RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-27_09:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.47 28.7291 0.962893 2 to 25 15.78 20.8926 0.768869 3 to 26 15.89 17.5793 0.584164 4 to 27 16.02 19.8275 0.716852 5 to 28 15.87 16.2001 0.490306 6 to 29 15.43 16.7854 0.531002 7 to 30 15.67 21.5920 0.799077 8 to 31 15.84 18.1001 0.617445 9 to 32 15.39 23.3726 0.862491 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.046274 Tough bday spacings test for dh-ranFile-2018-06-27_09:31: 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 9 32 78 93 104 71 55 29 17 8 4 (O-E)^2/E 0.0 0.6 0.3 0.2 0.4 0.7 0.2 0.0 0.3 0.3 0.0 Birthday Spacings: Sum(O-E)^2/E= 2.954, p= 0.018 RESULTS OF GCD FOR dh-ranFile-2018-06-27_09:31 Euclid's algorithm: p-value, steps to gcd: 0.367617 p-value, dist. of gcd's: 0.119144 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-27_09:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.717 0.990 0.975 0.281 0.680 0.339 0.621 0.273 Bits 8 to 15---> 0.355 0.008 0.763 0.094 0.742 0.801 0.804 0.188 Bits 16 to 23---> 0.213 0.095 0.924 0.867 0.166 0.472 0.714 0.918 Bits 24 to 31---> 0.795 0.210 0.202 0.106 0.893 0.749 0.393 0.360 KS test for the above 32 p values: 0.340 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-27_09:31, p-values for 5 runs: 0.3927, 0.6323, 0.5840, 0.3564, 0.0591 Rank test for binary matrices (31x31) for dh-ranFile-2018-06-27_09:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 215 211.4 0.061 0.061 r= 29 5155 5134.0 0.086 0.146 r= 30 23030 23103.0 0.231 0.377 r= 31 11600 11551.5 0.203 0.581 chi-square = 0.581 with df = 3; p-value = 0.099 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-06-27_09:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 194 211.4 1.435 1.435 r= 30 5151 5134.0 0.056 1.491 r= 31 23054 23103.0 0.104 1.595 r= 32 11601 11551.5 0.212 1.807 chi-square = 1.807 with df = 3; p-value = 0.387 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-06-27_09:31 b-rank test for bits 1 to 8, p=0.63959 b-rank test for bits 2 to 9, p=0.53473 b-rank test for bits 3 to 10, p=0.74616 b-rank test for bits 4 to 11, p=0.62223 b-rank test for bits 5 to 12, p=0.36803 b-rank test for bits 6 to 13, p=0.12529 b-rank test for bits 7 to 14, p=0.09505 b-rank test for bits 8 to 15, p=0.35791 b-rank test for bits 9 to 16, p=0.42248 b-rank test for bits 10 to 17, p=0.06189 b-rank test for bits 11 to 18, p=0.96535 b-rank test for bits 12 to 19, p=0.87753 b-rank test for bits 13 to 20, p=0.81248 b-rank test for bits 14 to 21, p=0.98036 b-rank test for bits 15 to 22, p=0.67007 b-rank test for bits 16 to 23, p=0.84944 b-rank test for bits 17 to 24, p=0.87417 b-rank test for bits 18 to 25, p=0.57504 b-rank test for bits 19 to 26, p=0.97885 b-rank test for bits 20 to 27, p=0.91703 b-rank test for bits 21 to 28, p=0.81656 b-rank test for bits 22 to 29, p=0.88296 b-rank test for bits 23 to 30, p=0.38967 b-rank test for bits 24 to 31, p=0.53610 b-rank test for bits 25 to 32, p=0.56906 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 = 0.040830 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-27_09:31 (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 141294 -1.44 0.075261 2 141570 -0.79 0.213939 3 141760 -0.35 0.363582 4 141848 -0.14 0.443029 5 142749 1.96 0.975110 6 141662 -0.58 0.281675 7 141655 -0.59 0.276180 8 142443 1.25 0.893782 9 142642 1.71 0.956537 10 142059 0.35 0.636717 11 142068 0.37 0.644579 12 141778 -0.31 0.379480 13 141694 -0.50 0.307444 14 142437 1.23 0.891189 15 142802 2.09 0.981496 16 141953 0.10 0.540635 17 141284 -1.46 0.072001 18 141159 -1.75 0.039792 19 141842 -0.16 0.437499 20 142802 2.09 0.981496 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-06-27_09:31 Bits used No. missing words z-score p-value 23 to 32 141449 -1.5873 0.056217 22 to 31 141862 -0.1632 0.435178 21 to 30 141999 0.3092 0.621418 20 to 29 141504 -1.3977 0.081103 19 to 28 141843 -0.2287 0.409542 18 to 27 142019 0.3782 0.647349 17 to 26 141773 -0.4701 0.319141 16 to 25 141889 -0.0701 0.472056 15 to 24 141328 -2.0046 0.022504 14 to 23 141667 -0.8356 0.201684 13 to 22 141907 -0.0080 0.496795 12 to 21 141505 -1.3942 0.081622 11 to 20 141938 0.0989 0.539376 10 to 19 141822 -0.3011 0.381655 9 to 18 141581 -1.1322 0.128781 8 to 17 142041 0.4540 0.675098 7 to 16 141692 -0.7494 0.226804 6 to 15 142148 0.8230 0.794746 5 to 14 141944 0.1196 0.547581 4 to 13 142179 0.9299 0.823788 3 to 12 142315 1.3989 0.919073 2 to 11 142069 0.5506 0.709041 1 to 10 142277 1.2678 0.897570 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-06-27_09:31 Bits used No. missing words z-score p-value 28 to 32 142011 0.3446 0.634819 27 to 31 142260 1.1887 0.882723 26 to 30 141762 -0.4994 0.308741 25 to 29 142091 0.6158 0.730997 24 to 28 142097 0.6362 0.737667 23 to 27 142067 0.5345 0.703493 22 to 26 142433 1.7752 0.962064 21 to 25 142141 0.7853 0.783868 20 to 24 141980 0.2396 0.594664 19 to 23 141713 -0.6655 0.252857 18 to 22 142364 1.5413 0.938373 17 to 21 142130 0.7480 0.772780 16 to 20 141983 0.2497 0.598602 15 to 19 142321 1.3955 0.918566 14 to 18 141984 0.2531 0.599912 13 to 17 141797 -0.3808 0.351683 12 to 16 142122 0.7209 0.764519 11 to 15 142388 1.6226 0.947664 10 to 14 141869 -0.1367 0.445629 9 to 13 142207 1.0091 0.843525 8 to 12 141657 -0.8554 0.196177 7 to 11 141607 -1.0248 0.152718 6 to 10 142459 1.8633 0.968789 5 to 9 141667 -0.8215 0.205693 4 to 8 141502 -1.3808 0.083673 3 to 7 141503 -1.3774 0.084196 2 to 6 141555 -1.2011 0.114853 1 to 5 142080 0.5785 0.718551 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-06-27_09:31 Bits used No. missing words z-score p-value 31 to 32 141592 -0.9361 0.174617 30 to 31 141878 -0.0924 0.463183 29 to 30 141542 -1.0836 0.139278 28 to 29 142201 0.8604 0.805211 27 to 28 142103 0.5713 0.716101 26 to 27 141986 0.2262 0.589464 25 to 26 142048 0.4091 0.658751 24 to 25 141880 -0.0865 0.465527 23 to 24 141274 -1.8741 0.030456 22 to 23 142197 0.8486 0.801944 21 to 22 142049 0.4120 0.659832 20 to 21 142212 0.8928 0.814026 19 to 20 142035 0.3707 0.644573 18 to 19 142156 0.7276 0.766583 17 to 18 141545 -1.0747 0.141250 16 to 17 142219 0.9135 0.819505 15 to 16 141594 -0.9302 0.176140 14 to 15 141335 -1.6942 0.045115 13 to 14 142018 0.3206 0.625728 12 to 13 141722 -0.5526 0.290270 11 to 12 141959 0.1465 0.558244 10 to 11 142016 0.3147 0.623490 9 to 10 141655 -0.7502 0.226556 8 to 9 141526 -1.1308 0.129077 7 to 8 142438 1.5595 0.940561 6 to 7 141559 -1.0334 0.150703 5 to 6 141944 0.1023 0.540729 4 to 5 141813 -0.2842 0.388144 3 to 4 141694 -0.6352 0.262652 2 to 3 141878 -0.0924 0.463183 1 to 2 142224 0.9282 0.823356 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-27_09:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2523.01 0.325 0.627545 Test results for specific bytes for dh-ranFile-2018-06-27_09:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2466.17 -0.478 0.316185 2 to 9 2580.54 1.139 0.872650 3 to 10 2455.58 -0.628 0.264940 4 to 11 2597.16 1.374 0.915296 5 to 12 2601.74 1.439 0.924907 6 to 13 2621.62 1.720 0.957282 7 to 14 2383.58 -1.646 0.049839 8 to 15 2580.36 1.137 0.872132 9 to 16 2416.68 -1.178 0.119344 10 to 17 2503.97 0.056 0.522379 11 to 18 2517.15 0.243 0.595825 12 to 19 2584.55 1.196 0.884083 13 to 20 2487.09 -0.183 0.427574 14 to 21 2436.53 -0.898 0.184692 15 to 22 2454.20 -0.648 0.258583 16 to 23 2615.71 1.636 0.949120 17 to 24 2523.65 0.334 0.630984 18 to 25 2433.23 -0.944 0.172506 19 to 26 2484.67 -0.217 0.414162 20 to 27 2499.18 -0.012 0.495388 21 to 28 2423.71 -1.079 0.140302 22 to 29 2478.85 -0.299 0.382437 23 to 30 2354.72 -2.055 0.019958 24 to 31 2597.59 1.380 0.916220 25 to 32 2550.30 0.711 0.761584 CDPARK for dh-ranFile-2018-06-27_09:31: 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 3550 1.2329 0.891189 3554 1.4155 0.921543 3520 -0.1370 0.445521 3542 0.8676 0.807188 3507 -0.7306 0.232514 3502 -0.9589 0.168804 3514 -0.4110 0.340551 3471 -2.3744 0.008788 3504 -0.8676 0.192812 3522 -0.0457 0.481790 Square side=100, avg. no. parked=3518.60 sample std.=23.90 p-value of the KSTEST for those 10 p-values: 0.726297 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-27_09:31 0.8947,0.1508,0.3734,0.3274,0.2009,0.9243,0.4075,0.8121,0.9345,0.5382, The KS test for those 10 p-values: 0.632728 The 3DSPHERES test for dh-ranFile-2018-06-27_09:31 sample no r^3 equiv. uni. 1 55.914 0.844920 2 8.615 0.249621 3 15.328 0.400063 4 0.786 0.025875 5 28.706 0.615911 6 56.697 0.848912 7 2.901 0.092162 8 91.300 0.952324 9 12.448 0.339612 10 9.187 0.263796 11 11.694 0.322819 12 1.578 0.051249 13 10.099 0.285827 14 41.622 0.750280 15 79.342 0.928975 16 1.660 0.053836 17 9.766 0.277869 18 28.013 0.606934 19 1.136 0.037148 20 107.529 0.972244 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.295526 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-27_09:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 -0.7 0.6 -0.3 -1.6 0.5 0.3 -1.2 -0.8 -1.4 -1.1 0.2 0.5 2.0 -0.1 1.9 -2.3 -0.9 0.2 1.1 1.1 -1.6 1.0 0.6 -0.1 0.6 -2.1 0.2 -1.0 0.9 1.0 0.8 -1.1 0.9 0.2 -1.4 -0.5 -1.3 -1.6 -0.7 -0.6 0.0 0.8 Chi-square with 42 degrees of freedom:47.772793 z-score=0.629863, p-value=0.750208 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-06-27_09:31 Test no p-value 1 0.195260 2 0.640587 3 0.120499 4 0.020125 5 0.036209 6 0.331303 7 0.583449 8 0.307828 9 0.476432 10 0.052098 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.019096 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-27_09:31: (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 66704 0.02 66802 0.27 3 25000.00 25072 0.21 25013 0.01 4 6666.67 6546 2.18 6553 1.94 5 1388.89 1407 0.24 1343 1.52 6 238.10 232 0.16 232 0.16 7 34.72 33 0.09 45 3.04 8 4.96 5 0.00 11 7.36 p=0.17750 p=0.97345 Number of rngs required: 688114, p-value: 0.370 RESULTS OF CRAPS TEST for dh-ranFile-2018-06-27_09:31 No. of wins: Observed Expected 98611 98585.9 z-score= 0.112, pvalue=0.54477 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66827 66666.7 0.386 0.386 2 37375 37654.3 2.072 2.458 3 26924 26954.7 0.035 2.493 4 19383 19313.5 0.250 2.743 5 13864 13851.4 0.011 2.754 6 10016 9943.5 0.528 3.282 7 7115 7145.0 0.126 3.409 8 5093 5139.1 0.413 3.822 9 3802 3699.9 2.819 6.641 10 2596 2666.3 1.853 8.494 11 1960 1923.3 0.699 9.194 12 1386 1388.7 0.005 9.199 13 1050 1003.7 2.134 11.333 14 693 726.1 1.513 12.846 15 540 525.8 0.382 13.227 16 387 381.2 0.090 13.317 17 286 276.5 0.324 13.641 18 205 200.8 0.087 13.728 19 132 146.0 1.340 15.067 20 98 106.2 0.635 15.703 21 268 287.1 1.272 16.975 Chisq= 16.98 for 20 degrees of freedom, p= 0.34540 SUMMARY of craptest p-value for no. of wins: 0.544766 p-value for throws/game: 0.345404 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-27_09:31 No. of wins: Observed Expected 98444 98585.9 z-score=-0.634, pvalue=0.26289 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66454 66666.7 0.678 0.678 2 37746 37654.3 0.223 0.902 3 27017 26954.7 0.144 1.045 4 19477 19313.5 1.385 2.430 5 14017 13851.4 1.979 4.410 6 10003 9943.5 0.356 4.765 7 7051 7145.0 1.237 6.002 8 5035 5139.1 2.108 8.110 9 3714 3699.9 0.054 8.164 10 2562 2666.3 4.080 12.244 11 1960 1923.3 0.699 12.943 12 1363 1388.7 0.477 13.420 13 973 1003.7 0.940 14.360 14 715 726.1 0.171 14.531 15 523 525.8 0.015 14.546 16 386 381.2 0.062 14.608 17 290 276.5 0.655 15.263 18 206 200.8 0.133 15.396 19 135 146.0 0.827 16.223 20 89 106.2 2.790 19.013 21 284 287.1 0.034 19.047 Chisq= 19.05 for 20 degrees of freedom, p= 0.48121 SUMMARY of craptest p-value for no. of wins: 0.262886 p-value for throws/game: 0.481209 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0079,0.0088,0.0175,0.0191,0.0200,0.0201,0.0225,0.0259,0.0305,0.0362, 0.0371,0.0398,0.0408,0.0451,0.0463,0.0498,0.0512,0.0521,0.0538,0.0562, 0.0591,0.0619,0.0720,0.0753,0.0811,0.0816,0.0837,0.0842,0.0922,0.0939, 0.0951,0.0954,0.0992,0.1064,0.1149,0.1191,0.1193,0.1205,0.1253,0.1288, 0.1291,0.1393,0.1403,0.1413,0.1507,0.1508,0.1527,0.1659,0.1688,0.1725, 0.1746,0.1761,0.1775,0.1847,0.1877,0.1928,0.1953,0.1962,0.2009,0.2017, 0.2021,0.2057,0.2104,0.2133,0.2139,0.2266,0.2268,0.2325,0.2496,0.2529, 0.2586,0.2627,0.2629,0.2638,0.2649,0.2726,0.2762,0.2779,0.2813,0.2817, 0.2858,0.2903,0.2955,0.3074,0.3078,0.3087,0.3162,0.3191,0.3228,0.3274, 0.3313,0.3386,0.3396,0.3402,0.3406,0.3454,0.3517,0.3553,0.3564,0.3579, 0.3595,0.3636,0.3676,0.3680,0.3697,0.3734,0.3795,0.3817,0.3824,0.3866, 0.3881,0.3897,0.3927,0.3934,0.4001,0.4075,0.4095,0.4142,0.4225,0.4276, 0.4352,0.4375,0.4430,0.4455,0.4456,0.4632,0.4632,0.4655,0.4715,0.4721, 0.4764,0.4812,0.4818,0.4903,0.4954,0.4968,0.5224,0.5310,0.5347,0.5361, 0.5382,0.5394,0.5406,0.5407,0.5448,0.5476,0.5582,0.5691,0.5750,0.5834, 0.5840,0.5842,0.5895,0.5947,0.5958,0.5986,0.5999,0.6069,0.6159,0.6174, 0.6209,0.6214,0.6222,0.6235,0.6257,0.6275,0.6310,0.6323,0.6327,0.6348, 0.6367,0.6396,0.6406,0.6446,0.6446,0.6473,0.6588,0.6598,0.6701,0.6751, 0.6801,0.7035,0.7090,0.7135,0.7161,0.7169,0.7169,0.7186,0.7263,0.7310, 0.7377,0.7424,0.7462,0.7491,0.7502,0.7503,0.7616,0.7628,0.7645,0.7666, 0.7689,0.7728,0.7839,0.7947,0.7952,0.7991,0.8007,0.8019,0.8042,0.8052, 0.8072,0.8121,0.8125,0.8140,0.8166,0.8195,0.8234,0.8238,0.8435,0.8449, 0.8489,0.8494,0.8625,0.8665,0.8721,0.8726,0.8742,0.8775,0.8827,0.8830, 0.8841,0.8912,0.8912,0.8929,0.8938,0.8947,0.8976,0.9153,0.9162,0.9170, 0.9177,0.9186,0.9191,0.9215,0.9235,0.9243,0.9249,0.9290,0.9345,0.9384, 0.9406,0.9477,0.9491,0.9523,0.9565,0.9573,0.9621,0.9629,0.9653,0.9688, 0.9722,0.9734,0.9750,0.9751,0.9788,0.9804,0.9815,0.9815,0.9897, Overall p-value after applying KStest on 269 p-values = 0.586811 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.