RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-03_08:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 16.01 12.4609 0.228542 2 to 25 15.89 10.3679 0.112524 3 to 26 15.82 9.2588 0.068210 4 to 27 15.84 11.2560 0.157049 5 to 28 15.52 16.8497 0.535409 6 to 29 15.70 16.3523 0.500991 7 to 30 15.87 19.2720 0.686854 8 to 31 15.93 18.1066 0.617853 9 to 32 15.84 10.3436 0.111415 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.117553 Tough bday spacings test for dh-ranFile-2018-07-03_08:31: 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 45 77 93 80 69 64 30 17 8 6 (O-E)^2/E 0.4 1.9 0.2 0.2 3.2 1.1 2.7 0.0 0.3 0.3 0.9 Birthday Spacings: Sum(O-E)^2/E= 11.200, p= 0.658 RESULTS OF GCD FOR dh-ranFile-2018-07-03_08:31 Euclid's algorithm: p-value, steps to gcd: 0.195499 p-value, dist. of gcd's: 0.581151 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-03_08:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.378 0.230 0.960 0.865 0.523 0.436 0.394 0.753 Bits 8 to 15---> 0.147 0.635 0.060 0.545 0.338 0.090 0.960 0.459 Bits 16 to 23---> 0.100 0.594 0.061 0.867 0.022 0.449 0.103 0.580 Bits 24 to 31---> 0.730 0.621 0.094 0.577 0.476 0.850 0.103 0.888 KS test for the above 32 p values: 0.411 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-03_08:31, p-values for 5 runs: 0.5704, 0.7640, 0.1075, 0.6373, 0.0113 Rank test for binary matrices (31x31) for dh-ranFile-2018-07-03_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 224 211.4 0.749 0.749 r= 29 5237 5134.0 2.066 2.815 r= 30 22915 23103.0 1.531 4.345 r= 31 11624 11551.5 0.455 4.800 chi-square = 4.800 with df = 3; p-value = 0.813 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-07-03_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 200 211.4 0.617 0.617 r= 30 5107 5134.0 0.142 0.759 r= 31 23133 23103.0 0.039 0.798 r= 32 11560 11551.5 0.006 0.804 chi-square = 0.804 with df = 3; p-value = 0.151 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-07-03_08:31 b-rank test for bits 1 to 8, p=0.77513 b-rank test for bits 2 to 9, p=0.33589 b-rank test for bits 3 to 10, p=0.53126 b-rank test for bits 4 to 11, p=0.38288 b-rank test for bits 5 to 12, p=0.07960 b-rank test for bits 6 to 13, p=0.52704 b-rank test for bits 7 to 14, p=0.33591 b-rank test for bits 8 to 15, p=0.31562 b-rank test for bits 9 to 16, p=0.63421 b-rank test for bits 10 to 17, p=0.36001 b-rank test for bits 11 to 18, p=0.86767 b-rank test for bits 12 to 19, p=0.92284 b-rank test for bits 13 to 20, p=0.92466 b-rank test for bits 14 to 21, p=0.79568 b-rank test for bits 15 to 22, p=0.49900 b-rank test for bits 16 to 23, p=0.17521 b-rank test for bits 17 to 24, p=0.50893 b-rank test for bits 18 to 25, p=0.08186 b-rank test for bits 19 to 26, p=0.23367 b-rank test for bits 20 to 27, p=0.01663 b-rank test for bits 21 to 28, p=0.06693 b-rank test for bits 22 to 29, p=0.13836 b-rank test for bits 23 to 30, p=0.87176 b-rank test for bits 24 to 31, p=0.06082 b-rank test for bits 25 to 32, p=0.59768 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 = 0.516167 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-03_08:31 (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 141570 -0.79 0.213939 2 142197 0.67 0.749248 3 141601 -0.72 0.235640 4 142088 0.42 0.661827 5 142571 1.55 0.938943 6 141482 -1.00 0.159034 7 142115 0.48 0.684577 8 142071 0.38 0.647186 9 142492 1.36 0.913303 10 142382 1.10 0.865284 11 141861 -0.11 0.455047 12 141980 0.17 0.565574 13 142065 0.36 0.641965 14 141692 -0.51 0.305804 15 141788 -0.28 0.388404 16 142037 0.30 0.617261 17 141863 -0.11 0.456900 18 141961 0.12 0.548045 19 141266 -1.50 0.066406 20 142367 1.07 0.857538 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-07-03_08:31 Bits used No. missing words z-score p-value 23 to 32 141873 -0.1253 0.450153 22 to 31 141939 0.1023 0.540745 21 to 30 141726 -0.6322 0.263637 20 to 29 141946 0.1264 0.550312 19 to 28 142005 0.3299 0.629261 18 to 27 142464 1.9127 0.972104 17 to 26 141817 -0.3184 0.375099 16 to 25 141882 -0.0942 0.462459 15 to 24 141863 -0.1598 0.436536 14 to 23 142215 1.0540 0.854066 13 to 22 141674 -0.8115 0.208544 12 to 21 141807 -0.3529 0.362096 11 to 20 142022 0.3885 0.651183 10 to 19 141479 -1.4839 0.068918 9 to 18 142194 0.9816 0.836857 8 to 17 141950 0.1402 0.555765 7 to 16 141994 0.2920 0.614844 6 to 15 142049 0.4816 0.684962 5 to 14 141989 0.2747 0.608236 4 to 13 142168 0.8920 0.813794 3 to 12 142526 2.1264 0.983267 2 to 11 142272 1.2506 0.894457 1 to 10 142197 0.9920 0.839393 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-07-03_08:31 Bits used No. missing words z-score p-value 28 to 32 141907 -0.0079 0.496849 27 to 31 141852 -0.1943 0.422955 26 to 30 141698 -0.7164 0.236881 25 to 29 142164 0.8633 0.806011 24 to 28 141928 0.0633 0.525232 23 to 27 142013 0.3514 0.637365 22 to 26 141570 -1.1503 0.125016 21 to 25 141927 0.0599 0.523882 20 to 24 141652 -0.8723 0.191521 19 to 23 141616 -0.9943 0.160029 18 to 22 141914 0.0158 0.506315 17 to 21 141986 0.2599 0.602529 16 to 20 141944 0.1175 0.546778 15 to 19 141729 -0.6113 0.270504 14 to 18 142263 1.1989 0.884713 13 to 17 141634 -0.9333 0.175327 12 to 16 141844 -0.2215 0.412368 11 to 15 142246 1.1413 0.873118 10 to 14 142134 0.7616 0.776849 9 to 13 142014 0.3548 0.638635 8 to 12 141689 -0.7469 0.227568 7 to 11 141407 -1.7028 0.044301 6 to 10 141598 -1.0554 0.145631 5 to 9 142197 0.9752 0.835258 4 to 8 141431 -1.6215 0.052460 3 to 7 141600 -1.0486 0.147187 2 to 6 142071 0.5480 0.708166 1 to 5 141654 -0.8655 0.193375 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-07-03_08:31 Bits used No. missing words z-score p-value 31 to 32 141927 0.0521 0.520785 30 to 31 141905 -0.0128 0.494905 29 to 30 141890 -0.0570 0.477264 28 to 29 142039 0.3825 0.648958 27 to 28 142714 2.3737 0.991194 26 to 27 142167 0.7601 0.776399 25 to 26 141629 -0.8269 0.204138 24 to 25 141785 -0.3668 0.356901 23 to 24 142196 0.8456 0.801122 22 to 23 142139 0.6775 0.750953 21 to 22 142008 0.2911 0.614498 20 to 21 142338 1.2645 0.896977 19 to 20 141906 -0.0098 0.496081 18 to 19 141791 -0.3491 0.363524 17 to 18 142088 0.5271 0.700921 16 to 17 141236 -1.9862 0.023504 15 to 16 141640 -0.7945 0.213457 14 to 15 141730 -0.5290 0.298404 13 to 14 141884 -0.0747 0.470219 12 to 13 142259 1.0315 0.848841 11 to 12 141857 -0.1544 0.438661 10 to 11 142163 0.7483 0.772857 9 to 10 141516 -1.1603 0.122970 8 to 9 142092 0.5388 0.705005 7 to 8 141788 -0.3579 0.360207 6 to 7 142572 1.9548 0.974695 5 to 6 141950 0.1200 0.547747 4 to 5 142342 1.2763 0.899078 3 to 4 141619 -0.8564 0.195880 2 to 3 141549 -1.0629 0.143909 1 to 2 142314 1.1937 0.883706 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-03_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2483.02 -0.240 0.405120 Test results for specific bytes for dh-ranFile-2018-07-03_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2475.97 -0.340 0.367009 2 to 9 2551.73 0.732 0.767772 3 to 10 2443.56 -0.798 0.212371 4 to 11 2538.07 0.538 0.704837 5 to 12 2378.14 -1.723 0.042418 6 to 13 2403.09 -1.370 0.085266 7 to 14 2608.36 1.532 0.937300 8 to 15 2575.33 1.065 0.856636 9 to 16 2595.92 1.356 0.912521 10 to 17 2594.26 1.333 0.908737 11 to 18 2389.75 -1.559 0.059478 12 to 19 2426.72 -1.036 0.150028 13 to 20 2589.35 1.264 0.896817 14 to 21 2532.67 0.462 0.677992 15 to 22 2487.56 -0.176 0.430167 16 to 23 2523.78 0.336 0.631662 17 to 24 2459.68 -0.570 0.284270 18 to 25 2476.78 -0.328 0.371293 19 to 26 2572.06 1.019 0.845934 20 to 27 2461.69 -0.542 0.293961 21 to 28 2476.49 -0.332 0.369782 22 to 29 2485.41 -0.206 0.418290 23 to 30 2423.48 -1.082 0.139587 24 to 31 2549.55 0.701 0.758289 25 to 32 2535.51 0.502 0.692224 CDPARK for dh-ranFile-2018-07-03_08:31: 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 3503 -0.9132 0.180558 3522 -0.0457 0.481790 3525 0.0913 0.536383 3564 1.8721 0.969407 3521 -0.0913 0.463617 3540 0.7763 0.781201 3487 -1.6438 0.050105 3525 0.0913 0.536383 3547 1.0959 0.863437 3542 0.8676 0.807188 Square side=100, avg. no. parked=3527.60 sample std.=20.99 p-value of the KSTEST for those 10 p-values: 0.746343 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-03_08:31 0.9388,0.9281,0.8842,0.7312,0.5462,0.9932,0.8277,0.3229,0.9782,0.9103, The KS test for those 10 p-values: 0.000406 The 3DSPHERES test for dh-ranFile-2018-07-03_08:31 sample no r^3 equiv. uni. 1 107.627 0.972335 2 75.911 0.920371 3 1.181 0.038614 4 74.801 0.917368 5 24.204 0.553716 6 10.738 0.300873 7 22.039 0.520312 8 22.488 0.527446 9 8.060 0.235605 10 42.450 0.757075 11 78.944 0.928027 12 12.143 0.332878 13 5.836 0.176770 14 6.434 0.193033 15 33.985 0.677877 16 39.225 0.729508 17 2.285 0.073350 18 62.502 0.875494 19 30.277 0.635506 20 29.498 0.625907 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.738653 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-03_08:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -1.2 -0.6 -0.4 1.1 -0.4 1.1 -1.1 0.0 0.3 0.1 0.5 -1.3 1.8 1.6 -0.5 0.0 -1.7 1.2 -0.6 0.4 -0.6 0.2 -0.6 -0.3 -0.1 -0.9 -0.5 -0.2 0.2 1.4 -0.5 0.3 1.6 0.2 1.0 0.3 -1.3 -0.4 -0.7 0.9 0.0 -0.1 Chi-square with 42 degrees of freedom:30.781544 z-score=-1.224034, p-value=0.100381 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-07-03_08:31 Test no p-value 1 0.899240 2 0.688242 3 0.340400 4 0.009294 5 0.114957 6 0.019971 7 0.695121 8 0.325648 9 0.250238 10 0.076415 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.074637 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-03_08:31: (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 66837 0.44 66792 0.24 3 25000.00 24796 1.66 24862 0.76 4 6666.67 6710 0.28 6673 0.01 5 1388.89 1368 0.31 1384 0.02 6 238.10 244 0.15 246 0.26 7 34.72 39 0.53 34 0.01 8 4.96 5 0.00 8 1.86 p=0.23882 p=0.21164 Number of rngs required: 687251, p-value: 0.090 RESULTS OF CRAPS TEST for dh-ranFile-2018-07-03_08:31 No. of wins: Observed Expected 98541 98585.9 z-score=-0.201, pvalue=0.42049 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66325 66666.7 1.751 1.751 2 37866 37654.3 1.190 2.941 3 26947 26954.7 0.002 2.943 4 19104 19313.5 2.272 5.215 5 13925 13851.4 0.391 5.606 6 10154 9943.5 4.454 10.060 7 7117 7145.0 0.110 10.170 8 5126 5139.1 0.033 10.203 9 3755 3699.9 0.822 11.025 10 2622 2666.3 0.736 11.761 11 1997 1923.3 2.822 14.583 12 1390 1388.7 0.001 14.584 13 1002 1003.7 0.003 14.587 14 720 726.1 0.052 14.639 15 544 525.8 0.627 15.266 16 396 381.2 0.579 15.845 17 297 276.5 1.514 17.359 18 192 200.8 0.388 17.747 19 133 146.0 1.155 18.902 20 121 106.2 2.058 20.960 21 267 287.1 1.409 22.369 Chisq= 22.37 for 20 degrees of freedom, p= 0.67916 SUMMARY of craptest p-value for no. of wins: 0.420492 p-value for throws/game: 0.679161 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-03_08:31 No. of wins: Observed Expected 98438 98585.9 z-score=-0.661, pvalue=0.25421 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66527 66666.7 0.293 0.293 2 37632 37654.3 0.013 0.306 3 27081 26954.7 0.591 0.897 4 19262 19313.5 0.137 1.034 5 13964 13851.4 0.915 1.949 6 9863 9943.5 0.652 2.602 7 7155 7145.0 0.014 2.616 8 5188 5139.1 0.466 3.082 9 3650 3699.9 0.672 3.754 10 2629 2666.3 0.522 4.275 11 1934 1923.3 0.059 4.335 12 1402 1388.7 0.127 4.461 13 1032 1003.7 0.797 5.258 14 763 726.1 1.871 7.129 15 536 525.8 0.196 7.326 16 378 381.2 0.026 7.352 17 275 276.5 0.009 7.360 18 190 200.8 0.584 7.944 19 150 146.0 0.110 8.055 20 96 106.2 0.982 9.037 21 293 287.1 0.121 9.158 Chisq= 9.16 for 20 degrees of freedom, p= 0.01900 SUMMARY of craptest p-value for no. of wins: 0.254207 p-value for throws/game: 0.018996 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0004,0.0093,0.0113,0.0166,0.0190,0.0200,0.0217,0.0235,0.0386,0.0424, 0.0443,0.0501,0.0525,0.0595,0.0598,0.0606,0.0608,0.0664,0.0669,0.0682, 0.0689,0.0734,0.0746,0.0764,0.0796,0.0819,0.0853,0.0898,0.0904,0.0939, 0.0997,0.1004,0.1026,0.1031,0.1075,0.1114,0.1125,0.1150,0.1176,0.1230, 0.1250,0.1384,0.1396,0.1439,0.1456,0.1467,0.1472,0.1500,0.1514,0.1570, 0.1590,0.1600,0.1752,0.1753,0.1768,0.1806,0.1915,0.1930,0.1934,0.1955, 0.1959,0.2041,0.2085,0.2116,0.2124,0.2135,0.2139,0.2276,0.2285,0.2301, 0.2337,0.2356,0.2356,0.2369,0.2388,0.2502,0.2542,0.2636,0.2705,0.2843, 0.2940,0.2984,0.3009,0.3058,0.3156,0.3229,0.3256,0.3329,0.3359,0.3359, 0.3383,0.3404,0.3569,0.3600,0.3602,0.3621,0.3635,0.3670,0.3698,0.3713, 0.3751,0.3776,0.3829,0.3884,0.3945,0.4051,0.4110,0.4124,0.4183,0.4205, 0.4230,0.4302,0.4365,0.4365,0.4387,0.4489,0.4502,0.4550,0.4569,0.4595, 0.4625,0.4636,0.4702,0.4758,0.4773,0.4818,0.4949,0.4961,0.4968,0.4990, 0.5010,0.5063,0.5089,0.5162,0.5203,0.5208,0.5233,0.5239,0.5252,0.5270, 0.5274,0.5313,0.5354,0.5364,0.5364,0.5407,0.5448,0.5462,0.5468,0.5477, 0.5480,0.5503,0.5537,0.5558,0.5656,0.5704,0.5765,0.5805,0.5812,0.5943, 0.5977,0.6025,0.6082,0.6145,0.6148,0.6173,0.6179,0.6211,0.6259,0.6293, 0.6317,0.6342,0.6352,0.6355,0.6373,0.6374,0.6386,0.6420,0.6472,0.6490, 0.6512,0.6579,0.6618,0.6779,0.6780,0.6792,0.6846,0.6850,0.6869,0.6882, 0.6922,0.6951,0.7009,0.7048,0.7050,0.7082,0.7295,0.7296,0.7312,0.7387, 0.7463,0.7492,0.7510,0.7531,0.7571,0.7583,0.7640,0.7678,0.7729,0.7751, 0.7764,0.7768,0.7812,0.7957,0.8011,0.8060,0.8072,0.8130,0.8138,0.8277, 0.8353,0.8369,0.8394,0.8459,0.8488,0.8504,0.8541,0.8566,0.8575,0.8634, 0.8649,0.8653,0.8673,0.8677,0.8718,0.8731,0.8755,0.8837,0.8842,0.8847, 0.8878,0.8945,0.8968,0.8970,0.8991,0.8992,0.9087,0.9103,0.9125,0.9133, 0.9174,0.9204,0.9228,0.9247,0.9280,0.9281,0.9373,0.9388,0.9389,0.9601, 0.9602,0.9694,0.9721,0.9723,0.9747,0.9782,0.9833,0.9912,0.9932, Overall p-value after applying KStest on 269 p-values = 0.827916 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.