RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-11-27_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 15.58 31.8524 0.984304 2 to 25 16.31 11.8911 0.193313 3 to 26 15.83 18.4880 0.641300 4 to 27 16.11 24.6121 0.896266 5 to 28 15.73 11.6467 0.178958 6 to 29 15.85 19.8033 0.715586 7 to 30 15.58 24.1292 0.884034 8 to 31 15.44 28.8618 0.964178 9 to 32 15.74 22.0151 0.815862 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.034815 Tough bday spacings test for dh-ranFile-2016-11-27_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 5 33 62 109 121 79 46 18 16 5 6 (O-E)^2/E 1.9 0.4 1.7 1.3 5.6 0.0 0.7 4.7 0.1 0.4 0.9 Birthday Spacings: Sum(O-E)^2/E= 17.630, p= 0.938 RESULTS OF GCD FOR dh-ranFile-2016-11-27_08:31 Euclid's algorithm: p-value, steps to gcd: 0.003343 p-value, dist. of gcd's: 0.040729 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-11-27_08:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.205 0.217 0.154 0.203 0.106 0.135 0.483 0.294 Bits 8 to 15---> 0.718 0.732 0.656 0.957 0.012 0.398 0.670 0.368 Bits 16 to 23---> 0.361 0.752 0.141 0.862 0.104 0.861 0.726 0.447 Bits 24 to 31---> 0.679 0.922 0.496 0.029 0.623 0.107 0.513 0.192 KS test for the above 32 p values: 0.584 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-11-27_08:31, p-values for 5 runs: 0.3558, 0.6243, 0.5843, 0.3919, 0.1939 Rank test for binary matrices (31x31) for dh-ranFile-2016-11-27_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 223 211.4 0.634 0.634 r= 29 5162 5134.0 0.153 0.787 r= 30 22964 23103.0 0.837 1.624 r= 31 11651 11551.5 0.857 2.481 chi-square = 2.481 with df = 3; p-value = 0.521 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-11-27_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 202 211.4 0.420 0.420 r= 30 5308 5134.0 5.896 6.316 r= 31 22951 23103.0 1.001 7.317 r= 32 11539 11551.5 0.014 7.330 chi-square = 7.330 with df = 3; p-value = 0.938 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-11-27_08:31 b-rank test for bits 1 to 8, p=0.88463 b-rank test for bits 2 to 9, p=0.42100 b-rank test for bits 3 to 10, p=0.75165 b-rank test for bits 4 to 11, p=0.26984 b-rank test for bits 5 to 12, p=0.82310 b-rank test for bits 6 to 13, p=0.71196 b-rank test for bits 7 to 14, p=0.53393 b-rank test for bits 8 to 15, p=0.27863 b-rank test for bits 9 to 16, p=0.02195 b-rank test for bits 10 to 17, p=0.62016 b-rank test for bits 11 to 18, p=0.07784 b-rank test for bits 12 to 19, p=0.52174 b-rank test for bits 13 to 20, p=0.48586 b-rank test for bits 14 to 21, p=0.35401 b-rank test for bits 15 to 22, p=0.90492 b-rank test for bits 16 to 23, p=0.31127 b-rank test for bits 17 to 24, p=0.86012 b-rank test for bits 18 to 25, p=0.46991 b-rank test for bits 19 to 26, p=0.85319 b-rank test for bits 20 to 27, p=0.39118 b-rank test for bits 21 to 28, p=0.78954 b-rank test for bits 22 to 29, p=0.39344 b-rank test for bits 23 to 30, p=0.16247 b-rank test for bits 24 to 31, p=0.52294 b-rank test for bits 25 to 32, p=0.06707 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 = 0.898942 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-11-27_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 142491 1.36 0.912933 2 141800 -0.26 0.399190 3 141990 0.19 0.574750 4 141782 -0.30 0.383042 5 142369 1.07 0.858588 6 141863 -0.11 0.456900 7 141418 -1.15 0.125491 8 142131 0.52 0.697743 9 142184 0.64 0.739483 10 142297 0.91 0.817471 11 141793 -0.27 0.392888 12 142377 1.09 0.862734 13 141330 -1.35 0.087936 14 141943 0.08 0.531352 15 142137 0.53 0.702616 16 141627 -0.66 0.254739 17 141668 -0.56 0.286426 18 141801 -0.25 0.400093 19 142723 1.90 0.971355 20 142412 1.17 0.879895 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-11-27_08:31 Bits used No. missing words z-score p-value 23 to 32 141854 -0.1908 0.424344 22 to 31 141730 -0.6184 0.268163 21 to 30 141185 -2.4977 0.006250 20 to 29 141847 -0.2149 0.414911 19 to 28 141615 -1.0149 0.155069 18 to 27 141966 0.1954 0.577466 17 to 26 141808 -0.3494 0.363389 16 to 25 141989 0.2747 0.608236 15 to 24 141218 -2.3839 0.008565 14 to 23 141970 0.2092 0.582857 13 to 22 142127 0.7506 0.773549 12 to 21 141933 0.0816 0.532526 11 to 20 142243 1.1506 0.875049 10 to 19 141795 -0.3942 0.346701 9 to 18 141828 -0.2804 0.389567 8 to 17 142015 0.3644 0.642213 7 to 16 141292 -2.1287 0.016639 6 to 15 141975 0.2264 0.589574 5 to 14 142245 1.1575 0.876462 4 to 13 141480 -1.4804 0.069377 3 to 12 142076 0.5747 0.717261 2 to 11 142360 1.5540 0.939912 1 to 10 142323 1.4264 0.923131 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-11-27_08:31 Bits used No. missing words z-score p-value 28 to 32 141925 0.0531 0.521181 27 to 31 142108 0.6735 0.749672 26 to 30 142118 0.7074 0.760327 25 to 29 141708 -0.6825 0.247470 24 to 28 141690 -0.7435 0.228592 23 to 27 142015 0.3582 0.639905 22 to 26 142213 1.0294 0.848352 21 to 25 141829 -0.2723 0.392694 20 to 24 141150 -2.5740 0.005027 19 to 23 141865 -0.1503 0.440275 18 to 22 142004 0.3209 0.625863 17 to 21 141913 0.0124 0.504963 16 to 20 142104 0.6599 0.745341 15 to 19 141891 -0.0621 0.475227 14 to 18 142089 0.6091 0.728755 13 to 17 141473 -1.4791 0.069559 12 to 16 141504 -1.3740 0.084721 11 to 15 141930 0.0701 0.527930 10 to 14 142219 1.0497 0.853079 9 to 13 141880 -0.0994 0.460401 8 to 12 141751 -0.5367 0.295733 7 to 11 141535 -1.2689 0.102236 6 to 10 141976 0.2260 0.589399 5 to 9 141912 0.0091 0.503611 4 to 8 142040 0.4429 0.671099 3 to 7 141587 -1.0926 0.137275 2 to 6 142351 1.4972 0.932828 1 to 5 142322 1.3989 0.919076 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-11-27_08:31 Bits used No. missing words z-score p-value 31 to 32 141775 -0.3963 0.345959 30 to 31 141279 -1.8594 0.031487 29 to 30 142016 0.3147 0.623490 28 to 29 141476 -1.2783 0.100579 27 to 28 141449 -1.3579 0.087247 26 to 27 141688 -0.6529 0.256913 25 to 26 141155 -2.2252 0.013035 24 to 25 141917 0.0226 0.509025 23 to 24 142025 0.3412 0.633527 22 to 23 142454 1.6067 0.945939 21 to 22 142003 0.2763 0.608846 20 to 21 142080 0.5035 0.692677 19 to 20 141257 -1.9243 0.027160 18 to 19 142452 1.6008 0.945289 17 to 18 141246 -1.9567 0.025190 16 to 17 142187 0.8191 0.793631 15 to 16 141988 0.2321 0.591756 14 to 15 141593 -0.9331 0.175377 13 to 14 142498 1.7365 0.958761 12 to 13 141601 -0.9095 0.181536 11 to 12 141675 -0.6912 0.244708 10 to 11 142048 0.4091 0.658751 9 to 10 142332 1.2468 0.893767 8 to 9 141109 -2.3609 0.009116 7 to 8 141890 -0.0570 0.477264 6 to 7 141521 -1.1455 0.125998 5 to 6 141481 -1.2635 0.103203 4 to 5 141449 -1.3579 0.087247 3 to 4 141650 -0.7650 0.222140 2 to 3 142116 0.6096 0.728952 1 to 2 141678 -0.6824 0.247496 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-11-27_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2468.18 -0.450 0.326369 Test results for specific bytes for dh-ranFile-2016-11-27_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2510.52 0.149 0.559125 2 to 9 2500.52 0.007 0.502936 3 to 10 2591.29 1.291 0.901656 4 to 11 2449.74 -0.711 0.238616 5 to 12 2459.28 -0.576 0.282373 6 to 13 2439.68 -0.853 0.196806 7 to 14 2562.21 0.880 0.810527 8 to 15 2508.34 0.118 0.546936 9 to 16 2587.19 1.233 0.891215 10 to 17 2481.66 -0.259 0.397674 11 to 18 2479.51 -0.290 0.386011 12 to 19 2509.29 0.131 0.552243 13 to 20 2346.40 -2.172 0.014917 14 to 21 2596.29 1.362 0.913368 15 to 22 2423.83 -1.077 0.140681 16 to 23 2480.06 -0.282 0.388994 17 to 24 2667.30 2.366 0.991008 18 to 25 2449.87 -0.709 0.239186 19 to 26 2582.62 1.168 0.878696 20 to 27 2552.29 0.740 0.770208 21 to 28 2523.03 0.326 0.627659 22 to 29 2513.79 0.195 0.577287 23 to 30 2474.53 -0.360 0.359326 24 to 31 2481.61 -0.260 0.397405 25 to 32 2459.73 -0.570 0.284508 CDPARK for dh-ranFile-2016-11-27_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 3513 -0.4566 0.323972 3530 0.3196 0.625377 3512 -0.5023 0.307734 3568 2.0548 0.980051 3523 0.0000 0.500000 3544 0.9589 0.831196 3512 -0.5023 0.307734 3524 0.0457 0.518210 3538 0.6849 0.753306 3488 -1.5982 0.055002 Square side=100, avg. no. parked=3525.20 sample std.=20.64 p-value of the KSTEST for those 10 p-values: 0.951147 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-11-27_08:31 0.3769,0.2621,0.4350,0.5266,0.4498,0.5893,0.1349,0.3242,0.6588,0.1815, The KS test for those 10 p-values: 0.191704 The 3DSPHERES test for dh-ranFile-2016-11-27_08:31 sample no r^3 equiv. uni. 1 30.187 0.634401 2 19.076 0.470522 3 11.288 0.313579 4 22.725 0.531166 5 27.730 0.603209 6 11.799 0.325181 7 29.185 0.621985 8 24.566 0.559063 9 16.318 0.419546 10 29.187 0.622012 11 7.063 0.209785 12 60.237 0.865729 13 50.981 0.817200 14 26.161 0.581894 15 41.192 0.746670 16 31.733 0.652765 17 14.524 0.383772 18 10.358 0.291959 19 25.650 0.574716 20 96.586 0.960026 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.137031 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-11-27_08:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.5 -1.8 -0.7 -0.7 -0.5 0.1 -1.8 -1.4 1.1 -0.5 -0.1 -0.2 1.3 0.7 -1.2 -2.0 -1.1 1.1 1.9 1.9 -0.9 -0.4 -1.0 0.1 0.6 0.3 1.4 0.8 -0.4 -0.4 0.1 -0.8 0.3 0.5 -0.5 -0.7 -0.4 0.5 0.4 -0.6 -1.0 0.8 Chi-square with 42 degrees of freedom:38.346130 z-score=-0.398670, p-value=0.367872 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-11-27_08:31 Test no p-value 1 0.767182 2 0.543748 3 0.120428 4 0.154490 5 0.043676 6 0.071946 7 0.576300 8 0.303803 9 0.002331 10 0.324301 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.024564 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-11-27_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 66772 0.17 66630 0.02 3 25000.00 24863 0.75 25065 0.17 4 6666.67 6673 0.01 6677 0.02 5 1388.89 1385 0.01 1342 1.58 6 238.10 254 1.06 245 0.20 7 34.72 44 2.48 40 0.80 8 4.96 8 1.86 0 4.96 p=0.61381 p=0.74311 Number of rngs required: 690042, p-value: 0.973 RESULTS OF CRAPS TEST for dh-ranFile-2016-11-27_08:31 No. of wins: Observed Expected 98535 98585.9 z-score=-0.227, pvalue=0.41003 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66846 66666.7 0.482 0.482 2 37627 37654.3 0.020 0.502 3 26861 26954.7 0.326 0.828 4 19154 19313.5 1.317 2.145 5 13773 13851.4 0.444 2.589 6 9942 9943.5 0.000 2.589 7 7173 7145.0 0.110 2.699 8 5180 5139.1 0.326 3.024 9 3710 3699.9 0.028 3.052 10 2685 2666.3 0.131 3.183 11 1924 1923.3 0.000 3.184 12 1368 1388.7 0.310 3.493 13 1044 1003.7 1.617 5.110 14 771 726.1 2.771 7.882 15 537 525.8 0.237 8.119 16 378 381.2 0.026 8.145 17 280 276.5 0.043 8.188 18 211 200.8 0.515 8.703 19 151 146.0 0.172 8.875 20 96 106.2 0.982 9.858 21 289 287.1 0.012 9.870 Chisq= 9.87 for 20 degrees of freedom, p= 0.02953 SUMMARY of craptest p-value for no. of wins: 0.410029 p-value for throws/game: 0.029534 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-11-27_08:31 No. of wins: Observed Expected 98567 98585.9 z-score=-0.084, pvalue=0.46639 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66254 66666.7 2.554 2.554 2 38031 37654.3 3.768 6.323 3 26959 26954.7 0.001 6.323 4 18998 19313.5 5.153 11.476 5 13940 13851.4 0.566 12.042 6 10068 9943.5 1.558 13.600 7 7165 7145.0 0.056 13.656 8 5144 5139.1 0.005 13.661 9 3802 3699.9 2.819 16.480 10 2635 2666.3 0.367 16.848 11 1870 1923.3 1.479 18.326 12 1407 1388.7 0.240 18.566 13 962 1003.7 1.734 20.300 14 735 726.1 0.108 20.408 15 566 525.8 3.068 23.476 16 376 381.2 0.070 23.545 17 284 276.5 0.201 23.747 18 210 200.8 0.419 24.165 19 166 146.0 2.744 26.910 20 108 106.2 0.030 26.940 21 320 287.1 3.767 30.707 Chisq= 30.71 for 20 degrees of freedom, p= 0.94081 SUMMARY of craptest p-value for no. of wins: 0.466390 p-value for throws/game: 0.940814 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0023,0.0033,0.0050,0.0063,0.0086,0.0091,0.0123,0.0130,0.0149,0.0166, 0.0219,0.0246,0.0252,0.0272,0.0293,0.0295,0.0315,0.0348,0.0407,0.0437, 0.0550,0.0671,0.0694,0.0696,0.0719,0.0778,0.0847,0.0872,0.0872,0.0879, 0.1006,0.1022,0.1032,0.1038,0.1059,0.1073,0.1204,0.1255,0.1260,0.1349, 0.1350,0.1370,0.1373,0.1407,0.1415,0.1543,0.1545,0.1551,0.1625,0.1754, 0.1790,0.1815,0.1815,0.1917,0.1918,0.1933,0.1939,0.1968,0.2028,0.2047, 0.2098,0.2169,0.2221,0.2286,0.2386,0.2392,0.2447,0.2475,0.2475,0.2547, 0.2569,0.2621,0.2682,0.2698,0.2786,0.2824,0.2845,0.2864,0.2920,0.2940, 0.2957,0.3038,0.3077,0.3077,0.3113,0.3136,0.3240,0.3242,0.3243,0.3252, 0.3264,0.3460,0.3467,0.3540,0.3558,0.3593,0.3607,0.3634,0.3679,0.3684, 0.3769,0.3830,0.3838,0.3860,0.3890,0.3896,0.3912,0.3919,0.3927,0.3929, 0.3934,0.3974,0.3977,0.3984,0.3992,0.4001,0.4100,0.4149,0.4195,0.4210, 0.4243,0.4350,0.4403,0.4473,0.4498,0.4569,0.4604,0.4664,0.4699,0.4705, 0.4752,0.4773,0.4832,0.4859,0.4956,0.5000,0.5029,0.5036,0.5050,0.5090, 0.5125,0.5182,0.5212,0.5212,0.5217,0.5229,0.5266,0.5279,0.5312,0.5314, 0.5325,0.5339,0.5437,0.5469,0.5522,0.5591,0.5591,0.5747,0.5748,0.5763, 0.5773,0.5775,0.5819,0.5829,0.5838,0.5843,0.5893,0.5894,0.5896,0.5918, 0.6032,0.6082,0.6088,0.6138,0.6202,0.6220,0.6220,0.6230,0.6235,0.6243, 0.6254,0.6259,0.6277,0.6335,0.6344,0.6399,0.6413,0.6422,0.6528,0.6565, 0.6588,0.6588,0.6702,0.6711,0.6794,0.6927,0.6977,0.7026,0.7120,0.7156, 0.7173,0.7179,0.7265,0.7288,0.7290,0.7319,0.7395,0.7431,0.7453,0.7467, 0.7497,0.7516,0.7516,0.7533,0.7603,0.7672,0.7702,0.7735,0.7895,0.7936, 0.8105,0.8159,0.8172,0.8175,0.8231,0.8312,0.8484,0.8531,0.8532,0.8586, 0.8601,0.8612,0.8616,0.8627,0.8657,0.8750,0.8765,0.8787,0.8799,0.8840, 0.8846,0.8912,0.8938,0.8963,0.8989,0.9017,0.9049,0.9129,0.9134,0.9191, 0.9224,0.9231,0.9328,0.9379,0.9385,0.9399,0.9408,0.9453,0.9459,0.9511, 0.9567,0.9588,0.9600,0.9642,0.9714,0.9733,0.9801,0.9843,0.9910, Overall p-value after applying KStest on 269 p-values = 0.404179 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.