RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-04-02_03:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.49 22.2047 0.823024 2 to 25 15.64 21.5027 0.795393 3 to 26 15.47 19.2040 0.683048 4 to 27 15.98 17.6234 0.587034 5 to 28 15.71 11.5070 0.170973 6 to 29 15.70 18.4463 0.638774 7 to 30 15.21 31.5760 0.983021 8 to 31 15.50 26.8190 0.939223 9 to 32 15.76 16.9218 0.540321 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.088633 Tough bday spacings test for dh-ranFile-2018-04-02_03:31: 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 15 36 66 96 101 71 59 30 13 10 3 (O-E)^2/E 3.7 0.0 0.7 0.0 0.1 0.7 0.9 0.0 0.2 1.7 0.3 Birthday Spacings: Sum(O-E)^2/E= 8.419, p= 0.412 RESULTS OF GCD FOR dh-ranFile-2018-04-02_03:31 Euclid's algorithm: p-value, steps to gcd: 0.485394 p-value, dist. of gcd's: 0.750949 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-04-02_03:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.048 0.958 0.264 0.217 0.612 0.423 0.878 0.792 Bits 8 to 15---> 0.398 0.749 0.195 0.971 0.375 0.078 0.276 0.587 Bits 16 to 23---> 0.425 0.942 0.576 0.844 0.038 0.276 0.879 0.046 Bits 24 to 31---> 0.042 0.025 0.273 0.178 0.996 0.875 0.935 0.550 KS test for the above 32 p values: 0.672 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-04-02_03:31, p-values for 5 runs: 0.4582, 0.2728, 0.1374, 0.7120, 0.6816 Rank test for binary matrices (31x31) for dh-ranFile-2018-04-02_03:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 189 211.4 2.377 2.377 r= 29 5131 5134.0 0.002 2.379 r= 30 23006 23103.0 0.408 2.787 r= 31 11674 11551.5 1.299 4.085 chi-square = 4.085 with df = 3; p-value = 0.748 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-04-02_03:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 199 211.4 0.729 0.729 r= 30 5181 5134.0 0.430 1.159 r= 31 23066 23103.0 0.059 1.219 r= 32 11554 11551.5 0.001 1.219 chi-square = 1.219 with df = 3; p-value = 0.252 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-04-02_03:31 b-rank test for bits 1 to 8, p=0.55525 b-rank test for bits 2 to 9, p=0.07972 b-rank test for bits 3 to 10, p=0.13055 b-rank test for bits 4 to 11, p=0.23687 b-rank test for bits 5 to 12, p=0.30135 b-rank test for bits 6 to 13, p=0.18999 b-rank test for bits 7 to 14, p=0.11523 b-rank test for bits 8 to 15, p=0.04022 b-rank test for bits 9 to 16, p=0.21836 b-rank test for bits 10 to 17, p=0.50853 b-rank test for bits 11 to 18, p=0.37442 b-rank test for bits 12 to 19, p=0.58987 b-rank test for bits 13 to 20, p=0.98473 b-rank test for bits 14 to 21, p=0.31499 b-rank test for bits 15 to 22, p=0.75169 b-rank test for bits 16 to 23, p=0.24900 b-rank test for bits 17 to 24, p=0.80200 b-rank test for bits 18 to 25, p=0.26968 b-rank test for bits 19 to 26, p=0.83727 b-rank test for bits 20 to 27, p=0.70093 b-rank test for bits 21 to 28, p=0.88041 b-rank test for bits 22 to 29, p=0.18971 b-rank test for bits 23 to 30, p=0.15272 b-rank test for bits 24 to 31, p=0.63426 b-rank test for bits 25 to 32, p=0.26186 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 = 0.183603 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-04-02_03:31 (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 141950 0.10 0.537852 2 141542 -0.86 0.195378 3 141858 -0.12 0.452269 4 142310 0.94 0.825401 5 141724 -0.43 0.332502 6 141489 -0.98 0.163030 7 142867 2.24 0.987375 8 141688 -0.52 0.302534 9 141795 -0.27 0.394686 10 141340 -1.33 0.091725 11 142122 0.50 0.690368 12 142059 0.35 0.636717 13 142932 2.39 0.991562 14 141725 -0.43 0.333351 15 142546 1.49 0.931565 16 141714 -0.46 0.324059 17 141657 -0.59 0.277744 18 142691 1.83 0.966100 19 141736 -0.40 0.342747 20 141632 -0.65 0.258503 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-04-02_03:31 Bits used No. missing words z-score p-value 23 to 32 141831 -0.2701 0.393540 22 to 31 141644 -0.9149 0.180114 21 to 30 141748 -0.5563 0.288999 20 to 29 141877 -0.1115 0.455617 19 to 28 142443 1.8402 0.967134 18 to 27 142119 0.7230 0.765160 17 to 26 141749 -0.5529 0.290179 16 to 25 142240 1.1402 0.872907 15 to 24 142046 0.4713 0.681278 14 to 23 142116 0.7127 0.761970 13 to 22 141805 -0.3598 0.359514 12 to 21 142100 0.6575 0.744565 11 to 20 142223 1.0816 0.860289 10 to 19 141363 -1.8839 0.029789 9 to 18 141970 0.2092 0.582857 8 to 17 141996 0.2989 0.617477 7 to 16 141687 -0.7667 0.221643 6 to 15 142447 1.8540 0.968133 5 to 14 141943 0.1161 0.546215 4 to 13 141881 -0.0977 0.461089 3 to 12 141716 -0.6667 0.252496 2 to 11 142004 0.3264 0.627957 1 to 10 141839 -0.2425 0.404190 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-04-02_03:31 Bits used No. missing words z-score p-value 28 to 32 142009 0.3379 0.632267 27 to 31 142035 0.4260 0.664946 26 to 30 142207 1.0091 0.843525 25 to 29 142298 1.3175 0.906169 24 to 28 141889 -0.0689 0.472529 23 to 27 142144 0.7955 0.786836 22 to 26 142063 0.5209 0.698787 21 to 25 141445 -1.5740 0.057744 20 to 24 141819 -0.3062 0.379725 19 to 23 142218 1.0463 0.852298 18 to 22 141840 -0.2350 0.407098 17 to 21 142054 0.4904 0.688077 16 to 20 141506 -1.3672 0.085778 15 to 19 142123 0.7243 0.765561 14 to 18 142065 0.5277 0.701145 13 to 17 141996 0.2938 0.615543 12 to 16 142326 1.4124 0.921090 11 to 15 141875 -0.1164 0.453679 10 to 14 142169 0.8802 0.810635 9 to 13 142226 1.0735 0.858467 8 to 12 142244 1.1345 0.871702 7 to 11 141695 -0.7265 0.233753 6 to 10 141973 0.2158 0.585440 5 to 9 142082 0.5853 0.720834 4 to 8 141785 -0.4215 0.336711 3 to 7 142292 1.2972 0.902717 2 to 6 141945 0.1209 0.548121 1 to 5 141167 -2.5164 0.005928 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-04-02_03:31 Bits used No. missing words z-score p-value 31 to 32 141467 -1.3048 0.095979 30 to 31 142143 0.6893 0.754680 29 to 30 142587 1.9990 0.977197 28 to 29 142123 0.6303 0.735749 27 to 28 142010 0.2970 0.616752 26 to 27 141325 -1.7237 0.042382 25 to 26 141835 -0.2193 0.413223 24 to 25 142038 0.3796 0.647863 23 to 24 142195 0.8427 0.800298 22 to 23 141660 -0.7355 0.231022 21 to 22 141901 -0.0246 0.490198 20 to 21 142268 1.0580 0.854978 19 to 20 142080 0.5035 0.692677 18 to 19 142241 0.9784 0.836056 17 to 18 141735 -0.5142 0.303539 16 to 17 141830 -0.2340 0.407488 15 to 16 141591 -0.9390 0.173859 14 to 15 142192 0.8338 0.797813 13 to 14 141980 0.2085 0.582568 12 to 13 141207 -2.0718 0.019143 11 to 12 141880 -0.0865 0.465527 10 to 11 142116 0.6096 0.728952 9 to 10 141772 -0.4051 0.342701 8 to 9 141435 -1.3992 0.080876 7 to 8 141990 0.2380 0.594046 6 to 7 141599 -0.9154 0.179984 5 to 6 141457 -1.3343 0.091052 4 to 5 142517 1.7925 0.963477 3 to 4 141610 -0.8830 0.188624 2 to 3 142341 1.2734 0.898555 1 to 2 142103 0.5713 0.716101 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-04-02_03:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2375.16 -1.765 0.038741 Test results for specific bytes for dh-ranFile-2018-04-02_03:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2515.02 0.212 0.584096 2 to 9 2479.79 -0.286 0.387495 3 to 10 2548.43 0.685 0.753277 4 to 11 2426.47 -1.040 0.149212 5 to 12 2499.32 -0.010 0.496190 6 to 13 2484.12 -0.225 0.411163 7 to 14 2495.85 -0.059 0.476602 8 to 15 2480.38 -0.278 0.390684 9 to 16 2459.37 -0.575 0.282802 10 to 17 2521.53 0.305 0.619629 11 to 18 2452.66 -0.670 0.251584 12 to 19 2465.78 -0.484 0.314194 13 to 20 2534.08 0.482 0.685068 14 to 21 2553.47 0.756 0.775237 15 to 22 2424.31 -1.070 0.142229 16 to 23 2548.60 0.687 0.754053 17 to 24 2493.21 -0.096 0.461762 18 to 25 2515.02 0.212 0.584128 19 to 26 2471.39 -0.405 0.342860 20 to 27 2510.12 0.143 0.556909 21 to 28 2513.88 0.196 0.577800 22 to 29 2495.96 -0.057 0.477199 23 to 30 2569.22 0.979 0.836206 24 to 31 2439.02 -0.862 0.194226 25 to 32 2616.66 1.650 0.950515 CDPARK for dh-ranFile-2018-04-02_03:31: 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 3492 -1.4155 0.078457 3521 -0.0913 0.463617 3516 -0.3196 0.374623 3528 0.2283 0.590298 3504 -0.8676 0.192812 3520 -0.1370 0.445521 3524 0.0457 0.518210 3552 1.3242 0.907282 3535 0.5479 0.708135 3521 -0.0913 0.463617 Square side=100, avg. no. parked=3521.30 sample std.=15.40 p-value of the KSTEST for those 10 p-values: 0.686543 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-04-02_03:31 0.3263,0.9286,0.5566,0.2188,0.6073,0.4811,0.1619,0.1206,0.3073,0.7397, The KS test for those 10 p-values: 0.807348 The 3DSPHERES test for dh-ranFile-2018-04-02_03:31 sample no r^3 equiv. uni. 1 16.861 0.429949 2 31.553 0.650674 3 48.863 0.803831 4 33.565 0.673340 5 10.036 0.284318 6 26.300 0.583828 7 38.879 0.726363 8 40.835 0.743642 9 192.597 0.998371 10 38.501 0.722896 11 44.191 0.770772 12 2.115 0.068069 13 79.273 0.928811 14 24.782 0.562237 15 20.289 0.491510 16 10.898 0.304589 17 1.121 0.036668 18 7.310 0.216248 19 8.820 0.254732 20 11.958 0.328737 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.814583 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-04-02_03:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 -1.2 -0.4 -0.1 -0.1 -0.6 -0.9 -1.0 0.7 -0.4 -2.5 0.3 0.4 -1.0 -0.1 -1.1 0.5 -1.1 -0.8 0.1 1.2 0.8 0.7 1.5 -0.2 1.6 1.0 0.8 -0.2 0.9 0.6 0.9 -1.1 -0.5 0.5 -0.1 1.0 1.8 -0.8 -0.1 -0.6 0.0 -0.1 Chi-square with 42 degrees of freedom:35.370280 z-score=-0.723362, p-value=0.244612 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-04-02_03:31 Test no p-value 1 0.465282 2 0.935604 3 0.201486 4 0.026131 5 0.893407 6 0.031239 7 0.513567 8 0.383392 9 0.083141 10 0.116263 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.120752 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-04-02_03:31: (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 66804 0.28 66527 0.29 3 25000.00 24814 1.38 25139 0.77 4 6666.67 6674 0.01 6671 0.00 5 1388.89 1430 1.22 1359 0.64 6 238.10 245 0.20 259 1.84 7 34.72 27 1.72 37 0.15 8 4.96 5 0.00 7 0.84 p=0.43143 p=0.39542 Number of rngs required: 688728, p-value: 0.646 RESULTS OF CRAPS TEST for dh-ranFile-2018-04-02_03:31 No. of wins: Observed Expected 98409 98585.9 z-score=-0.791, pvalue=0.21447 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66425 66666.7 0.876 0.876 2 37720 37654.3 0.115 0.991 3 27112 26954.7 0.918 1.908 4 19455 19313.5 1.037 2.945 5 13611 13851.4 4.173 7.118 6 9901 9943.5 0.182 7.300 7 7292 7145.0 3.023 10.324 8 5157 5139.1 0.063 10.386 9 3687 3699.9 0.045 10.431 10 2694 2666.3 0.288 10.719 11 1952 1923.3 0.427 11.146 12 1390 1388.7 0.001 11.147 13 948 1003.7 3.093 14.240 14 724 726.1 0.006 14.246 15 521 525.8 0.044 14.291 16 342 381.2 4.021 18.312 17 296 276.5 1.369 19.682 18 202 200.8 0.007 19.689 19 160 146.0 1.346 21.034 20 99 106.2 0.490 21.524 21 312 287.1 2.157 23.681 Chisq= 23.68 for 20 degrees of freedom, p= 0.74341 SUMMARY of craptest p-value for no. of wins: 0.214468 p-value for throws/game: 0.743410 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-04-02_03:31 No. of wins: Observed Expected 98323 98585.9 z-score=-1.176, pvalue=0.11987 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66819 66666.7 0.348 0.348 2 37760 37654.3 0.297 0.645 3 27055 26954.7 0.373 1.018 4 19357 19313.5 0.098 1.116 5 13711 13851.4 1.424 2.539 6 9912 9943.5 0.100 2.639 7 7065 7145.0 0.896 3.536 8 5047 5139.1 1.650 5.185 9 3667 3699.9 0.292 5.477 10 2735 2666.3 1.770 7.247 11 1916 1923.3 0.028 7.275 12 1363 1388.7 0.477 7.752 13 971 1003.7 1.066 8.819 14 733 726.1 0.065 8.884 15 516 525.8 0.184 9.068 16 392 381.2 0.309 9.376 17 282 276.5 0.108 9.484 18 191 200.8 0.481 9.965 19 136 146.0 0.683 10.648 20 95 106.2 1.184 11.832 21 277 287.1 0.356 12.189 Chisq= 12.19 for 20 degrees of freedom, p= 0.09057 SUMMARY of craptest p-value for no. of wins: 0.119866 p-value for throws/game: 0.090573 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0059,0.0191,0.0246,0.0261,0.0298,0.0312,0.0367,0.0384,0.0387,0.0402, 0.0422,0.0424,0.0464,0.0483,0.0577,0.0681,0.0775,0.0785,0.0797,0.0809, 0.0831,0.0858,0.0886,0.0906,0.0911,0.0917,0.0960,0.1152,0.1163,0.1199, 0.1206,0.1208,0.1306,0.1374,0.1422,0.1492,0.1527,0.1619,0.1630,0.1710, 0.1739,0.1782,0.1800,0.1801,0.1836,0.1886,0.1897,0.1900,0.1928,0.1942, 0.1949,0.1954,0.2015,0.2145,0.2162,0.2170,0.2184,0.2188,0.2216,0.2310, 0.2338,0.2369,0.2446,0.2490,0.2516,0.2516,0.2525,0.2547,0.2585,0.2619, 0.2644,0.2697,0.2728,0.2735,0.2759,0.2764,0.2777,0.2828,0.2843,0.2890, 0.2902,0.3013,0.3025,0.3035,0.3046,0.3073,0.3142,0.3150,0.3241,0.3263, 0.3287,0.3325,0.3334,0.3367,0.3427,0.3427,0.3429,0.3595,0.3744,0.3746, 0.3752,0.3797,0.3834,0.3875,0.3907,0.3935,0.3947,0.3954,0.3976,0.4042, 0.4071,0.4075,0.4112,0.4120,0.4132,0.4228,0.4247,0.4299,0.4314,0.4455, 0.4523,0.4537,0.4556,0.4582,0.4611,0.4618,0.4636,0.4636,0.4653,0.4655, 0.4725,0.4766,0.4772,0.4811,0.4854,0.4902,0.4915,0.4962,0.5085,0.5136, 0.5182,0.5379,0.5403,0.5462,0.5481,0.5497,0.5553,0.5566,0.5569,0.5622, 0.5755,0.5778,0.5826,0.5829,0.5838,0.5841,0.5841,0.5854,0.5870,0.5874, 0.5899,0.5903,0.5940,0.6073,0.6123,0.6155,0.6168,0.6175,0.6196,0.6280, 0.6323,0.6343,0.6367,0.6388,0.6459,0.6479,0.6507,0.6649,0.6716,0.6733, 0.6813,0.6816,0.6830,0.6851,0.6865,0.6881,0.6904,0.6927,0.6988,0.7009, 0.7011,0.7081,0.7120,0.7161,0.7208,0.7229,0.7264,0.7290,0.7357,0.7397, 0.7434,0.7436,0.7446,0.7476,0.7490,0.7509,0.7517,0.7533,0.7541,0.7547, 0.7620,0.7652,0.7656,0.7708,0.7752,0.7868,0.7916,0.7954,0.7978,0.8003, 0.8020,0.8038,0.8073,0.8106,0.8146,0.8230,0.8254,0.8361,0.8362,0.8373, 0.8435,0.8441,0.8523,0.8550,0.8585,0.8603,0.8717,0.8729,0.8754,0.8783, 0.8792,0.8804,0.8934,0.8986,0.9027,0.9062,0.9073,0.9211,0.9286,0.9288, 0.9316,0.9346,0.9356,0.9392,0.9415,0.9505,0.9581,0.9635,0.9661,0.9671, 0.9681,0.9713,0.9772,0.9830,0.9847,0.9874,0.9916,0.9961,0.9984, Overall p-value after applying KStest on 269 p-values = 0.972121 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.