RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-27_01:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.58 19.6264 0.706215 2 to 25 15.52 17.8287 0.600273 3 to 26 15.97 11.8110 0.188557 4 to 27 16.00 10.2416 0.106828 5 to 28 15.71 19.5213 0.700558 6 to 29 15.72 7.8969 0.031299 7 to 30 15.82 15.6934 0.454334 8 to 31 15.55 19.0414 0.673841 9 to 32 16.09 16.8671 0.536598 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.583551 Tough bday spacings test for dh-ranFile-2018-06-27_01:31: 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 30 74 102 99 60 67 32 15 7 3 (O-E)^2/E 0.4 1.2 0.0 0.2 0.0 4.2 4.3 0.2 0.0 0.0 0.3 Birthday Spacings: Sum(O-E)^2/E= 10.733, p= 0.621 RESULTS OF GCD FOR dh-ranFile-2018-06-27_01:31 Euclid's algorithm: p-value, steps to gcd: 0.530242 p-value, dist. of gcd's: 0.056831 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-27_01:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.054 0.394 0.669 0.866 0.125 0.016 0.995 0.458 Bits 8 to 15---> 0.240 0.919 0.041 0.852 0.948 0.722 0.151 0.691 Bits 16 to 23---> 0.007 0.324 0.625 0.082 0.999 0.659 0.994 0.077 Bits 24 to 31---> 0.740 0.506 0.773 0.558 0.822 0.430 0.055 0.459 KS test for the above 32 p values: 0.804 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-27_01:31, p-values for 5 runs: 0.9710, 0.3144, 0.2782, 0.4639, 0.1525 Rank test for binary matrices (31x31) for dh-ranFile-2018-06-27_01:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 209 211.4 0.028 0.028 r= 29 5071 5134.0 0.773 0.801 r= 30 23357 23103.0 2.791 3.592 r= 31 11363 11551.5 3.077 6.669 chi-square = 6.669 with df = 3; p-value = 0.917 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-06-27_01:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 225 211.4 0.873 0.873 r= 30 5149 5134.0 0.044 0.916 r= 31 23085 23103.0 0.014 0.930 r= 32 11541 11551.5 0.010 0.940 chi-square = 0.940 with df = 3; p-value = 0.184 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-06-27_01:31 b-rank test for bits 1 to 8, p=0.28947 b-rank test for bits 2 to 9, p=0.91743 b-rank test for bits 3 to 10, p=0.72751 b-rank test for bits 4 to 11, p=0.06962 b-rank test for bits 5 to 12, p=0.84269 b-rank test for bits 6 to 13, p=0.90143 b-rank test for bits 7 to 14, p=0.81616 b-rank test for bits 8 to 15, p=0.24462 b-rank test for bits 9 to 16, p=0.08219 b-rank test for bits 10 to 17, p=0.89395 b-rank test for bits 11 to 18, p=0.54721 b-rank test for bits 12 to 19, p=0.82440 b-rank test for bits 13 to 20, p=0.31809 b-rank test for bits 14 to 21, p=0.26265 b-rank test for bits 15 to 22, p=0.35658 b-rank test for bits 16 to 23, p=0.39561 b-rank test for bits 17 to 24, p=0.35350 b-rank test for bits 18 to 25, p=0.49820 b-rank test for bits 19 to 26, p=0.03112 b-rank test for bits 20 to 27, p=0.71549 b-rank test for bits 21 to 28, p=0.98213 b-rank test for bits 22 to 29, p=0.90120 b-rank test for bits 23 to 30, p=0.43574 b-rank test for bits 24 to 31, p=0.26780 b-rank test for bits 25 to 32, p=0.49393 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 = 0.769903 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-27_01:31 (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 141657 -0.59 0.277744 2 141580 -0.77 0.220809 3 142409 1.17 0.878486 4 142131 0.52 0.697743 5 141492 -0.98 0.164763 6 141563 -0.81 0.209205 7 142294 0.90 0.815610 8 142256 0.81 0.791023 9 141639 -0.63 0.263820 10 142046 0.32 0.625259 11 142593 1.60 0.944907 12 141816 -0.22 0.413691 13 141862 -0.11 0.455973 14 142260 0.82 0.793699 15 141966 0.13 0.552669 16 141658 -0.59 0.278528 17 142149 0.56 0.712252 18 142994 2.53 0.994366 19 141883 -0.06 0.475473 20 141707 -0.47 0.318202 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-06-27_01:31 Bits used No. missing words z-score p-value 23 to 32 141856 -0.1839 0.427047 22 to 31 142310 1.3816 0.916456 21 to 30 141499 -1.4149 0.078544 20 to 29 141641 -0.9253 0.177411 19 to 28 141805 -0.3598 0.359514 18 to 27 141638 -0.9356 0.174734 17 to 26 141594 -1.0873 0.138442 16 to 25 142328 1.4437 0.925587 15 to 24 142480 1.9678 0.975456 14 to 23 141743 -0.5736 0.283136 13 to 22 142248 1.1678 0.878562 12 to 21 141648 -0.9011 0.183758 11 to 20 142728 2.8230 0.997621 10 to 19 142039 0.4471 0.672612 9 to 18 141850 -0.2046 0.418948 8 to 17 141661 -0.8563 0.195913 7 to 16 141679 -0.7942 0.213528 6 to 15 141413 -1.7115 0.043496 5 to 14 141790 -0.4115 0.340359 4 to 13 142115 0.7092 0.760902 3 to 12 141801 -0.3736 0.354369 2 to 11 142173 0.9092 0.818380 1 to 10 141650 -0.8942 0.185596 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-06-27_01:31 Bits used No. missing words z-score p-value 28 to 32 141458 -1.5299 0.063017 27 to 31 141671 -0.8079 0.209575 26 to 30 142322 1.3989 0.919076 25 to 29 141779 -0.4418 0.329318 24 to 28 142275 1.2396 0.892431 23 to 27 142003 0.3175 0.624578 22 to 26 141822 -0.2960 0.383602 21 to 25 142256 1.1752 0.880033 20 to 24 142292 1.2972 0.902717 19 to 23 142079 0.5752 0.717406 18 to 22 142074 0.5582 0.711647 17 to 21 141911 0.0057 0.502258 16 to 20 141826 -0.2825 0.388790 15 to 19 141813 -0.3265 0.372007 14 to 18 141741 -0.5706 0.284132 13 to 17 141854 -0.1876 0.425611 12 to 16 142137 0.7718 0.779873 11 to 15 141614 -1.0011 0.158385 10 to 14 141785 -0.4215 0.336711 9 to 13 142190 0.9514 0.829305 8 to 12 141773 -0.4621 0.321992 7 to 11 141648 -0.8859 0.187845 6 to 10 141694 -0.7299 0.232716 5 to 9 142012 0.3480 0.636093 4 to 8 141692 -0.7367 0.230649 3 to 7 141925 0.0531 0.521181 2 to 6 141786 -0.4181 0.337949 1 to 5 141898 -0.0384 0.484682 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-06-27_01:31 Bits used No. missing words z-score p-value 31 to 32 142085 0.5182 0.697841 30 to 31 141951 0.1229 0.548915 29 to 30 141483 -1.2576 0.104266 28 to 29 141834 -0.2222 0.412074 27 to 28 142463 1.6332 0.948791 26 to 27 141715 -0.5732 0.283240 25 to 26 141296 -1.8092 0.035207 24 to 25 141654 -0.7532 0.225669 23 to 24 141494 -1.2252 0.110257 22 to 23 141523 -1.1396 0.127223 21 to 22 141595 -0.9272 0.176904 20 to 21 141755 -0.4553 0.324464 19 to 20 141705 -0.6027 0.273340 18 to 19 141786 -0.3638 0.358002 17 to 18 142187 0.8191 0.793631 16 to 17 141790 -0.3520 0.362417 15 to 16 141892 -0.0511 0.479615 14 to 15 141879 -0.0895 0.464355 13 to 14 141763 -0.4317 0.332997 12 to 13 142347 1.2911 0.901659 11 to 12 141723 -0.5496 0.291281 10 to 11 141685 -0.6617 0.254069 9 to 10 141869 -0.1190 0.452651 8 to 9 141887 -0.0659 0.473741 7 to 8 141896 -0.0393 0.484317 6 to 7 141638 -0.8004 0.211744 5 to 6 141774 -0.3992 0.344872 4 to 5 142040 0.3855 0.650051 3 to 4 142365 1.3442 0.910552 2 to 3 141561 -1.0275 0.152087 1 to 2 142046 0.4032 0.656583 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-27_01:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2649.92 2.120 0.983008 Test results for specific bytes for dh-ranFile-2018-06-27_01:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2357.16 -2.020 0.021691 2 to 9 2543.87 0.620 0.732518 3 to 10 2523.68 0.335 0.631144 4 to 11 2380.10 -1.696 0.044976 5 to 12 2535.28 0.499 0.691087 6 to 13 2453.98 -0.651 0.257600 7 to 14 2387.90 -1.585 0.056442 8 to 15 2564.57 0.913 0.819416 9 to 16 2448.58 -0.727 0.233534 10 to 17 2501.91 0.027 0.510773 11 to 18 2645.84 2.062 0.980417 12 to 19 2614.14 1.614 0.946751 13 to 20 2559.00 0.834 0.797958 14 to 21 2538.29 0.541 0.705911 15 to 22 2565.72 0.929 0.823664 16 to 23 2518.54 0.262 0.603392 17 to 24 2485.12 -0.210 0.416654 18 to 25 2587.45 1.237 0.891897 19 to 26 2466.48 -0.474 0.317713 20 to 27 2509.86 0.139 0.555429 21 to 28 2581.08 1.147 0.874232 22 to 29 2549.96 0.706 0.760054 23 to 30 2476.06 -0.339 0.367489 24 to 31 2595.36 1.349 0.911271 25 to 32 2413.64 -1.221 0.110981 CDPARK for dh-ranFile-2018-06-27_01:31: 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 3536 0.5936 0.723613 3524 0.0457 0.518210 3549 1.1872 0.882429 3559 1.6438 0.949895 3540 0.7763 0.781201 3561 1.7352 0.958644 3529 0.2740 0.607947 3506 -0.7763 0.218799 3532 0.4110 0.659449 3555 1.4612 0.928018 Square side=100, avg. no. parked=3539.10 sample std.=16.47 p-value of the KSTEST for those 10 p-values: 0.021116 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-27_01:31 0.2178,0.4511,0.7772,0.8846,0.7268,0.0617,0.5615,0.5316,0.3649,0.4151, The KS test for those 10 p-values: 0.931569 The 3DSPHERES test for dh-ranFile-2018-06-27_01:31 sample no r^3 equiv. uni. 1 75.547 0.919398 2 0.691 0.022785 3 22.383 0.525794 4 30.480 0.637962 5 5.036 0.154547 6 75.205 0.918473 7 21.766 0.515933 8 1.592 0.051693 9 6.985 0.207703 10 35.109 0.689721 11 65.477 0.887249 12 16.031 0.413958 13 10.342 0.291585 14 7.063 0.209783 15 16.409 0.421289 16 24.619 0.559852 17 46.440 0.787327 18 8.511 0.247002 19 37.113 0.709776 20 45.351 0.779463 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.997440 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-27_01:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.5 -0.1 -0.4 0.5 -0.7 -1.5 1.3 -1.0 -0.8 0.6 0.7 -0.4 -0.2 -0.4 -1.8 0.2 0.9 -0.6 0.8 -1.0 1.1 0.8 0.4 0.7 -0.3 0.2 0.2 0.8 0.2 -0.3 0.4 0.4 -0.4 -0.1 0.6 -1.4 1.1 -0.4 1.5 0.9 0.0 1.8 Chi-square with 42 degrees of freedom:27.690825 z-score=-1.561259, p-value=0.043633 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-06-27_01:31 Test no p-value 1 0.609188 2 0.903905 3 0.064459 4 0.464732 5 0.343506 6 0.147456 7 0.021543 8 0.011231 9 0.062636 10 0.665269 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.039286 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-27_01:31: (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 66796 0.25 66710 0.03 3 25000.00 24821 1.28 24976 0.02 4 6666.67 6766 1.48 6613 0.43 5 1388.89 1332 2.33 1446 2.35 6 238.10 255 1.20 220 1.38 7 34.72 23 3.96 27 1.72 8 4.96 6 0.22 7 0.84 p=0.90248 p=0.65662 Number of rngs required: 687617, p-value: 0.182 RESULTS OF CRAPS TEST for dh-ranFile-2018-06-27_01:31 No. of wins: Observed Expected 98629 98585.9 z-score= 0.193, pvalue=0.57650 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66811 66666.7 0.312 0.312 2 37779 37654.3 0.413 0.725 3 26774 26954.7 1.212 1.937 4 19217 19313.5 0.482 2.419 5 13968 13851.4 0.981 3.400 6 9878 9943.5 0.432 3.832 7 7176 7145.0 0.134 3.966 8 5151 5139.1 0.028 3.994 9 3585 3699.9 3.566 7.560 10 2631 2666.3 0.467 8.027 11 1936 1923.3 0.083 8.111 12 1375 1388.7 0.136 8.247 13 1115 1003.7 12.338 20.585 14 699 726.1 1.014 21.600 15 548 525.8 0.934 22.534 16 370 381.2 0.326 22.860 17 291 276.5 0.756 23.616 18 188 200.8 0.820 24.436 19 148 146.0 0.028 24.464 20 89 106.2 2.790 27.254 21 271 287.1 0.904 28.158 Chisq= 28.16 for 20 degrees of freedom, p= 0.89430 SUMMARY of craptest p-value for no. of wins: 0.576502 p-value for throws/game: 0.894298 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-27_01:31 No. of wins: Observed Expected 98879 98585.9 z-score= 1.311, pvalue=0.90509 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66762 66666.7 0.136 0.136 2 37480 37654.3 0.807 0.943 3 27026 26954.7 0.188 1.132 4 19275 19313.5 0.077 1.208 5 13949 13851.4 0.687 1.896 6 9767 9943.5 3.134 5.030 7 7173 7145.0 0.110 5.140 8 5206 5139.1 0.872 6.011 9 3705 3699.9 0.007 6.019 10 2666 2666.3 0.000 6.019 11 1914 1923.3 0.045 6.064 12 1383 1388.7 0.024 6.088 13 1037 1003.7 1.104 7.191 14 732 726.1 0.047 7.239 15 544 525.8 0.627 7.866 16 372 381.2 0.220 8.086 17 271 276.5 0.111 8.197 18 203 200.8 0.023 8.220 19 160 146.0 1.346 9.566 20 109 106.2 0.073 9.639 21 266 287.1 1.553 11.191 Chisq= 11.19 for 20 degrees of freedom, p= 0.05889 SUMMARY of craptest p-value for no. of wins: 0.905088 p-value for throws/game: 0.058895 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0066,0.0112,0.0161,0.0211,0.0215,0.0217,0.0228,0.0311,0.0313,0.0352, 0.0393,0.0415,0.0435,0.0436,0.0450,0.0517,0.0543,0.0548,0.0564,0.0568, 0.0589,0.0617,0.0626,0.0630,0.0645,0.0696,0.0771,0.0785,0.0820,0.0822, 0.1043,0.1068,0.1103,0.1110,0.1249,0.1272,0.1384,0.1475,0.1508,0.1521, 0.1525,0.1545,0.1584,0.1648,0.1747,0.1769,0.1774,0.1815,0.1838,0.1842, 0.1856,0.1878,0.1886,0.1959,0.2077,0.2092,0.2096,0.2098,0.2117,0.2135, 0.2178,0.2188,0.2208,0.2257,0.2306,0.2327,0.2335,0.2402,0.2446,0.2470, 0.2541,0.2576,0.2627,0.2638,0.2678,0.2733,0.2777,0.2782,0.2785,0.2831, 0.2832,0.2841,0.2895,0.2913,0.2916,0.3144,0.3177,0.3181,0.3182,0.3220, 0.3243,0.3245,0.3293,0.3330,0.3367,0.3379,0.3404,0.3435,0.3449,0.3535, 0.3544,0.3566,0.3580,0.3595,0.3624,0.3649,0.3675,0.3720,0.3836,0.3888, 0.3941,0.3956,0.4121,0.4137,0.4140,0.4151,0.4167,0.4189,0.4213,0.4256, 0.4270,0.4301,0.4357,0.4511,0.4527,0.4543,0.4560,0.4580,0.4595,0.4639, 0.4644,0.4647,0.4737,0.4755,0.4796,0.4843,0.4847,0.4939,0.4982,0.5023, 0.5056,0.5108,0.5159,0.5182,0.5212,0.5258,0.5302,0.5316,0.5366,0.5472, 0.5489,0.5527,0.5554,0.5580,0.5599,0.5615,0.5765,0.5836,0.6003,0.6034, 0.6079,0.6092,0.6213,0.6246,0.6248,0.6253,0.6311,0.6361,0.6380,0.6501, 0.6566,0.6566,0.6589,0.6594,0.6653,0.6692,0.6726,0.6738,0.6897,0.6906, 0.6911,0.6977,0.6978,0.7006,0.7059,0.7062,0.7098,0.7116,0.7123,0.7155, 0.7174,0.7225,0.7236,0.7268,0.7275,0.7325,0.7399,0.7601,0.7609,0.7699, 0.7730,0.7772,0.7795,0.7799,0.7812,0.7873,0.7910,0.7936,0.7937,0.7980, 0.8040,0.8156,0.8162,0.8184,0.8194,0.8218,0.8237,0.8244,0.8293,0.8427, 0.8516,0.8663,0.8742,0.8785,0.8786,0.8800,0.8824,0.8846,0.8872,0.8919, 0.8924,0.8939,0.8943,0.9012,0.9014,0.9017,0.9025,0.9027,0.9039,0.9051, 0.9106,0.9113,0.9165,0.9168,0.9174,0.9185,0.9187,0.9191,0.9194,0.9256, 0.9280,0.9316,0.9449,0.9468,0.9482,0.9488,0.9499,0.9586,0.9710,0.9755, 0.9804,0.9821,0.9830,0.9941,0.9944,0.9951,0.9974,0.9976,0.9992, Overall p-value after applying KStest on 269 p-values = 0.591348 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.