RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-04-03_13:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 16.12 13.3263 0.285919 2 to 25 15.76 17.4907 0.578370 3 to 26 15.87 16.9084 0.539412 4 to 27 15.69 14.6142 0.376752 5 to 28 16.25 16.6988 0.525056 6 to 29 15.81 19.9219 0.721755 7 to 30 15.99 13.3708 0.288970 8 to 31 15.47 16.0062 0.476603 9 to 32 15.79 27.0557 0.942745 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.505884 Tough bday spacings test for dh-ranFile-2018-04-03_13:31: 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 22 41 79 93 85 72 53 27 15 7 6 (O-E)^2/E 18.0 0.5 0.4 0.2 1.6 0.5 0.0 0.3 0.0 0.0 0.9 Birthday Spacings: Sum(O-E)^2/E= 22.550, p= 0.987 RESULTS OF GCD FOR dh-ranFile-2018-04-03_13:31 Euclid's algorithm: p-value, steps to gcd: 0.398824 p-value, dist. of gcd's: 0.112120 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-04-03_13:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.299 0.676 0.312 0.524 0.086 0.754 0.463 0.770 Bits 8 to 15---> 0.445 0.538 0.218 0.578 0.877 0.342 0.159 0.439 Bits 16 to 23---> 0.327 0.488 0.484 0.940 0.163 0.191 0.235 0.981 Bits 24 to 31---> 0.270 0.960 0.752 0.377 0.543 0.600 0.627 0.581 KS test for the above 32 p values: 0.532 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-04-03_13:31, p-values for 5 runs: 0.4540, 0.6815, 0.2083, 0.6149, 0.8889 Rank test for binary matrices (31x31) for dh-ranFile-2018-04-03_13:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 213 211.4 0.012 0.012 r= 29 5189 5134.0 0.589 0.601 r= 30 22923 23103.0 1.403 2.004 r= 31 11675 11551.5 1.320 3.324 chi-square = 3.324 with df = 3; p-value = 0.656 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-04-03_13:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 213 211.4 0.012 0.012 r= 30 5117 5134.0 0.056 0.068 r= 31 23130 23103.0 0.031 0.100 r= 32 11540 11551.5 0.011 0.111 chi-square = 0.111 with df = 3; p-value = 0.010 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-04-03_13:31 b-rank test for bits 1 to 8, p=0.95252 b-rank test for bits 2 to 9, p=0.11786 b-rank test for bits 3 to 10, p=0.62649 b-rank test for bits 4 to 11, p=0.55413 b-rank test for bits 5 to 12, p=0.00028 b-rank test for bits 6 to 13, p=0.94197 b-rank test for bits 7 to 14, p=0.09317 b-rank test for bits 8 to 15, p=0.19759 b-rank test for bits 9 to 16, p=0.85176 b-rank test for bits 10 to 17, p=0.30420 b-rank test for bits 11 to 18, p=0.91061 b-rank test for bits 12 to 19, p=0.80714 b-rank test for bits 13 to 20, p=0.54426 b-rank test for bits 14 to 21, p=0.69942 b-rank test for bits 15 to 22, p=0.45030 b-rank test for bits 16 to 23, p=0.68752 b-rank test for bits 17 to 24, p=0.96091 b-rank test for bits 18 to 25, p=0.61869 b-rank test for bits 19 to 26, p=0.25321 b-rank test for bits 20 to 27, p=0.86735 b-rank test for bits 21 to 28, p=0.53022 b-rank test for bits 22 to 29, p=0.72891 b-rank test for bits 23 to 30, p=0.32103 b-rank test for bits 24 to 31, p=0.72140 b-rank test for bits 25 to 32, p=0.93275 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 = 0.174306 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-04-03_13:31 (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 142010 0.24 0.592977 2 141862 -0.11 0.455973 3 141797 -0.26 0.396486 4 141873 -0.08 0.466177 5 141835 -0.17 0.431063 6 141898 -0.03 0.489440 7 142211 0.70 0.759544 8 142378 1.10 0.863247 9 142042 0.31 0.621711 10 142037 0.30 0.617261 11 142245 0.78 0.783561 12 141676 -0.55 0.292821 13 141355 -1.30 0.097632 14 141990 0.19 0.574750 15 141607 -0.71 0.239976 16 142649 1.73 0.958024 17 142042 0.31 0.621711 18 142358 1.05 0.852749 19 141930 0.05 0.519259 20 141736 -0.40 0.342747 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-04-03_13:31 Bits used No. missing words z-score p-value 23 to 32 141961 0.1782 0.570706 22 to 31 142088 0.6161 0.731087 21 to 30 141201 -2.4425 0.007293 20 to 29 141986 0.2644 0.604256 19 to 28 142007 0.3368 0.631864 18 to 27 141740 -0.5839 0.279645 17 to 26 141878 -0.1080 0.456984 16 to 25 141973 0.2196 0.586890 15 to 24 141918 0.0299 0.511925 14 to 23 141584 -1.1218 0.130968 13 to 22 141808 -0.3494 0.363389 12 to 21 141936 0.0920 0.536637 11 to 20 141402 -1.7494 0.040110 10 to 19 141632 -0.9563 0.169458 9 to 18 141676 -0.8046 0.210529 8 to 17 141996 0.2989 0.617477 7 to 16 142278 1.2713 0.898185 6 to 15 141923 0.0471 0.518798 5 to 14 141916 0.0230 0.509175 4 to 13 141400 -1.7563 0.039518 3 to 12 141787 -0.4218 0.336575 2 to 11 141901 -0.0287 0.488542 1 to 10 141746 -0.5632 0.286647 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-04-03_13:31 Bits used No. missing words z-score p-value 28 to 32 141901 -0.0282 0.488737 27 to 31 142461 1.8701 0.969263 26 to 30 141799 -0.3740 0.354202 25 to 29 141841 -0.2316 0.408414 24 to 28 141696 -0.7232 0.234793 23 to 27 141381 -1.7909 0.036651 22 to 26 142595 2.3243 0.989945 21 to 25 142354 1.5074 0.934140 20 to 24 141177 -2.4825 0.006524 19 to 23 141969 0.2023 0.580148 18 to 22 141764 -0.4926 0.311132 17 to 21 141760 -0.5062 0.306357 16 to 20 142001 0.3107 0.622003 15 to 19 142470 1.9006 0.971321 14 to 18 141660 -0.8452 0.199003 13 to 17 142090 0.6124 0.729877 12 to 16 141954 0.1514 0.560179 11 to 15 141442 -1.5842 0.056578 10 to 14 142298 1.3175 0.906169 9 to 13 141714 -0.6621 0.253942 8 to 12 141831 -0.2655 0.395302 7 to 11 141577 -1.1265 0.129968 6 to 10 142031 0.4124 0.659992 5 to 9 141894 -0.0520 0.479278 4 to 8 141860 -0.1672 0.433598 3 to 7 141900 -0.0316 0.487385 2 to 6 141542 -1.2452 0.106532 1 to 5 142234 1.1006 0.864459 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-04-03_13:31 Bits used No. missing words z-score p-value 31 to 32 141410 -1.4729 0.070382 30 to 31 142028 0.3501 0.636853 29 to 30 141930 0.0610 0.524310 28 to 29 141417 -1.4523 0.073209 27 to 28 142037 0.3766 0.646767 26 to 27 141575 -0.9862 0.162012 25 to 26 142204 0.8692 0.807640 24 to 25 142172 0.7748 0.780782 23 to 24 142062 0.4504 0.673772 22 to 23 142282 1.0993 0.864186 21 to 22 141605 -0.8977 0.184665 20 to 21 142239 0.9725 0.834594 19 to 20 142032 0.3619 0.641271 18 to 19 141674 -0.6942 0.243782 17 to 18 142206 0.8751 0.809249 16 to 17 142283 1.1023 0.864828 15 to 16 142101 0.5654 0.714099 14 to 15 141898 -0.0334 0.486669 13 to 14 141558 -1.0364 0.150014 12 to 13 142235 0.9607 0.831643 11 to 12 142322 1.2173 0.888258 10 to 11 141651 -0.7620 0.223019 9 to 10 141473 -1.2871 0.099028 8 to 9 142145 0.6952 0.756532 7 to 8 141841 -0.2016 0.420129 6 to 7 141618 -0.8594 0.195065 5 to 6 142236 0.9636 0.832384 4 to 5 142290 1.1229 0.869264 3 to 4 141686 -0.6588 0.255015 2 to 3 141826 -0.2458 0.402914 1 to 2 141997 0.2586 0.602033 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-04-03_13:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2544.94 0.635 0.737444 Test results for specific bytes for dh-ranFile-2018-04-03_13:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2588.60 1.253 0.894891 2 to 9 2597.72 1.382 0.916504 3 to 10 2459.35 -0.575 0.282684 4 to 11 2486.03 -0.198 0.421698 5 to 12 2401.68 -1.390 0.082200 6 to 13 2433.87 -0.935 0.174827 7 to 14 2562.03 0.877 0.809837 8 to 15 2706.19 2.916 0.998227 9 to 16 2640.68 1.989 0.976676 10 to 17 2578.93 1.116 0.867835 11 to 18 2518.11 0.256 0.601083 12 to 19 2441.96 -0.821 0.205864 13 to 20 2489.89 -0.143 0.443181 14 to 21 2545.69 0.646 0.740923 15 to 22 2425.52 -1.053 0.146104 16 to 23 2545.71 0.646 0.741001 17 to 24 2490.01 -0.141 0.443848 18 to 25 2412.02 -1.244 0.106712 19 to 26 2431.99 -0.962 0.168076 20 to 27 2523.20 0.328 0.628567 21 to 28 2483.53 -0.233 0.407885 22 to 29 2382.88 -1.656 0.048832 23 to 30 2487.41 -0.178 0.429350 24 to 31 2534.12 0.482 0.685268 25 to 32 2486.81 -0.186 0.426034 CDPARK for dh-ranFile-2018-04-03_13:31: 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 3529 0.2740 0.607947 3547 1.0959 0.863437 3527 0.1826 0.572463 3475 -2.1918 0.014198 3528 0.2283 0.590298 3539 0.7306 0.767486 3544 0.9589 0.831196 3506 -0.7763 0.218799 3562 1.7808 0.962529 3500 -1.0502 0.146807 Square side=100, avg. no. parked=3525.70 sample std.=24.33 p-value of the KSTEST for those 10 p-values: 0.696929 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-04-03_13:31 0.8702,0.6754,0.8606,0.6954,0.8052,0.6662,0.4579,0.7525,0.6268,0.3100, The KS test for those 10 p-values: 0.056933 The 3DSPHERES test for dh-ranFile-2018-04-03_13:31 sample no r^3 equiv. uni. 1 13.485 0.362048 2 1.123 0.036755 3 17.577 0.443403 4 30.683 0.640399 5 19.370 0.475684 6 93.769 0.956091 7 9.101 0.261675 8 34.306 0.681307 9 11.779 0.324724 10 79.681 0.929774 11 12.120 0.332355 12 41.173 0.746509 13 19.601 0.479703 14 27.236 0.596621 15 68.608 0.898421 16 30.404 0.637041 17 12.820 0.347758 18 0.643 0.021208 19 4.214 0.131038 20 80.878 0.932520 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.926050 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-04-03_13:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -0.7 2.3 -0.1 -0.8 2.6 0.2 -0.3 -0.3 -0.8 -0.3 2.1 -0.7 -2.0 0.8 -1.0 0.7 0.1 2.1 -0.9 1.3 1.0 -1.9 -1.3 0.4 -1.4 -1.1 1.1 0.6 1.3 0.9 -0.5 -0.4 -1.2 -1.7 1.0 -0.2 -0.7 0.5 -0.1 -0.6 0.0 -0.1 Chi-square with 42 degrees of freedom:52.679151 z-score=1.165191, p-value=0.874991 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-04-03_13:31 Test no p-value 1 0.188408 2 0.230647 3 0.215450 4 0.744200 5 0.862100 6 0.712010 7 0.037131 8 0.490113 9 0.501403 10 0.077487 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.518126 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-04-03_13:31: (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 66572 0.13 66666 0.00 3 25000.00 25084 0.28 25062 0.15 4 6666.67 6643 0.08 6647 0.06 5 1388.89 1400 0.09 1350 1.09 6 238.10 254 1.06 234 0.07 7 34.72 41 1.14 33 0.09 8 4.96 5 0.00 7 0.84 p=0.16508 p=0.10938 Number of rngs required: 688749, p-value: 0.655 RESULTS OF CRAPS TEST for dh-ranFile-2018-04-03_13:31 No. of wins: Observed Expected 98600 98585.9 z-score= 0.063, pvalue=0.52522 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66669 66666.7 0.000 0.000 2 37574 37654.3 0.171 0.171 3 26903 26954.7 0.099 0.271 4 19311 19313.5 0.000 0.271 5 13984 13851.4 1.269 1.540 6 10051 9943.5 1.161 2.701 7 7077 7145.0 0.648 3.349 8 5069 5139.1 0.955 4.304 9 3750 3699.9 0.679 4.984 10 2642 2666.3 0.221 5.205 11 1949 1923.3 0.343 5.548 12 1391 1388.7 0.004 5.551 13 967 1003.7 1.343 6.894 14 738 726.1 0.194 7.088 15 499 525.8 1.370 8.458 16 410 381.2 2.184 10.641 17 266 276.5 0.402 11.043 18 202 200.8 0.007 11.050 19 161 146.0 1.544 12.594 20 109 106.2 0.073 12.667 21 278 287.1 0.289 12.957 Chisq= 12.96 for 20 degrees of freedom, p= 0.12076 SUMMARY of craptest p-value for no. of wins: 0.525216 p-value for throws/game: 0.120762 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-04-03_13:31 No. of wins: Observed Expected 98608 98585.9 z-score= 0.099, pvalue=0.53944 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66812 66666.7 0.317 0.317 2 37907 37654.3 1.696 2.012 3 26926 26954.7 0.031 2.043 4 19212 19313.5 0.533 2.576 5 13664 13851.4 2.536 5.112 6 9988 9943.5 0.199 5.311 7 7019 7145.0 2.223 7.534 8 5042 5139.1 1.834 9.367 9 3799 3699.9 2.656 12.023 10 2679 2666.3 0.061 12.084 11 1934 1923.3 0.059 12.143 12 1365 1388.7 0.406 12.549 13 1028 1003.7 0.588 13.137 14 734 726.1 0.085 13.222 15 526 525.8 0.000 13.222 16 378 381.2 0.026 13.248 17 261 276.5 0.873 14.121 18 178 200.8 2.595 16.716 19 142 146.0 0.109 16.825 20 109 106.2 0.073 16.898 21 297 287.1 0.340 17.238 Chisq= 17.24 for 20 degrees of freedom, p= 0.36256 SUMMARY of craptest p-value for no. of wins: 0.539443 p-value for throws/game: 0.362557 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0003,0.0065,0.0073,0.0095,0.0142,0.0212,0.0367,0.0368,0.0371,0.0395, 0.0401,0.0488,0.0566,0.0569,0.0704,0.0732,0.0775,0.0822,0.0860,0.0932, 0.0976,0.0990,0.1065,0.1067,0.1094,0.1121,0.1179,0.1208,0.1300,0.1310, 0.1310,0.1461,0.1468,0.1500,0.1593,0.1620,0.1626,0.1651,0.1681,0.1695, 0.1743,0.1748,0.1847,0.1884,0.1912,0.1951,0.1976,0.1990,0.2059,0.2083, 0.2105,0.2154,0.2177,0.2188,0.2230,0.2306,0.2348,0.2350,0.2400,0.2438, 0.2532,0.2539,0.2550,0.2617,0.2703,0.2796,0.2827,0.2859,0.2866,0.2890, 0.2928,0.2990,0.3042,0.3064,0.3100,0.3111,0.3124,0.3210,0.3247,0.3272, 0.3324,0.3366,0.3417,0.3427,0.3478,0.3542,0.3620,0.3626,0.3634,0.3768, 0.3772,0.3953,0.3965,0.3988,0.4029,0.4079,0.4084,0.4201,0.4217,0.4260, 0.4293,0.4311,0.4336,0.4395,0.4432,0.4434,0.4438,0.4447,0.4503,0.4540, 0.4560,0.4570,0.4579,0.4626,0.4662,0.4757,0.4766,0.4793,0.4797,0.4843, 0.4867,0.4874,0.4883,0.4885,0.4887,0.4894,0.4901,0.5014,0.5059,0.5092, 0.5119,0.5181,0.5188,0.5193,0.5240,0.5243,0.5251,0.5252,0.5302,0.5316, 0.5366,0.5377,0.5394,0.5394,0.5427,0.5443,0.5541,0.5602,0.5707,0.5725, 0.5748,0.5781,0.5784,0.5801,0.5810,0.5869,0.5903,0.5930,0.5966,0.6001, 0.6011,0.6020,0.6043,0.6079,0.6149,0.6173,0.6175,0.6187,0.6217,0.6217, 0.6220,0.6265,0.6268,0.6274,0.6286,0.6319,0.6369,0.6370,0.6404,0.6413, 0.6468,0.6549,0.6557,0.6600,0.6662,0.6738,0.6754,0.6757,0.6813,0.6815, 0.6853,0.6875,0.6954,0.6969,0.6994,0.7120,0.7141,0.7214,0.7218,0.7289, 0.7299,0.7311,0.7374,0.7409,0.7410,0.7442,0.7465,0.7525,0.7525,0.7538, 0.7565,0.7595,0.7675,0.7701,0.7808,0.7836,0.8052,0.8071,0.8076,0.8092, 0.8098,0.8312,0.8316,0.8324,0.8346,0.8518,0.8527,0.8606,0.8621,0.8632, 0.8634,0.8642,0.8645,0.8648,0.8673,0.8678,0.8693,0.8702,0.8750,0.8775, 0.8883,0.8889,0.8949,0.8982,0.8984,0.9062,0.9106,0.9165,0.9260,0.9298, 0.9325,0.9327,0.9341,0.9402,0.9420,0.9427,0.9525,0.9561,0.9580,0.9603, 0.9609,0.9625,0.9693,0.9713,0.9767,0.9813,0.9875,0.9899,0.9982, Overall p-value after applying KStest on 269 p-values = 0.439028 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.