RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-02-23_19:31 (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 12.1982 0.212007 2 to 25 15.53 20.5814 0.754425 3 to 26 16.07 11.9670 0.197866 4 to 27 15.89 17.2188 0.560360 5 to 28 15.72 25.9754 0.925090 6 to 29 15.58 23.5540 0.867931 7 to 30 15.99 8.3883 0.042476 8 to 31 15.79 24.5208 0.894038 9 to 32 15.74 9.5044 0.076903 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.580576 Tough bday spacings test for dh-ranFile-2016-02-23_19:31: 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 33 86 97 103 68 60 30 7 8 2 (O-E)^2/E 1.1 0.4 2.2 0.0 0.3 1.3 1.2 0.0 4.2 0.3 1.0 Birthday Spacings: Sum(O-E)^2/E= 11.992, p= 0.714 RESULTS OF GCD FOR dh-ranFile-2016-02-23_19:31 Euclid's algorithm: p-value, steps to gcd: 0.687603 p-value, dist. of gcd's: 0.741843 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-02-23_19:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.886 0.995 0.390 0.250 0.642 0.161 0.297 0.926 Bits 8 to 15---> 0.267 0.506 0.569 0.771 0.849 0.276 0.360 0.865 Bits 16 to 23---> 0.746 0.245 0.812 0.863 0.582 0.488 0.307 0.693 Bits 24 to 31---> 0.080 0.049 0.083 0.351 0.880 0.911 0.677 0.354 KS test for the above 32 p values: 0.291 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-02-23_19:31, p-values for 5 runs: 0.5652, 0.1955, 0.6453, 0.1355, 0.4999 Rank test for binary matrices (31x31) for dh-ranFile-2016-02-23_19:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 231 211.4 1.814 1.814 r= 29 5217 5134.0 1.341 3.155 r= 30 22898 23103.0 1.820 4.975 r= 31 11654 11551.5 0.909 5.884 chi-square = 5.884 with df = 3; p-value = 0.883 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-02-23_19:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 203 211.4 0.335 0.335 r= 30 5191 5134.0 0.633 0.968 r= 31 23044 23103.0 0.151 1.119 r= 32 11562 11551.5 0.010 1.128 chi-square = 1.128 with df = 3; p-value = 0.230 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-02-23_19:31 b-rank test for bits 1 to 8, p=0.87350 b-rank test for bits 2 to 9, p=0.24752 b-rank test for bits 3 to 10, p=0.94954 b-rank test for bits 4 to 11, p=0.82457 b-rank test for bits 5 to 12, p=0.34298 b-rank test for bits 6 to 13, p=0.79846 b-rank test for bits 7 to 14, p=0.62678 b-rank test for bits 8 to 15, p=0.22181 b-rank test for bits 9 to 16, p=0.76609 b-rank test for bits 10 to 17, p=0.61611 b-rank test for bits 11 to 18, p=0.30371 b-rank test for bits 12 to 19, p=0.09596 b-rank test for bits 13 to 20, p=0.45257 b-rank test for bits 14 to 21, p=0.74167 b-rank test for bits 15 to 22, p=0.38144 b-rank test for bits 16 to 23, p=0.34393 b-rank test for bits 17 to 24, p=0.30856 b-rank test for bits 18 to 25, p=0.15429 b-rank test for bits 19 to 26, p=0.43220 b-rank test for bits 20 to 27, p=0.27664 b-rank test for bits 21 to 28, p=0.33610 b-rank test for bits 22 to 29, p=0.40568 b-rank test for bits 23 to 30, p=0.42500 b-rank test for bits 24 to 31, p=0.15209 b-rank test for bits 25 to 32, p=0.51783 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 = 0.345404 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-02-23_19:31 (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 141999 0.21 0.582975 2 142845 2.19 0.985597 3 141260 -1.52 0.064617 4 141231 -1.58 0.056496 5 142121 0.49 0.689543 6 142213 0.71 0.760996 7 141932 0.05 0.521121 8 141895 -0.03 0.486645 9 142737 1.93 0.973432 10 142261 0.82 0.794364 11 142140 0.54 0.705039 12 141904 -0.01 0.495032 13 141517 -0.92 0.179661 14 141957 0.11 0.544342 15 141958 0.11 0.545268 16 141581 -0.77 0.221503 17 141961 0.12 0.548045 18 142235 0.76 0.776645 19 142131 0.52 0.697743 20 141418 -1.15 0.125491 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-02-23_19:31 Bits used No. missing words z-score p-value 23 to 32 142244 1.1540 0.875757 22 to 31 141762 -0.5080 0.305715 21 to 30 141533 -1.2977 0.097197 20 to 29 142402 1.6989 0.955327 19 to 28 141815 -0.3253 0.372486 18 to 27 141510 -1.3770 0.084256 17 to 26 141737 -0.5942 0.276175 16 to 25 141697 -0.7322 0.232032 15 to 24 141893 -0.0563 0.477547 14 to 23 142106 0.6782 0.751169 13 to 22 142423 1.7713 0.961743 12 to 21 141993 0.2885 0.613525 11 to 20 142243 1.1506 0.875049 10 to 19 141703 -0.7115 0.238393 9 to 18 141633 -0.9529 0.170330 8 to 17 141910 0.0023 0.500922 7 to 16 141350 -1.9287 0.026883 6 to 15 141114 -2.7425 0.003049 5 to 14 141819 -0.3115 0.377717 4 to 13 142249 1.1713 0.879256 3 to 12 141912 0.0092 0.503673 2 to 11 141490 -1.4460 0.074093 1 to 10 142293 1.3230 0.907082 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-02-23_19:31 Bits used No. missing words z-score p-value 28 to 32 141807 -0.3469 0.364340 27 to 31 141809 -0.3401 0.366890 26 to 30 141901 -0.0282 0.488737 25 to 29 142184 0.9311 0.824095 24 to 28 141634 -0.9333 0.175327 23 to 27 141759 -0.5096 0.305168 22 to 26 141702 -0.7028 0.241086 21 to 25 142034 0.4226 0.663710 20 to 24 141895 -0.0486 0.480629 19 to 23 141616 -0.9943 0.160029 18 to 22 141966 0.1921 0.576169 17 to 21 142028 0.4023 0.656258 16 to 20 141752 -0.5333 0.296905 15 to 19 142145 0.7989 0.787820 14 to 18 141580 -1.1164 0.132131 13 to 17 141967 0.1955 0.577496 12 to 16 141946 0.1243 0.549463 11 to 15 141548 -1.2248 0.110316 10 to 14 142117 0.7040 0.759273 9 to 13 142230 1.0870 0.861485 8 to 12 142047 0.4667 0.679635 7 to 11 141735 -0.5909 0.277277 6 to 10 142287 1.2802 0.899769 5 to 9 141735 -0.5909 0.277277 4 to 8 141749 -0.5435 0.293396 3 to 7 141954 0.1514 0.560179 2 to 6 142286 1.2768 0.899172 1 to 5 142003 0.3175 0.624578 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-02-23_19:31 Bits used No. missing words z-score p-value 31 to 32 142622 2.1023 0.982235 30 to 31 141772 -0.4051 0.342701 29 to 30 141740 -0.4995 0.308714 28 to 29 141716 -0.5703 0.284239 27 to 28 142139 0.6775 0.750953 26 to 27 141829 -0.2370 0.406343 25 to 26 141730 -0.5290 0.298404 24 to 25 141831 -0.2311 0.408633 23 to 24 141523 -1.1396 0.127223 22 to 23 141230 -2.0039 0.022539 21 to 22 141168 -2.1868 0.014378 20 to 21 141674 -0.6942 0.243782 19 to 20 142121 0.6244 0.733816 18 to 19 142229 0.9430 0.827154 17 to 18 141238 -1.9803 0.023834 16 to 17 141741 -0.4965 0.309754 15 to 16 141976 0.1967 0.577956 14 to 15 141944 0.1023 0.540729 13 to 14 141985 0.2232 0.588316 12 to 13 141448 -1.3609 0.086780 11 to 12 141979 0.2055 0.581416 10 to 11 142399 1.4445 0.925694 9 to 10 142292 1.1288 0.870513 8 to 9 142132 0.6568 0.744359 7 to 8 142269 1.0610 0.855649 6 to 7 141524 -1.1367 0.127839 5 to 6 141084 -2.4346 0.007454 4 to 5 142275 1.0787 0.859633 3 to 4 141053 -2.5260 0.005768 2 to 3 142245 0.9902 0.838956 1 to 2 142296 1.1406 0.872986 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-02-23_19:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2446.86 -0.752 0.226155 Test results for specific bytes for dh-ranFile-2016-02-23_19:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2590.61 1.281 0.899975 2 to 9 2511.31 0.160 0.563543 3 to 10 2626.59 1.790 0.963291 4 to 11 2486.36 -0.193 0.423505 5 to 12 2433.52 -0.940 0.173583 6 to 13 2502.09 0.030 0.511772 7 to 14 2441.51 -0.827 0.204057 8 to 15 2388.12 -1.582 0.056799 9 to 16 2506.51 0.092 0.536671 10 to 17 2544.83 0.634 0.736960 11 to 18 2553.36 0.755 0.774780 12 to 19 2516.26 0.230 0.590931 13 to 20 2513.68 0.193 0.576711 14 to 21 2449.81 -0.710 0.238895 15 to 22 2622.27 1.729 0.958110 16 to 23 2550.91 0.720 0.764241 17 to 24 2538.69 0.547 0.707881 18 to 25 2622.81 1.737 0.958782 19 to 26 2473.47 -0.375 0.353754 20 to 27 2518.19 0.257 0.601522 21 to 28 2475.92 -0.341 0.366702 22 to 29 2437.65 -0.882 0.188966 23 to 30 2522.93 0.324 0.627132 24 to 31 2486.78 -0.187 0.425865 25 to 32 2499.48 -0.007 0.497042 CDPARK for dh-ranFile-2016-02-23_19:31: 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 3520 -0.1370 0.445521 3477 -2.1005 0.017844 3552 1.3242 0.907282 3540 0.7763 0.781201 3491 -1.4612 0.071982 3540 0.7763 0.781201 3484 -1.7808 0.037471 3484 -1.7808 0.037471 3538 0.6849 0.753306 3529 0.2740 0.607947 Square side=100, avg. no. parked=3515.50 sample std.=27.03 p-value of the KSTEST for those 10 p-values: 0.140749 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-02-23_19:31 0.8072,0.6839,0.0769,0.1922,0.8974,0.2577,0.8036,0.7508,0.6119,0.7473, The KS test for those 10 p-values: 0.407353 The 3DSPHERES test for dh-ranFile-2016-02-23_19:31 sample no r^3 equiv. uni. 1 14.585 0.385027 2 1.481 0.048169 3 17.365 0.439450 4 85.619 0.942386 5 80.343 0.931307 6 84.175 0.939543 7 5.730 0.173877 8 2.242 0.072015 9 10.419 0.293402 10 2.733 0.087061 11 85.639 0.942423 12 3.913 0.122297 13 8.206 0.239315 14 59.156 0.860805 15 10.230 0.288951 16 30.989 0.644053 17 68.200 0.897031 18 19.953 0.485772 19 0.527 0.017418 20 7.793 0.228774 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.205738 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-02-23_19:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -2.0 -1.8 0.5 -0.2 0.1 -1.0 0.5 0.2 0.1 0.7 -2.1 -0.6 -0.8 0.9 0.9 1.5 0.1 0.9 -0.2 -0.1 -1.4 -0.2 0.2 0.3 -0.6 -0.8 0.9 -1.7 -1.5 -0.4 1.0 1.5 0.9 1.7 -0.5 0.0 -1.3 3.4 1.5 -0.6 0.0 -0.1 Chi-square with 42 degrees of freedom:51.892842 z-score=1.079398, p-value=0.859074 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-02-23_19:31 Test no p-value 1 0.032388 2 0.826705 3 0.496018 4 0.447923 5 0.255258 6 0.103490 7 0.011818 8 0.084683 9 0.350605 10 0.091213 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.011575 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-02-23_19:31: (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 66632 0.02 66662 0.00 3 25000.00 25145 0.84 24976 0.02 4 6666.67 6583 1.05 6738 0.76 5 1388.89 1385 0.01 1365 0.41 6 238.10 219 1.53 223 0.96 7 34.72 33 0.09 29 0.94 8 4.96 2 1.77 6 0.22 p=0.49444 p=0.23159 Number of rngs required: 688734, p-value: 0.648 RESULTS OF CRAPS TEST for dh-ranFile-2016-02-23_19:31 No. of wins: Observed Expected 98821 98585.9 z-score= 1.052, pvalue=0.85353 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66892 66666.7 0.762 0.762 2 37696 37654.3 0.046 0.808 3 26979 26954.7 0.022 0.830 4 19226 19313.5 0.396 1.226 5 13733 13851.4 1.012 2.238 6 9793 9943.5 2.279 4.517 7 7030 7145.0 1.852 6.369 8 5201 5139.1 0.746 7.115 9 3734 3699.9 0.315 7.430 10 2751 2666.3 2.691 10.121 11 2026 1923.3 5.481 15.602 12 1392 1388.7 0.008 15.609 13 1018 1003.7 0.203 15.813 14 686 726.1 2.219 18.032 15 494 525.8 1.927 19.959 16 372 381.2 0.220 20.179 17 250 276.5 2.547 22.726 18 167 200.8 5.699 28.425 19 155 146.0 0.557 28.981 20 109 106.2 0.073 29.054 21 296 287.1 0.275 29.329 Chisq= 29.33 for 20 degrees of freedom, p= 0.91853 SUMMARY of craptest p-value for no. of wins: 0.853529 p-value for throws/game: 0.918526 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-02-23_19:31 No. of wins: Observed Expected 98932 98585.9 z-score= 1.548, pvalue=0.93921 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66361 66666.7 1.401 1.401 2 37684 37654.3 0.023 1.425 3 27018 26954.7 0.148 1.573 4 19500 19313.5 1.802 3.375 5 13817 13851.4 0.086 3.461 6 9997 9943.5 0.287 3.748 7 7162 7145.0 0.040 3.788 8 5019 5139.1 2.805 6.594 9 3743 3699.9 0.503 7.097 10 2636 2666.3 0.344 7.441 11 1941 1923.3 0.162 7.603 12 1421 1388.7 0.749 8.353 13 1030 1003.7 0.688 9.041 14 715 726.1 0.171 9.212 15 503 525.8 0.992 10.204 16 412 381.2 2.497 12.700 17 276 276.5 0.001 12.702 18 204 200.8 0.050 12.752 19 156 146.0 0.687 13.439 20 111 106.2 0.216 13.654 21 294 287.1 0.165 13.819 Chisq= 13.82 for 20 degrees of freedom, p= 0.16047 SUMMARY of craptest p-value for no. of wins: 0.939206 p-value for throws/game: 0.160466 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0030,0.0058,0.0075,0.0116,0.0118,0.0144,0.0174,0.0178,0.0225,0.0238, 0.0269,0.0324,0.0375,0.0375,0.0425,0.0482,0.0488,0.0565,0.0568,0.0646, 0.0720,0.0720,0.0741,0.0769,0.0769,0.0797,0.0829,0.0843,0.0847,0.0868, 0.0871,0.0912,0.0960,0.0972,0.1035,0.1103,0.1223,0.1255,0.1272,0.1278, 0.1321,0.1355,0.1407,0.1521,0.1543,0.1600,0.1605,0.1608,0.1703,0.1736, 0.1739,0.1753,0.1797,0.1890,0.1922,0.1955,0.1979,0.2041,0.2057,0.2120, 0.2215,0.2218,0.2262,0.2288,0.2297,0.2316,0.2320,0.2384,0.2389,0.2393, 0.2411,0.2438,0.2449,0.2475,0.2502,0.2553,0.2577,0.2667,0.2760,0.2762, 0.2766,0.2773,0.2773,0.2842,0.2890,0.2910,0.2934,0.2934,0.2969,0.2971, 0.2984,0.3037,0.3052,0.3057,0.3065,0.3086,0.3087,0.3098,0.3361,0.3427, 0.3430,0.3439,0.3454,0.3506,0.3511,0.3538,0.3544,0.3598,0.3643,0.3667, 0.3669,0.3725,0.3777,0.3814,0.3850,0.3903,0.4057,0.4063,0.4074,0.4086, 0.4235,0.4250,0.4259,0.4322,0.4395,0.4455,0.4479,0.4526,0.4775,0.4806, 0.4858,0.4866,0.4881,0.4887,0.4944,0.4950,0.4960,0.4970,0.4999,0.5009, 0.5037,0.5057,0.5118,0.5178,0.5211,0.5367,0.5407,0.5443,0.5453,0.5480, 0.5495,0.5602,0.5604,0.5635,0.5652,0.5695,0.5762,0.5767,0.5775,0.5780, 0.5806,0.5814,0.5824,0.5830,0.5883,0.5909,0.6015,0.6079,0.6119,0.6135, 0.6161,0.6246,0.6268,0.6271,0.6422,0.6441,0.6453,0.6485,0.6563,0.6637, 0.6771,0.6796,0.6839,0.6876,0.6895,0.6935,0.6977,0.7050,0.7079,0.7144, 0.7338,0.7370,0.7417,0.7418,0.7444,0.7462,0.7473,0.7508,0.7510,0.7512, 0.7533,0.7544,0.7593,0.7610,0.7642,0.7661,0.7710,0.7748,0.7766,0.7812, 0.7812,0.7878,0.7944,0.7985,0.8036,0.8072,0.8122,0.8241,0.8246,0.8267, 0.8272,0.8390,0.8489,0.8535,0.8556,0.8591,0.8596,0.8608,0.8615,0.8634, 0.8653,0.8679,0.8705,0.8730,0.8735,0.8750,0.8758,0.8793,0.8801,0.8826, 0.8856,0.8940,0.8970,0.8974,0.8992,0.8998,0.9000,0.9071,0.9073,0.9113, 0.9185,0.9251,0.9257,0.9261,0.9313,0.9392,0.9395,0.9424,0.9424,0.9495, 0.9553,0.9581,0.9588,0.9617,0.9633,0.9734,0.9822,0.9856,0.9949, Overall p-value after applying KStest on 269 p-values = 0.595678 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.