RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-03-18_11:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.70 14.5774 0.374111 2 to 25 16.02 23.3443 0.861625 3 to 26 15.86 20.0210 0.726842 4 to 27 15.65 16.7772 0.530441 5 to 28 15.68 12.9581 0.261013 6 to 29 15.94 17.8149 0.599394 7 to 30 15.87 13.1476 0.273748 8 to 31 15.69 25.3356 0.912554 9 to 32 15.61 30.6786 0.978154 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.416120 Tough bday spacings test for dh-ranFile-2018-03-18_11:31: 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 22 73 94 103 85 56 25 17 6 6 (O-E)^2/E 1.6 5.8 0.0 0.1 0.3 0.6 0.3 0.8 0.3 0.1 0.9 Birthday Spacings: Sum(O-E)^2/E= 10.820, p= 0.628 RESULTS OF GCD FOR dh-ranFile-2018-03-18_11:31 Euclid's algorithm: p-value, steps to gcd: 0.469523 p-value, dist. of gcd's: 0.351721 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-03-18_11:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.526 0.224 0.901 0.009 0.974 0.759 0.912 0.386 Bits 8 to 15---> 0.356 0.541 0.704 0.944 0.326 0.871 0.291 0.543 Bits 16 to 23---> 0.140 0.958 0.902 0.201 0.776 0.611 0.292 0.924 Bits 24 to 31---> 0.524 0.115 0.052 0.088 0.122 0.184 0.717 0.019 KS test for the above 32 p values: 0.392 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-03-18_11:31, p-values for 5 runs: 0.7433, 0.5017, 0.0906, 0.1582, 0.5835 Rank test for binary matrices (31x31) for dh-ranFile-2018-03-18_11:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 229 211.4 1.462 1.462 r= 29 5135 5134.0 0.000 1.462 r= 30 22991 23103.0 0.543 2.006 r= 31 11645 11551.5 0.756 2.762 chi-square = 2.762 with df = 3; p-value = 0.570 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-03-18_11:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 201 211.4 0.513 0.513 r= 30 5183 5134.0 0.467 0.981 r= 31 23180 23103.0 0.256 1.237 r= 32 11436 11551.5 1.155 2.392 chi-square = 2.392 with df = 3; p-value = 0.505 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-03-18_11:31 b-rank test for bits 1 to 8, p=0.27557 b-rank test for bits 2 to 9, p=0.43855 b-rank test for bits 3 to 10, p=0.05599 b-rank test for bits 4 to 11, p=0.67894 b-rank test for bits 5 to 12, p=0.20729 b-rank test for bits 6 to 13, p=0.03408 b-rank test for bits 7 to 14, p=0.22234 b-rank test for bits 8 to 15, p=0.13041 b-rank test for bits 9 to 16, p=0.11985 b-rank test for bits 10 to 17, p=0.93312 b-rank test for bits 11 to 18, p=0.98881 b-rank test for bits 12 to 19, p=0.94109 b-rank test for bits 13 to 20, p=0.38070 b-rank test for bits 14 to 21, p=0.19327 b-rank test for bits 15 to 22, p=0.55637 b-rank test for bits 16 to 23, p=0.50126 b-rank test for bits 17 to 24, p=0.08227 b-rank test for bits 18 to 25, p=0.57997 b-rank test for bits 19 to 26, p=0.71870 b-rank test for bits 20 to 27, p=0.70565 b-rank test for bits 21 to 28, p=0.98883 b-rank test for bits 22 to 29, p=0.98457 b-rank test for bits 23 to 30, p=0.86493 b-rank test for bits 24 to 31, p=0.63251 b-rank test for bits 25 to 32, p=0.82750 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 = 0.434548 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-03-18_11:31 (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 141731 -0.42 0.338464 2 141051 -2.01 0.022458 3 141374 -1.25 0.105509 4 142326 0.97 0.834855 5 141712 -0.46 0.322381 6 141944 0.08 0.532281 7 141136 -1.81 0.035393 8 142364 1.06 0.855953 9 141513 -0.93 0.177222 10 141767 -0.33 0.369738 11 141671 -0.56 0.288816 12 141818 -0.21 0.415512 13 142077 0.39 0.652379 14 142134 0.52 0.700184 15 141575 -0.78 0.217359 16 142286 0.88 0.810589 17 141459 -1.05 0.146360 18 141385 -1.23 0.110274 19 141656 -0.59 0.276961 20 142298 0.91 0.818089 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-03-18_11:31 Bits used No. missing words z-score p-value 23 to 32 141586 -1.1149 0.132440 22 to 31 141534 -1.2942 0.097791 21 to 30 142236 1.1264 0.870012 20 to 29 141754 -0.5356 0.296110 19 to 28 141775 -0.4632 0.321608 18 to 27 141902 -0.0253 0.489918 17 to 26 141538 -1.2804 0.100194 16 to 25 142327 1.4402 0.925100 15 to 24 142274 1.2575 0.895711 14 to 23 142496 2.0230 0.978463 13 to 22 141924 0.0506 0.520172 12 to 21 141849 -0.2080 0.417601 11 to 20 141744 -0.5701 0.284304 10 to 19 142128 0.7540 0.774586 9 to 18 142368 1.5816 0.943132 8 to 17 142087 0.6127 0.729948 7 to 16 142223 1.0816 0.860289 6 to 15 142414 1.7402 0.959092 5 to 14 142240 1.1402 0.872907 4 to 13 141678 -0.7977 0.212525 3 to 12 142074 0.5678 0.714924 2 to 11 141860 -0.1701 0.432464 1 to 10 142028 0.4092 0.658806 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-03-18_11:31 Bits used No. missing words z-score p-value 28 to 32 141911 0.0057 0.502258 27 to 31 141890 -0.0655 0.473878 26 to 30 142133 0.7582 0.775835 25 to 29 141853 -0.1909 0.424283 24 to 28 141715 -0.6587 0.255030 23 to 27 141498 -1.3943 0.081608 22 to 26 141946 0.1243 0.549463 21 to 25 141604 -1.0350 0.150331 20 to 24 142148 0.8091 0.790757 19 to 23 141806 -0.3503 0.363068 18 to 22 142061 0.5141 0.696421 17 to 21 142161 0.8531 0.803203 16 to 20 142383 1.6057 0.945826 15 to 19 142205 1.0023 0.841894 14 to 18 142227 1.0768 0.859226 13 to 17 141942 0.1107 0.544091 12 to 16 141790 -0.4045 0.342919 11 to 15 141889 -0.0689 0.472529 10 to 14 141527 -1.2960 0.097482 9 to 13 141510 -1.3537 0.087922 8 to 12 142479 1.9311 0.973264 7 to 11 141957 0.1616 0.564187 6 to 10 142083 0.5887 0.721973 5 to 9 141791 -0.4011 0.344166 4 to 8 141887 -0.0757 0.469831 3 to 7 142026 0.3955 0.653760 2 to 6 142272 1.2294 0.890537 1 to 5 142235 1.1040 0.865196 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-03-18_11:31 Bits used No. missing words z-score p-value 31 to 32 141087 -2.4258 0.007638 30 to 31 142149 0.7070 0.760214 29 to 30 142128 0.6450 0.740551 28 to 29 142115 0.6067 0.727974 27 to 28 142197 0.8486 0.801944 26 to 27 141789 -0.3550 0.361311 25 to 26 141535 -1.1042 0.134749 24 to 25 141572 -0.9951 0.159850 23 to 24 142342 1.2763 0.899078 22 to 23 141376 -1.5732 0.057831 21 to 22 141705 -0.6027 0.273340 20 to 21 141632 -0.8181 0.206655 19 to 20 141971 0.1819 0.572176 18 to 19 141207 -2.0718 0.019143 17 to 18 141957 0.1406 0.555915 16 to 17 142284 1.1052 0.865468 15 to 16 141927 0.0521 0.520785 14 to 15 141682 -0.6706 0.251241 13 to 14 141822 -0.2576 0.398354 12 to 13 142226 0.9341 0.824882 11 to 12 142266 1.0521 0.853629 10 to 11 142359 1.3265 0.907656 9 to 10 142822 2.6922 0.996451 8 to 9 141864 -0.1337 0.446813 7 to 8 141479 -1.2694 0.102147 6 to 7 142405 1.4622 0.928150 5 to 6 141894 -0.0452 0.481966 4 to 5 142172 0.7748 0.780782 3 to 4 141773 -0.4022 0.343786 2 to 3 142129 0.6480 0.741506 1 to 2 142134 0.6627 0.746253 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-03-18_11:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2515.41 0.218 0.586276 Test results for specific bytes for dh-ranFile-2018-03-18_11:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2447.97 -0.736 0.230916 2 to 9 2505.29 0.075 0.529822 3 to 10 2535.11 0.497 0.690250 4 to 11 2508.20 0.116 0.546136 5 to 12 2515.08 0.213 0.584466 6 to 13 2519.47 0.275 0.608475 7 to 14 2495.67 -0.061 0.475571 8 to 15 2553.27 0.753 0.774364 9 to 16 2410.73 -1.262 0.103400 10 to 17 2457.59 -0.600 0.274314 11 to 18 2521.21 0.300 0.617894 12 to 19 2474.53 -0.360 0.359349 13 to 20 2431.92 -0.963 0.167827 14 to 21 2493.03 -0.099 0.460726 15 to 22 2509.18 0.130 0.551670 16 to 23 2436.77 -0.894 0.185622 17 to 24 2532.99 0.467 0.679605 18 to 25 2590.47 1.279 0.899627 19 to 26 2475.54 -0.346 0.364704 20 to 27 2388.09 -1.583 0.056746 21 to 28 2419.56 -1.138 0.127635 22 to 29 2532.72 0.463 0.678216 23 to 30 2488.22 -0.167 0.433841 24 to 31 2439.57 -0.855 0.196386 25 to 32 2397.71 -1.447 0.074002 CDPARK for dh-ranFile-2018-03-18_11:31: 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 3549 1.1872 0.882429 3515 -0.3653 0.357445 3552 1.3242 0.907282 3534 0.5023 0.692266 3525 0.0913 0.536383 3529 0.2740 0.607947 3527 0.1826 0.572463 3549 1.1872 0.882429 3509 -0.6393 0.261324 3550 1.2329 0.891189 Square side=100, avg. no. parked=3533.90 sample std.=14.73 p-value of the KSTEST for those 10 p-values: 0.107332 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-03-18_11:31 0.0459,0.4574,0.2130,0.6433,0.7554,0.2513,0.6597,0.9695,0.0491,0.6153, The KS test for those 10 p-values: 0.850432 The 3DSPHERES test for dh-ranFile-2018-03-18_11:31 sample no r^3 equiv. uni. 1 20.743 0.499144 2 68.048 0.896510 3 10.477 0.294760 4 7.170 0.212587 5 25.465 0.572087 6 32.639 0.663098 7 7.107 0.210930 8 16.811 0.428994 9 9.792 0.278473 10 37.703 0.715424 11 15.508 0.403654 12 13.710 0.366817 13 19.583 0.479394 14 22.165 0.522333 15 10.506 0.295445 16 3.570 0.112183 17 13.921 0.371264 18 53.527 0.832073 19 72.037 0.909394 20 22.764 0.531773 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.398879 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-03-18_11:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 1.3 -1.6 -0.5 0.7 -0.3 -2.3 0.4 -1.3 1.7 0.4 -0.4 -0.4 -1.2 0.8 -1.0 0.3 -1.6 0.6 0.9 0.8 0.4 0.0 -0.1 0.8 0.6 -2.4 0.1 0.4 -0.1 2.4 -0.1 1.2 0.2 1.6 0.6 -0.7 -1.3 -0.8 2.1 0.1 -1.0 -0.1 Chi-square with 42 degrees of freedom:48.245369 z-score=0.681426, p-value=0.764936 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-03-18_11:31 Test no p-value 1 0.046503 2 0.361121 3 0.630202 4 0.139747 5 0.053540 6 0.597917 7 0.570236 8 0.062645 9 0.062605 10 0.057030 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.003564 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-03-18_11:31: (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 66919 0.96 66588 0.09 3 25000.00 24880 0.58 25039 0.06 4 6666.67 6556 1.84 6706 0.23 5 1388.89 1361 0.56 1418 0.61 6 238.10 244 0.15 213 2.65 7 34.72 35 0.00 34 0.01 8 4.96 4 0.19 1 3.16 p=0.35884 p=0.66194 Number of rngs required: 687886, p-value: 0.275 RESULTS OF CRAPS TEST for dh-ranFile-2018-03-18_11:31 No. of wins: Observed Expected 98833 98585.9 z-score= 1.105, pvalue=0.86550 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66511 66666.7 0.363 0.363 2 37614 37654.3 0.043 0.407 3 27255 26954.7 3.345 3.752 4 19615 19313.5 4.708 8.459 5 13947 13851.4 0.660 9.119 6 9730 9943.5 4.586 13.705 7 7143 7145.0 0.001 13.705 8 4998 5139.1 3.873 17.578 9 3801 3699.9 2.765 20.343 10 2635 2666.3 0.367 20.710 11 1826 1923.3 4.925 25.635 12 1381 1388.7 0.043 25.678 13 983 1003.7 0.428 26.106 14 705 726.1 0.615 26.721 15 495 525.8 1.808 28.530 16 373 381.2 0.174 28.704 17 280 276.5 0.043 28.747 18 220 200.8 1.830 30.577 19 129 146.0 1.976 32.553 20 95 106.2 1.184 33.737 21 264 287.1 1.861 35.598 Chisq= 35.60 for 20 degrees of freedom, p= 0.98286 SUMMARY of craptest p-value for no. of wins: 0.865498 p-value for throws/game: 0.982859 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-03-18_11:31 No. of wins: Observed Expected 98879 98585.9 z-score= 1.311, pvalue=0.90509 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66478 66666.7 0.534 0.534 2 37719 37654.3 0.111 0.645 3 26845 26954.7 0.447 1.092 4 19272 19313.5 0.089 1.181 5 13905 13851.4 0.207 1.388 6 9931 9943.5 0.016 1.404 7 7165 7145.0 0.056 1.460 8 5166 5139.1 0.141 1.601 9 3740 3699.9 0.435 2.036 10 2766 2666.3 3.728 5.764 11 1922 1923.3 0.001 5.765 12 1380 1388.7 0.055 5.820 13 1040 1003.7 1.312 7.132 14 723 726.1 0.014 7.146 15 534 525.8 0.127 7.272 16 386 381.2 0.062 7.334 17 290 276.5 0.655 7.989 18 207 200.8 0.190 8.179 19 139 146.0 0.334 8.513 20 110 106.2 0.135 8.648 21 282 287.1 0.091 8.739 Chisq= 8.74 for 20 degrees of freedom, p= 0.01426 SUMMARY of craptest p-value for no. of wins: 0.905088 p-value for throws/game: 0.014262 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0036,0.0076,0.0086,0.0143,0.0190,0.0191,0.0225,0.0341,0.0354,0.0459, 0.0465,0.0491,0.0520,0.0535,0.0560,0.0567,0.0570,0.0578,0.0626,0.0626, 0.0740,0.0816,0.0823,0.0879,0.0883,0.0906,0.0975,0.0978,0.1002,0.1021, 0.1034,0.1055,0.1073,0.1103,0.1122,0.1148,0.1199,0.1224,0.1276,0.1304, 0.1324,0.1347,0.1397,0.1397,0.1464,0.1503,0.1582,0.1599,0.1678,0.1772, 0.1839,0.1856,0.1933,0.1964,0.2007,0.2067,0.2073,0.2109,0.2125,0.2126, 0.2130,0.2174,0.2223,0.2236,0.2309,0.2512,0.2513,0.2550,0.2610,0.2613, 0.2733,0.2737,0.2743,0.2755,0.2756,0.2770,0.2785,0.2843,0.2888,0.2911, 0.2916,0.2948,0.2954,0.2961,0.3216,0.3224,0.3262,0.3385,0.3429,0.3438, 0.3442,0.3517,0.3563,0.3574,0.3588,0.3593,0.3611,0.3613,0.3631,0.3647, 0.3668,0.3697,0.3713,0.3741,0.3807,0.3861,0.3921,0.3984,0.3989,0.4037, 0.4155,0.4161,0.4176,0.4243,0.4290,0.4325,0.4338,0.4345,0.4385,0.4468, 0.4574,0.4607,0.4695,0.4698,0.4725,0.4739,0.4756,0.4794,0.4820,0.4899, 0.4991,0.5013,0.5017,0.5023,0.5050,0.5202,0.5208,0.5223,0.5237,0.5265, 0.5298,0.5304,0.5318,0.5323,0.5364,0.5412,0.5435,0.5441,0.5461,0.5495, 0.5517,0.5559,0.5564,0.5642,0.5702,0.5702,0.5721,0.5722,0.5725,0.5800, 0.5835,0.5845,0.5863,0.5979,0.5994,0.6079,0.6085,0.6109,0.6153,0.6179, 0.6283,0.6302,0.6325,0.6433,0.6524,0.6538,0.6588,0.6597,0.6619,0.6631, 0.6782,0.6789,0.6796,0.6903,0.6923,0.6964,0.7002,0.7041,0.7056,0.7149, 0.7154,0.7171,0.7187,0.7220,0.7268,0.7280,0.7299,0.7406,0.7415,0.7433, 0.7463,0.7554,0.7586,0.7602,0.7649,0.7744,0.7746,0.7758,0.7763,0.7808, 0.7908,0.8019,0.8032,0.8106,0.8181,0.8249,0.8275,0.8321,0.8349,0.8419, 0.8504,0.8536,0.8560,0.8592,0.8603,0.8616,0.8649,0.8652,0.8655,0.8655, 0.8700,0.8715,0.8729,0.8824,0.8824,0.8905,0.8912,0.8957,0.8965,0.8991, 0.8996,0.9005,0.9015,0.9051,0.9073,0.9077,0.9094,0.9116,0.9126,0.9237, 0.9251,0.9282,0.9331,0.9411,0.9431,0.9435,0.9458,0.9582,0.9591,0.9695, 0.9733,0.9741,0.9782,0.9785,0.9829,0.9846,0.9888,0.9888,0.9965, Overall p-value after applying KStest on 269 p-values = 0.987971 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.