RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-12-03_13:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.75 29.8360 0.972448 2 to 25 15.82 27.7662 0.952255 3 to 26 15.71 14.9461 0.400637 4 to 27 15.76 12.7925 0.250037 5 to 28 15.55 25.8549 0.922854 6 to 29 15.68 19.5149 0.700209 7 to 30 15.79 13.6797 0.310371 8 to 31 15.94 19.2551 0.685912 9 to 32 15.68 24.8480 0.901835 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.067864 Tough bday spacings test for dh-ranFile-2016-12-03_13:31: 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 6 36 75 104 89 69 51 38 16 11 5 (O-E)^2/E 1.1 0.0 0.0 0.4 0.8 1.1 0.0 2.3 0.1 2.9 0.2 Birthday Spacings: Sum(O-E)^2/E= 8.894, p= 0.458 RESULTS OF GCD FOR dh-ranFile-2016-12-03_13:31 Euclid's algorithm: p-value, steps to gcd: 0.668114 p-value, dist. of gcd's: 0.442510 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-12-03_13:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.339 0.867 0.629 0.317 0.947 0.565 0.380 0.921 Bits 8 to 15---> 0.410 0.164 0.287 0.403 0.334 0.265 0.170 0.630 Bits 16 to 23---> 0.008 0.120 0.858 0.806 0.864 0.951 0.038 0.418 Bits 24 to 31---> 0.381 0.424 0.349 0.044 0.496 0.779 0.734 0.388 KS test for the above 32 p values: 0.288 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-12-03_13:31, p-values for 5 runs: 0.4770, 0.7863, 0.8520, 0.6582, 0.8101 Rank test for binary matrices (31x31) for dh-ranFile-2016-12-03_13:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 199 211.4 0.729 0.729 r= 29 5090 5134.0 0.377 1.107 r= 30 23145 23103.0 0.076 1.183 r= 31 11566 11551.5 0.018 1.201 chi-square = 1.201 with df = 3; p-value = 0.247 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-12-03_13:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 201 211.4 0.513 0.513 r= 30 5102 5134.0 0.200 0.713 r= 31 23226 23103.0 0.654 1.367 r= 32 11471 11551.5 0.561 1.929 chi-square = 1.929 with df = 3; p-value = 0.413 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-12-03_13:31 b-rank test for bits 1 to 8, p=0.91259 b-rank test for bits 2 to 9, p=0.50384 b-rank test for bits 3 to 10, p=0.18961 b-rank test for bits 4 to 11, p=0.50798 b-rank test for bits 5 to 12, p=0.12041 b-rank test for bits 6 to 13, p=0.24567 b-rank test for bits 7 to 14, p=0.71464 b-rank test for bits 8 to 15, p=0.14987 b-rank test for bits 9 to 16, p=0.28851 b-rank test for bits 10 to 17, p=0.63219 b-rank test for bits 11 to 18, p=0.24749 b-rank test for bits 12 to 19, p=0.28606 b-rank test for bits 13 to 20, p=0.47084 b-rank test for bits 14 to 21, p=0.43650 b-rank test for bits 15 to 22, p=0.36251 b-rank test for bits 16 to 23, p=0.91772 b-rank test for bits 17 to 24, p=0.47603 b-rank test for bits 18 to 25, p=0.00742 b-rank test for bits 19 to 26, p=0.74669 b-rank test for bits 20 to 27, p=0.47280 b-rank test for bits 21 to 28, p=0.00500 b-rank test for bits 22 to 29, p=0.98470 b-rank test for bits 23 to 30, p=0.82731 b-rank test for bits 24 to 31, p=0.97452 b-rank test for bits 25 to 32, p=0.54399 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 = 0.760831 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-12-03_13:31 (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 142145 0.55 0.709057 2 142010 0.24 0.592977 3 142171 0.61 0.729526 4 142270 0.84 0.800298 5 141980 0.17 0.565574 6 142267 0.84 0.798332 7 142456 1.28 0.899246 8 141407 -1.17 0.120264 9 142319 0.96 0.830760 10 142453 1.27 0.898003 11 142023 0.27 0.604720 12 141946 0.09 0.534139 13 141895 -0.03 0.486645 14 142573 1.55 0.939505 15 142250 0.80 0.786972 16 142108 0.46 0.678741 17 141171 -1.73 0.042257 18 141689 -0.51 0.303350 19 142106 0.46 0.677066 20 141958 0.11 0.545268 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-12-03_13:31 Bits used No. missing words z-score p-value 23 to 32 142011 0.3506 0.637051 22 to 31 142275 1.2609 0.896333 21 to 30 141712 -0.6804 0.248110 20 to 29 142506 2.0575 0.980180 19 to 28 142112 0.6989 0.757681 18 to 27 142351 1.5230 0.936121 17 to 26 142123 0.7368 0.769376 16 to 25 142067 0.5437 0.706673 15 to 24 141900 -0.0322 0.487167 14 to 23 142460 1.8989 0.971209 13 to 22 141788 -0.4184 0.337835 12 to 21 141843 -0.2287 0.409542 11 to 20 142014 0.3609 0.640925 10 to 19 142208 1.0299 0.848471 9 to 18 141887 -0.0770 0.469312 8 to 17 142243 1.1506 0.875049 7 to 16 141715 -0.6701 0.251396 6 to 15 141657 -0.8701 0.192122 5 to 14 141687 -0.7667 0.221643 4 to 13 141933 0.0816 0.532526 3 to 12 142123 0.7368 0.769376 2 to 11 141901 -0.0287 0.488542 1 to 10 141999 0.3092 0.621418 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-12-03_13:31 Bits used No. missing words z-score p-value 28 to 32 142009 0.3379 0.632267 27 to 31 141926 0.0565 0.522532 26 to 30 141782 -0.4316 0.333006 25 to 29 142047 0.4667 0.679635 24 to 28 141743 -0.5638 0.286435 23 to 27 142136 0.7684 0.778867 22 to 26 141697 -0.7198 0.235836 21 to 25 141758 -0.5130 0.303982 20 to 24 141528 -1.2926 0.098067 19 to 23 142229 1.0836 0.860735 18 to 22 141671 -0.8079 0.209575 17 to 21 141657 -0.8554 0.196177 16 to 20 142018 0.3684 0.643702 15 to 19 141777 -0.4486 0.326869 14 to 18 142225 1.0701 0.857706 13 to 17 141605 -1.0316 0.151123 12 to 16 141586 -1.0960 0.136532 11 to 15 142066 0.5311 0.702320 10 to 14 142166 0.8701 0.807868 9 to 13 141962 0.1785 0.570852 8 to 12 141498 -1.3943 0.081608 7 to 11 142188 0.9446 0.827580 6 to 10 141603 -1.0384 0.149540 5 to 9 141493 -1.4113 0.079080 4 to 8 141615 -0.9977 0.159205 3 to 7 142118 0.7074 0.760327 2 to 6 142035 0.4260 0.664946 1 to 5 141951 0.1413 0.556166 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-12-03_13:31 Bits used No. missing words z-score p-value 31 to 32 142570 1.9489 0.974345 30 to 31 141902 -0.0216 0.491375 29 to 30 142017 0.3176 0.624610 28 to 29 141959 0.1465 0.558244 27 to 28 141614 -0.8712 0.191828 26 to 27 142150 0.7099 0.761130 25 to 26 141718 -0.5644 0.286243 24 to 25 142392 1.4238 0.922749 23 to 24 142396 1.4356 0.924443 22 to 23 141581 -0.9685 0.166391 21 to 22 141673 -0.6971 0.242858 20 to 21 141857 -0.1544 0.438661 19 to 20 141761 -0.4376 0.330856 18 to 19 141408 -1.4788 0.069590 17 to 18 142043 0.3943 0.653323 16 to 17 142235 0.9607 0.831643 15 to 16 142019 0.3235 0.626846 14 to 15 141231 -2.0010 0.022698 13 to 14 141940 0.0905 0.536044 12 to 13 142043 0.3943 0.653323 11 to 12 141852 -0.1691 0.432853 10 to 11 142644 2.1672 0.984889 9 to 10 141915 0.0167 0.506672 8 to 9 141648 -0.7709 0.220388 7 to 8 141780 -0.3815 0.351415 6 to 7 141786 -0.3638 0.358002 5 to 6 142145 0.6952 0.756532 4 to 5 141794 -0.3402 0.366851 3 to 4 141822 -0.2576 0.398354 2 to 3 141978 0.2026 0.580263 1 to 2 141690 -0.6470 0.258819 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-12-03_13:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2525.60 0.362 0.641314 Test results for specific bytes for dh-ranFile-2016-12-03_13:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2563.11 0.893 0.813945 2 to 9 2482.12 -0.253 0.400188 3 to 10 2648.87 2.105 0.982368 4 to 11 2207.98 -4.130 0.000018 5 to 12 2552.72 0.746 0.772053 6 to 13 2539.56 0.559 0.712081 7 to 14 2579.81 1.129 0.870495 8 to 15 2564.44 0.911 0.818922 9 to 16 2482.58 -0.246 0.402686 10 to 17 2497.57 -0.034 0.486284 11 to 18 2413.38 -1.225 0.110288 12 to 19 2373.85 -1.784 0.037214 13 to 20 2435.72 -0.909 0.181662 14 to 21 2622.87 1.738 0.958868 15 to 22 2591.67 1.296 0.902579 16 to 23 2521.91 0.310 0.621666 17 to 24 2500.99 0.014 0.505589 18 to 25 2563.87 0.903 0.816788 19 to 26 2517.54 0.248 0.597972 20 to 27 2704.89 2.898 0.998119 21 to 28 2445.37 -0.773 0.219880 22 to 29 2510.79 0.153 0.560664 23 to 30 2662.25 2.295 0.989120 24 to 31 2448.55 -0.728 0.233412 25 to 32 2456.74 -0.612 0.270361 CDPARK for dh-ranFile-2016-12-03_13:31: 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 3533 0.4566 0.676028 3538 0.6849 0.753306 3484 -1.7808 0.037471 3524 0.0457 0.518210 3524 0.0457 0.518210 3527 0.1826 0.572463 3503 -0.9132 0.180558 3529 0.2740 0.607947 3535 0.5479 0.708135 3513 -0.4566 0.323972 Square side=100, avg. no. parked=3521.00 sample std.=15.82 p-value of the KSTEST for those 10 p-values: 0.580726 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-12-03_13:31 0.7969,0.0104,0.8241,0.3320,0.1768,0.4086,0.0059,0.8821,0.7610,0.9174, The KS test for those 10 p-values: 0.276805 The 3DSPHERES test for dh-ranFile-2016-12-03_13:31 sample no r^3 equiv. uni. 1 28.850 0.617744 2 92.165 0.953680 3 52.893 0.828488 4 1.590 0.051620 5 5.119 0.156876 6 24.360 0.556033 7 69.730 0.902151 8 18.002 0.451226 9 7.324 0.216623 10 43.886 0.768429 11 32.314 0.659428 12 5.356 0.163505 13 19.902 0.484895 14 6.391 0.191876 15 9.698 0.276222 16 53.692 0.832996 17 27.367 0.598371 18 61.122 0.869631 19 20.084 0.488013 20 24.758 0.561883 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.895224 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-12-03_13:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 -1.2 2.0 -1.7 0.6 0.7 0.2 -0.4 0.1 -0.8 -0.2 0.9 0.0 -1.1 0.3 -1.0 0.6 0.4 0.7 -0.9 2.7 -0.7 -0.3 0.2 -1.9 0.0 -0.9 0.3 0.9 1.2 -1.6 0.8 -0.3 0.7 0.2 -1.9 0.0 -0.1 0.5 -0.7 0.1 0.0 -1.1 Chi-square with 42 degrees of freedom:39.182885 z-score=-0.307372, p-value=0.404664 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-12-03_13:31 Test no p-value 1 0.030492 2 0.059852 3 0.592688 4 0.819334 5 0.403702 6 0.786292 7 0.892837 8 0.007522 9 0.064420 10 0.059111 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.030906 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-12-03_13:31: (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 66771 0.16 3 25000.00 25088 0.31 24966 0.05 4 6666.67 6752 1.09 6645 0.07 5 1388.89 1336 2.01 1344 1.45 6 238.10 241 0.04 238 0.00 7 34.72 29 0.94 29 0.94 8 4.96 8 1.86 6 0.22 p=0.62829 p=0.17764 Number of rngs required: 689163, p-value: 0.810 RESULTS OF CRAPS TEST for dh-ranFile-2016-12-03_13:31 No. of wins: Observed Expected 98426 98585.9 z-score=-0.715, pvalue=0.23731 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66458 66666.7 0.653 0.653 2 37884 37654.3 1.401 2.054 3 26995 26954.7 0.060 2.114 4 19278 19313.5 0.065 2.179 5 13842 13851.4 0.006 2.186 6 10228 9943.5 8.138 10.323 7 7052 7145.0 1.211 11.534 8 5001 5139.1 3.710 15.244 9 3688 3699.9 0.038 15.282 10 2584 2666.3 2.540 17.822 11 1947 1923.3 0.291 18.114 12 1350 1388.7 1.081 19.194 13 1065 1003.7 3.742 22.936 14 678 726.1 3.192 26.128 15 530 525.8 0.033 26.161 16 381 381.2 0.000 26.161 17 300 276.5 1.990 28.151 18 218 200.8 1.468 29.619 19 135 146.0 0.827 30.446 20 95 106.2 1.184 31.630 21 291 287.1 0.053 31.682 Chisq= 31.68 for 20 degrees of freedom, p= 0.95320 SUMMARY of craptest p-value for no. of wins: 0.237310 p-value for throws/game: 0.953198 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-12-03_13:31 No. of wins: Observed Expected 98713 98585.9 z-score= 0.569, pvalue=0.71520 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66903 66666.7 0.838 0.838 2 37817 37654.3 0.703 1.541 3 26853 26954.7 0.384 1.925 4 19105 19313.5 2.250 4.175 5 13890 13851.4 0.107 4.282 6 10064 9943.5 1.459 5.741 7 7001 7145.0 2.903 8.645 8 5173 5139.1 0.224 8.869 9 3634 3699.9 1.173 10.041 10 2686 2666.3 0.146 10.187 11 1882 1923.3 0.888 11.075 12 1349 1388.7 1.137 12.212 13 994 1003.7 0.094 12.306 14 711 726.1 0.316 12.622 15 536 525.8 0.196 12.818 16 377 381.2 0.045 12.863 17 296 276.5 1.369 14.233 18 190 200.8 0.584 14.817 19 158 146.0 0.989 15.806 20 96 106.2 0.982 16.788 21 285 287.1 0.016 16.804 Chisq= 16.80 for 20 degrees of freedom, p= 0.33433 SUMMARY of craptest p-value for no. of wins: 0.715203 p-value for throws/game: 0.334325 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0000,0.0050,0.0059,0.0074,0.0075,0.0084,0.0104,0.0227,0.0305,0.0309, 0.0372,0.0375,0.0376,0.0423,0.0444,0.0516,0.0591,0.0599,0.0644,0.0679, 0.0696,0.0791,0.0816,0.0981,0.1103,0.1199,0.1203,0.1204,0.1365,0.1495, 0.1499,0.1511,0.1569,0.1592,0.1635,0.1645,0.1664,0.1704,0.1768,0.1776, 0.1806,0.1817,0.1896,0.1918,0.1919,0.1921,0.1962,0.2096,0.2166,0.2199, 0.2204,0.2216,0.2334,0.2358,0.2373,0.2429,0.2457,0.2472,0.2475,0.2481, 0.2500,0.2514,0.2588,0.2648,0.2704,0.2762,0.2768,0.2861,0.2862,0.2864, 0.2873,0.2877,0.2885,0.3034,0.3040,0.3104,0.3172,0.3240,0.3269,0.3309, 0.3320,0.3330,0.3335,0.3343,0.3378,0.3394,0.3488,0.3514,0.3580,0.3625, 0.3669,0.3801,0.3812,0.3882,0.3984,0.4002,0.4006,0.4027,0.4032,0.4037, 0.4047,0.4086,0.4095,0.4097,0.4126,0.4176,0.4242,0.4329,0.4365,0.4387, 0.4425,0.4512,0.4578,0.4693,0.4708,0.4728,0.4760,0.4770,0.4849,0.4863, 0.4866,0.4872,0.4880,0.4885,0.4914,0.4963,0.5038,0.5056,0.5067,0.5080, 0.5182,0.5182,0.5225,0.5325,0.5341,0.5360,0.5440,0.5453,0.5560,0.5562, 0.5582,0.5607,0.5619,0.5648,0.5656,0.5709,0.5725,0.5803,0.5807,0.5927, 0.5930,0.5980,0.5984,0.6047,0.6079,0.6177,0.6214,0.6217,0.6246,0.6268, 0.6283,0.6286,0.6305,0.6322,0.6323,0.6371,0.6409,0.6413,0.6437,0.6533, 0.6533,0.6582,0.6594,0.6649,0.6681,0.6760,0.6771,0.6787,0.6796,0.6859, 0.7002,0.7023,0.7067,0.7081,0.7091,0.7121,0.7146,0.7152,0.7295,0.7345, 0.7467,0.7533,0.7565,0.7577,0.7603,0.7608,0.7610,0.7611,0.7684,0.7694, 0.7694,0.7721,0.7787,0.7789,0.7863,0.7863,0.7870,0.7969,0.7983,0.8003, 0.8060,0.8079,0.8101,0.8103,0.8139,0.8168,0.8189,0.8193,0.8241,0.8273, 0.8276,0.8285,0.8308,0.8316,0.8330,0.8485,0.8520,0.8575,0.8577,0.8607, 0.8644,0.8673,0.8696,0.8705,0.8750,0.8821,0.8928,0.8952,0.8963,0.8980, 0.8992,0.9018,0.9022,0.9026,0.9126,0.9174,0.9177,0.9215,0.9227,0.9229, 0.9244,0.9361,0.9395,0.9467,0.9513,0.9523,0.9532,0.9537,0.9589,0.9712, 0.9724,0.9743,0.9745,0.9802,0.9824,0.9847,0.9849,0.9891,0.9981, Overall p-value after applying KStest on 269 p-values = 0.353212 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.