RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-01-28_18:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.77 39.2931 0.998373 2 to 25 16.03 10.9922 0.143028 3 to 26 15.77 14.9972 0.404314 4 to 27 15.35 21.8276 0.808559 5 to 28 15.68 13.1509 0.273975 6 to 29 15.50 26.9650 0.941417 7 to 30 15.60 16.0366 0.478756 8 to 31 15.87 16.8264 0.533812 9 to 32 15.75 19.6102 0.705349 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.446482 Tough bday spacings test for dh-ranFile-2017-01-28_18:31: 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 12 36 74 103 90 77 52 32 13 6 5 (O-E)^2/E 0.9 0.0 0.0 0.3 0.6 0.0 0.0 0.2 0.2 0.1 0.2 Birthday Spacings: Sum(O-E)^2/E= 2.489, p= 0.009 RESULTS OF GCD FOR dh-ranFile-2017-01-28_18:31 Euclid's algorithm: p-value, steps to gcd: 0.620591 p-value, dist. of gcd's: 0.125896 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-01-28_18:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.405 0.573 0.501 0.114 0.267 0.048 0.749 0.392 Bits 8 to 15---> 0.233 0.718 0.523 0.352 0.933 0.859 0.540 0.319 Bits 16 to 23---> 0.566 0.546 0.561 0.979 0.790 0.363 0.266 0.461 Bits 24 to 31---> 0.662 0.105 0.112 0.240 0.851 0.331 0.887 0.933 KS test for the above 32 p values: 0.107 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-01-28_18:31, p-values for 5 runs: 0.6006, 0.6701, 0.6887, 0.3601, 0.0836 Rank test for binary matrices (31x31) for dh-ranFile-2017-01-28_18:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 197 211.4 0.983 0.983 r= 29 5091 5134.0 0.360 1.344 r= 30 23069 23103.0 0.050 1.394 r= 31 11643 11551.5 0.724 2.118 chi-square = 2.118 with df = 3; p-value = 0.452 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2017-01-28_18:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 234 211.4 2.412 2.412 r= 30 5082 5134.0 0.527 2.939 r= 31 23228 23103.0 0.676 3.615 r= 32 11456 11551.5 0.790 4.405 chi-square = 4.405 with df = 3; p-value = 0.779 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2017-01-28_18:31 b-rank test for bits 1 to 8, p=0.69798 b-rank test for bits 2 to 9, p=0.29042 b-rank test for bits 3 to 10, p=0.98446 b-rank test for bits 4 to 11, p=0.88644 b-rank test for bits 5 to 12, p=0.19514 b-rank test for bits 6 to 13, p=0.12374 b-rank test for bits 7 to 14, p=0.35808 b-rank test for bits 8 to 15, p=0.34807 b-rank test for bits 9 to 16, p=0.20981 b-rank test for bits 10 to 17, p=0.10113 b-rank test for bits 11 to 18, p=0.39400 b-rank test for bits 12 to 19, p=0.65766 b-rank test for bits 13 to 20, p=0.43204 b-rank test for bits 14 to 21, p=0.36526 b-rank test for bits 15 to 22, p=0.80395 b-rank test for bits 16 to 23, p=0.92860 b-rank test for bits 17 to 24, p=0.05860 b-rank test for bits 18 to 25, p=0.96093 b-rank test for bits 19 to 26, p=0.87637 b-rank test for bits 20 to 27, p=0.45229 b-rank test for bits 21 to 28, p=0.20400 b-rank test for bits 22 to 29, p=0.59484 b-rank test for bits 23 to 30, p=0.79217 b-rank test for bits 24 to 31, p=0.69862 b-rank test for bits 25 to 32, p=0.64281 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 = 0.956617 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-01-28_18:31 (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 141464 -1.04 0.149056 2 142043 0.31 0.622599 3 142760 1.99 0.976569 4 142096 0.44 0.668634 5 140646 -2.95 0.001580 6 141746 -0.38 0.351375 7 142168 0.60 0.727201 8 141963 0.13 0.549895 9 141980 0.17 0.565574 10 142670 1.78 0.962238 11 141936 0.06 0.524843 12 142084 0.41 0.658403 13 141832 -0.18 0.428310 14 142235 0.76 0.776645 15 142327 0.98 0.835434 16 141633 -0.65 0.259259 17 141826 -0.19 0.422815 18 141326 -1.36 0.086454 19 141349 -1.31 0.095236 20 142368 1.07 0.858063 ---------------------------------------------------------------- OPSO test for dh-ranFile-2017-01-28_18:31 Bits used No. missing words z-score p-value 23 to 32 141650 -0.8942 0.185596 22 to 31 141907 -0.0080 0.496795 21 to 30 141934 0.0851 0.533897 20 to 29 142138 0.7885 0.784803 19 to 28 142380 1.6230 0.947705 18 to 27 141529 -1.3115 0.094847 17 to 26 141879 -0.1046 0.458352 16 to 25 142375 1.6058 0.945837 15 to 24 142352 1.5264 0.936551 14 to 23 141975 0.2264 0.589574 13 to 22 142618 2.4437 0.992731 12 to 21 142179 0.9299 0.823788 11 to 20 142538 2.1678 0.984914 10 to 19 142201 1.0058 0.842734 9 to 18 142086 0.6092 0.728806 8 to 17 142273 1.2540 0.895085 7 to 16 141729 -0.6218 0.267028 6 to 15 141905 -0.0149 0.494044 5 to 14 141650 -0.8942 0.185596 4 to 13 142487 1.9920 0.976813 3 to 12 141844 -0.2253 0.410882 2 to 11 141738 -0.5908 0.277330 1 to 10 142181 0.9368 0.825568 ----------------------------------------------------------------- OQSO test for dh-ranFile-2017-01-28_18:31 Bits used No. missing words z-score p-value 28 to 32 142263 1.1989 0.884713 27 to 31 141411 -1.6893 0.045585 26 to 30 141907 -0.0079 0.496849 25 to 29 142234 1.1006 0.864459 24 to 28 142355 1.5107 0.934573 23 to 27 141726 -0.6215 0.267149 22 to 26 142359 1.5243 0.936284 21 to 25 142187 0.9413 0.826713 20 to 24 141788 -0.4113 0.340431 19 to 23 141272 -2.1604 0.015369 18 to 22 142268 1.2158 0.887975 17 to 21 141333 -1.9537 0.025371 16 to 20 141818 -0.3096 0.378435 15 to 19 141759 -0.5096 0.305168 14 to 18 141363 -1.8520 0.032015 13 to 17 141868 -0.1401 0.444290 12 to 16 142215 1.0362 0.849938 11 to 15 141858 -0.1740 0.430933 10 to 14 141551 -1.2147 0.112244 9 to 13 141796 -0.3842 0.350426 8 to 12 141839 -0.2384 0.405783 7 to 11 141824 -0.2893 0.386193 6 to 10 142095 0.6294 0.735453 5 to 9 141882 -0.0926 0.463093 4 to 8 141748 -0.5469 0.292230 3 to 7 141745 -0.5571 0.288746 2 to 6 141744 -0.5604 0.287589 1 to 5 142705 2.6972 0.996504 ----------------------------------------------------------------- DNA test for dh-ranFile-2017-01-28_18:31 Bits used No. missing words z-score p-value 31 to 32 141702 -0.6116 0.270404 30 to 31 142066 0.4622 0.678014 29 to 30 142381 1.3914 0.917941 28 to 29 141644 -0.7827 0.216906 27 to 28 142770 2.5388 0.994439 26 to 27 142109 0.5890 0.722068 25 to 26 142129 0.6480 0.741506 24 to 25 141749 -0.4729 0.318125 23 to 24 141907 -0.0069 0.497258 22 to 23 142254 1.0167 0.845358 21 to 22 142039 0.3825 0.648958 20 to 21 141870 -0.1160 0.453819 19 to 20 141891 -0.0541 0.478439 18 to 19 141706 -0.5998 0.274322 17 to 18 141502 -1.2016 0.114766 16 to 17 142028 0.3501 0.636853 15 to 16 141562 -1.0246 0.152783 14 to 15 142165 0.7542 0.774632 13 to 14 142193 0.8368 0.798643 12 to 13 141738 -0.5054 0.306640 11 to 12 142263 1.0433 0.851589 10 to 11 141967 0.1701 0.567541 9 to 10 141614 -0.8712 0.191828 8 to 9 142037 0.3766 0.646767 7 to 8 142241 0.9784 0.836056 6 to 7 141670 -0.7060 0.240098 5 to 6 141691 -0.6440 0.259774 4 to 5 142282 1.0993 0.864186 3 to 4 141448 -1.3609 0.086780 2 to 3 141766 -0.4228 0.336220 1 to 2 142175 0.7837 0.783388 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2017-01-28_18:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2369.59 -1.844 0.032570 Test results for specific bytes for dh-ranFile-2017-01-28_18:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2516.50 0.233 0.592261 2 to 9 2652.94 2.163 0.984725 3 to 10 2569.56 0.984 0.837366 4 to 11 2387.12 -1.596 0.055206 5 to 12 2411.33 -1.254 0.104929 6 to 13 2410.95 -1.259 0.103939 7 to 14 2472.18 -0.394 0.346974 8 to 15 2521.73 0.307 0.620669 9 to 16 2532.53 0.460 0.677283 10 to 17 2611.40 1.575 0.942417 11 to 18 2578.78 1.114 0.867393 12 to 19 2447.68 -0.740 0.229657 13 to 20 2481.70 -0.259 0.397892 14 to 21 2447.08 -0.748 0.227092 15 to 22 2423.92 -1.076 0.140976 16 to 23 2523.07 0.326 0.627868 17 to 24 2557.02 0.806 0.789998 18 to 25 2437.93 -0.878 0.190017 19 to 26 2475.70 -0.344 0.365576 20 to 27 2512.17 0.172 0.568320 21 to 28 2557.78 0.817 0.793065 22 to 29 2588.36 1.250 0.894275 23 to 30 2438.66 -0.868 0.192826 24 to 31 2532.87 0.465 0.678967 25 to 32 2483.30 -0.236 0.406660 CDPARK for dh-ranFile-2017-01-28_18:31: 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 3476 -2.1461 0.015932 3512 -0.5023 0.307734 3508 -0.6849 0.246694 3521 -0.0913 0.463617 3539 0.7306 0.767486 3544 0.9589 0.831196 3476 -2.1461 0.015932 3547 1.0959 0.863437 3485 -1.7352 0.041356 3530 0.3196 0.625377 Square side=100, avg. no. parked=3513.80 sample std.=25.86 p-value of the KSTEST for those 10 p-values: 0.219941 Results for the MINIMUM DISTANCE test for dh-ranFile-2017-01-28_18:31 0.3858,0.7292,0.0877,0.2190,0.0261,0.8987,0.7100,0.3642,0.6099,0.4452, The KS test for those 10 p-values: 0.909205 The 3DSPHERES test for dh-ranFile-2017-01-28_18:31 sample no r^3 equiv. uni. 1 21.006 0.503514 2 11.335 0.314652 3 33.607 0.673794 4 26.860 0.591522 5 30.292 0.635681 6 31.831 0.653907 7 14.537 0.384040 8 1.920 0.061985 9 6.476 0.194159 10 1.885 0.060911 11 56.243 0.846608 12 6.496 0.194697 13 5.754 0.174524 14 25.675 0.575067 15 56.585 0.848349 16 20.041 0.487279 17 4.690 0.144735 18 12.399 0.338531 19 59.009 0.860120 20 53.596 0.832458 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.806115 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-01-28_18:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -0.3 0.3 -0.4 -1.5 -0.1 -1.8 1.9 0.5 -0.7 1.7 -0.2 -0.4 -1.4 0.9 0.3 -0.4 1.5 -0.1 1.0 -1.8 -1.7 -0.4 2.4 0.6 -0.2 -1.4 0.5 -0.3 -0.1 0.6 -1.7 -1.1 0.4 -0.4 0.6 0.3 0.2 0.9 -0.7 0.9 -1.0 0.8 Chi-square with 42 degrees of freedom:43.208800 z-score=0.131891, p-value=0.580548 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2017-01-28_18:31 Test no p-value 1 0.121065 2 0.857688 3 0.705092 4 0.135283 5 0.423841 6 0.005908 7 0.108646 8 0.042262 9 0.000542 10 0.159365 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.001584 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-01-28_18:31: (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 66617 0.04 66677 0.00 3 25000.00 25007 0.00 24991 0.00 4 6666.67 6692 0.10 6694 0.11 5 1388.89 1405 0.19 1372 0.21 6 238.10 242 0.06 226 0.61 7 34.72 31 0.40 34 0.01 8 4.96 5 0.00 5 0.00 p=0.00753 p=0.01263 Number of rngs required: 687520, p-value: 0.153 RESULTS OF CRAPS TEST for dh-ranFile-2017-01-28_18:31 No. of wins: Observed Expected 98795 98585.9 z-score= 0.935, pvalue=0.82521 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66874 66666.7 0.645 0.645 2 37424 37654.3 1.409 2.054 3 27172 26954.7 1.751 3.805 4 19314 19313.5 0.000 3.805 5 13632 13851.4 3.476 7.281 6 9988 9943.5 0.199 7.479 7 7060 7145.0 1.012 8.491 8 5141 5139.1 0.001 8.492 9 3787 3699.9 2.052 10.544 10 2629 2666.3 0.522 11.066 11 1868 1923.3 1.592 12.658 12 1418 1388.7 0.616 13.274 13 1035 1003.7 0.975 14.249 14 750 726.1 0.784 15.033 15 527 525.8 0.003 15.036 16 385 381.2 0.039 15.075 17 269 276.5 0.206 15.280 18 216 200.8 1.146 16.426 19 119 146.0 4.988 21.414 20 97 106.2 0.800 22.213 21 295 287.1 0.217 22.430 Chisq= 22.43 for 20 degrees of freedom, p= 0.68236 SUMMARY of craptest p-value for no. of wins: 0.825210 p-value for throws/game: 0.682361 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2017-01-28_18:31 No. of wins: Observed Expected 98540 98585.9 z-score=-0.205, pvalue=0.41874 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66618 66666.7 0.036 0.036 2 37645 37654.3 0.002 0.038 3 27064 26954.7 0.443 0.481 4 19385 19313.5 0.265 0.746 5 13821 13851.4 0.067 0.813 6 9948 9943.5 0.002 0.815 7 7097 7145.0 0.323 1.137 8 5107 5139.1 0.200 1.338 9 3702 3699.9 0.001 1.339 10 2636 2666.3 0.344 1.683 11 1951 1923.3 0.398 2.081 12 1398 1388.7 0.062 2.143 13 999 1003.7 0.022 2.165 14 712 726.1 0.275 2.440 15 514 525.8 0.266 2.707 16 375 381.2 0.099 2.806 17 298 276.5 1.665 4.471 18 185 200.8 1.248 5.719 19 157 146.0 0.831 6.550 20 99 106.2 0.490 7.041 21 289 287.1 0.012 7.053 Chisq= 7.05 for 20 degrees of freedom, p= 0.00349 SUMMARY of craptest p-value for no. of wins: 0.418745 p-value for throws/game: 0.003492 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0005,0.0016,0.0016,0.0035,0.0059,0.0075,0.0090,0.0126,0.0154,0.0159, 0.0159,0.0254,0.0261,0.0320,0.0326,0.0414,0.0423,0.0456,0.0475,0.0552, 0.0586,0.0609,0.0620,0.0836,0.0865,0.0868,0.0877,0.0948,0.0952,0.1011, 0.1039,0.1049,0.1051,0.1073,0.1086,0.1120,0.1122,0.1143,0.1148,0.1211, 0.1237,0.1259,0.1353,0.1410,0.1430,0.1447,0.1491,0.1528,0.1531,0.1594, 0.1745,0.1856,0.1856,0.1900,0.1918,0.1928,0.1942,0.1947,0.1951,0.2040, 0.2098,0.2169,0.2190,0.2199,0.2271,0.2297,0.2333,0.2398,0.2401,0.2467, 0.2593,0.2598,0.2663,0.2667,0.2670,0.2671,0.2704,0.2740,0.2743,0.2773, 0.2876,0.2887,0.2904,0.2922,0.3052,0.3066,0.3077,0.3147,0.3181,0.3187, 0.3307,0.3362,0.3385,0.3404,0.3470,0.3481,0.3504,0.3514,0.3521,0.3581, 0.3601,0.3627,0.3642,0.3653,0.3656,0.3784,0.3840,0.3858,0.3862,0.3924, 0.3940,0.3979,0.4043,0.4048,0.4058,0.4067,0.4109,0.4187,0.4228,0.4238, 0.4283,0.4309,0.4320,0.4443,0.4452,0.4465,0.4518,0.4523,0.4538,0.4584, 0.4608,0.4631,0.4636,0.4784,0.4788,0.4873,0.4940,0.4968,0.4968,0.4973, 0.5013,0.5035,0.5231,0.5248,0.5338,0.5339,0.5401,0.5465,0.5499,0.5605, 0.5656,0.5660,0.5675,0.5683,0.5731,0.5751,0.5805,0.5896,0.5915,0.5923, 0.5948,0.6006,0.6099,0.6206,0.6207,0.6226,0.6254,0.6279,0.6357,0.6369, 0.6428,0.6468,0.6490,0.6539,0.6577,0.6584,0.6617,0.6686,0.6701,0.6738, 0.6773,0.6780,0.6790,0.6824,0.6887,0.6980,0.6986,0.7051,0.7053,0.7100, 0.7181,0.7221,0.7272,0.7288,0.7292,0.7355,0.7415,0.7487,0.7675,0.7746, 0.7766,0.7790,0.7834,0.7848,0.7900,0.7902,0.7922,0.7931,0.7986,0.8039, 0.8061,0.8086,0.8238,0.8252,0.8256,0.8267,0.8312,0.8325,0.8354,0.8361, 0.8374,0.8427,0.8454,0.8466,0.8483,0.8499,0.8506,0.8516,0.8577,0.8581, 0.8589,0.8601,0.8634,0.8642,0.8645,0.8674,0.8764,0.8847,0.8864,0.8865, 0.8880,0.8943,0.8951,0.8987,0.9092,0.9179,0.9286,0.9326,0.9329,0.9346, 0.9363,0.9366,0.9414,0.9424,0.9458,0.9477,0.9566,0.9609,0.9622,0.9766, 0.9768,0.9791,0.9845,0.9847,0.9849,0.9927,0.9944,0.9965,0.9984, Overall p-value after applying KStest on 269 p-values = 0.631330 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.