RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-08-29_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 15.52 14.8363 0.392726 2 to 25 15.66 25.9857 0.925279 3 to 26 15.98 21.2263 0.783668 4 to 27 15.65 17.4381 0.574914 5 to 28 15.65 13.5567 0.301804 6 to 29 15.84 17.3256 0.567473 7 to 30 15.66 20.1211 0.731918 8 to 31 15.75 24.5575 0.894938 9 to 32 15.67 12.0654 0.203837 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.560379 Tough bday spacings test for dh-ranFile-2016-08-29_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 43 85 97 99 58 49 29 19 11 1 (O-E)^2/E 0.0 1.1 1.9 0.0 0.0 5.2 0.2 0.0 1.1 2.9 2.3 Birthday Spacings: Sum(O-E)^2/E= 14.766, p= 0.859 RESULTS OF GCD FOR dh-ranFile-2016-08-29_09:31 Euclid's algorithm: p-value, steps to gcd: 0.046826 p-value, dist. of gcd's: 0.042590 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-08-29_09:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.924 0.852 0.781 0.432 0.755 0.343 0.310 0.004 Bits 8 to 15---> 0.499 0.598 0.376 0.694 0.938 0.807 0.092 0.790 Bits 16 to 23---> 0.207 0.053 0.431 0.767 0.523 0.876 0.242 0.422 Bits 24 to 31---> 0.868 0.853 0.152 0.398 0.928 0.911 0.817 0.848 KS test for the above 32 p values: 0.865 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-08-29_09:31, p-values for 5 runs: 0.4237, 0.8306, 0.1054, 0.7031, 0.8065 Rank test for binary matrices (31x31) for dh-ranFile-2016-08-29_09:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 203 211.4 0.335 0.335 r= 29 5065 5134.0 0.928 1.263 r= 30 23227 23103.0 0.665 1.928 r= 31 11505 11551.5 0.187 2.115 chi-square = 2.115 with df = 3; p-value = 0.451 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-08-29_09:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 193 211.4 1.605 1.605 r= 30 5136 5134.0 0.001 1.605 r= 31 23102 23103.0 0.000 1.605 r= 32 11569 11551.5 0.026 1.632 chi-square = 1.632 with df = 3; p-value = 0.348 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-08-29_09:31 b-rank test for bits 1 to 8, p=0.64351 b-rank test for bits 2 to 9, p=0.47084 b-rank test for bits 3 to 10, p=0.48910 b-rank test for bits 4 to 11, p=0.19875 b-rank test for bits 5 to 12, p=0.87351 b-rank test for bits 6 to 13, p=0.40012 b-rank test for bits 7 to 14, p=0.06139 b-rank test for bits 8 to 15, p=0.23401 b-rank test for bits 9 to 16, p=0.14310 b-rank test for bits 10 to 17, p=0.68175 b-rank test for bits 11 to 18, p=0.86648 b-rank test for bits 12 to 19, p=0.36531 b-rank test for bits 13 to 20, p=0.51698 b-rank test for bits 14 to 21, p=0.21562 b-rank test for bits 15 to 22, p=0.90246 b-rank test for bits 16 to 23, p=0.95310 b-rank test for bits 17 to 24, p=0.89785 b-rank test for bits 18 to 25, p=0.78379 b-rank test for bits 19 to 26, p=0.11476 b-rank test for bits 20 to 27, p=0.77013 b-rank test for bits 21 to 28, p=0.82000 b-rank test for bits 22 to 29, p=0.54223 b-rank test for bits 23 to 30, p=0.78304 b-rank test for bits 24 to 31, p=0.19886 b-rank test for bits 25 to 32, p=0.28530 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 = 0.857422 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-08-29_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 142901 2.32 0.989748 2 141442 -1.09 0.137440 3 141729 -0.42 0.336756 4 142036 0.30 0.616369 5 141659 -0.58 0.279313 6 142021 0.26 0.602920 7 141495 -0.97 0.166507 8 142323 0.97 0.833108 9 141457 -1.06 0.145291 10 141552 -0.83 0.201892 11 141795 -0.27 0.394686 12 142355 1.04 0.851128 13 142319 0.96 0.830760 14 140820 -2.55 0.005461 15 141530 -0.89 0.187732 16 141770 -0.33 0.372387 17 142034 0.29 0.614583 18 141727 -0.43 0.335052 19 142115 0.48 0.684577 20 142117 0.49 0.686236 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-08-29_09:31 Bits used No. missing words z-score p-value 23 to 32 141902 -0.0253 0.489918 22 to 31 142091 0.6264 0.734490 21 to 30 141665 -0.8425 0.199749 20 to 29 142066 0.5402 0.705485 19 to 28 141476 -1.4942 0.067556 18 to 27 141553 -1.2287 0.109588 17 to 26 141920 0.0368 0.514675 16 to 25 142044 0.4644 0.678812 15 to 24 142152 0.8368 0.798646 14 to 23 142155 0.8471 0.801541 13 to 22 142079 0.5851 0.720749 12 to 21 142087 0.6127 0.729948 11 to 20 141822 -0.3011 0.381655 10 to 19 142656 2.5747 0.994984 9 to 18 142281 1.2816 0.900012 8 to 17 141847 -0.2149 0.414911 7 to 16 141819 -0.3115 0.377717 6 to 15 141771 -0.4770 0.316681 5 to 14 141496 -1.4253 0.077039 4 to 13 141653 -0.8839 0.188376 3 to 12 141877 -0.1115 0.455617 2 to 11 141878 -0.1080 0.456984 1 to 10 142144 0.8092 0.790802 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-08-29_09:31 Bits used No. missing words z-score p-value 28 to 32 141971 0.2091 0.582796 27 to 31 142162 0.8565 0.804142 26 to 30 142258 1.1819 0.881384 25 to 29 141695 -0.7265 0.233753 24 to 28 141877 -0.1096 0.456366 23 to 27 141950 0.1379 0.554826 22 to 26 141564 -1.1706 0.120878 21 to 25 141967 0.1955 0.577496 20 to 24 142208 1.0124 0.844336 19 to 23 142128 0.7413 0.770730 18 to 22 141140 -2.6079 0.004555 17 to 21 142217 1.0429 0.851514 16 to 20 142148 0.8091 0.790757 15 to 19 142309 1.3548 0.912262 14 to 18 141564 -1.1706 0.120878 13 to 17 141956 0.1582 0.562852 12 to 16 141888 -0.0723 0.471180 11 to 15 141720 -0.6418 0.260503 10 to 14 141529 -1.2893 0.098655 9 to 13 141807 -0.3469 0.364340 8 to 12 141593 -1.0723 0.141792 7 to 11 141576 -1.1299 0.129252 6 to 10 141611 -1.0113 0.155939 5 to 9 142138 0.7752 0.780875 4 to 8 142046 0.4633 0.678421 3 to 7 142293 1.3006 0.903298 2 to 6 141966 0.1921 0.576169 1 to 5 141946 0.1243 0.549463 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-08-29_09:31 Bits used No. missing words z-score p-value 31 to 32 141783 -0.3727 0.354703 30 to 31 142225 0.9312 0.824120 29 to 30 141962 0.1554 0.561735 28 to 29 141806 -0.3048 0.380256 27 to 28 141481 -1.2635 0.103203 26 to 27 142098 0.5565 0.711082 25 to 26 142218 0.9105 0.818729 24 to 25 141824 -0.2517 0.400632 23 to 24 142347 1.2911 0.901659 22 to 23 141871 -0.1131 0.454988 21 to 22 141536 -1.1013 0.135390 20 to 21 141997 0.2586 0.602033 19 to 20 141980 0.2085 0.582568 18 to 19 142016 0.3147 0.623490 17 to 18 141776 -0.3933 0.347048 16 to 17 141877 -0.0954 0.462011 15 to 16 141357 -1.6293 0.051626 14 to 15 142196 0.8456 0.801122 13 to 14 142188 0.8220 0.794472 12 to 13 142065 0.4592 0.676956 11 to 12 141982 0.2144 0.584869 10 to 11 142089 0.5300 0.701944 9 to 10 142372 1.3648 0.913843 8 to 9 141839 -0.2075 0.417824 7 to 8 141547 -1.0688 0.142575 6 to 7 141959 0.1465 0.558244 5 to 6 141112 -2.3520 0.009336 4 to 5 141880 -0.0865 0.465527 3 to 4 141816 -0.2753 0.391539 2 to 3 141979 0.2055 0.581416 1 to 2 141155 -2.2252 0.013035 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-08-29_09:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2536.12 0.511 0.695257 Test results for specific bytes for dh-ranFile-2016-08-29_09:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2591.69 1.297 0.902622 2 to 9 2451.74 -0.683 0.247442 3 to 10 2494.55 -0.077 0.469281 4 to 11 2403.88 -1.359 0.087013 5 to 12 2462.45 -0.531 0.297692 6 to 13 2438.73 -0.866 0.193109 7 to 14 2493.24 -0.096 0.461904 8 to 15 2462.51 -0.530 0.297972 9 to 16 2423.57 -1.081 0.139865 10 to 17 2497.89 -0.030 0.488083 11 to 18 2470.70 -0.414 0.339321 12 to 19 2531.31 0.443 0.671052 13 to 20 2332.04 -2.375 0.008767 14 to 21 2437.03 -0.891 0.186587 15 to 22 2406.93 -1.316 0.094054 16 to 23 2491.32 -0.123 0.451139 17 to 24 2465.06 -0.494 0.310601 18 to 25 2462.55 -0.530 0.298192 19 to 26 2446.62 -0.755 0.225165 20 to 27 2448.12 -0.734 0.231560 21 to 28 2419.24 -1.142 0.126695 22 to 29 2541.76 0.591 0.722608 23 to 30 2477.44 -0.319 0.374859 24 to 31 2530.50 0.431 0.666904 25 to 32 2493.66 -0.090 0.464297 CDPARK for dh-ranFile-2016-08-29_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 3567 2.0091 0.977738 3505 -0.8219 0.205562 3550 1.2329 0.891189 3543 0.9132 0.819442 3517 -0.2740 0.392053 3551 1.2785 0.899470 3513 -0.4566 0.323972 3559 1.6438 0.949895 3474 -2.2374 0.012629 3520 -0.1370 0.445521 Square side=100, avg. no. parked=3529.90 sample std.=27.46 p-value of the KSTEST for those 10 p-values: 0.221163 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-08-29_09:31 0.7060,0.1325,0.1472,0.0051,0.2838,0.5100,0.4140,0.4513,0.6509,0.9149, The KS test for those 10 p-values: 0.634617 The 3DSPHERES test for dh-ranFile-2016-08-29_09:31 sample no r^3 equiv. uni. 1 1.104 0.036120 2 31.976 0.655573 3 11.483 0.318036 4 11.518 0.318816 5 12.117 0.332289 6 14.705 0.387478 7 65.174 0.886104 8 17.330 0.438797 9 6.930 0.206259 10 24.101 0.552183 11 9.607 0.274027 12 20.912 0.501964 13 2.370 0.075952 14 16.435 0.421808 15 1.433 0.046656 16 76.132 0.920956 17 12.899 0.349468 18 2.518 0.080519 19 58.408 0.857287 20 59.227 0.861131 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.349798 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-08-29_09:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 1.8 0.1 1.1 -0.7 0.4 0.6 -1.3 0.6 -1.6 -0.8 -0.7 -1.6 -1.7 -1.4 -0.4 0.1 1.0 -0.0 3.2 -0.1 2.1 0.9 -1.3 -0.2 -0.0 1.8 0.4 0.3 -1.2 -0.3 0.8 -0.7 0.1 -0.2 0.8 0.0 -0.7 0.5 -0.1 -0.6 0.0 -0.1 Chi-square with 42 degrees of freedom:44.339162 z-score=0.255224, p-value=0.626699 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-08-29_09:31 Test no p-value 1 0.615159 2 0.464887 3 0.457828 4 0.294909 5 0.261098 6 0.048868 7 0.569875 8 0.782466 9 0.366299 10 0.925554 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.908715 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-08-29_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 66730 0.06 66716 0.04 3 25000.00 25133 0.71 25118 0.56 4 6666.67 6561 1.67 6564 1.58 5 1388.89 1323 3.13 1319 3.52 6 238.10 226 0.61 248 0.41 7 34.72 20 6.24 32 0.21 8 4.96 6 0.22 2 1.77 p=0.95091 p=0.76792 Number of rngs required: 688192, p-value: 0.404 RESULTS OF CRAPS TEST for dh-ranFile-2016-08-29_09:31 No. of wins: Observed Expected 98943 98585.9 z-score= 1.597, pvalue=0.94491 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66802 66666.7 0.275 0.275 2 37497 37654.3 0.657 0.932 3 27036 26954.7 0.245 1.177 4 19378 19313.5 0.216 1.393 5 13877 13851.4 0.047 1.440 6 9918 9943.5 0.066 1.506 7 7139 7145.0 0.005 1.511 8 5107 5139.1 0.200 1.711 9 3705 3699.9 0.007 1.718 10 2665 2666.3 0.001 1.719 11 1924 1923.3 0.000 1.719 12 1330 1388.7 2.485 4.203 13 1010 1003.7 0.039 4.243 14 695 726.1 1.335 5.578 15 541 525.8 0.437 6.015 16 366 381.2 0.602 6.618 17 268 276.5 0.264 6.881 18 214 200.8 0.864 7.745 19 138 146.0 0.437 8.182 20 114 106.2 0.571 8.752 21 276 287.1 0.430 9.183 Chisq= 9.18 for 20 degrees of freedom, p= 0.01931 SUMMARY of craptest p-value for no. of wins: 0.944906 p-value for throws/game: 0.019305 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-08-29_09:31 No. of wins: Observed Expected 98517 98585.9 z-score=-0.308, pvalue=0.37905 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66821 66666.7 0.357 0.357 2 37565 37654.3 0.212 0.569 3 27020 26954.7 0.158 0.727 4 19175 19313.5 0.993 1.720 5 13774 13851.4 0.433 2.153 6 9780 9943.5 2.690 4.842 7 7294 7145.0 3.106 7.949 8 5150 5139.1 0.023 7.972 9 3748 3699.9 0.626 8.598 10 2705 2666.3 0.562 9.160 11 1910 1923.3 0.092 9.252 12 1457 1388.7 3.355 12.607 13 999 1003.7 0.022 12.629 14 695 726.1 1.335 13.965 15 544 525.8 0.627 14.592 16 378 381.2 0.026 14.618 17 242 276.5 4.314 18.932 18 214 200.8 0.864 19.796 19 154 146.0 0.440 20.236 20 111 106.2 0.216 20.452 21 264 287.1 1.861 22.312 Chisq= 22.31 for 20 degrees of freedom, p= 0.67620 SUMMARY of craptest p-value for no. of wins: 0.379050 p-value for throws/game: 0.676200 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0045,0.0046,0.0051,0.0055,0.0088,0.0093,0.0126,0.0130,0.0193,0.0361, 0.0426,0.0467,0.0468,0.0489,0.0516,0.0532,0.0614,0.0676,0.0760,0.0770, 0.0805,0.0870,0.0925,0.0941,0.0987,0.1032,0.1054,0.1096,0.1148,0.1209, 0.1209,0.1267,0.1293,0.1325,0.1354,0.1374,0.1399,0.1418,0.1426,0.1431, 0.1453,0.1472,0.1521,0.1559,0.1665,0.1866,0.1877,0.1884,0.1931,0.1987, 0.1989,0.1997,0.2019,0.2038,0.2056,0.2063,0.2065,0.2156,0.2212,0.2252, 0.2316,0.2338,0.2340,0.2420,0.2474,0.2605,0.2611,0.2740,0.2793,0.2838, 0.2853,0.2949,0.2977,0.2980,0.2982,0.3018,0.3096,0.3106,0.3167,0.3180, 0.3188,0.3240,0.3323,0.3351,0.3368,0.3393,0.3429,0.3470,0.3478,0.3495, 0.3498,0.3547,0.3643,0.3653,0.3663,0.3724,0.3749,0.3760,0.3777,0.3791, 0.3803,0.3817,0.3875,0.3915,0.3921,0.3927,0.3947,0.3977,0.4001,0.4006, 0.4041,0.4140,0.4149,0.4178,0.4216,0.4218,0.4237,0.4310,0.4316,0.4388, 0.4455,0.4511,0.4512,0.4513,0.4550,0.4556,0.4564,0.4570,0.4578,0.4619, 0.4620,0.4643,0.4649,0.4655,0.4693,0.4708,0.4712,0.4881,0.4891,0.4899, 0.4989,0.5020,0.5100,0.5147,0.5170,0.5228,0.5422,0.5495,0.5522,0.5548, 0.5582,0.5604,0.5617,0.5629,0.5675,0.5699,0.5749,0.5762,0.5775,0.5814, 0.5826,0.5828,0.5849,0.5977,0.6020,0.6029,0.6146,0.6152,0.6164,0.6235, 0.6267,0.6346,0.6435,0.6509,0.6556,0.6669,0.6711,0.6762,0.6770,0.6784, 0.6788,0.6817,0.6846,0.6862,0.6940,0.6953,0.7019,0.7031,0.7055,0.7060, 0.7111,0.7207,0.7226,0.7299,0.7319,0.7345,0.7549,0.7674,0.7679,0.7701, 0.7707,0.7809,0.7811,0.7825,0.7830,0.7837,0.7838,0.7899,0.7908,0.7908, 0.7945,0.7986,0.8011,0.8015,0.8041,0.8065,0.8073,0.8171,0.8187,0.8194, 0.8200,0.8241,0.8306,0.8308,0.8331,0.8443,0.8481,0.8511,0.8515,0.8525, 0.8531,0.8573,0.8574,0.8592,0.8611,0.8650,0.8665,0.8679,0.8735,0.8755, 0.8814,0.8861,0.8912,0.8949,0.8979,0.8995,0.9000,0.9017,0.9025,0.9026, 0.9033,0.9087,0.9114,0.9123,0.9138,0.9149,0.9210,0.9235,0.9253,0.9256, 0.9282,0.9384,0.9449,0.9499,0.9509,0.9531,0.9777,0.9897,0.9950, Overall p-value after applying KStest on 269 p-values = 0.593479 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.