rank test for binary matrices (31x31) for dh-ranFile-2015-10-02_11:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 200 211.4 0.617 0.617 r= 29 5193 5134.0 0.678 1.294 r= 30 23148 23103.0 0.087 1.382 r= 31 11459 11551.5 0.741 2.123 chi-square = 2.123 with df = 3; p-value = 0.453 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-10-02_11:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 206 211.4 0.139 0.139 r= 30 5159 5134.0 0.122 0.260 r= 31 22937 23103.0 1.193 1.454 r= 32 11698 11551.5 1.857 3.311 chi-square = 3.311 with df = 3; p-value = 0.654 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-10-02_11:31 b-rank test for bits 1 to 8, p=0.72356 b-rank test for bits 2 to 9, p=0.53432 b-rank test for bits 3 to 10, p=0.86695 b-rank test for bits 4 to 11, p=0.08389 b-rank test for bits 5 to 12, p=0.41021 b-rank test for bits 6 to 13, p=0.76542 b-rank test for bits 7 to 14, p=0.02754 b-rank test for bits 8 to 15, p=0.76445 b-rank test for bits 9 to 16, p=0.38358 b-rank test for bits 10 to 17, p=0.81353 b-rank test for bits 11 to 18, p=0.59350 b-rank test for bits 12 to 19, p=0.04709 b-rank test for bits 13 to 20, p=0.69965 b-rank test for bits 14 to 21, p=0.52132 b-rank test for bits 15 to 22, p=0.35363 b-rank test for bits 16 to 23, p=0.39361 b-rank test for bits 17 to 24, p=0.08514 b-rank test for bits 18 to 25, p=0.83470 b-rank test for bits 19 to 26, p=0.88917 b-rank test for bits 20 to 27, p=0.35926 b-rank test for bits 21 to 28, p=0.38975 b-rank test for bits 22 to 29, p=0.23742 b-rank test for bits 23 to 30, p=0.64549 b-rank test for bits 24 to 31, p=0.36400 b-rank test for bits 25 to 32, p=0.15370 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 = 0.786010 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-10-02_11:31 (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 142306 0.93 0.822985 2 141377 -1.24 0.106794 3 141523 -0.90 0.183358 4 142299 0.91 0.818706 5 141584 -0.76 0.223592 6 141382 -1.23 0.108960 7 141187 -1.69 0.045736 8 141037 -2.04 0.020767 9 141169 -1.73 0.041838 10 141378 -1.24 0.107224 11 141917 0.02 0.507149 12 141977 0.16 0.562814 13 142108 0.46 0.678741 14 141761 -0.35 0.364459 15 141999 0.21 0.582975 16 141695 -0.50 0.308266 17 141755 -0.36 0.359205 18 141455 -1.06 0.144227 19 142080 0.40 0.654966 20 141611 -0.70 0.242891 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-10-02_11:31 Bits used No. missing words z-score p-value 23 to 32 141822 -0.3011 0.381655 22 to 31 141876 -0.1149 0.454250 21 to 30 141992 0.2851 0.612204 20 to 29 142199 0.9989 0.841069 19 to 28 141845 -0.2218 0.412224 18 to 27 142159 0.8609 0.805362 17 to 26 142407 1.7161 0.956928 16 to 25 141770 -0.4804 0.315454 15 to 24 141872 -0.1287 0.448788 14 to 23 142221 1.0747 0.858751 13 to 22 142174 0.9127 0.819288 12 to 21 142080 0.5885 0.721907 11 to 20 142126 0.7471 0.772510 10 to 19 141777 -0.4563 0.324083 9 to 18 141403 -1.7460 0.040408 8 to 17 141596 -1.0804 0.139971 7 to 16 142311 1.3851 0.916984 6 to 15 142193 0.9782 0.836006 5 to 14 141671 -0.8218 0.205588 4 to 13 141820 -0.3080 0.379028 3 to 12 141856 -0.1839 0.427047 2 to 11 142296 1.3333 0.908791 1 to 10 141945 0.1230 0.548947 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-10-02_11:31 Bits used No. missing words z-score p-value 28 to 32 142064 0.5243 0.699967 27 to 31 141912 0.0091 0.503611 26 to 30 142375 1.5785 0.942779 25 to 29 141783 -0.4282 0.334239 24 to 28 142160 0.8497 0.802262 23 to 27 141875 -0.1164 0.453679 22 to 26 141346 -1.9096 0.028093 21 to 25 141865 -0.1503 0.440275 20 to 24 142296 1.3107 0.905028 19 to 23 141889 -0.0689 0.472529 18 to 22 141662 -0.8384 0.200901 17 to 21 141838 -0.2418 0.404469 16 to 20 141611 -1.0113 0.155939 15 to 19 142098 0.6396 0.738770 14 to 18 141932 0.0768 0.530628 13 to 17 141866 -0.1469 0.441613 12 to 16 141951 0.1413 0.556166 11 to 15 142458 1.8599 0.968550 10 to 14 141915 0.0192 0.507667 9 to 13 142197 0.9752 0.835258 8 to 12 142195 0.9684 0.833571 7 to 11 142005 0.3243 0.627147 6 to 10 141943 0.1141 0.545435 5 to 9 142327 1.4158 0.921587 4 to 8 141936 0.0904 0.536018 3 to 7 141909 -0.0011 0.499554 2 to 6 141851 -0.1977 0.421629 1 to 5 141766 -0.4859 0.313532 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-10-02_11:31 Bits used No. missing words z-score p-value 31 to 32 141685 -0.6617 0.254069 30 to 31 141932 0.0669 0.526659 29 to 30 142227 0.9371 0.825641 28 to 29 142208 0.8810 0.810850 27 to 28 141704 -0.6057 0.272359 26 to 27 141486 -1.2488 0.105876 25 to 26 141596 -0.9243 0.177671 24 to 25 141711 -0.5850 0.279259 23 to 24 141810 -0.2930 0.384758 22 to 23 141956 0.1377 0.554749 21 to 22 142210 0.8869 0.812442 20 to 21 141390 -1.5319 0.062768 19 to 20 141757 -0.4494 0.326589 18 to 19 141974 0.1908 0.575646 17 to 18 141875 -0.1013 0.459669 16 to 17 141687 -0.6558 0.255963 15 to 16 142022 0.3324 0.630191 14 to 15 142468 1.6480 0.950323 13 to 14 141572 -0.9951 0.159850 12 to 13 141635 -0.8092 0.209191 11 to 12 141707 -0.5968 0.275306 10 to 11 142457 1.6155 0.946904 9 to 10 142597 2.0285 0.978747 8 to 9 142402 1.4533 0.926930 7 to 8 142206 0.8751 0.809249 6 to 7 141856 -0.1573 0.437498 5 to 6 142628 2.1200 0.982996 4 to 5 141946 0.1082 0.543070 3 to 4 141931 0.0639 0.525484 2 to 3 141686 -0.6588 0.255015 1 to 2 141910 0.0020 0.500789 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-10-02_11:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2460.19 -0.563 0.286717 Test results for specific bytes for dh-ranFile-2015-10-02_11:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2555.50 0.785 0.783726 2 to 9 2604.63 1.480 0.930531 3 to 10 2570.82 1.002 0.841725 4 to 11 2675.96 2.488 0.993584 5 to 12 2518.52 0.262 0.603311 6 to 13 2611.94 1.583 0.943297 7 to 14 2486.83 -0.186 0.426114 8 to 15 2578.30 1.107 0.865917 9 to 16 2443.84 -0.794 0.213533 10 to 17 2430.58 -0.982 0.163096 11 to 18 2586.11 1.218 0.888343 12 to 19 2385.60 -1.618 0.052842 13 to 20 2414.75 -1.206 0.113984 14 to 21 2512.98 0.184 0.572828 15 to 22 2477.78 -0.314 0.376669 16 to 23 2524.00 0.339 0.632839 17 to 24 2529.99 0.424 0.664240 18 to 25 2512.19 0.172 0.568452 19 to 26 2458.21 -0.591 0.277257 20 to 27 2534.05 0.481 0.684914 21 to 28 2418.42 -1.154 0.124322 22 to 29 2471.66 -0.401 0.344290 23 to 30 2490.04 -0.141 0.443987 24 to 31 2541.68 0.589 0.722218 25 to 32 2435.63 -0.910 0.181315 CDPARK for dh-ranFile-2015-10-02_11:31: 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 3523 0.0000 0.500000 3516 -0.3196 0.374623 3486 -1.6895 0.045562 3504 -0.8676 0.192812 3532 0.4110 0.659449 3515 -0.3653 0.357445 3528 0.2283 0.590298 3548 1.1416 0.873180 3496 -1.2329 0.108811 3527 0.1826 0.572463 Square side=100, avg. no. parked=3517.50 sample std.=17.37 p-value of the KSTEST for those 10 p-values: 0.709933 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-10-02_11:31 0.7433,0.4899,0.6837,0.4218,0.9249,0.1908,0.2806,0.6994,0.7527,0.3299, The KS test for those 10 p-values: 0.688725 The 3DSPHERES test for dh-ranFile-2015-10-02_11:31 sample no r^3 equiv. uni. 1 0.934 0.030651 2 13.576 0.363981 3 16.528 0.423594 4 10.609 0.297861 5 57.956 0.855124 6 54.239 0.836013 7 3.932 0.122853 8 39.273 0.729940 9 18.313 0.456888 10 12.777 0.346814 11 17.887 0.449124 12 20.309 0.491851 13 16.570 0.424402 14 0.689 0.022695 15 52.664 0.827174 16 11.895 0.327326 17 10.348 0.291739 18 13.389 0.360019 19 13.850 0.369778 20 0.581 0.019174 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.101915 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-10-02_11:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 1.8 -0.8 -0.7 1.2 -1.6 -0.2 0.7 -2.1 0.9 -1.0 -1.5 0.4 0.6 1.3 0.7 -1.1 1.7 0.3 0.3 -0.5 -1.1 -0.4 -0.6 -0.2 0.0 -1.9 0.9 1.0 -0.1 0.2 0.2 2.4 0.1 2.4 0.1 -0.2 0.8 1.3 -0.1 1.6 1.0 -1.1 Chi-square with 42 degrees of freedom:51.965818 z-score=1.087360, p-value=0.860613 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-10-02_11:31 Test no p-value 1 0.730501 2 0.016572 3 0.603086 4 0.720423 5 0.448787 6 0.049144 7 0.931333 8 0.067997 9 0.934457 10 0.810636 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.360159 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-10-02_11:31: (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 66797 0.25 66593 0.08 3 25000.00 24909 0.33 24957 0.07 4 6666.67 6612 0.45 6748 0.99 5 1388.89 1417 0.57 1429 1.16 6 238.10 231 0.21 235 0.04 7 34.72 26 2.19 32 0.21 8 4.96 7 0.84 5 0.00 p=0.43600 p=0.13825 Number of rngs required: 687721, p-value: 0.215 RESULTS OF CRAPS TEST for dh-ranFile-2015-10-02_11:31 No. of wins: Observed Expected 98717 98585.9 z-score= 0.587, pvalue=0.72124 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66874 66666.7 0.645 0.645 2 37981 37654.3 2.834 3.479 3 26888 26954.7 0.165 3.644 4 19305 19313.5 0.004 3.648 5 13726 13851.4 1.136 4.784 6 9861 9943.5 0.685 5.469 7 7081 7145.0 0.574 6.042 8 5092 5139.1 0.431 6.474 9 3615 3699.9 1.947 8.420 10 2598 2666.3 1.749 10.170 11 1992 1923.3 2.452 12.621 12 1372 1388.7 0.202 12.823 13 991 1003.7 0.161 12.984 14 727 726.1 0.001 12.985 15 507 525.8 0.675 13.660 16 384 381.2 0.021 13.681 17 271 276.5 0.111 13.792 18 175 200.8 3.322 17.114 19 155 146.0 0.557 17.671 20 112 106.2 0.315 17.986 21 293 287.1 0.121 18.107 Chisq= 18.11 for 20 degrees of freedom, p= 0.41964 SUMMARY of craptest p-value for no. of wins: 0.721244 p-value for throws/game: 0.419640 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-10-02_11:31 No. of wins: Observed Expected 98840 98585.9 z-score= 1.137, pvalue=0.87216 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66936 66666.7 1.088 1.088 2 37337 37654.3 2.674 3.762 3 26707 26954.7 2.277 6.039 4 19377 19313.5 0.209 6.248 5 13840 13851.4 0.009 6.258 6 9964 9943.5 0.042 6.300 7 7252 7145.0 1.602 7.901 8 5183 5139.1 0.375 8.277 9 3724 3699.9 0.157 8.434 10 2652 2666.3 0.077 8.511 11 1914 1923.3 0.045 8.556 12 1388 1388.7 0.000 8.556 13 1042 1003.7 1.460 10.017 14 732 726.1 0.047 10.064 15 544 525.8 0.627 10.691 16 417 381.2 3.372 14.063 17 268 276.5 0.264 14.327 18 180 200.8 2.160 16.487 19 139 146.0 0.334 16.822 20 118 106.2 1.308 18.129 21 286 287.1 0.004 18.133 Chisq= 18.13 for 20 degrees of freedom, p= 0.42139 SUMMARY of craptest p-value for no. of wins: 0.872162 p-value for throws/game: 0.421386 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0006,0.0051,0.0166,0.0192,0.0208,0.0227,0.0275,0.0281,0.0307,0.0404, 0.0418,0.0456,0.0457,0.0471,0.0491,0.0528,0.0628,0.0680,0.0768,0.0773, 0.0839,0.0851,0.0879,0.1019,0.1059,0.1068,0.1072,0.1088,0.1089,0.1090, 0.1093,0.1140,0.1229,0.1243,0.1290,0.1383,0.1400,0.1442,0.1537,0.1539, 0.1559,0.1599,0.1617,0.1631,0.1687,0.1757,0.1777,0.1813,0.1834,0.1908, 0.1925,0.1928,0.2009,0.2056,0.2092,0.2135,0.2153,0.2184,0.2236,0.2374, 0.2429,0.2523,0.2541,0.2550,0.2560,0.2635,0.2724,0.2753,0.2763,0.2773, 0.2793,0.2806,0.2867,0.2881,0.2917,0.2979,0.3063,0.3083,0.3135,0.3155, 0.3241,0.3255,0.3266,0.3273,0.3299,0.3342,0.3443,0.3468,0.3517,0.3536, 0.3564,0.3574,0.3592,0.3593,0.3600,0.3602,0.3640,0.3640,0.3645,0.3698, 0.3746,0.3758,0.3767,0.3790,0.3817,0.3836,0.3848,0.3892,0.3898,0.3936, 0.4045,0.4047,0.4102,0.4122,0.4154,0.4196,0.4214,0.4216,0.4218,0.4220, 0.4236,0.4244,0.4261,0.4270,0.4360,0.4375,0.4403,0.4416,0.4440,0.4488, 0.4488,0.4491,0.4499,0.4523,0.4527,0.4537,0.4542,0.4569,0.4597,0.4635, 0.4725,0.4899,0.4919,0.4996,0.5000,0.5008,0.5036,0.5071,0.5077,0.5213, 0.5255,0.5267,0.5306,0.5343,0.5360,0.5431,0.5454,0.5489,0.5524,0.5547, 0.5562,0.5586,0.5628,0.5673,0.5685,0.5725,0.5728,0.5756,0.5777,0.5779, 0.5830,0.5903,0.5935,0.6031,0.6033,0.6122,0.6271,0.6302,0.6328,0.6455, 0.6539,0.6549,0.6550,0.6594,0.6642,0.6666,0.6787,0.6837,0.6849,0.6887, 0.6955,0.6994,0.6996,0.7000,0.7099,0.7204,0.7212,0.7219,0.7222,0.7236, 0.7252,0.7299,0.7305,0.7388,0.7433,0.7476,0.7527,0.7644,0.7654,0.7725, 0.7837,0.7851,0.7860,0.8023,0.8054,0.8092,0.8106,0.8108,0.8124,0.8135, 0.8187,0.8193,0.8230,0.8256,0.8272,0.8336,0.8347,0.8353,0.8360,0.8360, 0.8411,0.8417,0.8541,0.8551,0.8588,0.8606,0.8659,0.8670,0.8722,0.8732, 0.8883,0.8892,0.8924,0.9050,0.9088,0.9107,0.9170,0.9216,0.9249,0.9269, 0.9305,0.9313,0.9323,0.9345,0.9349,0.9388,0.9396,0.9401,0.9428,0.9433, 0.9469,0.9503,0.9569,0.9686,0.9787,0.9811,0.9830,0.9908,0.9936, Overall p-value after applying KStest on 269 p-values = 0.597817 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.