RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-05-28_08:31 (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 29.9439 0.973247 2 to 25 15.65 16.1323 0.485523 3 to 26 15.77 10.4128 0.114588 4 to 27 15.80 22.1266 0.820099 5 to 28 15.56 21.0647 0.776591 6 to 29 15.80 29.2921 0.968074 7 to 30 15.42 30.4445 0.976688 8 to 31 15.54 17.9236 0.606322 9 to 32 15.75 18.2791 0.628560 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.026788 Tough bday spacings test for dh-ranFile-2016-05-28_08:31: 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 34 82 88 107 70 54 34 15 4 4 (O-E)^2/E 0.1 0.2 1.0 1.0 0.9 0.8 0.1 0.6 0.0 1.0 0.0 Birthday Spacings: Sum(O-E)^2/E= 5.782, p= 0.167 RESULTS OF GCD FOR dh-ranFile-2016-05-28_08:31 Euclid's algorithm: p-value, steps to gcd: 0.021174 p-value, dist. of gcd's: 0.150284 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-05-28_08:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.516 0.623 0.888 0.139 0.823 0.313 0.821 0.249 Bits 8 to 15---> 0.961 0.269 0.508 0.766 0.751 0.901 0.033 0.062 Bits 16 to 23---> 0.215 0.402 0.539 0.455 0.196 0.545 0.748 0.858 Bits 24 to 31---> 0.508 0.134 0.323 0.659 0.914 0.945 0.786 0.588 KS test for the above 32 p values: 0.293 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-05-28_08:31, p-values for 5 runs: 0.8150, 0.7652, 0.9694, 0.8460, 0.3469 Rank test for binary matrices (31x31) for dh-ranFile-2016-05-28_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 212 211.4 0.002 0.002 r= 29 5092 5134.0 0.344 0.345 r= 30 23184 23103.0 0.284 0.629 r= 31 11512 11551.5 0.135 0.764 chi-square = 0.764 with df = 3; p-value = 0.142 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-05-28_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 206 211.4 0.139 0.139 r= 30 5112 5134.0 0.094 0.233 r= 31 23194 23103.0 0.358 0.591 r= 32 11488 11551.5 0.349 0.941 chi-square = 0.941 with df = 3; p-value = 0.184 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-05-28_08:31 b-rank test for bits 1 to 8, p=0.22308 b-rank test for bits 2 to 9, p=0.68881 b-rank test for bits 3 to 10, p=0.46531 b-rank test for bits 4 to 11, p=0.02307 b-rank test for bits 5 to 12, p=0.55383 b-rank test for bits 6 to 13, p=0.75005 b-rank test for bits 7 to 14, p=0.40072 b-rank test for bits 8 to 15, p=0.02124 b-rank test for bits 9 to 16, p=0.47315 b-rank test for bits 10 to 17, p=0.03215 b-rank test for bits 11 to 18, p=0.54608 b-rank test for bits 12 to 19, p=0.46398 b-rank test for bits 13 to 20, p=0.04861 b-rank test for bits 14 to 21, p=0.34833 b-rank test for bits 15 to 22, p=0.46251 b-rank test for bits 16 to 23, p=0.43690 b-rank test for bits 17 to 24, p=0.10334 b-rank test for bits 18 to 25, p=0.23766 b-rank test for bits 19 to 26, p=0.55110 b-rank test for bits 20 to 27, p=0.23381 b-rank test for bits 21 to 28, p=0.40769 b-rank test for bits 22 to 29, p=0.00278 b-rank test for bits 23 to 30, p=0.02189 b-rank test for bits 24 to 31, p=0.96361 b-rank test for bits 25 to 32, p=0.46229 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 = 0.007692 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-05-28_08:31 (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 142058 0.35 0.635840 2 142257 0.81 0.791694 3 142348 1.02 0.847302 4 141800 -0.26 0.399190 5 141879 -0.07 0.471753 6 141763 -0.34 0.366216 7 141252 -1.54 0.062292 8 141227 -1.59 0.055442 9 142558 1.52 0.935188 10 142479 1.33 0.908406 11 142146 0.55 0.709857 12 141888 -0.05 0.480126 13 141672 -0.55 0.289615 14 141863 -0.11 0.456900 15 141587 -0.75 0.225693 16 141388 -1.22 0.111600 17 141884 -0.06 0.476404 18 141716 -0.45 0.325741 19 142160 0.59 0.720954 20 141846 -0.15 0.441184 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-05-28_08:31 Bits used No. missing words z-score p-value 23 to 32 142104 0.6713 0.748978 22 to 31 141444 -1.6046 0.054292 21 to 30 141601 -1.0632 0.143844 20 to 29 141808 -0.3494 0.363389 19 to 28 141931 0.0747 0.529783 18 to 27 142173 0.9092 0.818380 17 to 26 141721 -0.6494 0.258036 16 to 25 141838 -0.2460 0.402855 15 to 24 142011 0.3506 0.637051 14 to 23 141458 -1.5563 0.059817 13 to 22 142560 2.2437 0.987574 12 to 21 142073 0.5644 0.713752 11 to 20 142083 0.5989 0.725368 10 to 19 141906 -0.0115 0.495419 9 to 18 141857 -0.1804 0.428400 8 to 17 141575 -1.1529 0.124484 7 to 16 141290 -2.1356 0.016355 6 to 15 141879 -0.1046 0.458352 5 to 14 141988 0.2713 0.606911 4 to 13 141894 -0.0529 0.478921 3 to 12 142465 1.9161 0.972324 2 to 11 141818 -0.3149 0.376407 1 to 10 141557 -1.2149 0.112196 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-05-28_08:31 Bits used No. missing words z-score p-value 28 to 32 142072 0.5514 0.709328 27 to 31 141883 -0.0893 0.464440 26 to 30 141621 -0.9774 0.164188 25 to 29 141645 -0.8960 0.185117 24 to 28 142137 0.7718 0.779873 23 to 27 141682 -0.7706 0.220469 22 to 26 142302 1.3311 0.908419 21 to 25 142438 1.7921 0.963442 20 to 24 141934 0.0836 0.533324 19 to 23 142276 1.2429 0.893057 18 to 22 141992 0.2802 0.610352 17 to 21 141821 -0.2994 0.382308 16 to 20 141436 -1.6045 0.054301 15 to 19 142036 0.4294 0.666180 14 to 18 141642 -0.9062 0.182414 13 to 17 141676 -0.7909 0.214487 12 to 16 141939 0.1006 0.540057 11 to 15 142352 1.5006 0.933267 10 to 14 141853 -0.1909 0.424283 9 to 13 141848 -0.2079 0.417654 8 to 12 142069 0.5413 0.705834 7 to 11 142110 0.6802 0.751823 6 to 10 142280 1.2565 0.895534 5 to 9 141971 0.2091 0.582796 4 to 8 142210 1.0192 0.845951 3 to 7 141635 -0.9299 0.176203 2 to 6 141493 -1.4113 0.079080 1 to 5 141701 -0.7062 0.240031 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-05-28_08:31 Bits used No. missing words z-score p-value 31 to 32 142299 1.1495 0.874819 30 to 31 141717 -0.5673 0.285240 29 to 30 142576 1.9666 0.975384 28 to 29 141739 -0.5024 0.307676 27 to 28 141772 -0.4051 0.342701 26 to 27 142005 0.2822 0.611110 25 to 26 141817 -0.2724 0.392673 24 to 25 141734 -0.5172 0.302509 23 to 24 142488 1.7070 0.956088 22 to 23 141941 0.0934 0.537216 21 to 22 141452 -1.3491 0.088660 20 to 21 142064 0.4563 0.675896 19 to 20 141717 -0.5673 0.285240 18 to 19 141691 -0.6440 0.259774 17 to 18 142200 0.8574 0.804397 16 to 17 142119 0.6185 0.731876 15 to 16 142085 0.5182 0.697841 14 to 15 141999 0.2645 0.604308 13 to 14 141979 0.2055 0.581416 12 to 13 142050 0.4150 0.660913 11 to 12 141611 -0.8800 0.189422 10 to 11 141985 0.2232 0.588316 9 to 10 142241 0.9784 0.836056 8 to 9 141555 -1.0452 0.147960 7 to 8 141903 -0.0187 0.492551 6 to 7 141786 -0.3638 0.358002 5 to 6 141615 -0.8682 0.192634 4 to 5 141991 0.2409 0.595189 3 to 4 142094 0.5447 0.707037 2 to 3 142300 1.1524 0.875426 1 to 2 141688 -0.6529 0.256913 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-05-28_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2506.59 0.093 0.537154 Test results for specific bytes for dh-ranFile-2016-05-28_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2607.81 1.525 0.936324 2 to 9 2513.09 0.185 0.573438 3 to 10 2475.44 -0.347 0.364153 4 to 11 2505.30 0.075 0.529875 5 to 12 2590.40 1.278 0.899444 6 to 13 2547.17 0.667 0.747631 7 to 14 2542.47 0.601 0.725931 8 to 15 2586.14 1.218 0.888426 9 to 16 2560.02 0.849 0.802026 10 to 17 2335.34 -2.329 0.009940 11 to 18 2523.00 0.325 0.627514 12 to 19 2429.52 -0.997 0.159463 13 to 20 2476.13 -0.338 0.367847 14 to 21 2432.09 -0.960 0.168420 15 to 22 2491.40 -0.122 0.451623 16 to 23 2375.46 -1.761 0.039095 17 to 24 2457.58 -0.600 0.274296 18 to 25 2437.29 -0.887 0.187584 19 to 26 2571.13 1.006 0.842780 20 to 27 2424.90 -1.062 0.144111 21 to 28 2531.25 0.442 0.670709 22 to 29 2469.38 -0.433 0.332485 23 to 30 2540.82 0.577 0.718118 24 to 31 2539.15 0.554 0.710077 25 to 32 2518.64 0.264 0.603985 CDPARK for dh-ranFile-2016-05-28_08:31: 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 3523 0.0000 0.500000 3531 0.3653 0.642555 3516 -0.3196 0.374623 3536 0.5936 0.723613 3494 -1.3242 0.092718 3512 -0.5023 0.307734 3536 0.5936 0.723613 3506 -0.7763 0.218799 3547 1.0959 0.863437 3558 1.5982 0.944998 Square side=100, avg. no. parked=3525.90 sample std.=18.49 p-value of the KSTEST for those 10 p-values: 0.980416 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-05-28_08:31 0.8583,0.0699,0.6033,0.2427,0.9568,0.3304,0.0745,0.9313,0.7721,0.4276, The KS test for those 10 p-values: 0.846165 The 3DSPHERES test for dh-ranFile-2016-05-28_08:31 sample no r^3 equiv. uni. 1 37.526 0.713740 2 36.135 0.700161 3 4.580 0.141573 4 29.200 0.622181 5 7.448 0.219861 6 43.084 0.762152 7 9.022 0.259732 8 32.852 0.665487 9 15.860 0.410604 10 4.127 0.128531 11 14.513 0.383552 12 0.226 0.007517 13 2.147 0.069060 14 2.768 0.088130 15 4.761 0.146759 16 23.545 0.543797 17 29.173 0.621834 18 103.636 0.968398 19 67.244 0.893697 20 6.669 0.199326 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.408366 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-05-28_08:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 3.4 0.1 0.6 -0.1 0.5 -0.2 -0.6 0.9 0.8 0.5 0.4 -2.3 0.8 0.4 0.1 2.3 -1.1 0.1 -0.1 -0.7 -1.5 -1.7 2.9 0.5 0.3 -1.1 -0.3 0.1 0.1 -0.9 -0.6 -0.2 -0.0 0.4 -0.6 0.6 -0.5 -0.4 0.1 -1.8 0.1 1.0 0.8 Chi-square with 42 degrees of freedom:49.768705 z-score=0.847635, p-value=0.808434 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-05-28_08:31 Test no p-value 1 0.030956 2 0.000439 3 0.065208 4 0.055848 5 0.064361 6 0.462192 7 0.863940 8 0.063613 9 0.972610 10 0.003768 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000084 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-05-28_08:31: (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 66610 0.05 66424 0.88 3 25000.00 25196 1.54 25261 2.72 4 6666.67 6586 0.98 6671 0.00 5 1388.89 1319 3.52 1385 0.01 6 238.10 247 0.33 219 1.53 7 34.72 35 0.00 33 0.09 8 4.96 6 0.22 6 0.22 p=0.64370 p=0.51328 Number of rngs required: 688442, p-value: 0.518 RESULTS OF CRAPS TEST for dh-ranFile-2016-05-28_08:31 No. of wins: Observed Expected 98571 98585.9 z-score=-0.066, pvalue=0.47351 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66375 66666.7 1.276 1.276 2 37659 37654.3 0.001 1.277 3 26866 26954.7 0.292 1.569 4 19358 19313.5 0.103 1.671 5 13818 13851.4 0.081 1.752 6 9924 9943.5 0.038 1.790 7 7254 7145.0 1.662 3.453 8 5115 5139.1 0.113 3.565 9 3790 3699.9 2.196 5.761 10 2723 2666.3 1.206 6.967 11 1959 1923.3 0.662 7.629 12 1423 1388.7 0.845 8.474 13 1005 1003.7 0.002 8.475 14 767 726.1 2.299 10.775 15 510 525.8 0.477 11.251 16 404 381.2 1.370 12.621 17 301 276.5 2.164 14.785 18 191 200.8 0.481 15.266 19 139 146.0 0.334 15.600 20 117 106.2 1.095 16.695 21 302 287.1 0.772 17.467 Chisq= 17.47 for 20 degrees of freedom, p= 0.37752 SUMMARY of craptest p-value for no. of wins: 0.473507 p-value for throws/game: 0.377521 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-05-28_08:31 No. of wins: Observed Expected 98506 98585.9 z-score=-0.357, pvalue=0.36048 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66615 66666.7 0.040 0.040 2 37937 37654.3 2.122 2.162 3 26711 26954.7 2.204 4.366 4 19267 19313.5 0.112 4.478 5 14107 13851.4 4.716 9.194 6 9898 9943.5 0.209 9.402 7 7080 7145.0 0.592 9.994 8 5127 5139.1 0.028 10.022 9 3625 3699.9 1.515 11.537 10 2595 2666.3 1.907 13.444 11 1937 1923.3 0.097 13.541 12 1377 1388.7 0.099 13.640 13 1026 1003.7 0.495 14.135 14 722 726.1 0.024 14.159 15 542 525.8 0.497 14.655 16 382 381.2 0.002 14.657 17 275 276.5 0.009 14.666 18 171 200.8 4.431 19.097 19 172 146.0 4.636 23.733 20 131 106.2 5.783 29.516 21 303 287.1 0.879 30.395 Chisq= 30.40 for 20 degrees of freedom, p= 0.93630 SUMMARY of craptest p-value for no. of wins: 0.360481 p-value for throws/game: 0.936303 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0001,0.0004,0.0028,0.0038,0.0075,0.0077,0.0099,0.0164,0.0212,0.0212, 0.0219,0.0231,0.0268,0.0310,0.0322,0.0325,0.0391,0.0486,0.0543,0.0543, 0.0554,0.0558,0.0598,0.0619,0.0623,0.0636,0.0644,0.0652,0.0691,0.0699, 0.0745,0.0791,0.0881,0.0887,0.0927,0.1033,0.1116,0.1122,0.1146,0.1245, 0.1285,0.1341,0.1393,0.1416,0.1420,0.1438,0.1441,0.1468,0.1480,0.1503, 0.1595,0.1642,0.1667,0.1684,0.1762,0.1824,0.1844,0.1851,0.1876,0.1894, 0.1926,0.1958,0.1993,0.2145,0.2152,0.2188,0.2199,0.2205,0.2231,0.2257, 0.2338,0.2377,0.2400,0.2427,0.2487,0.2569,0.2580,0.2597,0.2598,0.2685, 0.2743,0.2852,0.2852,0.2896,0.2930,0.3025,0.3077,0.3077,0.3126,0.3226, 0.3257,0.3304,0.3325,0.3427,0.3469,0.3483,0.3580,0.3605,0.3634,0.3642, 0.3662,0.3678,0.3746,0.3764,0.3775,0.3823,0.3836,0.3927,0.3992,0.4007, 0.4019,0.4029,0.4077,0.4084,0.4106,0.4177,0.4243,0.4276,0.4284,0.4369, 0.4412,0.4516,0.4549,0.4569,0.4584,0.4622,0.4623,0.4625,0.4640,0.4644, 0.4653,0.4718,0.4732,0.4735,0.4764,0.4789,0.4801,0.4855,0.4926,0.4954, 0.5000,0.5082,0.5083,0.5133,0.5161,0.5179,0.5298,0.5299,0.5333,0.5372, 0.5372,0.5386,0.5401,0.5438,0.5450,0.5461,0.5511,0.5538,0.5734,0.5814, 0.5828,0.5883,0.5884,0.5952,0.6033,0.6040,0.6043,0.6063,0.6069,0.6104, 0.6111,0.6218,0.6222,0.6228,0.6275,0.6286,0.6358,0.6371,0.6426,0.6437, 0.6592,0.6609,0.6655,0.6662,0.6707,0.6759,0.6888,0.6978,0.7002,0.7058, 0.7070,0.7093,0.7099,0.7101,0.7137,0.7138,0.7181,0.7210,0.7236,0.7236, 0.7254,0.7259,0.7319,0.7476,0.7483,0.7490,0.7500,0.7509,0.7518,0.7622, 0.7652,0.7660,0.7721,0.7766,0.7799,0.7861,0.7917,0.8020,0.8044,0.8084, 0.8150,0.8184,0.8201,0.8214,0.8231,0.8361,0.8428,0.8460,0.8460,0.8462, 0.8473,0.8577,0.8583,0.8634,0.8639,0.8748,0.8754,0.8879,0.8884,0.8931, 0.8937,0.8955,0.8994,0.9014,0.9084,0.9084,0.9136,0.9313,0.9333,0.9352, 0.9363,0.9363,0.9446,0.9450,0.9561,0.9568,0.9609,0.9634,0.9636,0.9681, 0.9684,0.9694,0.9723,0.9726,0.9732,0.9754,0.9767,0.9804,0.9876, Overall p-value after applying KStest on 269 p-values = 0.417784 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.