RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-10-25_18:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.46 21.5449 0.797141 2 to 25 15.81 10.6377 0.125236 3 to 26 15.57 13.5136 0.298820 4 to 27 15.73 33.9574 0.991497 5 to 28 15.80 9.6029 0.080568 6 to 29 15.79 22.7527 0.842525 7 to 30 15.55 23.0731 0.853113 8 to 31 15.65 18.3160 0.630826 9 to 32 15.70 25.4862 0.915657 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.203480 Tough bday spacings test for dh-ranFile-2015-10-25_18:31: 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 4 25 83 110 98 79 50 34 8 7 2 (O-E)^2/E 2.9 3.7 1.3 1.6 0.0 0.0 0.1 0.6 3.2 0.0 1.0 Birthday Spacings: Sum(O-E)^2/E= 14.398, p= 0.844 RESULTS OF GCD FOR dh-ranFile-2015-10-25_18:31 Euclid's algorithm: p-value, steps to gcd: 0.910513 p-value, dist. of gcd's: 0.137551 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-10-25_18:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.175 0.872 0.432 0.906 0.879 0.148 0.918 0.249 Bits 8 to 15---> 0.338 0.306 0.681 0.687 0.349 0.185 0.618 0.219 Bits 16 to 23---> 0.473 0.722 0.151 0.858 0.304 0.921 0.042 0.879 Bits 24 to 31---> 0.184 0.217 0.304 0.489 0.604 0.607 0.284 0.777 KS test for the above 32 p values: 0.331 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-10-25_18:31, p-values for 5 runs: 0.1202, 0.3660, 0.4527, 0.2954, 0.7125 Rank test for binary matrices (31x31) for dh-ranFile-2015-10-25_18:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 210 211.4 0.010 0.010 r= 29 5061 5134.0 1.038 1.048 r= 30 23210 23103.0 0.495 1.543 r= 31 11519 11551.5 0.092 1.634 chi-square = 1.634 with df = 3; p-value = 0.348 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-10-25_18:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 188 211.4 2.594 2.594 r= 30 4996 5134.0 3.710 6.304 r= 31 23195 23103.0 0.366 6.670 r= 32 11621 11551.5 0.418 7.088 chi-square = 7.088 with df = 3; p-value = 0.931 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-10-25_18:31 b-rank test for bits 1 to 8, p=0.23441 b-rank test for bits 2 to 9, p=0.95333 b-rank test for bits 3 to 10, p=0.71704 b-rank test for bits 4 to 11, p=0.81136 b-rank test for bits 5 to 12, p=0.84234 b-rank test for bits 6 to 13, p=0.55652 b-rank test for bits 7 to 14, p=0.11112 b-rank test for bits 8 to 15, p=0.54806 b-rank test for bits 9 to 16, p=0.08124 b-rank test for bits 10 to 17, p=0.16292 b-rank test for bits 11 to 18, p=0.37775 b-rank test for bits 12 to 19, p=0.13949 b-rank test for bits 13 to 20, p=0.76225 b-rank test for bits 14 to 21, p=0.48747 b-rank test for bits 15 to 22, p=0.78643 b-rank test for bits 16 to 23, p=0.92157 b-rank test for bits 17 to 24, p=0.44879 b-rank test for bits 18 to 25, p=0.10861 b-rank test for bits 19 to 26, p=0.79420 b-rank test for bits 20 to 27, p=0.66080 b-rank test for bits 21 to 28, p=0.87172 b-rank test for bits 22 to 29, p=0.74524 b-rank test for bits 23 to 30, p=0.65389 b-rank test for bits 24 to 31, p=0.46044 b-rank test for bits 25 to 32, p=0.86267 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 = 0.366654 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-10-25_18:31 (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 142667 1.77 0.961658 2 141846 -0.15 0.441184 3 142437 1.23 0.891189 4 141720 -0.44 0.329114 5 141810 -0.23 0.408238 6 141768 -0.33 0.370621 7 142222 0.73 0.767469 8 141603 -0.72 0.237081 9 142215 0.71 0.762443 10 141909 -0.00 0.499692 11 141715 -0.45 0.324899 12 142475 1.32 0.906859 13 142542 1.48 0.930323 14 141250 -1.54 0.061720 15 141675 -0.55 0.292018 16 141882 -0.06 0.474543 17 141342 -1.33 0.092497 18 141431 -1.12 0.131870 19 142191 0.66 0.744765 20 141921 0.03 0.510876 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-10-25_18:31 Bits used No. missing words z-score p-value 23 to 32 141675 -0.8080 0.209535 22 to 31 141697 -0.7322 0.232032 21 to 30 141354 -1.9149 0.027751 20 to 29 141445 -1.6011 0.054673 19 to 28 142040 0.4506 0.673856 18 to 27 142216 1.0575 0.854854 17 to 26 142189 0.9644 0.832572 16 to 25 141717 -0.6632 0.253599 15 to 24 141948 0.1333 0.553040 14 to 23 141910 0.0023 0.500922 13 to 22 141546 -1.2529 0.105128 12 to 21 141786 -0.4253 0.335318 11 to 20 141057 -2.9391 0.001646 10 to 19 141905 -0.0149 0.494044 9 to 18 141857 -0.1804 0.428400 8 to 17 142331 1.4540 0.927032 7 to 16 142294 1.3264 0.907654 6 to 15 142682 2.6644 0.996143 5 to 14 142000 0.3127 0.622729 4 to 13 141673 -0.8149 0.207556 3 to 12 141848 -0.2115 0.416255 2 to 11 141432 -1.6460 0.049885 1 to 10 141549 -1.2425 0.107023 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-10-25_18:31 Bits used No. missing words z-score p-value 28 to 32 141850 -0.2011 0.420303 27 to 31 141820 -0.3028 0.381016 26 to 30 141834 -0.2554 0.399224 25 to 29 142090 0.6124 0.729877 24 to 28 141737 -0.5842 0.279553 23 to 27 141535 -1.2689 0.102236 22 to 26 142330 1.4260 0.923066 21 to 25 141281 -2.1299 0.016589 20 to 24 141531 -1.2825 0.099838 19 to 23 142168 0.8768 0.809715 18 to 22 141935 0.0870 0.534671 17 to 21 142236 1.1074 0.865930 16 to 20 141828 -0.2757 0.391391 15 to 19 141184 -2.4587 0.006971 14 to 18 142035 0.4260 0.664946 13 to 17 141828 -0.2757 0.391391 12 to 16 141712 -0.6689 0.251775 11 to 15 142617 2.3989 0.991777 10 to 14 141636 -0.9265 0.177082 9 to 13 142229 1.0836 0.860735 8 to 12 142080 0.5785 0.718551 7 to 11 141702 -0.7028 0.241086 6 to 10 142322 1.3989 0.919076 5 to 9 142349 1.4904 0.931941 4 to 8 142247 1.1446 0.873822 3 to 7 141753 -0.5299 0.298080 2 to 6 141822 -0.2960 0.383602 1 to 5 142051 0.4802 0.684471 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-10-25_18:31 Bits used No. missing words z-score p-value 31 to 32 142071 0.4769 0.683284 30 to 31 141876 -0.0983 0.460840 29 to 30 141374 -1.5791 0.057151 28 to 29 141904 -0.0157 0.493728 27 to 28 141443 -1.3756 0.084472 26 to 27 142244 0.9872 0.838234 25 to 26 142183 0.8073 0.790249 24 to 25 142311 1.1849 0.881965 23 to 24 141676 -0.6883 0.245635 22 to 23 142277 1.0846 0.860944 21 to 22 141430 -1.4140 0.078688 20 to 21 141611 -0.8800 0.189422 19 to 20 141877 -0.0954 0.462011 18 to 19 141774 -0.3992 0.344872 17 to 18 142113 0.6008 0.726012 16 to 17 141418 -1.4494 0.073620 15 to 16 142183 0.8073 0.790249 14 to 15 141993 0.2468 0.597474 13 to 14 142603 2.0462 0.979633 12 to 13 141543 -1.0806 0.139933 11 to 12 141486 -1.2488 0.105876 10 to 11 141414 -1.4612 0.071987 9 to 10 141877 -0.0954 0.462011 8 to 9 141746 -0.4818 0.314974 7 to 8 142146 0.6981 0.757456 6 to 7 141929 0.0580 0.523135 5 to 6 142039 0.3825 0.648958 4 to 5 141450 -1.3550 0.087716 3 to 4 141677 -0.6853 0.246565 2 to 3 141792 -0.3461 0.364632 1 to 2 141850 -0.1750 0.430534 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-10-25_18:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2405.53 -1.336 0.090766 Test results for specific bytes for dh-ranFile-2015-10-25_18:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2562.87 0.889 0.813041 2 to 9 2513.31 0.188 0.574639 3 to 10 2531.91 0.451 0.674124 4 to 11 2374.53 -1.774 0.037995 5 to 12 2538.43 0.543 0.706593 6 to 13 2419.11 -1.144 0.126320 7 to 14 2370.86 -1.826 0.033903 8 to 15 2536.68 0.519 0.698016 9 to 16 2493.02 -0.099 0.460689 10 to 17 2400.94 -1.401 0.080618 11 to 18 2643.51 2.030 0.978797 12 to 19 2581.89 1.158 0.876593 13 to 20 2476.57 -0.331 0.370175 14 to 21 2477.71 -0.315 0.376275 15 to 22 2477.78 -0.314 0.376667 16 to 23 2390.86 -1.543 0.061367 17 to 24 2532.87 0.465 0.678992 18 to 25 2487.74 -0.173 0.431170 19 to 26 2631.76 1.863 0.968793 20 to 27 2350.96 -2.108 0.017527 21 to 28 2527.72 0.392 0.652500 22 to 29 2448.37 -0.730 0.232636 23 to 30 2514.75 0.209 0.582594 24 to 31 2480.84 -0.271 0.393207 25 to 32 2519.27 0.273 0.607389 CDPARK for dh-ranFile-2015-10-25_18:31: 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 3541 0.8219 0.794438 3536 0.5936 0.723613 3499 -1.0959 0.136563 3534 0.5023 0.692266 3503 -0.9132 0.180558 3504 -0.8676 0.192812 3514 -0.4110 0.340551 3504 -0.8676 0.192812 3532 0.4110 0.659449 3516 -0.3196 0.374623 Square side=100, avg. no. parked=3518.30 sample std.=15.17 p-value of the KSTEST for those 10 p-values: 0.479193 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-10-25_18:31 0.8984,0.0970,0.3968,0.8638,0.2503,0.6959,0.7685,0.6859,0.7201,0.1442, The KS test for those 10 p-values: 0.737469 The 3DSPHERES test for dh-ranFile-2015-10-25_18:31 sample no r^3 equiv. uni. 1 106.234 0.971020 2 63.894 0.881137 3 5.610 0.170550 4 47.668 0.795856 5 26.757 0.590126 6 137.169 0.989666 7 6.568 0.196629 8 7.321 0.216534 9 0.913 0.029981 10 27.921 0.605728 11 3.291 0.103893 12 37.498 0.713475 13 94.594 0.957282 14 23.066 0.536466 15 23.974 0.550278 16 14.084 0.374656 17 72.936 0.912069 18 5.193 0.158947 19 7.665 0.225460 20 1.793 0.058017 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.561519 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-10-25_18:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 -0.7 1.8 -2.3 0.1 1.8 0.8 0.3 -1.0 0.5 -0.8 0.9 -0.3 2.3 -1.2 -1.5 0.1 -0.2 1.4 0.2 0.5 -1.1 -0.6 1.1 -0.2 0.1 -1.1 0.7 -0.5 -0.4 -0.5 -0.4 -1.0 -1.0 0.6 0.1 1.2 -0.1 0.5 -0.1 -1.3 -1.0 1.8 Chi-square with 42 degrees of freedom:42.860036 z-score=0.093838, p-value=0.565883 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-10-25_18:31 Test no p-value 1 0.493601 2 0.116919 3 0.198556 4 0.369440 5 0.488163 6 0.158473 7 0.113524 8 0.577360 9 0.024133 10 0.400994 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.036727 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-10-25_18:31: (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 66509 0.37 66684 0.00 3 25000.00 25110 0.48 24875 0.62 4 6666.67 6703 0.20 6743 0.87 5 1388.89 1391 0.00 1420 0.70 6 238.10 255 1.20 230 0.28 7 34.72 30 0.64 38 0.31 8 4.96 1 3.16 9 3.29 p=0.58367 p=0.58527 Number of rngs required: 691001, p-value: 0.999 RESULTS OF CRAPS TEST for dh-ranFile-2015-10-25_18:31 No. of wins: Observed Expected 98612 98585.9 z-score= 0.117, pvalue=0.54654 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66948 66666.7 1.187 1.187 2 37443 37654.3 1.186 2.373 3 26904 26954.7 0.095 2.469 4 19295 19313.5 0.018 2.486 5 13804 13851.4 0.162 2.649 6 10051 9943.5 1.161 3.810 7 7023 7145.0 2.084 5.894 8 5103 5139.1 0.253 6.147 9 3702 3699.9 0.001 6.148 10 2705 2666.3 0.562 6.710 11 1875 1923.3 1.214 7.925 12 1404 1388.7 0.168 8.092 13 1031 1003.7 0.742 8.834 14 765 726.1 2.080 10.913 15 551 525.8 1.204 12.118 16 348 381.2 2.883 15.001 17 272 276.5 0.075 15.076 18 204 200.8 0.050 15.126 19 163 146.0 1.983 17.109 20 108 106.2 0.030 17.139 21 301 287.1 0.672 17.810 Chisq= 17.81 for 20 degrees of freedom, p= 0.40011 SUMMARY of craptest p-value for no. of wins: 0.546538 p-value for throws/game: 0.400106 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-10-25_18:31 No. of wins: Observed Expected 98665 98585.9 z-score= 0.354, pvalue=0.63832 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66533 66666.7 0.268 0.268 2 37834 37654.3 0.857 1.125 3 26817 26954.7 0.704 1.829 4 19355 19313.5 0.089 1.919 5 13787 13851.4 0.300 2.218 6 9935 9943.5 0.007 2.225 7 7086 7145.0 0.488 2.713 8 5302 5139.1 5.165 7.878 9 3757 3699.9 0.882 8.761 10 2650 2666.3 0.100 8.860 11 1953 1923.3 0.458 9.318 12 1396 1388.7 0.038 9.356 13 950 1003.7 2.875 12.231 14 713 726.1 0.238 12.469 15 539 525.8 0.330 12.798 16 391 381.2 0.255 13.053 17 314 276.5 5.074 18.127 18 198 200.8 0.040 18.167 19 127 146.0 2.469 20.636 20 102 106.2 0.167 20.803 21 261 287.1 2.375 23.178 Chisq= 23.18 for 20 degrees of freedom, p= 0.71987 SUMMARY of craptest p-value for no. of wins: 0.638318 p-value for throws/game: 0.719870 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0016,0.0070,0.0166,0.0175,0.0241,0.0278,0.0300,0.0339,0.0367,0.0380, 0.0416,0.0499,0.0547,0.0572,0.0580,0.0614,0.0617,0.0720,0.0736,0.0787, 0.0806,0.0806,0.0812,0.0845,0.0877,0.0908,0.0925,0.0970,0.0998,0.1022, 0.1039,0.1051,0.1059,0.1070,0.1086,0.1111,0.1135,0.1169,0.1202,0.1252, 0.1263,0.1319,0.1366,0.1376,0.1395,0.1399,0.1442,0.1479,0.1510,0.1585, 0.1589,0.1629,0.1705,0.1751,0.1771,0.1806,0.1841,0.1855,0.1894,0.1928, 0.1928,0.1966,0.1986,0.2035,0.2076,0.2095,0.2165,0.2166,0.2190,0.2255, 0.2320,0.2326,0.2344,0.2371,0.2411,0.2456,0.2466,0.2491,0.2503,0.2518, 0.2536,0.2796,0.2841,0.2920,0.2954,0.2981,0.2988,0.3035,0.3038,0.3056, 0.3150,0.3249,0.3291,0.3307,0.3353,0.3375,0.3406,0.3449,0.3484,0.3495, 0.3646,0.3660,0.3667,0.3694,0.3702,0.3706,0.3746,0.3747,0.3763,0.3767, 0.3777,0.3810,0.3836,0.3914,0.3914,0.3932,0.3968,0.3992,0.4001,0.4010, 0.4082,0.4163,0.4203,0.4284,0.4305,0.4312,0.4324,0.4412,0.4488,0.4527, 0.4604,0.4607,0.4608,0.4620,0.4620,0.4728,0.4745,0.4792,0.4875,0.4882, 0.4889,0.4936,0.4937,0.4940,0.4997,0.5009,0.5109,0.5231,0.5347,0.5365, 0.5465,0.5481,0.5503,0.5530,0.5565,0.5615,0.5659,0.5746,0.5774,0.5826, 0.5837,0.5853,0.5901,0.5975,0.6036,0.6057,0.6074,0.6074,0.6175,0.6227, 0.6308,0.6383,0.6490,0.6525,0.6539,0.6594,0.6608,0.6649,0.6739,0.6741, 0.6790,0.6810,0.6833,0.6845,0.6859,0.6867,0.6923,0.6959,0.6980,0.7066, 0.7125,0.7135,0.7170,0.7186,0.7199,0.7201,0.7221,0.7236,0.7260,0.7299, 0.7375,0.7448,0.7452,0.7575,0.7622,0.7624,0.7675,0.7685,0.7771,0.7864, 0.7902,0.7902,0.7942,0.7944,0.7959,0.7971,0.8097,0.8114,0.8130,0.8326, 0.8382,0.8423,0.8425,0.8444,0.8531,0.8549,0.8577,0.8607,0.8609,0.8627, 0.8638,0.8659,0.8717,0.8722,0.8738,0.8766,0.8789,0.8793,0.8811,0.8820, 0.8912,0.8984,0.9061,0.9069,0.9077,0.9105,0.9121,0.9157,0.9177,0.9191, 0.9210,0.9216,0.9231,0.9270,0.9303,0.9308,0.9319,0.9533,0.9573,0.9617, 0.9688,0.9710,0.9788,0.9796,0.9897,0.9915,0.9918,0.9961,0.9992, Overall p-value after applying KStest on 269 p-values = 0.621489 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.