RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-04-14_21:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.94 17.6848 0.591017 2 to 25 15.66 24.2980 0.888439 3 to 26 15.69 14.5196 0.369959 4 to 27 15.61 22.4677 0.832607 5 to 28 16.02 12.9395 0.259772 6 to 29 15.78 6.7666 0.013626 7 to 30 15.72 9.2434 0.067686 8 to 31 15.58 14.7543 0.386823 9 to 32 15.65 19.1614 0.680654 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.873892 Tough bday spacings test for dh-ranFile-2018-04-14_21:31: 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 11 37 70 90 95 87 52 27 23 5 3 (O-E)^2/E 0.4 0.0 0.1 0.6 0.1 1.0 0.0 0.3 4.4 0.4 0.3 Birthday Spacings: Sum(O-E)^2/E= 7.557, p= 0.328 RESULTS OF GCD FOR dh-ranFile-2018-04-14_21:31 Euclid's algorithm: p-value, steps to gcd: 0.198893 p-value, dist. of gcd's: 0.454014 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-04-14_21:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.396 0.454 0.547 0.331 0.912 0.716 0.787 0.835 Bits 8 to 15---> 0.891 0.337 0.396 0.833 0.499 0.759 0.912 0.385 Bits 16 to 23---> 0.001 0.638 0.756 0.175 0.721 0.110 0.711 0.964 Bits 24 to 31---> 0.102 0.648 0.750 0.022 0.314 0.319 0.957 0.289 KS test for the above 32 p values: 0.462 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-04-14_21:31, p-values for 5 runs: 0.3871, 0.3659, 0.4741, 0.8861, 0.6297 Rank test for binary matrices (31x31) for dh-ranFile-2018-04-14_21:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 218 211.4 0.205 0.205 r= 29 5071 5134.0 0.773 0.978 r= 30 23045 23103.0 0.146 1.124 r= 31 11666 11551.5 1.134 2.259 chi-square = 2.259 with df = 3; p-value = 0.479 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-04-14_21:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 197 211.4 0.983 0.983 r= 30 5215 5134.0 1.278 2.261 r= 31 23193 23103.0 0.350 2.611 r= 32 11395 11551.5 2.121 4.732 chi-square = 4.732 with df = 3; p-value = 0.807 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-04-14_21:31 b-rank test for bits 1 to 8, p=0.17334 b-rank test for bits 2 to 9, p=0.71044 b-rank test for bits 3 to 10, p=0.54423 b-rank test for bits 4 to 11, p=0.65660 b-rank test for bits 5 to 12, p=0.97277 b-rank test for bits 6 to 13, p=0.01251 b-rank test for bits 7 to 14, p=0.92695 b-rank test for bits 8 to 15, p=0.72937 b-rank test for bits 9 to 16, p=0.87478 b-rank test for bits 10 to 17, p=0.60425 b-rank test for bits 11 to 18, p=0.27140 b-rank test for bits 12 to 19, p=0.70842 b-rank test for bits 13 to 20, p=0.82274 b-rank test for bits 14 to 21, p=0.80406 b-rank test for bits 15 to 22, p=0.61657 b-rank test for bits 16 to 23, p=0.43274 b-rank test for bits 17 to 24, p=0.62904 b-rank test for bits 18 to 25, p=0.28836 b-rank test for bits 19 to 26, p=0.91473 b-rank test for bits 20 to 27, p=0.98075 b-rank test for bits 21 to 28, p=0.16986 b-rank test for bits 22 to 29, p=0.69887 b-rank test for bits 23 to 30, p=0.56112 b-rank test for bits 24 to 31, p=0.29945 b-rank test for bits 25 to 32, p=0.39392 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 = 0.187309 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-04-14_21:31 (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 141722 -0.44 0.330807 2 142058 0.35 0.635840 3 141689 -0.51 0.303350 4 140995 -2.14 0.016328 5 142069 0.37 0.645448 6 142186 0.65 0.740998 7 142149 0.56 0.712252 8 141844 -0.15 0.439341 9 142671 1.78 0.962430 10 142765 2.00 0.977208 11 141843 -0.15 0.438420 12 141615 -0.69 0.245825 13 141676 -0.55 0.292821 14 142272 0.85 0.801603 15 142007 0.23 0.590255 16 141637 -0.64 0.262295 17 141983 0.17 0.568331 18 141777 -0.31 0.378591 19 142179 0.63 0.735676 20 142006 0.23 0.589347 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-04-14_21:31 Bits used No. missing words z-score p-value 23 to 32 141577 -1.1460 0.125905 22 to 31 141323 -2.0218 0.021597 21 to 30 142017 0.3713 0.644784 20 to 29 141680 -0.7908 0.214532 19 to 28 141749 -0.5529 0.290179 18 to 27 141864 -0.1563 0.437894 17 to 26 142508 2.0644 0.980509 16 to 25 141804 -0.3632 0.358225 15 to 24 141438 -1.6253 0.052052 14 to 23 141978 0.2368 0.593591 13 to 22 141905 -0.0149 0.494044 12 to 21 141525 -1.3253 0.092540 11 to 20 142200 1.0023 0.841903 10 to 19 141920 0.0368 0.514675 9 to 18 142539 2.1713 0.985045 8 to 17 142027 0.4058 0.657540 7 to 16 141562 -1.1977 0.115519 6 to 15 141601 -1.0632 0.143844 5 to 14 141533 -1.2977 0.097197 4 to 13 141484 -1.4667 0.071235 3 to 12 141588 -1.1080 0.133923 2 to 11 141943 0.1161 0.546215 1 to 10 142001 0.3161 0.624038 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-04-14_21:31 Bits used No. missing words z-score p-value 28 to 32 141810 -0.3367 0.368167 27 to 31 141597 -1.0587 0.144858 26 to 30 142320 1.3921 0.918054 25 to 29 141778 -0.4452 0.328093 24 to 28 141872 -0.1265 0.449651 23 to 27 141643 -0.9028 0.183312 22 to 26 141639 -0.9164 0.179736 21 to 25 142567 2.2294 0.987106 20 to 24 142582 2.2802 0.988703 19 to 23 142064 0.5243 0.699967 18 to 22 142243 1.1311 0.870990 17 to 21 142186 0.9379 0.825843 16 to 20 141623 -0.9706 0.165871 15 to 19 141865 -0.1503 0.440275 14 to 18 141949 0.1345 0.553486 13 to 17 141790 -0.4045 0.342919 12 to 16 142022 0.3819 0.648744 11 to 15 142092 0.6192 0.732114 10 to 14 141702 -0.7028 0.241086 9 to 13 141634 -0.9333 0.175327 8 to 12 142339 1.4565 0.927374 7 to 11 141993 0.2836 0.611652 6 to 10 141865 -0.1503 0.440275 5 to 9 141656 -0.8587 0.195240 4 to 8 142104 0.6599 0.745341 3 to 7 142144 0.7955 0.786836 2 to 6 142067 0.5345 0.703493 1 to 5 142140 0.7819 0.782873 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-04-14_21:31 Bits used No. missing words z-score p-value 31 to 32 141502 -1.2016 0.114766 30 to 31 141936 0.0787 0.531354 29 to 30 141227 -2.0128 0.022069 28 to 29 142112 0.5978 0.725029 27 to 28 141351 -1.6470 0.049780 26 to 27 141546 -1.0718 0.141912 25 to 26 142112 0.5978 0.725029 24 to 25 142060 0.4445 0.671643 23 to 24 141858 -0.1514 0.439824 22 to 23 142399 1.4445 0.925694 21 to 22 141996 0.2557 0.600895 20 to 21 142598 2.0315 0.978897 19 to 20 142658 2.2085 0.986394 18 to 19 141857 -0.1544 0.438661 17 to 18 141800 -0.3225 0.373534 16 to 17 142002 0.2734 0.607713 15 to 16 141387 -1.5408 0.061683 14 to 15 141944 0.1023 0.540729 13 to 14 142097 0.5536 0.710073 12 to 13 141664 -0.7237 0.234629 11 to 12 141865 -0.1308 0.447980 10 to 11 141775 -0.3963 0.345959 9 to 10 141740 -0.4995 0.308714 8 to 9 141676 -0.6883 0.245635 7 to 8 141604 -0.9007 0.183880 6 to 7 142004 0.2793 0.609978 5 to 6 142234 0.9577 0.830900 4 to 5 142038 0.3796 0.647863 3 to 4 141997 0.2586 0.602033 2 to 3 141396 -1.5142 0.064982 1 to 2 141281 -1.8535 0.031907 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-04-14_21:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2523.92 0.338 0.632410 Test results for specific bytes for dh-ranFile-2018-04-14_21:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2465.55 -0.487 0.313083 2 to 9 2529.81 0.422 0.663336 3 to 10 2521.73 0.307 0.620690 4 to 11 2427.22 -1.029 0.151691 5 to 12 2490.63 -0.133 0.447289 6 to 13 2553.27 0.753 0.774378 7 to 14 2486.46 -0.192 0.424048 8 to 15 2530.00 0.424 0.664291 9 to 16 2517.25 0.244 0.596358 10 to 17 2506.84 0.097 0.538510 11 to 18 2421.53 -1.110 0.133568 12 to 19 2489.06 -0.155 0.438509 13 to 20 2504.26 0.060 0.524015 14 to 21 2357.11 -2.021 0.021655 15 to 22 2421.97 -1.104 0.134897 16 to 23 2479.70 -0.287 0.387007 17 to 24 2413.64 -1.221 0.110974 18 to 25 2481.49 -0.262 0.396776 19 to 26 2556.16 0.794 0.786466 20 to 27 2432.23 -0.958 0.168944 21 to 28 2516.05 0.227 0.589794 22 to 29 2418.30 -1.155 0.123970 23 to 30 2520.88 0.295 0.616114 24 to 31 2571.50 1.011 0.844019 25 to 32 2638.60 1.960 0.975006 CDPARK for dh-ranFile-2018-04-14_21:31: 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 3528 0.2283 0.590298 3515 -0.3653 0.357445 3519 -0.1826 0.427537 3531 0.3653 0.642555 3569 2.1005 0.982156 3521 -0.0913 0.463617 3494 -1.3242 0.092718 3554 1.4155 0.921543 3525 0.0913 0.536383 3554 1.4155 0.921543 Square side=100, avg. no. parked=3531.00 sample std.=21.01 p-value of the KSTEST for those 10 p-values: 0.407211 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-04-14_21:31 0.1814,0.3615,0.2556,0.4301,0.7893,0.8409,0.1136,0.5401,0.6335,0.8703, The KS test for those 10 p-values: 0.984746 The 3DSPHERES test for dh-ranFile-2018-04-14_21:31 sample no r^3 equiv. uni. 1 50.369 0.813436 2 0.113 0.003758 3 34.320 0.681462 4 76.609 0.922203 5 14.473 0.382717 6 16.858 0.429901 7 40.671 0.742229 8 37.038 0.709053 9 63.722 0.880454 10 8.263 0.240745 11 5.952 0.179954 12 30.790 0.641679 13 4.558 0.140948 14 15.168 0.396852 15 9.001 0.259207 16 47.330 0.793546 17 55.922 0.844957 18 15.143 0.396348 19 12.221 0.334608 20 35.341 0.692120 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.792831 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-04-14_21:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -0.7 -1.8 -1.3 0.5 0.8 1.4 0.3 -0.7 1.4 0.1 -1.0 -0.0 -0.6 -0.1 1.4 -0.4 -0.2 -0.7 0.6 0.4 -0.7 -1.0 0.9 0.4 -0.2 0.6 0.5 0.3 -1.2 1.5 -1.4 -0.7 -0.6 -0.6 -0.7 -1.4 0.5 -0.8 2.6 0.1 2.0 -0.1 Chi-square with 42 degrees of freedom:40.237051 z-score=-0.192354, p-value=0.451435 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-04-14_21:31 Test no p-value 1 0.991496 2 0.756205 3 0.416311 4 0.354312 5 0.139596 6 0.480888 7 0.514785 8 0.827809 9 0.114297 10 0.746139 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.895843 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-04-14_21:31: (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 66857 0.54 66682 0.00 3 25000.00 24823 1.25 25022 0.02 4 6666.67 6623 0.29 6631 0.19 5 1388.89 1427 1.05 1380 0.06 6 238.10 230 0.28 254 1.06 7 34.72 37 0.15 26 2.19 8 4.96 2 1.77 4 0.19 p=0.49649 p=0.28400 Number of rngs required: 689152, p-value: 0.807 RESULTS OF CRAPS TEST for dh-ranFile-2018-04-14_21:31 No. of wins: Observed Expected 98789 98585.9 z-score= 0.909, pvalue=0.81821 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67062 66666.7 2.344 2.344 2 37275 37654.3 3.821 6.166 3 26809 26954.7 0.788 6.953 4 19354 19313.5 0.085 7.039 5 13787 13851.4 0.300 7.338 6 9976 9943.5 0.106 7.444 7 7207 7145.0 0.538 7.982 8 5239 5139.1 1.943 9.925 9 3678 3699.9 0.129 10.054 10 2657 2666.3 0.032 10.086 11 1896 1923.3 0.388 10.475 12 1378 1388.7 0.083 10.558 13 1074 1003.7 4.922 15.479 14 689 726.1 1.900 17.379 15 522 525.8 0.028 17.407 16 382 381.2 0.002 17.409 17 267 276.5 0.329 17.738 18 185 200.8 1.248 18.986 19 144 146.0 0.027 19.013 20 129 106.2 4.888 23.900 21 290 287.1 0.029 23.929 Chisq= 23.93 for 20 degrees of freedom, p= 0.75451 SUMMARY of craptest p-value for no. of wins: 0.818211 p-value for throws/game: 0.754511 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-04-14_21:31 No. of wins: Observed Expected 98425 98585.9 z-score=-0.719, pvalue=0.23593 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66528 66666.7 0.288 0.288 2 37525 37654.3 0.444 0.733 3 26959 26954.7 0.001 0.733 4 19411 19313.5 0.493 1.226 5 13777 13851.4 0.400 1.626 6 10084 9943.5 1.984 3.610 7 7173 7145.0 0.110 3.719 8 5139 5139.1 0.000 3.719 9 3776 3699.9 1.567 5.286 10 2635 2666.3 0.367 5.653 11 1983 1923.3 1.851 7.505 12 1366 1388.7 0.372 7.877 13 988 1003.7 0.246 8.123 14 665 726.1 5.148 13.271 15 524 525.8 0.006 13.277 16 426 381.2 5.277 18.555 17 296 276.5 1.369 19.924 18 195 200.8 0.169 20.093 19 168 146.0 3.320 23.414 20 94 106.2 1.405 24.818 21 288 287.1 0.003 24.821 Chisq= 24.82 for 20 degrees of freedom, p= 0.79164 SUMMARY of craptest p-value for no. of wins: 0.235931 p-value for throws/game: 0.791640 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0013,0.0038,0.0125,0.0136,0.0163,0.0216,0.0217,0.0218,0.0221,0.0319, 0.0498,0.0521,0.0617,0.0650,0.0677,0.0712,0.0925,0.0927,0.0972,0.1023, 0.1096,0.1110,0.1136,0.1143,0.1148,0.1155,0.1240,0.1259,0.1336,0.1339, 0.1349,0.1396,0.1409,0.1419,0.1438,0.1449,0.1517,0.1659,0.1689,0.1699, 0.1733,0.1753,0.1753,0.1797,0.1800,0.1814,0.1833,0.1839,0.1873,0.1952, 0.1989,0.2145,0.2346,0.2359,0.2407,0.2411,0.2456,0.2458,0.2556,0.2592, 0.2598,0.2623,0.2714,0.2840,0.2884,0.2892,0.2902,0.2928,0.2994,0.3034, 0.3087,0.3131,0.3138,0.3191,0.3279,0.3281,0.3308,0.3310,0.3346,0.3366, 0.3429,0.3460,0.3543,0.3574,0.3582,0.3615,0.3659,0.3682,0.3700,0.3735, 0.3786,0.3827,0.3846,0.3868,0.3870,0.3871,0.3939,0.3956,0.3959,0.3963, 0.3968,0.3969,0.4072,0.4163,0.4240,0.4275,0.4299,0.4301,0.4327,0.4379, 0.4384,0.4385,0.4387,0.4393,0.4398,0.4403,0.4403,0.4473,0.4480,0.4497, 0.4514,0.4537,0.4540,0.4623,0.4636,0.4741,0.4795,0.4809,0.4940,0.4965, 0.4987,0.5147,0.5148,0.5240,0.5314,0.5364,0.5385,0.5401,0.5407,0.5442, 0.5462,0.5474,0.5535,0.5611,0.5683,0.5893,0.5898,0.5903,0.5903,0.5910, 0.5936,0.5964,0.6009,0.6020,0.6043,0.6077,0.6100,0.6117,0.6161,0.6166, 0.6207,0.6240,0.6290,0.6297,0.6324,0.6335,0.6358,0.6377,0.6417,0.6426, 0.6448,0.6454,0.6477,0.6479,0.6487,0.6566,0.6575,0.6633,0.6643,0.6716, 0.6807,0.6815,0.6921,0.6989,0.7000,0.7035,0.7084,0.7091,0.7101,0.7104, 0.7110,0.7123,0.7156,0.7213,0.7250,0.7250,0.7294,0.7321,0.7357,0.7410, 0.7422,0.7453,0.7461,0.7501,0.7545,0.7558,0.7562,0.7592,0.7744,0.7829, 0.7865,0.7868,0.7874,0.7893,0.7916,0.7928,0.7935,0.8016,0.8041,0.8068, 0.8075,0.8134,0.8182,0.8227,0.8258,0.8278,0.8309,0.8326,0.8327,0.8349, 0.8409,0.8419,0.8440,0.8450,0.8703,0.8710,0.8739,0.8748,0.8805,0.8861, 0.8884,0.8915,0.8958,0.9118,0.9121,0.9147,0.9181,0.9215,0.9215,0.9222, 0.9257,0.9270,0.9274,0.9572,0.9624,0.9636,0.9728,0.9750,0.9772,0.9789, 0.9805,0.9807,0.9822,0.9847,0.9850,0.9864,0.9871,0.9887,0.9915, Overall p-value after applying KStest on 269 p-values = 0.409558 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.