RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-10-09_06:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.59 28.1755 0.957071 2 to 25 15.92 19.1154 0.678053 3 to 26 15.96 11.4309 0.166691 4 to 27 16.05 13.6801 0.310397 5 to 28 15.83 28.8263 0.963839 6 to 29 15.78 17.4770 0.577472 7 to 30 15.52 16.8427 0.534931 8 to 31 15.67 22.0923 0.818806 9 to 32 15.53 29.3028 0.968166 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.091197 Tough bday spacings test for dh-ranFile-2015-10-09_06:31: 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 5 47 59 112 103 63 53 36 14 6 2 (O-E)^2/E 1.9 2.9 2.8 2.1 0.3 2.9 0.0 1.3 0.1 0.1 1.0 Birthday Spacings: Sum(O-E)^2/E= 15.402, p= 0.882 RESULTS OF GCD FOR dh-ranFile-2015-10-09_06:31 Euclid's algorithm: p-value, steps to gcd: 0.875164 p-value, dist. of gcd's: 0.925791 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-10-09_06:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.884 0.322 0.403 0.434 0.231 0.388 0.274 0.274 Bits 8 to 15---> 0.732 0.509 0.327 0.105 0.605 0.768 0.610 0.425 Bits 16 to 23---> 0.651 0.472 0.292 0.806 0.825 0.286 0.452 0.009 Bits 24 to 31---> 0.032 0.155 0.585 0.844 0.229 0.920 0.682 0.205 KS test for the above 32 p values: 0.496 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-10-09_06:31, p-values for 5 runs: 0.4401, 0.2469, 0.2271, 0.5050, 0.3407 Rank test for binary matrices (31x31) for dh-ranFile-2015-10-09_06:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 227 211.4 1.148 1.148 r= 29 5080 5134.0 0.568 1.717 r= 30 23146 23103.0 0.080 1.796 r= 31 11547 11551.5 0.002 1.798 chi-square = 1.798 with df = 3; p-value = 0.385 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-10-09_06:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 202 211.4 0.420 0.420 r= 30 5167 5134.0 0.212 0.632 r= 31 23048 23103.0 0.131 0.763 r= 32 11583 11551.5 0.086 0.848 chi-square = 0.848 with df = 3; p-value = 0.162 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-10-09_06:31 b-rank test for bits 1 to 8, p=0.54236 b-rank test for bits 2 to 9, p=0.00824 b-rank test for bits 3 to 10, p=0.57761 b-rank test for bits 4 to 11, p=0.47313 b-rank test for bits 5 to 12, p=0.20502 b-rank test for bits 6 to 13, p=0.45397 b-rank test for bits 7 to 14, p=0.80197 b-rank test for bits 8 to 15, p=0.07800 b-rank test for bits 9 to 16, p=0.83797 b-rank test for bits 10 to 17, p=0.98124 b-rank test for bits 11 to 18, p=0.53932 b-rank test for bits 12 to 19, p=0.19584 b-rank test for bits 13 to 20, p=0.56909 b-rank test for bits 14 to 21, p=0.99759 b-rank test for bits 15 to 22, p=0.27966 b-rank test for bits 16 to 23, p=0.40451 b-rank test for bits 17 to 24, p=0.77015 b-rank test for bits 18 to 25, p=0.71965 b-rank test for bits 19 to 26, p=0.28109 b-rank test for bits 20 to 27, p=0.83719 b-rank test for bits 21 to 28, p=0.27833 b-rank test for bits 22 to 29, p=0.79995 b-rank test for bits 23 to 30, p=0.73300 b-rank test for bits 24 to 31, p=0.47180 b-rank test for bits 25 to 32, p=0.23558 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 = 0.816253 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-10-09_06:31 (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 142754 1.97 0.975782 2 142132 0.52 0.698558 3 142165 0.60 0.724866 4 141466 -1.04 0.150144 5 142480 1.33 0.908790 6 142148 0.56 0.711455 7 142161 0.59 0.721739 8 142056 0.34 0.634083 9 142306 0.93 0.822985 10 140942 -2.26 0.011907 11 142080 0.40 0.654966 12 142086 0.41 0.660116 13 141909 -0.00 0.499692 14 142071 0.38 0.647186 15 142469 1.31 0.904502 16 141332 -1.35 0.088684 17 142126 0.51 0.693655 18 142110 0.47 0.680413 19 141979 0.16 0.564654 20 142048 0.32 0.627029 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-10-09_06:31 Bits used No. missing words z-score p-value 23 to 32 141780 -0.4460 0.327811 22 to 31 142037 0.4402 0.670119 21 to 30 141980 0.2437 0.596264 20 to 29 141943 0.1161 0.546215 19 to 28 142572 2.2851 0.988846 18 to 27 141771 -0.4770 0.316681 17 to 26 142243 1.1506 0.875049 16 to 25 141762 -0.5080 0.305715 15 to 24 142129 0.7575 0.775620 14 to 23 141964 0.1885 0.574764 13 to 22 141514 -1.3632 0.086409 12 to 21 142159 0.8609 0.805362 11 to 20 142209 1.0333 0.849279 10 to 19 142290 1.3127 0.905350 9 to 18 141797 -0.3873 0.349251 8 to 17 141313 -2.0563 0.019876 7 to 16 141987 0.2678 0.605584 6 to 15 141703 -0.7115 0.238393 5 to 14 141870 -0.1356 0.446061 4 to 13 141958 0.1678 0.566641 3 to 12 141816 -0.3218 0.373792 2 to 11 142170 0.8989 0.815637 1 to 10 141737 -0.5942 0.276175 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-10-09_06:31 Bits used No. missing words z-score p-value 28 to 32 141897 -0.0418 0.483330 27 to 31 142018 0.3684 0.643702 26 to 30 142208 1.0124 0.844336 25 to 29 141931 0.0735 0.529279 24 to 28 141939 0.1006 0.540057 23 to 27 141795 -0.3876 0.349171 22 to 26 141685 -0.7604 0.223496 21 to 25 141895 -0.0486 0.480629 20 to 24 141601 -1.0452 0.147968 19 to 23 141658 -0.8520 0.197116 18 to 22 141987 0.2633 0.603836 17 to 21 141680 -0.7774 0.218464 16 to 20 141804 -0.3571 0.360527 15 to 19 142272 1.2294 0.890537 14 to 18 142066 0.5311 0.702320 13 to 17 142009 0.3379 0.632267 12 to 16 141532 -1.2791 0.100434 11 to 15 141400 -1.7265 0.042125 10 to 14 141894 -0.0520 0.479278 9 to 13 141834 -0.2554 0.399224 8 to 12 141763 -0.4960 0.309935 7 to 11 142221 1.0565 0.854632 6 to 10 141471 -1.4859 0.068658 5 to 9 142259 1.1853 0.882055 4 to 8 141944 0.1175 0.546778 3 to 7 141566 -1.1638 0.122246 2 to 6 142135 0.7650 0.777859 1 to 5 141595 -1.0655 0.143319 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-10-09_06:31 Bits used No. missing words z-score p-value 31 to 32 141221 -2.0305 0.021154 30 to 31 142253 1.0138 0.844655 29 to 30 142168 0.7630 0.777280 28 to 29 141685 -0.6617 0.254069 27 to 28 141558 -1.0364 0.150014 26 to 27 142309 1.1790 0.880794 25 to 26 141942 0.0964 0.538387 24 to 25 141814 -0.2812 0.389275 23 to 24 141955 0.1347 0.553583 22 to 23 141964 0.1613 0.564059 21 to 22 141229 -2.0069 0.022382 20 to 21 142111 0.5949 0.724044 19 to 20 141409 -1.4759 0.069985 18 to 19 141322 -1.7325 0.041589 17 to 18 141567 -1.0098 0.156290 16 to 17 141742 -0.4936 0.310795 15 to 16 141580 -0.9715 0.165656 14 to 15 141829 -0.2370 0.406343 13 to 14 141685 -0.6617 0.254069 12 to 13 141973 0.1878 0.574490 11 to 12 141753 -0.4612 0.322345 10 to 11 141841 -0.2016 0.420129 9 to 10 141959 0.1465 0.558244 8 to 9 142217 0.9076 0.817950 7 to 8 141527 -1.1278 0.129699 6 to 7 142143 0.6893 0.754680 5 to 6 142054 0.4268 0.665221 4 to 5 142171 0.7719 0.779910 3 to 4 141847 -0.1839 0.427060 2 to 3 141653 -0.7561 0.224784 1 to 2 141550 -1.0600 0.144579 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-10-09_06:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2484.46 -0.220 0.413020 Test results for specific bytes for dh-ranFile-2015-10-09_06:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2555.42 0.784 0.783412 2 to 9 2452.39 -0.673 0.250367 3 to 10 2556.64 0.801 0.788433 4 to 11 2649.24 2.111 0.982595 5 to 12 2453.61 -0.656 0.255900 6 to 13 2514.41 0.204 0.580718 7 to 14 2533.49 0.474 0.682092 8 to 15 2671.07 2.419 0.992226 9 to 16 2499.80 -0.003 0.498880 10 to 17 2426.36 -1.041 0.148855 11 to 18 2621.05 1.712 0.956545 12 to 19 2390.70 -1.546 0.061090 13 to 20 2475.29 -0.350 0.363349 14 to 21 2630.61 1.847 0.967638 15 to 22 2514.47 0.205 0.581091 16 to 23 2678.44 2.524 0.994192 17 to 24 2476.55 -0.332 0.370058 18 to 25 2514.74 0.208 0.582546 19 to 26 2546.40 0.656 0.744131 20 to 27 2497.75 -0.032 0.487325 21 to 28 2441.41 -0.829 0.203687 22 to 29 2643.10 2.024 0.978504 23 to 30 2507.23 0.102 0.540695 24 to 31 2357.67 -2.013 0.022066 25 to 32 2359.55 -1.986 0.023499 CDPARK for dh-ranFile-2015-10-09_06:31: 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 3522 -0.0457 0.481790 3534 0.5023 0.692266 3501 -1.0046 0.157553 3524 0.0457 0.518210 3512 -0.5023 0.307734 3516 -0.3196 0.374623 3506 -0.7763 0.218799 3541 0.8219 0.794438 3529 0.2740 0.607947 3512 -0.5023 0.307734 Square side=100, avg. no. parked=3519.70 sample std.=11.99 p-value of the KSTEST for those 10 p-values: 0.495772 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-10-09_06:31 0.1555,0.4277,0.1341,0.1066,0.2092,0.3626,0.4344,0.9968,0.3981,0.3819, The KS test for those 10 p-values: 0.086905 The 3DSPHERES test for dh-ranFile-2015-10-09_06:31 sample no r^3 equiv. uni. 1 21.212 0.506904 2 4.008 0.125050 3 27.588 0.601326 4 54.718 0.838609 5 18.958 0.468431 6 8.196 0.239070 7 0.715 0.023556 8 4.140 0.128888 9 8.297 0.241613 10 21.951 0.518908 11 26.194 0.582353 12 33.839 0.676314 13 9.484 0.271045 14 1.815 0.058705 15 70.884 0.905843 16 16.759 0.428001 17 6.710 0.200408 18 5.261 0.160862 19 89.899 0.950046 20 2.806 0.089292 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.210582 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-10-09_06:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 0.5 -1.1 -1.3 -0.8 -1.3 0.3 -0.6 0.3 0.4 -0.6 1.6 0.1 -0.3 -0.4 0.7 -0.2 -0.3 -0.2 0.9 0.4 -0.9 1.2 -1.4 0.5 -0.7 0.4 -2.0 -0.5 0.2 1.3 1.2 1.1 -0.3 -1.2 -1.2 0.3 -2.3 0.5 -0.7 -0.6 -1.0 -1.1 Chi-square with 42 degrees of freedom:36.483712 z-score=-0.601876, p-value=0.288831 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-10-09_06:31 Test no p-value 1 0.359971 2 0.720214 3 0.503961 4 0.168033 5 0.456523 6 0.634681 7 0.973946 8 0.371016 9 0.114731 10 0.040868 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.793411 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-10-09_06:31: (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 66750 0.10 66467 0.60 3 25000.00 24909 0.33 25095 0.36 4 6666.67 6614 0.42 6801 2.71 5 1388.89 1454 3.05 1354 0.88 6 238.10 226 0.61 241 0.04 7 34.72 42 1.53 33 0.09 8 4.96 4 0.19 8 1.86 p=0.60213 p=0.63309 Number of rngs required: 687606, p-value: 0.178 RESULTS OF CRAPS TEST for dh-ranFile-2015-10-09_06:31 No. of wins: Observed Expected 98390 98585.9 z-score=-0.876, pvalue=0.19052 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66402 66666.7 1.051 1.051 2 37822 37654.3 0.747 1.797 3 27050 26954.7 0.337 2.134 4 19239 19313.5 0.287 2.421 5 13755 13851.4 0.671 3.092 6 10096 9943.5 2.338 5.430 7 6998 7145.0 3.025 8.455 8 5212 5139.1 1.035 9.490 9 3679 3699.9 0.118 9.608 10 2632 2666.3 0.441 10.049 11 1988 1923.3 2.175 12.224 12 1428 1388.7 1.110 13.333 13 997 1003.7 0.045 13.378 14 789 726.1 5.442 18.820 15 519 525.8 0.089 18.909 16 402 381.2 1.140 20.049 17 263 276.5 0.663 20.712 18 202 200.8 0.007 20.719 19 151 146.0 0.172 20.891 20 97 106.2 0.800 21.691 21 279 287.1 0.229 21.920 Chisq= 21.92 for 20 degrees of freedom, p= 0.65514 SUMMARY of craptest p-value for no. of wins: 0.190517 p-value for throws/game: 0.655138 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-10-09_06:31 No. of wins: Observed Expected 98655 98585.9 z-score= 0.309, pvalue=0.62143 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66503 66666.7 0.402 0.402 2 37681 37654.3 0.019 0.421 3 26901 26954.7 0.107 0.528 4 19158 19313.5 1.251 1.779 5 14066 13851.4 3.324 5.103 6 9984 9943.5 0.165 5.268 7 7240 7145.0 1.262 6.530 8 5188 5139.1 0.466 6.996 9 3651 3699.9 0.645 7.642 10 2658 2666.3 0.026 7.667 11 1933 1923.3 0.049 7.716 12 1408 1388.7 0.267 7.983 13 990 1003.7 0.187 8.171 14 727 726.1 0.001 8.172 15 499 525.8 1.370 9.541 16 402 381.2 1.140 10.682 17 275 276.5 0.009 10.690 18 191 200.8 0.481 11.171 19 149 146.0 0.062 11.234 20 105 106.2 0.014 11.248 21 291 287.1 0.053 11.300 Chisq= 11.30 for 20 degrees of freedom, p= 0.06194 SUMMARY of craptest p-value for no. of wins: 0.621431 p-value for throws/game: 0.061935 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0082,0.0090,0.0119,0.0199,0.0212,0.0221,0.0224,0.0235,0.0236,0.0316, 0.0409,0.0416,0.0421,0.0587,0.0611,0.0619,0.0687,0.0700,0.0780,0.0864, 0.0869,0.0887,0.0893,0.0912,0.1004,0.1052,0.1066,0.1147,0.1222,0.1251, 0.1289,0.1297,0.1341,0.1433,0.1446,0.1480,0.1489,0.1500,0.1501,0.1555, 0.1555,0.1563,0.1576,0.1609,0.1622,0.1657,0.1667,0.1680,0.1781,0.1905, 0.1958,0.1971,0.2004,0.2037,0.2050,0.2054,0.2092,0.2106,0.2185,0.2188, 0.2235,0.2248,0.2271,0.2286,0.2307,0.2356,0.2384,0.2391,0.2416,0.2469, 0.2504,0.2541,0.2541,0.2559,0.2710,0.2737,0.2738,0.2762,0.2783,0.2797, 0.2811,0.2862,0.2888,0.2924,0.3057,0.3077,0.3077,0.3099,0.3104,0.3108, 0.3167,0.3218,0.3223,0.3273,0.3278,0.3407,0.3492,0.3493,0.3600,0.3605, 0.3626,0.3633,0.3701,0.3710,0.3738,0.3746,0.3819,0.3847,0.3880,0.3893, 0.3981,0.3992,0.4026,0.4045,0.4063,0.4130,0.4201,0.4251,0.4271,0.4277, 0.4280,0.4340,0.4344,0.4401,0.4461,0.4519,0.4540,0.4565,0.4684,0.4716, 0.4718,0.4731,0.4793,0.4806,0.4818,0.4833,0.4873,0.4958,0.4958,0.4989, 0.4997,0.5040,0.5050,0.5069,0.5093,0.5182,0.5189,0.5293,0.5349,0.5384, 0.5393,0.5401,0.5407,0.5424,0.5462,0.5468,0.5536,0.5582,0.5641,0.5647, 0.5666,0.5691,0.5745,0.5748,0.5775,0.5776,0.5807,0.5811,0.5824,0.5825, 0.5849,0.5963,0.6013,0.6021,0.6038,0.6054,0.6056,0.6079,0.6097,0.6214, 0.6270,0.6323,0.6331,0.6341,0.6347,0.6437,0.6472,0.6508,0.6550,0.6551, 0.6601,0.6652,0.6701,0.6763,0.6781,0.6804,0.6819,0.6821,0.6923,0.6937, 0.6986,0.7023,0.7115,0.7196,0.7202,0.7217,0.7240,0.7249,0.7315,0.7330, 0.7441,0.7547,0.7678,0.7701,0.7756,0.7773,0.7779,0.7799,0.7834,0.7884, 0.7934,0.7944,0.7999,0.8020,0.8054,0.8060,0.8156,0.8163,0.8180,0.8188, 0.8230,0.8249,0.8372,0.8380,0.8386,0.8437,0.8443,0.8447,0.8493,0.8546, 0.8750,0.8752,0.8808,0.8819,0.8821,0.8837,0.8905,0.9045,0.9054,0.9058, 0.9088,0.9199,0.9258,0.9500,0.9565,0.9571,0.9638,0.9676,0.9682,0.9739, 0.9758,0.9785,0.9812,0.9826,0.9888,0.9922,0.9942,0.9968,0.9976, Overall p-value after applying KStest on 269 p-values = 0.395795 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.