RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-09-18_16:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.83 18.3526 0.633071 2 to 25 15.76 26.6870 0.937179 3 to 26 15.70 11.1430 0.150964 4 to 27 15.52 18.9451 0.668306 5 to 28 15.77 21.6987 0.803414 6 to 29 15.96 22.6084 0.837561 7 to 30 16.01 9.0401 0.061006 8 to 31 15.92 9.9232 0.093199 9 to 32 15.64 11.1856 0.153245 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.563366 Tough bday spacings test for dh-ranFile-2016-09-18_16:31: 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 9 40 65 108 90 88 55 21 13 6 5 (O-E)^2/E 0.0 0.3 0.9 1.1 0.6 1.2 0.2 2.6 0.2 0.1 0.2 Birthday Spacings: Sum(O-E)^2/E= 7.436, p= 0.316 RESULTS OF GCD FOR dh-ranFile-2016-09-18_16:31 Euclid's algorithm: p-value, steps to gcd: 0.508186 p-value, dist. of gcd's: 0.941216 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-09-18_16:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.895 0.866 0.516 0.562 0.411 0.358 0.901 0.837 Bits 8 to 15---> 0.296 0.545 0.249 0.562 0.584 0.767 0.354 0.799 Bits 16 to 23---> 0.276 0.167 0.080 0.587 0.993 0.634 0.693 0.539 Bits 24 to 31---> 0.667 0.067 0.416 0.914 0.344 0.129 0.618 0.166 KS test for the above 32 p values: 0.213 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-09-18_16:31, p-values for 5 runs: 0.4230, 0.2289, 0.7165, 0.2552, 0.8260 Rank test for binary matrices (31x31) for dh-ranFile-2016-09-18_16:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 204 211.4 0.260 0.260 r= 29 5153 5134.0 0.070 0.331 r= 30 22936 23103.0 1.208 1.538 r= 31 11707 11551.5 2.093 3.631 chi-square = 3.631 with df = 3; p-value = 0.696 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-09-18_16:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 198 211.4 0.852 0.852 r= 30 5229 5134.0 1.757 2.609 r= 31 23066 23103.0 0.059 2.668 r= 32 11507 11551.5 0.172 2.840 chi-square = 2.840 with df = 3; p-value = 0.583 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-09-18_16:31 b-rank test for bits 1 to 8, p=0.35250 b-rank test for bits 2 to 9, p=0.88419 b-rank test for bits 3 to 10, p=0.30780 b-rank test for bits 4 to 11, p=0.60702 b-rank test for bits 5 to 12, p=0.86897 b-rank test for bits 6 to 13, p=0.49997 b-rank test for bits 7 to 14, p=0.38771 b-rank test for bits 8 to 15, p=0.84344 b-rank test for bits 9 to 16, p=0.57569 b-rank test for bits 10 to 17, p=0.12151 b-rank test for bits 11 to 18, p=0.23882 b-rank test for bits 12 to 19, p=0.40024 b-rank test for bits 13 to 20, p=0.31444 b-rank test for bits 14 to 21, p=0.73144 b-rank test for bits 15 to 22, p=0.15996 b-rank test for bits 16 to 23, p=0.38314 b-rank test for bits 17 to 24, p=0.34843 b-rank test for bits 18 to 25, p=0.54348 b-rank test for bits 19 to 26, p=0.94645 b-rank test for bits 20 to 27, p=0.77224 b-rank test for bits 21 to 28, p=0.52300 b-rank test for bits 22 to 29, p=0.82366 b-rank test for bits 23 to 30, p=0.67962 b-rank test for bits 24 to 31, p=0.30222 b-rank test for bits 25 to 32, p=0.82066 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 = 0.452892 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-09-18_16:31 (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 141729 -0.42 0.336756 2 141087 -1.92 0.027345 3 141322 -1.37 0.084990 4 142872 2.25 0.987751 5 141704 -0.48 0.315705 6 141924 0.03 0.513671 7 141944 0.08 0.532281 8 141881 -0.07 0.473613 9 142658 1.75 0.959874 10 142667 1.77 0.961658 11 141887 -0.05 0.479196 12 141819 -0.21 0.416424 13 141377 -1.24 0.106794 14 142370 1.08 0.859111 15 142203 0.69 0.753689 16 141114 -1.86 0.031567 17 141617 -0.68 0.247299 18 141664 -0.57 0.283254 19 141832 -0.18 0.428310 20 141495 -0.97 0.166507 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-09-18_16:31 Bits used No. missing words z-score p-value 23 to 32 142027 0.4058 0.657540 22 to 31 141468 -1.5218 0.064026 21 to 30 141974 0.2230 0.588232 20 to 29 141802 -0.3701 0.355653 19 to 28 141824 -0.2942 0.384287 18 to 27 142184 0.9471 0.828216 17 to 26 141991 0.2816 0.610883 16 to 25 141615 -1.0149 0.155069 15 to 24 142124 0.7402 0.770423 14 to 23 141661 -0.8563 0.195913 13 to 22 141702 -0.7149 0.237326 12 to 21 141484 -1.4667 0.071235 11 to 20 142013 0.3575 0.639635 10 to 19 141781 -0.4425 0.329058 9 to 18 142015 0.3644 0.642213 8 to 17 141965 0.1920 0.576115 7 to 16 142419 1.7575 0.960582 6 to 15 142154 0.8437 0.800579 5 to 14 141864 -0.1563 0.437894 4 to 13 142040 0.4506 0.673856 3 to 12 141997 0.3023 0.618792 2 to 11 141949 0.1368 0.554403 1 to 10 142088 0.6161 0.731087 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-09-18_16:31 Bits used No. missing words z-score p-value 28 to 32 141757 -0.5164 0.302797 27 to 31 141745 -0.5571 0.288746 26 to 30 142345 1.4768 0.930142 25 to 29 141875 -0.1164 0.453679 24 to 28 141842 -0.2282 0.409731 23 to 27 141755 -0.5232 0.300434 22 to 26 141267 -2.1774 0.014726 21 to 25 141947 0.1277 0.550805 20 to 24 142305 1.3413 0.910081 19 to 23 142154 0.8294 0.796558 18 to 22 141531 -1.2825 0.099838 17 to 21 141911 0.0057 0.502258 16 to 20 141616 -0.9943 0.160029 15 to 19 142130 0.7480 0.772780 14 to 18 142139 0.7785 0.781875 13 to 17 141899 -0.0350 0.486033 12 to 16 141951 0.1413 0.556166 11 to 15 142005 0.3243 0.627147 10 to 14 141982 0.2463 0.597290 9 to 13 142582 2.2802 0.988703 8 to 12 141666 -0.8248 0.204729 7 to 11 141741 -0.5706 0.284132 6 to 10 142498 1.9955 0.977005 5 to 9 141938 0.0972 0.538711 4 to 8 141672 -0.8045 0.210552 3 to 7 141973 0.2158 0.585440 2 to 6 141933 0.0802 0.531976 1 to 5 141700 -0.7096 0.238978 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-09-18_16:31 Bits used No. missing words z-score p-value 31 to 32 141923 0.0403 0.516083 30 to 31 141821 -0.2606 0.397216 29 to 30 142292 1.1288 0.870513 28 to 29 142047 0.4061 0.657668 27 to 28 141963 0.1583 0.562897 26 to 27 141849 -0.1780 0.429375 25 to 26 142029 0.3530 0.637959 24 to 25 141387 -1.5408 0.061683 23 to 24 141511 -1.1750 0.119994 22 to 23 141761 -0.4376 0.330856 21 to 22 141716 -0.5703 0.284239 20 to 21 141327 -1.7178 0.042918 19 to 20 141438 -1.3904 0.082211 18 to 19 142359 1.3265 0.907656 17 to 18 141758 -0.4464 0.327654 16 to 17 142461 1.6273 0.948168 15 to 16 141682 -0.6706 0.251241 14 to 15 141872 -0.1101 0.456158 13 to 14 142056 0.4327 0.667367 12 to 13 141925 0.0462 0.518434 11 to 12 141940 0.0905 0.536044 10 to 11 141857 -0.1544 0.438661 9 to 10 141845 -0.1898 0.424747 8 to 9 141444 -1.3727 0.084930 7 to 8 142636 2.1436 0.983966 6 to 7 141666 -0.7178 0.236444 5 to 6 142335 1.2557 0.895381 4 to 5 142022 0.3324 0.630191 3 to 4 141536 -1.1013 0.135390 2 to 3 141935 0.0757 0.530180 1 to 2 141986 0.2262 0.589464 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-09-18_16:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2438.23 -0.874 0.191192 Test results for specific bytes for dh-ranFile-2016-09-18_16:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2446.85 -0.752 0.226134 2 to 9 2611.28 1.574 0.942223 3 to 10 2404.32 -1.353 0.088018 4 to 11 2424.72 -1.065 0.143533 5 to 12 2556.89 0.805 0.789448 6 to 13 2455.88 -0.624 0.266338 7 to 14 2356.68 -2.027 0.021337 8 to 15 2480.19 -0.280 0.389683 9 to 16 2525.90 0.366 0.642930 10 to 17 2527.69 0.392 0.652325 11 to 18 2431.34 -0.971 0.165781 12 to 19 2520.96 0.296 0.616540 13 to 20 2620.42 1.703 0.955714 14 to 21 2462.86 -0.525 0.299706 15 to 22 2504.98 0.070 0.528055 16 to 23 2517.89 0.253 0.599868 17 to 24 2416.30 -1.184 0.118273 18 to 25 2415.41 -1.196 0.115789 19 to 26 2424.27 -1.071 0.142075 20 to 27 2603.42 1.463 0.928214 21 to 28 2563.16 0.893 0.814114 22 to 29 2507.18 0.102 0.540434 23 to 30 2481.76 -0.258 0.398230 24 to 31 2563.27 0.895 0.814557 25 to 32 2497.57 -0.034 0.486292 CDPARK for dh-ranFile-2016-09-18_16:31: 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 3523 0.0000 0.500000 3524 0.0457 0.518210 3465 -2.6484 0.004044 3568 2.0548 0.980051 3517 -0.2740 0.392053 3517 -0.2740 0.392053 3519 -0.1826 0.427537 3505 -0.8219 0.205562 3513 -0.4566 0.323972 3559 1.6438 0.949895 Square side=100, avg. no. parked=3521.00 sample std.=26.75 p-value of the KSTEST for those 10 p-values: 0.441344 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-09-18_16:31 0.4385,0.7010,0.1034,0.7427,0.0103,0.9505,0.1274,0.3816,0.6844,0.1222, The KS test for those 10 p-values: 0.496823 The 3DSPHERES test for dh-ranFile-2016-09-18_16:31 sample no r^3 equiv. uni. 1 78.903 0.927930 2 22.532 0.528142 3 31.421 0.649141 4 9.247 0.265267 5 31.907 0.654773 6 20.156 0.489243 7 3.547 0.111498 8 1.413 0.046001 9 106.689 0.971456 10 122.441 0.983115 11 21.600 0.513241 12 2.426 0.077682 13 9.387 0.268680 14 22.484 0.527382 15 31.860 0.654233 16 33.098 0.668211 17 33.877 0.676720 18 27.825 0.604453 19 26.169 0.582013 20 31.387 0.648739 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.374671 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-09-18_16:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 1.3 -1.2 2.3 1.4 0.2 -0.3 1.6 -0.8 -1.1 0.1 2.0 0.3 0.3 -2.6 -0.9 0.5 -1.1 -2.3 0.0 1.2 1.9 0.7 -0.0 1.1 -0.8 0.3 1.7 0.4 0.7 -0.9 0.4 0.4 -0.1 0.2 -0.9 -1.0 -1.4 -0.7 0.1 -0.1 -0.6 1.0 -1.1 Chi-square with 42 degrees of freedom:52.532170 z-score=1.149154, p-value=0.872127 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-09-18_16:31 Test no p-value 1 0.554470 2 0.158535 3 0.905597 4 0.806990 5 0.848059 6 0.770669 7 0.212577 8 0.016299 9 0.070651 10 0.069105 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.295143 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-09-18_16:31: (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 66729 0.06 66847 0.49 3 25000.00 24828 1.18 24839 1.04 4 6666.67 6774 1.73 6631 0.19 5 1388.89 1375 0.14 1381 0.04 6 238.10 244 0.15 263 2.61 7 34.72 41 1.14 34 0.01 8 4.96 8 1.86 4 0.19 p=0.60466 p=0.39946 Number of rngs required: 687878, p-value: 0.272 RESULTS OF CRAPS TEST for dh-ranFile-2016-09-18_16:31 No. of wins: Observed Expected 98407 98585.9 z-score=-0.800, pvalue=0.21187 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66909 66666.7 0.881 0.881 2 37528 37654.3 0.424 1.305 3 26811 26954.7 0.766 2.071 4 19290 19313.5 0.029 2.100 5 13694 13851.4 1.789 3.889 6 10077 9943.5 1.791 5.680 7 7295 7145.0 3.148 8.828 8 5132 5139.1 0.010 8.838 9 3695 3699.9 0.006 8.844 10 2621 2666.3 0.770 9.613 11 2012 1923.3 4.088 13.701 12 1321 1388.7 3.304 17.006 13 1018 1003.7 0.203 17.209 14 671 726.1 4.187 21.396 15 535 525.8 0.160 21.556 16 402 381.2 1.140 22.696 17 296 276.5 1.369 24.066 18 173 200.8 3.857 27.922 19 127 146.0 2.469 30.391 20 112 106.2 0.315 30.706 21 281 287.1 0.130 30.836 Chisq= 30.84 for 20 degrees of freedom, p= 0.94261 SUMMARY of craptest p-value for no. of wins: 0.211867 p-value for throws/game: 0.942613 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-09-18_16:31 No. of wins: Observed Expected 98607 98585.9 z-score= 0.095, pvalue=0.53767 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66736 66666.7 0.072 0.072 2 37472 37654.3 0.883 0.955 3 27035 26954.7 0.239 1.194 4 19424 19313.5 0.633 1.827 5 13934 13851.4 0.492 2.319 6 9933 9943.5 0.011 2.330 7 7060 7145.0 1.012 3.342 8 5216 5139.1 1.152 4.493 9 3656 3699.9 0.520 5.013 10 2622 2666.3 0.736 5.749 11 1986 1923.3 2.042 7.792 12 1335 1388.7 2.080 9.871 13 979 1003.7 0.609 10.480 14 713 726.1 0.238 10.718 15 504 525.8 0.907 11.624 16 383 381.2 0.009 11.633 17 260 276.5 0.989 12.622 18 203 200.8 0.023 12.646 19 150 146.0 0.110 12.756 20 113 106.2 0.433 13.190 21 286 287.1 0.004 13.194 Chisq= 13.19 for 20 degrees of freedom, p= 0.13110 SUMMARY of craptest p-value for no. of wins: 0.537667 p-value for throws/game: 0.131097 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0040,0.0103,0.0147,0.0163,0.0213,0.0273,0.0316,0.0429,0.0460,0.0610, 0.0617,0.0640,0.0670,0.0691,0.0707,0.0712,0.0777,0.0800,0.0822,0.0849, 0.0850,0.0880,0.0932,0.0998,0.1034,0.1068,0.1115,0.1158,0.1183,0.1200, 0.1215,0.1222,0.1274,0.1292,0.1311,0.1354,0.1421,0.1435,0.1510,0.1532, 0.1551,0.1585,0.1600,0.1600,0.1658,0.1661,0.1665,0.1673,0.1912,0.1959, 0.2047,0.2056,0.2106,0.2119,0.2126,0.2127,0.2261,0.2289,0.2364,0.2373, 0.2388,0.2390,0.2473,0.2488,0.2512,0.2552,0.2653,0.2663,0.2687,0.2724, 0.2763,0.2833,0.2841,0.2842,0.2887,0.2951,0.2956,0.2997,0.3004,0.3022, 0.3028,0.3078,0.3144,0.3157,0.3163,0.3240,0.3277,0.3291,0.3309,0.3368, 0.3436,0.3484,0.3525,0.3535,0.3557,0.3577,0.3747,0.3816,0.3831,0.3843, 0.3877,0.3897,0.3921,0.3921,0.3972,0.3982,0.3995,0.4002,0.4097,0.4106, 0.4159,0.4164,0.4230,0.4247,0.4275,0.4283,0.4294,0.4379,0.4385,0.4387, 0.4413,0.4529,0.4537,0.4562,0.4736,0.4792,0.4860,0.4863,0.4892,0.4968, 0.5000,0.5000,0.5023,0.5082,0.5132,0.5137,0.5159,0.5161,0.5182,0.5184, 0.5230,0.5274,0.5281,0.5281,0.5302,0.5320,0.5323,0.5360,0.5377,0.5387, 0.5390,0.5404,0.5435,0.5449,0.5508,0.5544,0.5545,0.5562,0.5618,0.5619, 0.5629,0.5634,0.5757,0.5761,0.5820,0.5831,0.5839,0.5854,0.5875,0.5882, 0.5895,0.5973,0.5999,0.6045,0.6047,0.6070,0.6109,0.6165,0.6183,0.6188, 0.6271,0.6302,0.6331,0.6342,0.6380,0.6396,0.6422,0.6429,0.6487,0.6491, 0.6523,0.6542,0.6548,0.6575,0.6577,0.6668,0.6674,0.6682,0.6683,0.6739, 0.6767,0.6796,0.6844,0.6927,0.6958,0.7010,0.7165,0.7311,0.7314,0.7427, 0.7537,0.7674,0.7704,0.7707,0.7722,0.7728,0.7819,0.7894,0.7966,0.7990, 0.8006,0.8034,0.8070,0.8141,0.8146,0.8207,0.8237,0.8260,0.8282,0.8371, 0.8376,0.8434,0.8481,0.8591,0.8664,0.8690,0.8705,0.8721,0.8842,0.8948, 0.8954,0.9008,0.9056,0.9077,0.9101,0.9138,0.9279,0.9282,0.9301,0.9372, 0.9412,0.9422,0.9426,0.9464,0.9482,0.9499,0.9505,0.9557,0.9599,0.9606, 0.9617,0.9715,0.9770,0.9801,0.9831,0.9840,0.9878,0.9887,0.9933, Overall p-value after applying KStest on 269 p-values = 0.432616 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.