RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-29_18:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.51 16.3087 0.497938 2 to 25 15.55 24.8611 0.902137 3 to 26 15.74 20.1871 0.735227 4 to 27 15.67 20.7765 0.763553 5 to 28 15.77 19.7581 0.713212 6 to 29 15.65 14.7890 0.389326 7 to 30 15.77 21.4065 0.791368 8 to 31 15.68 21.8982 0.811335 9 to 32 15.86 12.7418 0.246711 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.143716 Tough bday spacings test for dh-ranFile-2018-06-29_18:31: 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 13 38 67 109 91 74 60 25 15 4 4 (O-E)^2/E 1.6 0.1 0.5 1.3 0.5 0.2 1.2 0.8 0.0 1.0 0.0 Birthday Spacings: Sum(O-E)^2/E= 7.186, p= 0.292 RESULTS OF GCD FOR dh-ranFile-2018-06-29_18:31 Euclid's algorithm: p-value, steps to gcd: 0.220003 p-value, dist. of gcd's: 0.854034 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-29_18:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.406 0.920 0.371 0.856 0.378 0.319 0.573 0.970 Bits 8 to 15---> 0.137 0.518 0.227 0.590 0.745 0.822 0.240 0.392 Bits 16 to 23---> 0.133 0.581 0.098 0.526 0.562 0.569 0.645 0.983 Bits 24 to 31---> 0.489 0.767 0.073 0.901 0.252 0.277 0.313 0.213 KS test for the above 32 p values: 0.175 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-29_18:31, p-values for 5 runs: 0.9033, 0.9576, 0.7891, 0.7850, 0.4735 Rank test for binary matrices (31x31) for dh-ranFile-2018-06-29_18:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 194 211.4 1.435 1.435 r= 29 5192 5134.0 0.655 2.090 r= 30 23034 23103.0 0.206 2.296 r= 31 11580 11551.5 0.070 2.367 chi-square = 2.367 with df = 3; p-value = 0.500 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-06-29_18:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 203 211.4 0.335 0.335 r= 30 5279 5134.0 4.095 4.430 r= 31 22995 23103.0 0.505 4.935 r= 32 11523 11551.5 0.070 5.006 chi-square = 5.006 with df = 3; p-value = 0.829 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-06-29_18:31 b-rank test for bits 1 to 8, p=0.88887 b-rank test for bits 2 to 9, p=0.02202 b-rank test for bits 3 to 10, p=0.87337 b-rank test for bits 4 to 11, p=0.08074 b-rank test for bits 5 to 12, p=0.47317 b-rank test for bits 6 to 13, p=0.30224 b-rank test for bits 7 to 14, p=0.99644 b-rank test for bits 8 to 15, p=0.86267 b-rank test for bits 9 to 16, p=0.24826 b-rank test for bits 10 to 17, p=0.35678 b-rank test for bits 11 to 18, p=0.84889 b-rank test for bits 12 to 19, p=0.18825 b-rank test for bits 13 to 20, p=0.44879 b-rank test for bits 14 to 21, p=0.09217 b-rank test for bits 15 to 22, p=0.96459 b-rank test for bits 16 to 23, p=0.07643 b-rank test for bits 17 to 24, p=0.32540 b-rank test for bits 18 to 25, p=0.12492 b-rank test for bits 19 to 26, p=0.72759 b-rank test for bits 20 to 27, p=0.50681 b-rank test for bits 21 to 28, p=0.07764 b-rank test for bits 22 to 29, p=0.73672 b-rank test for bits 23 to 30, p=0.54869 b-rank test for bits 24 to 31, p=0.28423 b-rank test for bits 25 to 32, p=0.14108 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 = 0.358184 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-29_18:31 (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 141827 -0.19 0.423730 2 142369 1.07 0.858588 3 141889 -0.05 0.481057 4 141996 0.20 0.580237 5 141872 -0.09 0.465249 6 141945 0.08 0.533210 7 141766 -0.33 0.368857 8 142311 0.94 0.826001 9 141611 -0.70 0.242891 10 141873 -0.08 0.466177 11 142333 0.99 0.838884 12 141621 -0.67 0.250261 13 142059 0.35 0.636717 14 142129 0.51 0.696111 15 141895 -0.03 0.486645 16 142022 0.26 0.603820 17 141477 -1.01 0.156220 18 141646 -0.62 0.269193 19 141984 0.17 0.569249 20 142439 1.24 0.892058 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-06-29_18:31 Bits used No. missing words z-score p-value 23 to 32 141832 -0.2667 0.394867 22 to 31 141973 0.2196 0.586890 21 to 30 141404 -1.7425 0.040709 20 to 29 141916 0.0230 0.509175 19 to 28 141457 -1.5598 0.059408 18 to 27 142078 0.5816 0.719589 17 to 26 141961 0.1782 0.570706 16 to 25 142443 1.8402 0.967134 15 to 24 141859 -0.1736 0.431109 14 to 23 142325 1.4333 0.924120 13 to 22 141873 -0.1253 0.450153 12 to 21 142429 1.7920 0.963431 11 to 20 142322 1.4230 0.922632 10 to 19 141854 -0.1908 0.424344 9 to 18 142157 0.8540 0.803457 8 to 17 142293 1.3230 0.907082 7 to 16 142044 0.4644 0.678812 6 to 15 141619 -1.0011 0.158380 5 to 14 141650 -0.8942 0.185596 4 to 13 141607 -1.0425 0.148586 3 to 12 141844 -0.2253 0.410882 2 to 11 141739 -0.5873 0.278486 1 to 10 141673 -0.8149 0.207556 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-06-29_18:31 Bits used No. missing words z-score p-value 28 to 32 141613 -1.0045 0.157567 27 to 31 141806 -0.3503 0.363068 26 to 30 141696 -0.7232 0.234793 25 to 29 142232 1.0938 0.862978 24 to 28 141804 -0.3571 0.360527 23 to 27 142150 0.8158 0.792702 22 to 26 142022 0.3819 0.648744 21 to 25 141552 -1.2113 0.112893 20 to 24 142220 1.0531 0.853857 19 to 23 141998 0.3006 0.618131 18 to 22 142406 1.6836 0.953873 17 to 21 141796 -0.3842 0.350426 16 to 20 142009 0.3379 0.632267 15 to 19 141522 -1.3130 0.094594 14 to 18 142022 0.3819 0.648744 13 to 17 141678 -0.7842 0.216470 12 to 16 142120 0.7141 0.762428 11 to 15 141688 -0.7503 0.226546 10 to 14 141505 -1.3706 0.085248 9 to 13 142014 0.3548 0.638635 8 to 12 141787 -0.4147 0.339189 7 to 11 142089 0.6091 0.728755 6 to 10 141936 0.0904 0.536018 5 to 9 141858 -0.1740 0.430933 4 to 8 141530 -1.2859 0.099245 3 to 7 142611 2.3785 0.991309 2 to 6 141849 -0.2045 0.418978 1 to 5 141894 -0.0520 0.479278 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-06-29_18:31 Bits used No. missing words z-score p-value 31 to 32 141767 -0.4199 0.337297 30 to 31 141912 0.0079 0.503142 29 to 30 142289 1.1200 0.868637 28 to 29 142104 0.5742 0.717100 27 to 28 142987 3.1790 0.999261 26 to 27 142061 0.4474 0.672708 25 to 26 142320 1.2114 0.887132 24 to 25 141906 -0.0098 0.496081 23 to 24 142260 1.0344 0.849531 22 to 23 141746 -0.4818 0.314974 21 to 22 142256 1.0226 0.846758 20 to 21 142671 2.2468 0.987674 19 to 20 142043 0.3943 0.653323 18 to 19 142619 2.0934 0.981844 17 to 18 141739 -0.5024 0.307676 16 to 17 141936 0.0787 0.531354 15 to 16 141844 -0.1927 0.423592 14 to 15 142095 0.5477 0.708051 13 to 14 142100 0.5624 0.713095 12 to 13 141730 -0.5290 0.298404 11 to 12 142278 1.0875 0.861597 10 to 11 141235 -1.9892 0.023341 9 to 10 141845 -0.1898 0.424747 8 to 9 141623 -0.8446 0.199158 7 to 8 141666 -0.7178 0.236444 6 to 7 141610 -0.8830 0.188624 5 to 6 142113 0.6008 0.726012 4 to 5 142246 0.9931 0.839676 3 to 4 142110 0.5919 0.723057 2 to 3 142203 0.8663 0.806833 1 to 2 142060 0.4445 0.671643 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-29_18:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2456.63 -0.613 0.269830 Test results for specific bytes for dh-ranFile-2018-06-29_18:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2510.68 0.151 0.560006 2 to 9 2478.83 -0.299 0.382318 3 to 10 2453.03 -0.664 0.253264 4 to 11 2517.92 0.253 0.600038 5 to 12 2556.27 0.796 0.786929 6 to 13 2446.13 -0.762 0.223065 7 to 14 2453.83 -0.653 0.256881 8 to 15 2569.07 0.977 0.835682 9 to 16 2484.90 -0.214 0.415462 10 to 17 2483.38 -0.235 0.407108 11 to 18 2448.38 -0.730 0.232701 12 to 19 2490.19 -0.139 0.444855 13 to 20 2549.75 0.704 0.759168 14 to 21 2471.68 -0.400 0.344400 15 to 22 2622.88 1.738 0.958879 16 to 23 2457.79 -0.597 0.275290 17 to 24 2602.64 1.451 0.926678 18 to 25 2581.49 1.152 0.875417 19 to 26 2569.82 0.987 0.838291 20 to 27 2467.10 -0.465 0.320878 21 to 28 2387.72 -1.588 0.056154 22 to 29 2489.71 -0.145 0.442166 23 to 30 2512.76 0.180 0.571595 24 to 31 2500.49 0.007 0.502743 25 to 32 2621.87 1.723 0.957600 CDPARK for dh-ranFile-2018-06-29_18:31: 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 3507 -0.7306 0.232514 3516 -0.3196 0.374623 3537 0.6393 0.738676 3558 1.5982 0.944998 3552 1.3242 0.907282 3504 -0.8676 0.192812 3505 -0.8219 0.205562 3488 -1.5982 0.055002 3528 0.2283 0.590298 3507 -0.7306 0.232514 Square side=100, avg. no. parked=3520.20 sample std.=21.63 p-value of the KSTEST for those 10 p-values: 0.671901 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-29_18:31 0.1587,0.5715,0.4358,0.3162,0.7738,0.8693,0.9897,0.6009,0.8128,0.1878, The KS test for those 10 p-values: 0.736285 The 3DSPHERES test for dh-ranFile-2018-06-29_18:31 sample no r^3 equiv. uni. 1 11.713 0.323227 2 60.618 0.867422 3 9.346 0.267665 4 29.647 0.627761 5 11.168 0.310825 6 26.791 0.590585 7 8.817 0.254651 8 10.136 0.286701 9 16.481 0.422691 10 29.599 0.627172 11 66.361 0.890522 12 50.182 0.812268 13 35.284 0.691526 14 0.409 0.013548 15 100.464 0.964874 16 0.579 0.019109 17 47.836 0.796996 18 50.616 0.814963 19 29.503 0.625980 20 9.597 0.273784 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.756116 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-29_18:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -0.7 1.8 0.3 -0.8 -1.6 -1.9 1.0 -0.3 1.2 -0.2 -0.1 0.6 0.5 0.1 0.9 -0.2 0.2 -0.9 -2.1 0.5 -0.4 1.3 0.2 1.2 -0.6 -0.3 -1.7 0.9 -0.6 0.5 -0.9 0.6 0.4 -0.2 -0.7 2.4 -0.1 0.5 2.1 0.1 0.0 0.8 Chi-square with 42 degrees of freedom:41.718038 z-score=-0.030765, p-value=0.516762 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-06-29_18:31 Test no p-value 1 0.761229 2 0.363934 3 0.087058 4 0.107884 5 0.016461 6 0.732753 7 0.043701 8 0.409886 9 0.000106 10 0.192864 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.004534 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-29_18:31: (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 66543 0.23 66453 0.68 3 25000.00 25011 0.00 25114 0.52 4 6666.67 6762 1.36 6707 0.24 5 1388.89 1395 0.03 1433 1.40 6 238.10 256 1.35 258 1.66 7 34.72 27 1.72 30 0.64 8 4.96 5 0.00 4 0.19 p=0.41554 p=0.49913 Number of rngs required: 688161, p-value: 0.390 RESULTS OF CRAPS TEST for dh-ranFile-2018-06-29_18:31 No. of wins: Observed Expected 98373 98585.9 z-score=-0.952, pvalue=0.17054 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66556 66666.7 0.184 0.184 2 37931 37654.3 2.033 2.217 3 26771 26954.7 1.252 3.469 4 19375 19313.5 0.196 3.665 5 13903 13851.4 0.192 3.857 6 10089 9943.5 2.128 5.985 7 6999 7145.0 2.984 8.969 8 5063 5139.1 1.126 10.095 9 3730 3699.9 0.245 10.341 10 2688 2666.3 0.177 10.518 11 1918 1923.3 0.015 10.532 12 1398 1388.7 0.062 10.594 13 975 1003.7 0.822 11.416 14 723 726.1 0.014 11.429 15 509 525.8 0.539 11.968 16 386 381.2 0.062 12.030 17 244 276.5 3.829 15.859 18 207 200.8 0.190 16.048 19 138 146.0 0.437 16.485 20 126 106.2 3.685 20.170 21 271 287.1 0.904 21.075 Chisq= 21.07 for 20 degrees of freedom, p= 0.60725 SUMMARY of craptest p-value for no. of wins: 0.170541 p-value for throws/game: 0.607252 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-29_18:31 No. of wins: Observed Expected 98464 98585.9 z-score=-0.545, pvalue=0.29287 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66552 66666.7 0.197 0.197 2 37725 37654.3 0.133 0.330 3 26926 26954.7 0.031 0.361 4 19313 19313.5 0.000 0.361 5 13896 13851.4 0.143 0.504 6 9974 9943.5 0.093 0.597 7 7207 7145.0 0.538 1.135 8 5053 5139.1 1.442 2.576 9 3797 3699.9 2.550 5.127 10 2705 2666.3 0.562 5.688 11 1870 1923.3 1.479 7.167 12 1378 1388.7 0.083 7.250 13 998 1003.7 0.033 7.283 14 747 726.1 0.599 7.882 15 471 525.8 5.718 13.600 16 394 381.2 0.433 14.034 17 256 276.5 1.526 15.559 18 187 200.8 0.952 16.511 19 151 146.0 0.172 16.684 20 110 106.2 0.135 16.819 21 290 287.1 0.029 16.848 Chisq= 16.85 for 20 degrees of freedom, p= 0.33716 SUMMARY of craptest p-value for no. of wins: 0.292869 p-value for throws/game: 0.337156 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0001,0.0045,0.0135,0.0165,0.0191,0.0220,0.0233,0.0407,0.0437,0.0550, 0.0562,0.0594,0.0727,0.0764,0.0776,0.0807,0.0852,0.0871,0.0922,0.0946, 0.0977,0.0992,0.1079,0.1129,0.1249,0.1331,0.1368,0.1411,0.1437,0.1486, 0.1562,0.1576,0.1584,0.1587,0.1705,0.1751,0.1856,0.1878,0.1882,0.1886, 0.1928,0.1929,0.1992,0.2056,0.2076,0.2128,0.2165,0.2200,0.2231,0.2265, 0.2265,0.2325,0.2325,0.2327,0.2348,0.2364,0.2403,0.2429,0.2467,0.2483, 0.2503,0.2516,0.2533,0.2547,0.2569,0.2677,0.2692,0.2698,0.2738,0.2753, 0.2767,0.2785,0.2842,0.2867,0.2922,0.2929,0.2984,0.3022,0.3077,0.3108, 0.3135,0.3150,0.3162,0.3189,0.3209,0.3232,0.3254,0.3372,0.3373,0.3392, 0.3444,0.3504,0.3568,0.3582,0.3605,0.3631,0.3639,0.3689,0.3705,0.3746, 0.3779,0.3823,0.3893,0.3903,0.3923,0.3949,0.4060,0.4071,0.4099,0.4109, 0.4155,0.4155,0.4190,0.4227,0.4236,0.4237,0.4243,0.4247,0.4309,0.4311, 0.4358,0.4422,0.4449,0.4488,0.4502,0.4652,0.4662,0.4732,0.4735,0.4793, 0.4811,0.4866,0.4889,0.4961,0.4979,0.4991,0.5001,0.5027,0.5031,0.5068, 0.5092,0.5168,0.5181,0.5258,0.5314,0.5332,0.5360,0.5487,0.5600,0.5619, 0.5688,0.5692,0.5707,0.5715,0.5716,0.5731,0.5802,0.5810,0.5869,0.5900, 0.5903,0.5906,0.6000,0.6009,0.6038,0.6073,0.6181,0.6260,0.6272,0.6278, 0.6323,0.6367,0.6386,0.6454,0.6487,0.6487,0.6533,0.6716,0.6719,0.6727, 0.6788,0.6915,0.6961,0.7081,0.7131,0.7132,0.7171,0.7196,0.7231,0.7260, 0.7276,0.7288,0.7328,0.7352,0.7363,0.7367,0.7387,0.7450,0.7561,0.7592, 0.7612,0.7624,0.7636,0.7666,0.7738,0.7850,0.7869,0.7891,0.7914,0.7927, 0.7970,0.8035,0.8068,0.8113,0.8123,0.8128,0.8150,0.8224,0.8260,0.8286, 0.8357,0.8383,0.8389,0.8397,0.8468,0.8489,0.8495,0.8539,0.8540,0.8557, 0.8586,0.8616,0.8627,0.8630,0.8674,0.8686,0.8693,0.8734,0.8754,0.8871, 0.8889,0.8905,0.8921,0.9005,0.9021,0.9033,0.9071,0.9073,0.9201,0.9226, 0.9241,0.9267,0.9450,0.9539,0.9576,0.9576,0.9589,0.9634,0.9646,0.9649, 0.9671,0.9703,0.9818,0.9834,0.9877,0.9897,0.9913,0.9964,0.9993, Overall p-value after applying KStest on 269 p-values = 0.573454 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.