RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-03-19_07:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.79 10.3859 0.113346 2 to 25 15.94 20.1668 0.734214 3 to 26 15.42 24.5853 0.895616 4 to 27 15.63 29.9994 0.973651 5 to 28 15.67 26.2125 0.929326 6 to 29 15.55 18.6468 0.650821 7 to 30 15.91 23.1251 0.854776 8 to 31 16.08 15.1032 0.411952 9 to 32 15.85 20.2432 0.738019 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.050874 Tough bday spacings test for dh-ranFile-2016-03-19_07:31: 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 44 74 99 93 88 47 20 14 8 5 (O-E)^2/E 0.1 1.5 0.0 0.0 0.2 1.2 0.5 3.2 0.1 0.3 0.2 Birthday Spacings: Sum(O-E)^2/E= 7.383, p= 0.311 RESULTS OF GCD FOR dh-ranFile-2016-03-19_07:31 Euclid's algorithm: p-value, steps to gcd: 0.804584 p-value, dist. of gcd's: 0.792127 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-03-19_07:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.829 0.654 0.012 0.831 0.639 0.155 0.859 0.253 Bits 8 to 15---> 0.529 0.122 0.683 0.759 0.684 0.584 0.666 0.970 Bits 16 to 23---> 0.657 0.099 0.526 0.478 0.659 0.267 0.119 0.740 Bits 24 to 31---> 0.973 0.861 0.738 0.434 0.673 0.172 0.462 0.322 KS test for the above 32 p values: 0.574 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-03-19_07:31, p-values for 5 runs: 0.1643, 0.4475, 0.8732, 0.3804, 0.4219 Rank test for binary matrices (31x31) for dh-ranFile-2016-03-19_07:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 225 211.4 0.873 0.873 r= 29 5039 5134.0 1.758 2.631 r= 30 23302 23103.0 1.713 4.344 r= 31 11434 11551.5 1.196 5.540 chi-square = 5.540 with df = 3; p-value = 0.864 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-03-19_07:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 207 211.4 0.092 0.092 r= 30 5078 5134.0 0.611 0.703 r= 31 23054 23103.0 0.104 0.808 r= 32 11661 11551.5 1.038 1.845 chi-square = 1.845 with df = 3; p-value = 0.395 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-03-19_07:31 b-rank test for bits 1 to 8, p=0.81100 b-rank test for bits 2 to 9, p=0.52666 b-rank test for bits 3 to 10, p=0.60700 b-rank test for bits 4 to 11, p=0.41665 b-rank test for bits 5 to 12, p=0.00824 b-rank test for bits 6 to 13, p=0.40953 b-rank test for bits 7 to 14, p=0.09122 b-rank test for bits 8 to 15, p=0.26243 b-rank test for bits 9 to 16, p=0.29747 b-rank test for bits 10 to 17, p=0.18746 b-rank test for bits 11 to 18, p=0.86812 b-rank test for bits 12 to 19, p=0.68456 b-rank test for bits 13 to 20, p=0.39820 b-rank test for bits 14 to 21, p=0.87658 b-rank test for bits 15 to 22, p=0.88188 b-rank test for bits 16 to 23, p=0.94188 b-rank test for bits 17 to 24, p=0.52136 b-rank test for bits 18 to 25, p=0.25500 b-rank test for bits 19 to 26, p=0.48639 b-rank test for bits 20 to 27, p=0.14610 b-rank test for bits 21 to 28, p=0.38119 b-rank test for bits 22 to 29, p=0.60400 b-rank test for bits 23 to 30, p=0.15840 b-rank test for bits 24 to 31, p=0.18288 b-rank test for bits 25 to 32, p=0.78805 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 = 0.893199 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-03-19_07:31 (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 141587 -0.75 0.225693 2 141704 -0.48 0.315705 3 141808 -0.24 0.406425 4 141507 -0.94 0.173603 5 142274 0.85 0.802902 6 142035 0.29 0.615476 7 141308 -1.40 0.080014 8 141523 -0.90 0.183358 9 141605 -0.71 0.238526 10 141518 -0.91 0.180274 11 142487 1.35 0.911443 12 141683 -0.53 0.298469 13 140893 -2.37 0.008784 14 142390 1.12 0.869294 15 142399 1.14 0.873707 16 141044 -2.02 0.021599 17 141737 -0.40 0.343607 18 142919 2.36 0.990839 19 141967 0.13 0.553593 20 142008 0.23 0.591163 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-03-19_07:31 Bits used No. missing words z-score p-value 23 to 32 142190 0.9678 0.833435 22 to 31 141868 -0.1425 0.443336 21 to 30 142276 1.2644 0.896953 20 to 29 142438 1.8230 0.965848 19 to 28 141664 -0.8460 0.198786 18 to 27 142265 1.2264 0.889985 17 to 26 141698 -0.7287 0.233085 16 to 25 142374 1.6023 0.945457 15 to 24 141941 0.1092 0.543481 14 to 23 141920 0.0368 0.514675 13 to 22 141721 -0.6494 0.258036 12 to 21 141961 0.1782 0.570706 11 to 20 141698 -0.7287 0.233085 10 to 19 141839 -0.2425 0.404190 9 to 18 142078 0.5816 0.719589 8 to 17 141739 -0.5873 0.278486 7 to 16 141893 -0.0563 0.477547 6 to 15 141824 -0.2942 0.384287 5 to 14 142179 0.9299 0.823788 4 to 13 141991 0.2816 0.610883 3 to 12 141961 0.1782 0.570706 2 to 11 141329 -2.0011 0.022689 1 to 10 141714 -0.6736 0.250298 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-03-19_07:31 Bits used No. missing words z-score p-value 28 to 32 141774 -0.4587 0.323208 27 to 31 141999 0.3040 0.619423 26 to 30 142263 1.1989 0.884713 25 to 29 141915 0.0192 0.507667 24 to 28 142160 0.8497 0.802262 23 to 27 142384 1.6091 0.946197 22 to 26 142257 1.1785 0.880710 21 to 25 141896 -0.0452 0.481979 20 to 24 141752 -0.5333 0.296905 19 to 23 141608 -1.0215 0.153519 18 to 22 141958 0.1650 0.565521 17 to 21 141760 -0.5062 0.306357 16 to 20 141896 -0.0452 0.481979 15 to 19 142615 2.3921 0.991624 14 to 18 142124 0.7277 0.766600 13 to 17 141762 -0.4994 0.308741 12 to 16 142017 0.3650 0.642438 11 to 15 141965 0.1887 0.574841 10 to 14 142141 0.7853 0.783868 9 to 13 141357 -1.8723 0.030582 8 to 12 142213 1.0294 0.848352 7 to 11 142068 0.5379 0.704665 6 to 10 141978 0.2328 0.592034 5 to 9 141902 -0.0248 0.490088 4 to 8 142385 1.6124 0.946567 3 to 7 141749 -0.5435 0.293396 2 to 6 142059 0.5074 0.694048 1 to 5 142027 0.3989 0.655010 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-03-19_07:31 Bits used No. missing words z-score p-value 31 to 32 142041 0.3884 0.651143 30 to 31 141976 0.1967 0.577956 29 to 30 142460 1.6244 0.947854 28 to 29 141571 -0.9980 0.159134 27 to 28 141792 -0.3461 0.364632 26 to 27 141928 0.0551 0.521960 25 to 26 141923 0.0403 0.516083 24 to 25 141956 0.1377 0.554749 23 to 24 141243 -1.9656 0.024674 22 to 23 141706 -0.5998 0.274322 21 to 22 141798 -0.3284 0.371302 20 to 21 141834 -0.2222 0.412074 19 to 20 141781 -0.3786 0.352509 18 to 19 141955 0.1347 0.553583 17 to 18 141743 -0.4906 0.311837 16 to 17 141867 -0.1249 0.450314 15 to 16 141237 -1.9833 0.023668 14 to 15 141834 -0.2222 0.412074 13 to 14 142161 0.7424 0.771074 12 to 13 141882 -0.0806 0.467872 11 to 12 141666 -0.7178 0.236444 10 to 11 142097 0.5536 0.710073 9 to 10 142580 1.9784 0.976057 8 to 9 141881 -0.0836 0.466699 7 to 8 141558 -1.0364 0.150014 6 to 7 141093 -2.4081 0.008019 5 to 6 142063 0.4533 0.674835 4 to 5 141663 -0.7266 0.233724 3 to 4 141649 -0.7679 0.221263 2 to 3 142181 0.8014 0.788546 1 to 2 141515 -1.1632 0.122371 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-03-19_07:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2374.92 -1.769 0.038458 Test results for specific bytes for dh-ranFile-2016-03-19_07:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2643.07 2.023 0.978477 2 to 9 2522.72 0.321 0.625991 3 to 10 2561.33 0.867 0.807138 4 to 11 2431.30 -0.972 0.165632 5 to 12 2480.22 -0.280 0.389839 6 to 13 2531.05 0.439 0.669705 7 to 14 2309.37 -2.696 0.003510 8 to 15 2427.29 -1.028 0.151926 9 to 16 2584.32 1.192 0.883461 10 to 17 2548.35 0.684 0.752959 11 to 18 2518.87 0.267 0.605204 12 to 19 2399.40 -1.423 0.077403 13 to 20 2479.51 -0.290 0.385978 14 to 21 2530.18 0.427 0.665238 15 to 22 2512.79 0.181 0.571768 16 to 23 2482.24 -0.251 0.400853 17 to 24 2530.29 0.428 0.665815 18 to 25 2560.62 0.857 0.804372 19 to 26 2497.31 -0.038 0.484805 20 to 27 2499.29 -0.010 0.495972 21 to 28 2564.54 0.913 0.819316 22 to 29 2589.56 1.267 0.897334 23 to 30 2483.10 -0.239 0.405529 24 to 31 2401.97 -1.386 0.082828 25 to 32 2478.38 -0.306 0.379916 CDPARK for dh-ranFile-2016-03-19_07:31: 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 3494 -1.3242 0.092718 3530 0.3196 0.625377 3536 0.5936 0.723613 3536 0.5936 0.723613 3531 0.3653 0.642555 3527 0.1826 0.572463 3496 -1.2329 0.108811 3517 -0.2740 0.392053 3564 1.8721 0.969407 3542 0.8676 0.807188 Square side=100, avg. no. parked=3527.30 sample std.=19.82 p-value of the KSTEST for those 10 p-values: 0.626199 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-03-19_07:31 0.8183,0.8700,0.3620,0.2484,0.6507,0.0064,0.3711,0.8941,0.6156,0.8415, The KS test for those 10 p-values: 0.536456 The 3DSPHERES test for dh-ranFile-2016-03-19_07:31 sample no r^3 equiv. uni. 1 80.270 0.931138 2 184.435 0.997862 3 44.003 0.769334 4 17.993 0.451058 5 8.636 0.250131 6 1.069 0.035019 7 28.964 0.619197 8 22.155 0.522164 9 17.952 0.450314 10 36.509 0.703877 11 124.927 0.984459 12 48.830 0.803615 13 7.679 0.225823 14 8.451 0.245501 15 10.922 0.305145 16 29.452 0.625335 17 5.708 0.173270 18 7.314 0.216368 19 21.460 0.510963 20 36.500 0.703782 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.750999 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-03-19_07:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.5 -0.4 0.9 0.3 1.6 0.1 0.1 -0.4 1.2 -0.1 0.0 -0.4 -1.0 0.7 -0.7 0.3 0.2 -0.7 1.6 -0.8 -0.8 1.4 -0.1 -1.4 1.2 -0.7 -0.4 0.2 -1.5 0.7 1.3 1.9 -0.4 0.1 -0.3 0.7 -1.3 -1.2 0.4 -0.6 -1.0 -0.1 Chi-square with 42 degrees of freedom:31.630835 z-score=-1.131369, p-value=0.121749 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-03-19_07:31 Test no p-value 1 0.087644 2 0.875361 3 0.041414 4 0.727964 5 0.054624 6 0.028143 7 0.392930 8 0.027855 9 0.469241 10 0.709857 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.026889 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-03-19_07:31: (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 66816 0.33 66948 1.19 3 25000.00 24759 2.32 24822 1.27 4 6666.67 6679 0.02 6584 1.03 5 1388.89 1460 3.64 1352 0.98 6 238.10 246 0.26 256 1.35 7 34.72 38 0.31 35 0.00 8 4.96 1 3.16 2 1.77 p=0.87765 p=0.72905 Number of rngs required: 687174, p-value: 0.076 RESULTS OF CRAPS TEST for dh-ranFile-2016-03-19_07:31 No. of wins: Observed Expected 98505 98585.9 z-score=-0.362, pvalue=0.35881 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66748 66666.7 0.099 0.099 2 37618 37654.3 0.035 0.134 3 27024 26954.7 0.178 0.312 4 19169 19313.5 1.081 1.393 5 13714 13851.4 1.363 2.756 6 9969 9943.5 0.065 2.821 7 7194 7145.0 0.336 3.157 8 5182 5139.1 0.359 3.516 9 3743 3699.9 0.503 4.019 10 2602 2666.3 1.551 5.569 11 1979 1923.3 1.611 7.180 12 1410 1388.7 0.325 7.506 13 1003 1003.7 0.001 7.506 14 706 726.1 0.559 8.065 15 525 525.8 0.001 8.066 16 400 381.2 0.932 8.999 17 265 276.5 0.482 9.480 18 212 200.8 0.621 10.101 19 155 146.0 0.557 10.658 20 116 106.2 0.901 11.559 21 266 287.1 1.553 13.112 Chisq= 13.11 for 20 degrees of freedom, p= 0.12748 SUMMARY of craptest p-value for no. of wins: 0.358808 p-value for throws/game: 0.127482 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-03-19_07:31 No. of wins: Observed Expected 98730 98585.9 z-score= 0.645, pvalue=0.74043 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66690 66666.7 0.008 0.008 2 37612 37654.3 0.048 0.056 3 27082 26954.7 0.601 0.657 4 19248 19313.5 0.222 0.879 5 13784 13851.4 0.328 1.207 6 9849 9943.5 0.899 2.106 7 7170 7145.0 0.087 2.193 8 5140 5139.1 0.000 2.193 9 3684 3699.9 0.068 2.261 10 2695 2666.3 0.309 2.570 11 1931 1923.3 0.031 2.601 12 1373 1388.7 0.178 2.779 13 1000 1003.7 0.014 2.793 14 742 726.1 0.346 3.139 15 570 525.8 3.709 6.848 16 385 381.2 0.039 6.887 17 273 276.5 0.045 6.933 18 202 200.8 0.007 6.939 19 137 146.0 0.553 7.492 20 135 106.2 7.801 15.293 21 298 287.1 0.413 15.706 Chisq= 15.71 for 20 degrees of freedom, p= 0.26531 SUMMARY of craptest p-value for no. of wins: 0.740434 p-value for throws/game: 0.265308 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0035,0.0064,0.0080,0.0082,0.0088,0.0122,0.0216,0.0227,0.0237,0.0247, 0.0269,0.0279,0.0281,0.0306,0.0350,0.0385,0.0414,0.0509,0.0546,0.0758, 0.0774,0.0800,0.0828,0.0876,0.0912,0.0927,0.0986,0.1088,0.1133,0.1186, 0.1217,0.1218,0.1224,0.1275,0.1461,0.1500,0.1519,0.1535,0.1554,0.1584, 0.1591,0.1643,0.1656,0.1723,0.1733,0.1736,0.1803,0.1829,0.1834,0.1875, 0.1988,0.2164,0.2213,0.2257,0.2258,0.2331,0.2331,0.2337,0.2364,0.2385, 0.2455,0.2484,0.2501,0.2503,0.2532,0.2550,0.2580,0.2624,0.2653,0.2670, 0.2743,0.2785,0.2934,0.2969,0.2975,0.2985,0.3051,0.3064,0.3087,0.3111, 0.3118,0.3157,0.3220,0.3232,0.3436,0.3525,0.3588,0.3620,0.3646,0.3711, 0.3713,0.3799,0.3804,0.3812,0.3843,0.3860,0.3898,0.3921,0.3929,0.3948, 0.3982,0.4009,0.4042,0.4055,0.4064,0.4095,0.4120,0.4121,0.4121,0.4166, 0.4219,0.4336,0.4433,0.4475,0.4503,0.4503,0.4511,0.4617,0.4667,0.4679, 0.4692,0.4775,0.4782,0.4820,0.4820,0.4848,0.4864,0.4901,0.4960,0.5077, 0.5110,0.5147,0.5161,0.5214,0.5220,0.5222,0.5264,0.5267,0.5289,0.5365, 0.5435,0.5536,0.5536,0.5547,0.5655,0.5707,0.5707,0.5718,0.5725,0.5744, 0.5748,0.5780,0.5836,0.5912,0.5920,0.6040,0.6052,0.6070,0.6109,0.6155, 0.6156,0.6192,0.6194,0.6253,0.6254,0.6260,0.6262,0.6393,0.6424,0.6426, 0.6507,0.6508,0.6511,0.6541,0.6550,0.6570,0.6595,0.6652,0.6658,0.6661, 0.6697,0.6732,0.6748,0.6826,0.6840,0.6846,0.6940,0.7038,0.7039,0.7047, 0.7099,0.7101,0.7196,0.7236,0.7236,0.7280,0.7291,0.7342,0.7380,0.7381, 0.7402,0.7404,0.7510,0.7530,0.7593,0.7666,0.7693,0.7711,0.7839,0.7881, 0.7885,0.7921,0.8023,0.8029,0.8036,0.8044,0.8046,0.8071,0.8072,0.8110, 0.8183,0.8193,0.8238,0.8289,0.8309,0.8334,0.8415,0.8484,0.8548,0.8591, 0.8610,0.8637,0.8681,0.8693,0.8700,0.8732,0.8737,0.8754,0.8766,0.8777, 0.8807,0.8819,0.8835,0.8847,0.8900,0.8932,0.8941,0.8956,0.8970,0.8973, 0.9114,0.9293,0.9311,0.9419,0.9455,0.9462,0.9466,0.9479,0.9658,0.9694, 0.9702,0.9733,0.9737,0.9761,0.9785,0.9845,0.9908,0.9916,0.9979, Overall p-value after applying KStest on 269 p-values = 0.796702 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.