RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-04-14_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 16.18 23.2143 0.857598 2 to 25 15.85 18.3836 0.634965 3 to 26 15.72 13.3606 0.288267 4 to 27 15.87 18.5862 0.647208 5 to 28 15.70 23.8648 0.876843 6 to 29 15.72 23.2006 0.857166 7 to 30 15.88 13.0037 0.264064 8 to 31 15.59 16.6846 0.524074 9 to 32 15.55 18.0063 0.611559 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.278082 Tough bday spacings test for dh-ranFile-2018-04-14_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 6 30 89 96 113 81 42 26 10 6 1 (O-E)^2/E 1.1 1.2 3.4 0.0 2.4 0.1 2.0 0.5 1.6 0.1 2.3 Birthday Spacings: Sum(O-E)^2/E= 14.612, p= 0.853 RESULTS OF GCD FOR dh-ranFile-2018-04-14_01:31 Euclid's algorithm: p-value, steps to gcd: 0.621751 p-value, dist. of gcd's: 0.710090 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-04-14_01:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.310 0.357 0.646 0.244 0.931 0.740 0.241 0.418 Bits 8 to 15---> 0.475 0.358 0.080 0.284 0.107 0.808 0.888 0.572 Bits 16 to 23---> 0.202 0.143 0.681 0.172 0.968 0.352 0.144 0.457 Bits 24 to 31---> 0.673 0.078 0.134 0.063 0.803 0.208 0.351 0.563 KS test for the above 32 p values: 0.830 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-04-14_01:31, p-values for 5 runs: 0.0380, 0.3892, 0.4843, 0.5641, 0.0224 Rank test for binary matrices (31x31) for dh-ranFile-2018-04-14_01:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 214 211.4 0.032 0.032 r= 29 5016 5134.0 2.713 2.744 r= 30 22971 23103.0 0.755 3.499 r= 31 11799 11551.5 5.302 8.801 chi-square = 8.801 with df = 3; p-value = 0.968 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-04-14_01:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 225 211.4 0.873 0.873 r= 30 5111 5134.0 0.103 0.976 r= 31 23043 23103.0 0.156 1.132 r= 32 11621 11551.5 0.418 1.550 chi-square = 1.550 with df = 3; p-value = 0.329 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-04-14_01:31 b-rank test for bits 1 to 8, p=0.35527 b-rank test for bits 2 to 9, p=0.46915 b-rank test for bits 3 to 10, p=0.44464 b-rank test for bits 4 to 11, p=0.23046 b-rank test for bits 5 to 12, p=0.02446 b-rank test for bits 6 to 13, p=0.70925 b-rank test for bits 7 to 14, p=0.27262 b-rank test for bits 8 to 15, p=0.93132 b-rank test for bits 9 to 16, p=0.34219 b-rank test for bits 10 to 17, p=0.68852 b-rank test for bits 11 to 18, p=0.96140 b-rank test for bits 12 to 19, p=0.66490 b-rank test for bits 13 to 20, p=0.69600 b-rank test for bits 14 to 21, p=0.18060 b-rank test for bits 15 to 22, p=0.54639 b-rank test for bits 16 to 23, p=0.21249 b-rank test for bits 17 to 24, p=0.02957 b-rank test for bits 18 to 25, p=0.94405 b-rank test for bits 19 to 26, p=0.24319 b-rank test for bits 20 to 27, p=0.95873 b-rank test for bits 21 to 28, p=0.71119 b-rank test for bits 22 to 29, p=0.24004 b-rank test for bits 23 to 30, p=0.80113 b-rank test for bits 24 to 31, p=0.93131 b-rank test for bits 25 to 32, p=0.79312 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 = 0.638140 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-04-14_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 141978 0.16 0.563734 2 141703 -0.48 0.314875 3 141010 -2.10 0.017810 4 141931 0.05 0.520190 5 141804 -0.25 0.402803 6 142023 0.27 0.604720 7 142230 0.75 0.773140 8 141547 -0.85 0.198619 9 142140 0.54 0.705039 10 143009 2.57 0.994905 11 141203 -1.65 0.049440 12 141913 0.01 0.503421 13 142979 2.50 0.993777 14 141668 -0.56 0.286426 15 141435 -1.11 0.133877 16 142154 0.57 0.716223 17 142482 1.34 0.909554 18 142025 0.27 0.606519 19 141981 0.17 0.566493 20 142424 1.20 0.885415 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-04-14_01:31 Bits used No. missing words z-score p-value 23 to 32 141131 -2.6839 0.003638 22 to 31 141461 -1.5460 0.061056 21 to 30 141344 -1.9494 0.025623 20 to 29 141442 -1.6115 0.053537 19 to 28 141713 -0.6770 0.249203 18 to 27 141642 -0.9218 0.178309 17 to 26 141741 -0.5804 0.280806 16 to 25 142104 0.6713 0.748978 15 to 24 142080 0.5885 0.721907 14 to 23 142008 0.3402 0.633163 13 to 22 141762 -0.5080 0.305715 12 to 21 142139 0.7920 0.785810 11 to 20 142056 0.5058 0.693487 10 to 19 142171 0.9023 0.816554 9 to 18 141963 0.1851 0.573413 8 to 17 141729 -0.6218 0.267028 7 to 16 142012 0.3540 0.638344 6 to 15 142220 1.0713 0.857977 5 to 14 142019 0.3782 0.647349 4 to 13 141560 -1.2046 0.114182 3 to 12 141758 -0.5218 0.300895 2 to 11 141685 -0.7736 0.219598 1 to 10 141826 -0.2873 0.386924 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-04-14_01:31 Bits used No. missing words z-score p-value 28 to 32 142276 1.2429 0.893057 27 to 31 141306 -2.0452 0.020418 26 to 30 142266 1.2091 0.886678 25 to 29 142137 0.7718 0.779873 24 to 28 142167 0.8735 0.808793 23 to 27 142000 0.3074 0.620714 22 to 26 142177 0.9074 0.817891 21 to 25 141955 0.1548 0.561516 20 to 24 141980 0.2396 0.594664 19 to 23 142187 0.9413 0.826713 18 to 22 141714 -0.6621 0.253942 17 to 21 141952 0.1446 0.557504 16 to 20 141548 -1.2248 0.110316 15 to 19 141666 -0.8248 0.204729 14 to 18 141537 -1.2621 0.103450 13 to 17 142095 0.6294 0.735453 12 to 16 142587 2.2972 0.989196 11 to 15 142004 0.3209 0.625863 10 to 14 141831 -0.2655 0.395302 9 to 13 141721 -0.6384 0.261605 8 to 12 142019 0.3718 0.644965 7 to 11 141512 -1.3469 0.089009 6 to 10 141479 -1.4587 0.072318 5 to 9 141903 -0.0215 0.491440 4 to 8 141998 0.3006 0.618131 3 to 7 142074 0.5582 0.711647 2 to 6 142368 1.5548 0.940005 1 to 5 141981 0.2429 0.595978 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-04-14_01:31 Bits used No. missing words z-score p-value 31 to 32 141943 0.0993 0.539559 30 to 31 142685 2.2881 0.988935 29 to 30 141987 0.2291 0.590610 28 to 29 142730 2.4209 0.992258 27 to 28 141659 -0.7384 0.230125 26 to 27 142032 0.3619 0.641271 25 to 26 141355 -1.6352 0.051004 24 to 25 141824 -0.2517 0.400632 23 to 24 141714 -0.5762 0.282242 22 to 23 141171 -2.1780 0.014704 21 to 22 142103 0.5713 0.716101 20 to 21 141925 0.0462 0.518434 19 to 20 141661 -0.7325 0.231921 18 to 19 141822 -0.2576 0.398354 17 to 18 141769 -0.4140 0.339454 16 to 17 141947 0.1111 0.544240 15 to 16 142454 1.6067 0.945939 14 to 15 142026 0.3442 0.634637 13 to 14 141512 -1.1721 0.120586 12 to 13 142068 0.4681 0.680127 11 to 12 141645 -0.7797 0.217774 10 to 11 142015 0.3117 0.622370 9 to 10 141681 -0.6735 0.250302 8 to 9 141423 -1.4346 0.075700 7 to 8 142074 0.4858 0.686429 6 to 7 141561 -1.0275 0.152087 5 to 6 141734 -0.5172 0.302509 4 to 5 142830 2.7158 0.996695 3 to 4 141551 -1.0570 0.145251 2 to 3 142384 1.4002 0.919274 1 to 2 142265 1.0492 0.852951 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-04-14_01:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2513.02 0.184 0.573063 Test results for specific bytes for dh-ranFile-2018-04-14_01:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2537.99 0.537 0.704465 2 to 9 2518.24 0.258 0.601752 3 to 10 2583.53 1.181 0.881248 4 to 11 2532.95 0.466 0.679400 5 to 12 2440.96 -0.835 0.201880 6 to 13 2529.01 0.410 0.659174 7 to 14 2350.05 -2.121 0.016975 8 to 15 2497.70 -0.033 0.487023 9 to 16 2470.85 -0.412 0.340082 10 to 17 2528.02 0.396 0.654061 11 to 18 2487.88 -0.171 0.431926 12 to 19 2594.12 1.331 0.908408 13 to 20 2416.36 -1.183 0.118431 14 to 21 2564.62 0.914 0.819589 15 to 22 2539.20 0.554 0.710330 16 to 23 2449.43 -0.715 0.237247 17 to 24 2556.77 0.803 0.788974 18 to 25 2578.41 1.109 0.866261 19 to 26 2588.68 1.254 0.895112 20 to 27 2416.35 -1.183 0.118399 21 to 28 2536.61 0.518 0.697698 22 to 29 2531.81 0.450 0.673601 23 to 30 2457.59 -0.600 0.274324 24 to 31 2519.54 0.276 0.608864 25 to 32 2508.56 0.121 0.548160 CDPARK for dh-ranFile-2018-04-14_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 3539 0.7306 0.767486 3540 0.7763 0.781201 3491 -1.4612 0.071982 3517 -0.2740 0.392053 3551 1.2785 0.899470 3543 0.9132 0.819442 3544 0.9589 0.831196 3535 0.5479 0.708135 3506 -0.7763 0.218799 3549 1.1872 0.882429 Square side=100, avg. no. parked=3531.50 sample std.=19.02 p-value of the KSTEST for those 10 p-values: 0.129823 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-04-14_01:31 0.0959,0.9665,0.0864,0.3839,0.0727,0.0444,0.8527,0.4128,0.0767,0.0403, The KS test for those 10 p-values: 0.007489 The 3DSPHERES test for dh-ranFile-2018-04-14_01:31 sample no r^3 equiv. uni. 1 2.894 0.091957 2 2.238 0.071872 3 12.117 0.332285 4 11.373 0.315518 5 4.017 0.125308 6 30.358 0.636489 7 18.308 0.456791 8 16.486 0.422779 9 16.439 0.421868 10 7.291 0.215758 11 0.459 0.015180 12 19.609 0.479855 13 7.465 0.220287 14 44.422 0.772531 15 18.801 0.465642 16 10.649 0.298793 17 8.976 0.258577 18 5.170 0.158290 19 3.096 0.098067 20 73.952 0.914996 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.018871 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-04-14_01:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 1.3 -0.3 0.8 0.2 1.9 -0.4 -0.4 0.3 0.2 1.1 -0.5 -2.2 -0.6 1.3 0.7 -1.4 1.7 0.6 -1.9 1.4 0.5 -0.1 0.4 0.3 0.2 -0.7 -2.9 -0.0 -0.5 0.0 1.9 1.0 -1.4 -1.0 -0.4 -1.0 0.5 -1.3 1.3 -0.7 0.1 -1.0 -0.1 Chi-square with 42 degrees of freedom:50.316557 z-score=0.907411, p-value=0.822595 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-04-14_01:31 Test no p-value 1 0.016937 2 0.925006 3 0.988614 4 0.001279 5 0.882656 6 0.202436 7 0.501675 8 0.008896 9 0.020198 10 0.666637 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.009445 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-04-14_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 66502 0.41 66423 0.89 3 25000.00 25002 0.00 25228 2.08 4 6666.67 6780 1.93 6631 0.19 5 1388.89 1436 1.60 1419 0.65 6 238.10 241 0.04 255 1.20 7 34.72 29 0.94 39 0.53 8 4.96 9 3.29 4 0.19 p=0.77617 p=0.54557 Number of rngs required: 689619, p-value: 0.922 RESULTS OF CRAPS TEST for dh-ranFile-2018-04-14_01:31 No. of wins: Observed Expected 98659 98585.9 z-score= 0.327, pvalue=0.62822 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66706 66666.7 0.023 0.023 2 37759 37654.3 0.291 0.314 3 27023 26954.7 0.173 0.487 4 19142 19313.5 1.522 2.009 5 13958 13851.4 0.820 2.829 6 9959 9943.5 0.024 2.853 7 7127 7145.0 0.045 2.899 8 5069 5139.1 0.955 3.854 9 3633 3699.9 1.208 5.063 10 2612 2666.3 1.106 6.168 11 1901 1923.3 0.259 6.428 12 1317 1388.7 3.706 10.134 13 1025 1003.7 0.451 10.585 14 753 726.1 0.994 11.579 15 542 525.8 0.497 12.075 16 391 381.2 0.255 12.330 17 288 276.5 0.475 12.805 18 233 200.8 5.153 17.958 19 144 146.0 0.027 17.985 20 119 106.2 1.539 19.524 21 299 287.1 0.492 20.016 Chisq= 20.02 for 20 degrees of freedom, p= 0.54307 SUMMARY of craptest p-value for no. of wins: 0.628216 p-value for throws/game: 0.543074 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-04-14_01:31 No. of wins: Observed Expected 98310 98585.9 z-score=-1.234, pvalue=0.10864 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66677 66666.7 0.002 0.002 2 37250 37654.3 4.341 4.343 3 27031 26954.7 0.216 4.559 4 19282 19313.5 0.051 4.610 5 13889 13851.4 0.102 4.712 6 10002 9943.5 0.344 5.056 7 7158 7145.0 0.024 5.079 8 5219 5139.1 1.243 6.322 9 3717 3699.9 0.079 6.402 10 2662 2666.3 0.007 6.409 11 1972 1923.3 1.232 7.640 12 1427 1388.7 1.054 8.694 13 1060 1003.7 3.156 11.851 14 686 726.1 2.219 14.070 15 521 525.8 0.044 14.114 16 390 381.2 0.205 14.320 17 308 276.5 3.579 17.899 18 212 200.8 0.621 18.520 19 137 146.0 0.553 19.073 20 103 106.2 0.097 19.170 21 297 287.1 0.340 19.511 Chisq= 19.51 for 20 degrees of freedom, p= 0.51111 SUMMARY of craptest p-value for no. of wins: 0.108639 p-value for throws/game: 0.511106 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0013,0.0036,0.0075,0.0089,0.0094,0.0147,0.0152,0.0169,0.0170,0.0178, 0.0189,0.0202,0.0204,0.0224,0.0245,0.0256,0.0296,0.0380,0.0403,0.0444, 0.0494,0.0510,0.0535,0.0611,0.0633,0.0719,0.0720,0.0723,0.0727,0.0757, 0.0767,0.0778,0.0804,0.0864,0.0890,0.0920,0.0959,0.0981,0.1035,0.1070, 0.1086,0.1103,0.1142,0.1184,0.1184,0.1206,0.1253,0.1298,0.1339,0.1343, 0.1435,0.1440,0.1453,0.1521,0.1583,0.1716,0.1783,0.1806,0.1986,0.2019, 0.2023,0.2024,0.2047,0.2079,0.2125,0.2158,0.2178,0.2188,0.2196,0.2203, 0.2301,0.2305,0.2319,0.2372,0.2400,0.2406,0.2432,0.2441,0.2492,0.2503, 0.2539,0.2586,0.2616,0.2641,0.2670,0.2726,0.2743,0.2781,0.2808,0.2822, 0.2837,0.2864,0.2883,0.2988,0.3009,0.3025,0.3057,0.3099,0.3149,0.3155, 0.3291,0.3323,0.3395,0.3401,0.3422,0.3513,0.3518,0.3553,0.3569,0.3576, 0.3839,0.3869,0.3892,0.3921,0.3953,0.3984,0.4006,0.4028,0.4128,0.4180, 0.4219,0.4228,0.4319,0.4446,0.4568,0.4575,0.4656,0.4692,0.4749,0.4799, 0.4843,0.4870,0.4914,0.5017,0.5034,0.5111,0.5184,0.5202,0.5241,0.5396, 0.5431,0.5442,0.5456,0.5464,0.5482,0.5575,0.5615,0.5635,0.5637,0.5641, 0.5665,0.5722,0.5731,0.5734,0.5906,0.5947,0.5960,0.6018,0.6047,0.6065, 0.6089,0.6116,0.6181,0.6207,0.6218,0.6224,0.6259,0.6282,0.6332,0.6346, 0.6350,0.6365,0.6381,0.6383,0.6413,0.6450,0.6458,0.6472,0.6473,0.6541, 0.6592,0.6649,0.6666,0.6732,0.6736,0.6794,0.6801,0.6814,0.6864,0.6885, 0.6935,0.6960,0.6977,0.7045,0.7050,0.7081,0.7092,0.7101,0.7103,0.7112, 0.7116,0.7161,0.7162,0.7219,0.7355,0.7399,0.7490,0.7675,0.7725,0.7731, 0.7762,0.7799,0.7812,0.7858,0.7890,0.7931,0.8011,0.8032,0.8084,0.8088, 0.8166,0.8179,0.8194,0.8196,0.8226,0.8267,0.8303,0.8312,0.8527,0.8530, 0.8531,0.8572,0.8576,0.8580,0.8663,0.8768,0.8812,0.8824,0.8827,0.8854, 0.8867,0.8881,0.8931,0.8951,0.8995,0.9084,0.9096,0.9150,0.9193,0.9220, 0.9250,0.9313,0.9313,0.9315,0.9400,0.9441,0.9459,0.9587,0.9614,0.9665, 0.9679,0.9681,0.9886,0.9889,0.9892,0.9923,0.9938,0.9949,0.9967, Overall p-value after applying KStest on 269 p-values = 0.179211 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.