RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-02-29_02:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.87 9.3394 0.070993 2 to 25 15.62 29.5471 0.970198 3 to 26 15.73 22.2653 0.825268 4 to 27 15.74 18.6164 0.649008 5 to 28 15.84 16.7653 0.529628 6 to 29 15.61 28.9254 0.964779 7 to 30 15.88 21.3378 0.788457 8 to 31 15.96 23.1427 0.855337 9 to 32 15.96 20.2518 0.738445 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.033241 Tough bday spacings test for dh-ranFile-2016-02-29_02:31: 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 7 49 72 87 98 70 61 29 15 7 5 (O-E)^2/E 0.5 4.2 0.0 1.2 0.0 0.8 1.5 0.0 0.0 0.0 0.2 Birthday Spacings: Sum(O-E)^2/E= 8.504, p= 0.420 RESULTS OF GCD FOR dh-ranFile-2016-02-29_02:31 Euclid's algorithm: p-value, steps to gcd: 0.700257 p-value, dist. of gcd's: 0.102655 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-02-29_02:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.931 0.039 0.443 0.902 0.071 0.775 0.150 0.249 Bits 8 to 15---> 0.607 0.906 0.921 0.833 0.352 0.900 0.907 0.895 Bits 16 to 23---> 0.217 0.536 0.628 0.685 0.419 0.055 0.099 0.440 Bits 24 to 31---> 0.633 0.062 0.738 0.094 0.758 0.733 0.673 0.458 KS test for the above 32 p values: 0.553 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-02-29_02:31, p-values for 5 runs: 0.0018, 0.4265, 0.2681, 0.6481, 0.2859 Rank test for binary matrices (31x31) for dh-ranFile-2016-02-29_02:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 195 211.4 1.275 1.275 r= 29 5053 5134.0 1.278 2.553 r= 30 23152 23103.0 0.104 2.657 r= 31 11600 11551.5 0.203 2.860 chi-square = 2.860 with df = 3; p-value = 0.586 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-02-29_02:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 234 211.4 2.412 2.412 r= 30 5246 5134.0 2.443 4.855 r= 31 22974 23103.0 0.721 5.576 r= 32 11546 11551.5 0.003 5.578 chi-square = 5.578 with df = 3; p-value = 0.866 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-02-29_02:31 b-rank test for bits 1 to 8, p=0.10588 b-rank test for bits 2 to 9, p=0.13888 b-rank test for bits 3 to 10, p=0.02341 b-rank test for bits 4 to 11, p=0.93683 b-rank test for bits 5 to 12, p=0.66648 b-rank test for bits 6 to 13, p=0.62609 b-rank test for bits 7 to 14, p=0.95183 b-rank test for bits 8 to 15, p=0.83751 b-rank test for bits 9 to 16, p=0.94139 b-rank test for bits 10 to 17, p=0.62566 b-rank test for bits 11 to 18, p=0.11813 b-rank test for bits 12 to 19, p=0.35933 b-rank test for bits 13 to 20, p=0.16624 b-rank test for bits 14 to 21, p=0.47686 b-rank test for bits 15 to 22, p=0.62593 b-rank test for bits 16 to 23, p=0.73990 b-rank test for bits 17 to 24, p=0.08084 b-rank test for bits 18 to 25, p=0.63349 b-rank test for bits 19 to 26, p=0.25206 b-rank test for bits 20 to 27, p=0.34715 b-rank test for bits 21 to 28, p=0.61321 b-rank test for bits 22 to 29, p=0.97382 b-rank test for bits 23 to 30, p=0.95479 b-rank test for bits 24 to 31, p=0.46311 b-rank test for bits 25 to 32, p=0.99690 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 = 0.310247 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-02-29_02:31 (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 142252 0.80 0.788327 2 142464 1.30 0.902505 3 142011 0.24 0.593884 4 141170 -1.73 0.042047 5 142116 0.48 0.685407 6 141669 -0.56 0.287222 7 142214 0.71 0.761720 8 142315 0.95 0.828391 9 141574 -0.78 0.216672 10 141742 -0.39 0.347914 11 141728 -0.42 0.335904 12 142284 0.88 0.809321 13 142023 0.27 0.604720 14 141999 0.21 0.582975 15 141693 -0.51 0.306624 16 141522 -0.90 0.182739 17 141748 -0.38 0.353109 18 141832 -0.18 0.428310 19 142625 1.67 0.952750 20 141675 -0.55 0.292018 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-02-29_02:31 Bits used No. missing words z-score p-value 23 to 32 141889 -0.0701 0.472056 22 to 31 141994 0.2920 0.614844 21 to 30 141945 0.1230 0.548947 20 to 29 142346 1.5058 0.933935 19 to 28 142083 0.5989 0.725368 18 to 27 141862 -0.1632 0.435178 17 to 26 141751 -0.5460 0.292545 16 to 25 141575 -1.1529 0.124484 15 to 24 141932 0.0782 0.531155 14 to 23 142019 0.3782 0.647349 13 to 22 142025 0.3989 0.655003 12 to 21 141877 -0.1115 0.455617 11 to 20 142298 1.3402 0.909917 10 to 19 141947 0.1299 0.551676 9 to 18 141769 -0.4839 0.314230 8 to 17 141654 -0.8804 0.189308 7 to 16 141445 -1.6011 0.054673 6 to 15 141242 -2.3011 0.010692 5 to 14 142068 0.5471 0.707858 4 to 13 142085 0.6058 0.727663 3 to 12 141727 -0.6287 0.264765 2 to 11 142389 1.6540 0.950940 1 to 10 141702 -0.7149 0.237326 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-02-29_02:31 Bits used No. missing words z-score p-value 28 to 32 141684 -0.7638 0.222484 27 to 31 141390 -1.7604 0.039167 26 to 30 141554 -1.2045 0.114197 25 to 29 142075 0.5616 0.712803 24 to 28 141671 -0.8079 0.209575 23 to 27 141856 -0.1808 0.428270 22 to 26 142395 1.6463 0.950153 21 to 25 141649 -0.8825 0.188760 20 to 24 141743 -0.5638 0.286435 19 to 23 142352 1.5006 0.933267 18 to 22 141613 -1.0045 0.157567 17 to 21 141788 -0.4113 0.340431 16 to 20 141896 -0.0452 0.481979 15 to 19 142143 0.7921 0.785849 14 to 18 141854 -0.1876 0.425611 13 to 17 142146 0.8023 0.788802 12 to 16 142479 1.9311 0.973264 11 to 15 142126 0.7345 0.768670 10 to 14 141850 -0.2011 0.420303 9 to 13 141721 -0.6384 0.261605 8 to 12 142093 0.6226 0.733230 7 to 11 142048 0.4701 0.680847 6 to 10 141565 -1.1672 0.121561 5 to 9 141995 0.2904 0.614248 4 to 8 142254 1.1684 0.878672 3 to 7 142445 1.8158 0.965302 2 to 6 141923 0.0463 0.518480 1 to 5 141778 -0.4452 0.328093 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-02-29_02:31 Bits used No. missing words z-score p-value 31 to 32 141919 0.0285 0.511378 30 to 31 141762 -0.4346 0.331926 29 to 30 142069 0.4710 0.681181 28 to 29 142120 0.6214 0.732847 27 to 28 142352 1.3058 0.904192 26 to 27 142042 0.3914 0.652233 25 to 26 141170 -2.1809 0.014595 24 to 25 142278 1.0875 0.861597 23 to 24 141551 -1.0570 0.145251 22 to 23 141624 -0.8417 0.199983 21 to 22 142422 1.5123 0.934771 20 to 21 142158 0.7335 0.768385 19 to 20 141926 0.0492 0.519610 18 to 19 142355 1.3147 0.905688 17 to 18 142059 0.4415 0.670576 16 to 17 141532 -1.1131 0.132840 15 to 16 141996 0.2557 0.600895 14 to 15 141423 -1.4346 0.075700 13 to 14 141944 0.1023 0.540729 12 to 13 142867 2.8250 0.997636 11 to 12 141944 0.1023 0.540729 10 to 11 141448 -1.3609 0.086780 9 to 10 142039 0.3825 0.648958 8 to 9 142277 1.0846 0.860944 7 to 8 142128 0.6450 0.740551 6 to 7 141711 -0.5850 0.279259 5 to 6 142404 1.4592 0.927745 4 to 5 142073 0.4828 0.685382 3 to 4 141472 -1.2901 0.098515 2 to 3 142288 1.1170 0.868007 1 to 2 141746 -0.4818 0.314974 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-02-29_02:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2441.66 -0.825 0.204670 Test results for specific bytes for dh-ranFile-2016-02-29_02:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2513.31 0.188 0.574667 2 to 9 2629.18 1.827 0.966145 3 to 10 2543.67 0.618 0.731572 4 to 11 2472.31 -0.392 0.347678 5 to 12 2516.31 0.231 0.591209 6 to 13 2477.67 -0.316 0.376106 7 to 14 2578.96 1.117 0.867919 8 to 15 2351.52 -2.100 0.017873 9 to 16 2522.94 0.324 0.627173 10 to 17 2545.14 0.638 0.738398 11 to 18 2558.96 0.834 0.797804 12 to 19 2445.05 -0.777 0.218529 13 to 20 2543.90 0.621 0.732665 14 to 21 2464.90 -0.496 0.309805 15 to 22 2464.72 -0.499 0.308923 16 to 23 2462.40 -0.532 0.297459 17 to 24 2508.58 0.121 0.548316 18 to 25 2584.95 1.201 0.885187 19 to 26 2579.16 1.120 0.868542 20 to 27 2471.11 -0.409 0.341411 21 to 28 2487.02 -0.184 0.427151 22 to 29 2532.36 0.458 0.676372 23 to 30 2471.92 -0.397 0.345638 24 to 31 2395.60 -1.476 0.069920 25 to 32 2547.27 0.669 0.748097 CDPARK for dh-ranFile-2016-02-29_02:31: 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 3492 -1.4155 0.078457 3553 1.3699 0.914635 3557 1.5525 0.939730 3517 -0.2740 0.392053 3543 0.9132 0.819442 3521 -0.0913 0.463617 3552 1.3242 0.907282 3515 -0.3653 0.357445 3568 2.0548 0.980051 3542 0.8676 0.807188 Square side=100, avg. no. parked=3536.00 sample std.=22.49 p-value of the KSTEST for those 10 p-values: 0.060974 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-02-29_02:31 0.3078,0.1401,0.8532,0.3182,0.6341,0.7951,0.4463,0.3752,0.2693,0.6522, The KS test for those 10 p-values: 0.753172 The 3DSPHERES test for dh-ranFile-2016-02-29_02:31 sample no r^3 equiv. uni. 1 0.983 0.032244 2 13.383 0.359881 3 1.132 0.037035 4 7.669 0.225580 5 1.619 0.052527 6 3.818 0.119510 7 13.091 0.353609 8 25.808 0.576950 9 57.019 0.850525 10 49.356 0.807025 11 2.125 0.068387 12 52.387 0.825571 13 24.575 0.559194 14 44.931 0.776358 15 119.423 0.981329 16 30.623 0.639681 17 3.457 0.108832 18 28.373 0.611618 19 47.825 0.796923 20 113.091 0.976941 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.439164 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-02-29_02:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 2.2 0.6 0.6 -1.3 -0.2 1.3 0.7 -0.7 1.6 0.0 -1.8 1.1 -0.1 0.0 1.7 0.2 0.1 0.1 -2.0 -0.6 0.4 -0.7 0.9 -1.9 -0.2 1.3 0.4 0.2 -0.1 -0.9 -0.1 -0.2 0.7 1.5 0.8 -1.2 0.8 -0.4 -1.3 -1.3 -1.0 -0.1 Chi-square with 42 degrees of freedom:41.480878 z-score=-0.056641, p-value=0.506391 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-02-29_02:31 Test no p-value 1 0.496249 2 0.092583 3 0.081598 4 0.816390 5 0.577183 6 0.049130 7 0.126476 8 0.032089 9 0.741223 10 0.567723 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.090332 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-02-29_02:31: (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 66545 0.22 66462 0.63 3 25000.00 24990 0.00 25158 1.00 4 6666.67 6798 2.59 6699 0.16 5 1388.89 1373 0.18 1406 0.21 6 238.10 257 1.50 235 0.04 7 34.72 34 0.01 36 0.05 8 4.96 2 1.77 3 0.77 p=0.60716 p=0.17336 Number of rngs required: 691198, p-value: 1.000 RESULTS OF CRAPS TEST for dh-ranFile-2016-02-29_02:31 No. of wins: Observed Expected 98608 98585.9 z-score= 0.099, pvalue=0.53944 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66807 66666.7 0.295 0.295 2 37501 37654.3 0.624 0.920 3 26920 26954.7 0.045 0.964 4 19309 19313.5 0.001 0.965 5 13826 13851.4 0.047 1.012 6 9956 9943.5 0.016 1.028 7 7063 7145.0 0.942 1.969 8 5100 5139.1 0.297 2.266 9 3837 3699.9 5.083 7.349 10 2695 2666.3 0.309 7.658 11 1829 1923.3 4.626 12.285 12 1321 1388.7 3.304 15.589 13 1082 1003.7 6.106 21.695 14 751 726.1 0.851 22.546 15 597 525.8 9.631 32.177 16 379 381.2 0.012 32.189 17 271 276.5 0.111 32.300 18 208 200.8 0.256 32.556 19 136 146.0 0.683 33.239 20 117 106.2 1.095 34.334 21 295 287.1 0.217 34.550 Chisq= 34.55 for 20 degrees of freedom, p= 0.97737 SUMMARY of craptest p-value for no. of wins: 0.539443 p-value for throws/game: 0.977367 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-02-29_02:31 No. of wins: Observed Expected 99135 98585.9 z-score= 2.456, pvalue=0.99298 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66760 66666.7 0.131 0.131 2 37520 37654.3 0.479 0.610 3 26724 26954.7 1.975 2.585 4 19404 19313.5 0.424 3.009 5 13906 13851.4 0.215 3.224 6 9898 9943.5 0.209 3.433 7 7235 7145.0 1.133 4.566 8 5122 5139.1 0.057 4.623 9 3727 3699.9 0.199 4.822 10 2733 2666.3 1.669 6.490 11 1930 1923.3 0.023 6.514 12 1415 1388.7 0.497 7.010 13 911 1003.7 8.564 15.574 14 780 726.1 3.995 19.569 15 535 525.8 0.160 19.729 16 367 381.2 0.525 20.254 17 266 276.5 0.402 20.656 18 187 200.8 0.952 21.608 19 146 146.0 0.000 21.608 20 114 106.2 0.571 22.179 21 320 287.1 3.767 25.946 Chisq= 25.95 for 20 degrees of freedom, p= 0.83239 SUMMARY of craptest p-value for no. of wins: 0.992977 p-value for throws/game: 0.832386 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0018,0.0107,0.0146,0.0179,0.0234,0.0321,0.0322,0.0332,0.0370,0.0392, 0.0395,0.0420,0.0491,0.0525,0.0546,0.0547,0.0610,0.0623,0.0684,0.0699, 0.0710,0.0710,0.0757,0.0785,0.0808,0.0816,0.0868,0.0903,0.0926,0.0942, 0.0985,0.0994,0.1027,0.1059,0.1088,0.1142,0.1181,0.1195,0.1216,0.1245, 0.1265,0.1328,0.1389,0.1401,0.1453,0.1503,0.1576,0.1662,0.1734,0.1827, 0.1888,0.1893,0.2000,0.2047,0.2096,0.2167,0.2168,0.2185,0.2225,0.2256, 0.2373,0.2494,0.2521,0.2616,0.2648,0.2681,0.2693,0.2793,0.2859,0.2864, 0.2872,0.2920,0.2925,0.2975,0.3066,0.3078,0.3089,0.3098,0.3102,0.3142, 0.3150,0.3182,0.3281,0.3319,0.3359,0.3404,0.3414,0.3456,0.3471,0.3477, 0.3479,0.3517,0.3531,0.3536,0.3574,0.3593,0.3599,0.3752,0.3761,0.3921, 0.4187,0.4203,0.4203,0.4256,0.4265,0.4272,0.4283,0.4283,0.4352,0.4392, 0.4399,0.4430,0.4463,0.4556,0.4580,0.4631,0.4636,0.4721,0.4769,0.4820, 0.4962,0.5064,0.5114,0.5185,0.5196,0.5296,0.5312,0.5362,0.5394,0.5407, 0.5407,0.5483,0.5489,0.5517,0.5534,0.5592,0.5677,0.5747,0.5770,0.5772, 0.5830,0.5863,0.5912,0.5939,0.6009,0.6047,0.6065,0.6072,0.6116,0.6132, 0.6142,0.6148,0.6257,0.6259,0.6261,0.6272,0.6285,0.6331,0.6335,0.6341, 0.6397,0.6473,0.6481,0.6490,0.6490,0.6522,0.6522,0.6550,0.6665,0.6706, 0.6729,0.6764,0.6808,0.6812,0.6848,0.6854,0.6854,0.7003,0.7079,0.7128, 0.7254,0.7277,0.7316,0.7326,0.7327,0.7328,0.7332,0.7380,0.7384,0.7384, 0.7399,0.7406,0.7412,0.7481,0.7532,0.7580,0.7617,0.7684,0.7687,0.7751, 0.7764,0.7858,0.7883,0.7885,0.7888,0.7951,0.7969,0.7978,0.8070,0.8072, 0.8093,0.8164,0.8194,0.8253,0.8256,0.8284,0.8324,0.8329,0.8375,0.8505, 0.8532,0.8553,0.8609,0.8616,0.8660,0.8679,0.8680,0.8685,0.8787,0.8852, 0.8947,0.9001,0.9019,0.9025,0.9042,0.9057,0.9063,0.9068,0.9073,0.9099, 0.9146,0.9206,0.9277,0.9314,0.9333,0.9339,0.9348,0.9368,0.9397,0.9414, 0.9502,0.9509,0.9518,0.9528,0.9548,0.9648,0.9653,0.9661,0.9702,0.9733, 0.9738,0.9769,0.9774,0.9801,0.9813,0.9930,0.9969,0.9976,0.9997, Overall p-value after applying KStest on 269 p-values = 0.173936 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.