RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-09_23:31 (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 13.2252 0.279013 2 to 25 15.64 29.5556 0.970266 3 to 26 15.97 15.2836 0.424940 4 to 27 15.67 22.9282 0.848396 5 to 28 15.44 27.8648 0.953457 6 to 29 15.77 15.3284 0.428160 7 to 30 15.64 24.1069 0.883441 8 to 31 15.86 10.3483 0.111627 9 to 32 15.46 29.9875 0.973564 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.057401 Tough bday spacings test for dh-ranFile-2018-07-09_23:31: 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 8 30 76 105 95 75 53 35 15 7 1 (O-E)^2/E 0.1 1.2 0.1 0.5 0.1 0.1 0.0 0.9 0.0 0.0 2.3 Birthday Spacings: Sum(O-E)^2/E= 5.467, p= 0.142 RESULTS OF GCD FOR dh-ranFile-2018-07-09_23:31 Euclid's algorithm: p-value, steps to gcd: 0.931191 p-value, dist. of gcd's: 0.926617 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-09_23:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.612 0.531 0.641 0.470 0.335 0.644 0.844 0.561 Bits 8 to 15---> 0.673 0.153 0.941 0.343 0.319 0.662 0.676 0.389 Bits 16 to 23---> 0.312 0.581 0.208 0.113 0.343 0.913 0.577 0.975 Bits 24 to 31---> 0.676 0.053 0.416 0.796 0.130 0.017 0.762 0.052 KS test for the above 32 p values: 0.095 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-09_23:31, p-values for 5 runs: 0.1514, 0.4859, 0.9603, 0.7011, 0.7580 Rank test for binary matrices (31x31) for dh-ranFile-2018-07-09_23:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 218 211.4 0.205 0.205 r= 29 5213 5134.0 1.215 1.420 r= 30 22853 23103.0 2.706 4.127 r= 31 11716 11551.5 2.342 6.468 chi-square = 6.468 with df = 3; p-value = 0.909 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-07-09_23:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 207 211.4 0.092 0.092 r= 30 5153 5134.0 0.070 0.163 r= 31 23185 23103.0 0.291 0.453 r= 32 11455 11551.5 0.807 1.260 chi-square = 1.260 with df = 3; p-value = 0.261 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-07-09_23:31 b-rank test for bits 1 to 8, p=0.20515 b-rank test for bits 2 to 9, p=0.38037 b-rank test for bits 3 to 10, p=0.00368 b-rank test for bits 4 to 11, p=0.05575 b-rank test for bits 5 to 12, p=0.36308 b-rank test for bits 6 to 13, p=0.63181 b-rank test for bits 7 to 14, p=0.10613 b-rank test for bits 8 to 15, p=0.16531 b-rank test for bits 9 to 16, p=0.99226 b-rank test for bits 10 to 17, p=0.47850 b-rank test for bits 11 to 18, p=0.27202 b-rank test for bits 12 to 19, p=0.35036 b-rank test for bits 13 to 20, p=0.68626 b-rank test for bits 14 to 21, p=0.64551 b-rank test for bits 15 to 22, p=0.33030 b-rank test for bits 16 to 23, p=0.11693 b-rank test for bits 17 to 24, p=0.27803 b-rank test for bits 18 to 25, p=0.28288 b-rank test for bits 19 to 26, p=0.30237 b-rank test for bits 20 to 27, p=0.00899 b-rank test for bits 21 to 28, p=0.52286 b-rank test for bits 22 to 29, p=0.51357 b-rank test for bits 23 to 30, p=0.10226 b-rank test for bits 24 to 31, p=0.77066 b-rank test for bits 25 to 32, p=0.51275 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 = 0.023874 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-09_23:31 (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 141193 -1.67 0.047098 2 141265 -1.51 0.066105 3 142279 0.86 0.806128 4 141713 -0.46 0.323219 5 142052 0.33 0.630562 6 141938 0.07 0.526704 7 141939 0.07 0.527634 8 141277 -1.48 0.069783 9 141530 -0.89 0.187732 10 142137 0.53 0.702616 11 142036 0.30 0.616369 12 141916 0.02 0.506217 13 143295 3.24 0.999397 14 141728 -0.42 0.335904 15 141772 -0.32 0.374157 16 141793 -0.27 0.392888 17 142284 0.88 0.809321 18 141762 -0.34 0.365337 19 141898 -0.03 0.489440 20 142269 0.84 0.799644 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-07-09_23:31 Bits used No. missing words z-score p-value 23 to 32 142022 0.3885 0.651183 22 to 31 141346 -1.9425 0.026037 21 to 30 141898 -0.0391 0.484418 20 to 29 141588 -1.1080 0.133923 19 to 28 142005 0.3299 0.629261 18 to 27 141753 -0.5391 0.294920 17 to 26 141462 -1.5425 0.061474 16 to 25 142008 0.3402 0.633163 15 to 24 142363 1.5644 0.941136 14 to 23 141609 -1.0356 0.150190 13 to 22 141933 0.0816 0.532526 12 to 21 141566 -1.1839 0.118227 11 to 20 141859 -0.1736 0.431109 10 to 19 141904 -0.0184 0.492668 9 to 18 142386 1.6437 0.949880 8 to 17 142369 1.5851 0.943525 7 to 16 141371 -1.8563 0.031705 6 to 15 141632 -0.9563 0.169458 5 to 14 141898 -0.0391 0.484418 4 to 13 142333 1.4609 0.927983 3 to 12 142454 1.8782 0.969821 2 to 11 141245 -2.2908 0.010988 1 to 10 141924 0.0506 0.520172 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-07-09_23:31 Bits used No. missing words z-score p-value 28 to 32 141875 -0.1164 0.453679 27 to 31 142110 0.6802 0.751823 26 to 30 142298 1.3175 0.906169 25 to 29 141696 -0.7232 0.234793 24 to 28 142192 0.9582 0.831020 23 to 27 141858 -0.1740 0.430933 22 to 26 142202 0.9921 0.839426 21 to 25 141682 -0.7706 0.220469 20 to 24 141961 0.1752 0.569520 19 to 23 142154 0.8294 0.796558 18 to 22 141551 -1.2147 0.112244 17 to 21 142020 0.3752 0.646227 16 to 20 141932 0.0768 0.530628 15 to 19 141852 -0.1943 0.422955 14 to 18 142298 1.3175 0.906169 13 to 17 141853 -0.1909 0.424283 12 to 16 141945 0.1209 0.548121 11 to 15 141544 -1.2384 0.107783 10 to 14 141934 0.0836 0.533324 9 to 13 142009 0.3379 0.632267 8 to 12 142394 1.6429 0.949803 7 to 11 142016 0.3616 0.641172 6 to 10 141778 -0.4452 0.328093 5 to 9 141466 -1.5028 0.066444 4 to 8 141991 0.2768 0.609051 3 to 7 141881 -0.0960 0.461747 2 to 6 142233 1.0972 0.863720 1 to 5 142259 1.1853 0.882055 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-07-09_23:31 Bits used No. missing words z-score p-value 31 to 32 141503 -1.1986 0.115339 30 to 31 142319 1.2085 0.886566 29 to 30 141910 0.0020 0.500789 28 to 29 142371 1.3619 0.913379 27 to 28 142587 1.9990 0.977197 26 to 27 141422 -1.4376 0.075281 25 to 26 141682 -0.6706 0.251241 24 to 25 141810 -0.2930 0.384758 23 to 24 141623 -0.8446 0.199158 22 to 23 141508 -1.1839 0.118233 21 to 22 142153 0.7188 0.763865 20 to 21 141404 -1.4906 0.068027 19 to 20 141808 -0.2989 0.382505 18 to 19 141795 -0.3373 0.367962 17 to 18 141919 0.0285 0.511378 16 to 17 141877 -0.0954 0.462011 15 to 16 141484 -1.2547 0.104801 14 to 15 140846 -3.1367 0.000854 13 to 14 141555 -1.0452 0.147960 12 to 13 142131 0.6539 0.743410 11 to 12 141885 -0.0718 0.471393 10 to 11 141780 -0.3815 0.351415 9 to 10 141641 -0.7915 0.214316 8 to 9 141735 -0.5142 0.303539 7 to 8 142221 0.9194 0.821052 6 to 7 141829 -0.2370 0.406343 5 to 6 141798 -0.3284 0.371302 4 to 5 141838 -0.2104 0.416673 3 to 4 141937 0.0816 0.532527 2 to 3 141653 -0.7561 0.224784 1 to 2 141741 -0.4965 0.309754 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-09_23:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2499.08 -0.013 0.494829 Test results for specific bytes for dh-ranFile-2018-07-09_23:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2524.55 0.347 0.635764 2 to 9 2474.77 -0.357 0.360644 3 to 10 2523.55 0.333 0.630430 4 to 11 2507.06 0.100 0.539789 5 to 12 2530.92 0.437 0.669053 6 to 13 2433.14 -0.945 0.172204 7 to 14 2437.27 -0.887 0.187508 8 to 15 2490.61 -0.133 0.447177 9 to 16 2526.14 0.370 0.644206 10 to 17 2437.93 -0.878 0.190035 11 to 18 2439.13 -0.861 0.194665 12 to 19 2432.98 -0.948 0.171601 13 to 20 2497.82 -0.031 0.487677 14 to 21 2498.82 -0.017 0.493369 15 to 22 2518.73 0.265 0.604467 16 to 23 2518.40 0.260 0.602657 17 to 24 2505.99 0.085 0.533752 18 to 25 2466.15 -0.479 0.316082 19 to 26 2524.51 0.347 0.635564 20 to 27 2479.28 -0.293 0.384762 21 to 28 2462.33 -0.533 0.297112 22 to 29 2544.19 0.625 0.733991 23 to 30 2441.60 -0.826 0.204434 24 to 31 2484.06 -0.225 0.410811 25 to 32 2522.91 0.324 0.627034 CDPARK for dh-ranFile-2018-07-09_23:31: 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 3537 0.6393 0.738676 3514 -0.4110 0.340551 3541 0.8219 0.794438 3522 -0.0457 0.481790 3498 -1.1416 0.126820 3499 -1.0959 0.136563 3500 -1.0502 0.146807 3506 -0.7763 0.218799 3554 1.4155 0.921543 3470 -2.4201 0.007758 Square side=100, avg. no. parked=3514.10 sample std.=23.66 p-value of the KSTEST for those 10 p-values: 0.297692 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-09_23:31 0.6512,0.9709,0.8106,0.4640,0.1817,0.9412,0.3110,0.0554,0.7446,0.4094, The KS test for those 10 p-values: 0.897948 The 3DSPHERES test for dh-ranFile-2018-07-09_23:31 sample no r^3 equiv. uni. 1 20.587 0.496524 2 2.383 0.076364 3 8.383 0.243800 4 34.778 0.686279 5 33.242 0.669808 6 23.429 0.542043 7 1.722 0.055796 8 14.381 0.380820 9 3.596 0.112972 10 0.675 0.022235 11 5.681 0.172530 12 50.617 0.814970 13 7.606 0.223933 14 8.500 0.246723 15 5.982 0.180767 16 82.690 0.936475 17 1.111 0.036355 18 41.892 0.752511 19 14.555 0.384399 20 2.460 0.078728 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.033028 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-09_23:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -0.3 -0.8 -1.3 0.9 -0.6 0.3 1.7 0.3 -0.3 -0.7 -0.9 -0.4 -0.4 -0.1 -0.9 0.3 -0.0 2.1 -0.1 -1.3 1.8 0.2 0.8 -0.4 -0.9 -0.1 0.6 -1.4 -0.1 1.1 -0.3 -1.8 0.5 0.2 -0.3 0.7 1.5 0.5 -0.7 -1.3 -1.0 -1.1 Chi-square with 42 degrees of freedom:35.318530 z-score=-0.729008, p-value=0.242628 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-07-09_23:31 Test no p-value 1 0.202904 2 0.017046 3 0.337789 4 0.052680 5 0.003862 6 0.159864 7 0.602861 8 0.850412 9 0.679038 10 0.008805 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.005529 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-09_23:31: (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 66559 0.17 66652 0.00 3 25000.00 25042 0.07 25059 0.14 4 6666.67 6820 3.53 6633 0.17 5 1388.89 1341 1.65 1387 0.00 6 238.10 197 7.09 217 1.87 7 34.72 36 0.05 48 5.08 8 4.96 4 0.19 3 0.77 p=0.95279 p=0.76467 Number of rngs required: 687959, p-value: 0.304 RESULTS OF CRAPS TEST for dh-ranFile-2018-07-09_23:31 No. of wins: Observed Expected 98676 98585.9 z-score= 0.403, pvalue=0.65659 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66446 66666.7 0.730 0.730 2 38013 37654.3 3.417 4.147 3 26839 26954.7 0.497 4.644 4 19109 19313.5 2.165 6.808 5 13810 13851.4 0.124 6.932 6 10011 9943.5 0.458 7.390 7 7284 7145.0 2.703 10.093 8 5123 5139.1 0.050 10.143 9 3677 3699.9 0.141 10.285 10 2767 2666.3 3.803 14.088 11 1886 1923.3 0.725 14.813 12 1392 1388.7 0.008 14.820 13 1034 1003.7 0.914 15.734 14 711 726.1 0.316 16.050 15 512 525.8 0.364 16.414 16 354 381.2 1.934 18.348 17 275 276.5 0.009 18.356 18 243 200.8 8.855 27.211 19 133 146.0 1.155 28.366 20 85 106.2 4.237 32.604 21 296 287.1 0.275 32.879 Chisq= 32.88 for 20 degrees of freedom, p= 0.96521 SUMMARY of craptest p-value for no. of wins: 0.656587 p-value for throws/game: 0.965210 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-09_23:31 No. of wins: Observed Expected 98727 98585.9 z-score= 0.631, pvalue=0.73607 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66645 66666.7 0.007 0.007 2 37687 37654.3 0.028 0.035 3 26779 26954.7 1.146 1.181 4 19425 19313.5 0.644 1.825 5 13874 13851.4 0.037 1.862 6 10057 9943.5 1.295 3.157 7 7138 7145.0 0.007 3.164 8 5191 5139.1 0.525 3.688 9 3658 3699.9 0.474 4.162 10 2688 2666.3 0.177 4.339 11 1953 1923.3 0.458 4.796 12 1323 1388.7 3.112 7.908 13 989 1003.7 0.216 8.124 14 716 726.1 0.142 8.266 15 546 525.8 0.773 9.039 16 366 381.2 0.602 9.641 17 227 276.5 8.875 18.516 18 207 200.8 0.190 18.705 19 152 146.0 0.248 18.953 20 114 106.2 0.571 19.524 21 265 287.1 1.703 21.227 Chisq= 21.23 for 20 degrees of freedom, p= 0.61612 SUMMARY of craptest p-value for no. of wins: 0.736067 p-value for throws/game: 0.616116 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0009,0.0037,0.0039,0.0055,0.0078,0.0088,0.0090,0.0110,0.0170,0.0171, 0.0222,0.0239,0.0260,0.0317,0.0330,0.0364,0.0471,0.0520,0.0527,0.0532, 0.0554,0.0557,0.0558,0.0574,0.0615,0.0661,0.0664,0.0680,0.0698,0.0753, 0.0764,0.0787,0.0948,0.1023,0.1048,0.1061,0.1078,0.1116,0.1122,0.1130, 0.1130,0.1153,0.1169,0.1182,0.1182,0.1268,0.1297,0.1339,0.1366,0.1421, 0.1468,0.1480,0.1502,0.1514,0.1532,0.1599,0.1653,0.1695,0.1716,0.1722, 0.1725,0.1808,0.1817,0.1875,0.1877,0.1900,0.1947,0.1992,0.2029,0.2044, 0.2052,0.2084,0.2143,0.2188,0.2205,0.2239,0.2248,0.2348,0.2426,0.2438, 0.2467,0.2512,0.2613,0.2720,0.2780,0.2790,0.2829,0.2949,0.2971,0.2977, 0.3024,0.3035,0.3044,0.3098,0.3110,0.3122,0.3161,0.3189,0.3232,0.3281, 0.3303,0.3348,0.3359,0.3378,0.3406,0.3426,0.3430,0.3504,0.3514,0.3606, 0.3631,0.3653,0.3680,0.3713,0.3742,0.3804,0.3808,0.3825,0.3844,0.3848, 0.3848,0.3892,0.3929,0.4063,0.4094,0.4108,0.4157,0.4167,0.4230,0.4243, 0.4249,0.4282,0.4309,0.4311,0.4472,0.4537,0.4617,0.4620,0.4640,0.4704, 0.4714,0.4785,0.4818,0.4844,0.4844,0.4859,0.4877,0.4894,0.4927,0.4934, 0.4948,0.4965,0.5008,0.5062,0.5114,0.5127,0.5136,0.5202,0.5229,0.5267, 0.5276,0.5306,0.5310,0.5325,0.5325,0.5333,0.5338,0.5398,0.5420,0.5481, 0.5608,0.5695,0.5772,0.5812,0.6027,0.6029,0.6045,0.6091,0.6117,0.6161, 0.6164,0.6270,0.6293,0.6304,0.6306,0.6318,0.6323,0.6332,0.6356,0.6358, 0.6407,0.6412,0.6441,0.6442,0.6455,0.6462,0.6512,0.6512,0.6566,0.6625, 0.6691,0.6698,0.6731,0.6757,0.6760,0.6790,0.6863,0.6863,0.7011,0.7026, 0.7340,0.7361,0.7387,0.7434,0.7446,0.7518,0.7525,0.7580,0.7616,0.7639, 0.7647,0.7707,0.7944,0.7956,0.7966,0.7996,0.8061,0.8093,0.8106,0.8150, 0.8211,0.8310,0.8394,0.8441,0.8484,0.8504,0.8637,0.8821,0.8834,0.8866, 0.8979,0.9062,0.9062,0.9091,0.9130,0.9134,0.9215,0.9266,0.9280,0.9312, 0.9365,0.9411,0.9412,0.9412,0.9435,0.9498,0.9499,0.9528,0.9535,0.9603, 0.9652,0.9698,0.9703,0.9709,0.9736,0.9747,0.9772,0.9923,0.9994, Overall p-value after applying KStest on 269 p-values = 0.017212 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.