RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-03-11_15:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.76 20.3634 0.743936 2 to 25 15.72 12.5178 0.232182 3 to 26 16.03 16.0974 0.483062 4 to 27 15.81 17.6865 0.591131 5 to 28 15.68 19.4199 0.695028 6 to 29 15.37 29.6919 0.971345 7 to 30 15.70 20.1818 0.734962 8 to 31 15.81 17.0823 0.551193 9 to 32 15.91 17.2445 0.562079 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.226926 Tough bday spacings test for dh-ranFile-2016-03-11_15:31: 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 31 71 102 117 70 39 32 17 4 4 (O-E)^2/E 1.6 0.9 0.1 0.2 3.8 0.8 3.3 0.2 0.3 1.0 0.0 Birthday Spacings: Sum(O-E)^2/E= 12.203, p= 0.728 RESULTS OF GCD FOR dh-ranFile-2016-03-11_15:31 Euclid's algorithm: p-value, steps to gcd: 0.568027 p-value, dist. of gcd's: 0.777499 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-03-11_15:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.183 0.841 0.035 0.666 0.259 0.970 0.733 0.196 Bits 8 to 15---> 0.767 0.130 0.237 0.906 0.858 0.285 0.418 0.999 Bits 16 to 23---> 0.735 0.891 0.588 0.623 0.847 0.493 0.858 0.244 Bits 24 to 31---> 0.429 0.630 0.370 0.948 0.217 0.754 0.350 0.809 KS test for the above 32 p values: 0.760 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-03-11_15:31, p-values for 5 runs: 0.2190, 0.0427, 0.0551, 0.5943, 0.2704 Rank test for binary matrices (31x31) for dh-ranFile-2016-03-11_15:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 217 211.4 0.147 0.147 r= 29 5041 5134.0 1.685 1.832 r= 30 23074 23103.0 0.037 1.869 r= 31 11668 11551.5 1.174 3.043 chi-square = 3.043 with df = 3; p-value = 0.615 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-03-11_15:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 235 211.4 2.630 2.630 r= 30 5197 5134.0 0.773 3.403 r= 31 22991 23103.0 0.543 3.947 r= 32 11577 11551.5 0.056 4.003 chi-square = 4.003 with df = 3; p-value = 0.739 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-03-11_15:31 b-rank test for bits 1 to 8, p=0.32523 b-rank test for bits 2 to 9, p=0.66143 b-rank test for bits 3 to 10, p=0.11454 b-rank test for bits 4 to 11, p=0.48904 b-rank test for bits 5 to 12, p=0.28256 b-rank test for bits 6 to 13, p=0.14170 b-rank test for bits 7 to 14, p=0.91669 b-rank test for bits 8 to 15, p=0.84463 b-rank test for bits 9 to 16, p=0.99926 b-rank test for bits 10 to 17, p=0.90145 b-rank test for bits 11 to 18, p=0.78550 b-rank test for bits 12 to 19, p=0.11024 b-rank test for bits 13 to 20, p=0.21709 b-rank test for bits 14 to 21, p=0.08708 b-rank test for bits 15 to 22, p=0.25118 b-rank test for bits 16 to 23, p=0.53514 b-rank test for bits 17 to 24, p=0.17334 b-rank test for bits 18 to 25, p=0.74708 b-rank test for bits 19 to 26, p=0.43748 b-rank test for bits 20 to 27, p=0.32658 b-rank test for bits 21 to 28, p=0.65226 b-rank test for bits 22 to 29, p=0.94771 b-rank test for bits 23 to 30, p=0.91170 b-rank test for bits 24 to 31, p=0.73450 b-rank test for bits 25 to 32, p=0.37284 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 = 0.772919 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-03-11_15:31 (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 141730 -0.42 0.337610 2 141913 0.01 0.503421 3 142339 1.00 0.842287 4 142224 0.74 0.768894 5 141895 -0.03 0.486645 6 141696 -0.50 0.309089 7 142453 1.27 0.898003 8 142552 1.50 0.933395 9 141835 -0.17 0.431063 10 141353 -1.30 0.096829 11 142507 1.40 0.918707 12 141602 -0.72 0.236360 13 140984 -2.16 0.015310 14 141318 -1.38 0.083545 15 142241 0.77 0.780809 16 141221 -1.61 0.053890 17 141372 -1.26 0.104659 18 142087 0.42 0.660972 19 142281 0.87 0.807409 20 141650 -0.61 0.272287 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-03-11_15:31 Bits used No. missing words z-score p-value 23 to 32 142143 0.8058 0.789809 22 to 31 142000 0.3127 0.622729 21 to 30 142314 1.3954 0.918554 20 to 29 141408 -1.7287 0.041929 19 to 28 141628 -0.9701 0.165998 18 to 27 141618 -1.0046 0.157548 17 to 26 142254 1.1885 0.882685 16 to 25 142065 0.5368 0.704295 15 to 24 142054 0.4989 0.691062 14 to 23 142007 0.3368 0.631864 13 to 22 142020 0.3816 0.648629 12 to 21 141939 0.1023 0.540745 11 to 20 141560 -1.2046 0.114182 10 to 19 141724 -0.6391 0.261389 9 to 18 141854 -0.1908 0.424344 8 to 17 141501 -1.4080 0.079560 7 to 16 142112 0.6989 0.757681 6 to 15 141524 -1.3287 0.091970 5 to 14 141977 0.2333 0.592253 4 to 13 141785 -0.4287 0.334062 3 to 12 141525 -1.3253 0.092540 2 to 11 141700 -0.7218 0.235200 1 to 10 142069 0.5506 0.709041 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-03-11_15:31 Bits used No. missing words z-score p-value 28 to 32 141545 -1.2350 0.108412 27 to 31 142184 0.9311 0.824095 26 to 30 142297 1.3141 0.905600 25 to 29 142083 0.5887 0.721973 24 to 28 142161 0.8531 0.803203 23 to 27 141917 0.0260 0.510371 22 to 26 142169 0.8802 0.810635 21 to 25 141455 -1.5401 0.061768 20 to 24 141569 -1.1537 0.124320 19 to 23 142148 0.8091 0.790757 18 to 22 142305 1.3413 0.910081 17 to 21 141556 -1.1977 0.115511 16 to 20 141487 -1.4316 0.076125 15 to 19 142139 0.7785 0.781875 14 to 18 141479 -1.4587 0.072318 13 to 17 141690 -0.7435 0.228592 12 to 16 141072 -2.8384 0.002267 11 to 15 141781 -0.4350 0.331775 10 to 14 141848 -0.2079 0.417654 9 to 13 141747 -0.5503 0.291067 8 to 12 142395 1.6463 0.950153 7 to 11 141908 -0.0045 0.498201 6 to 10 142472 1.9074 0.971763 5 to 9 141722 -0.6350 0.262709 4 to 8 142299 1.3209 0.906735 3 to 7 141630 -0.9469 0.171850 2 to 6 141649 -0.8825 0.188760 1 to 5 142360 1.5277 0.936706 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-03-11_15:31 Bits used No. missing words z-score p-value 31 to 32 141679 -0.6794 0.248430 30 to 31 141925 0.0462 0.518434 29 to 30 142138 0.6745 0.750017 28 to 29 142059 0.4415 0.670576 27 to 28 141757 -0.4494 0.326589 26 to 27 142129 0.6480 0.741506 25 to 26 141912 0.0079 0.503142 24 to 25 142302 1.1583 0.876633 23 to 24 141874 -0.1042 0.458498 22 to 23 142115 0.6067 0.727974 21 to 22 141729 -0.5319 0.297381 20 to 21 142118 0.6155 0.730903 19 to 20 142962 3.1052 0.999049 18 to 19 142115 0.6067 0.727974 17 to 18 141670 -0.7060 0.240098 16 to 17 142572 1.9548 0.974695 15 to 16 142497 1.7335 0.958500 14 to 15 141936 0.0787 0.531354 13 to 14 141729 -0.5319 0.297381 12 to 13 141660 -0.7355 0.231022 11 to 12 141864 -0.1337 0.446813 10 to 11 141707 -0.5968 0.275306 9 to 10 141989 0.2350 0.592901 8 to 9 142450 1.5949 0.944632 7 to 8 141494 -1.2252 0.110257 6 to 7 141863 -0.1367 0.445647 5 to 6 142238 0.9695 0.833859 4 to 5 142149 0.7070 0.760214 3 to 4 141743 -0.4906 0.311837 2 to 3 142303 1.1613 0.877234 1 to 2 142186 0.8161 0.792789 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-03-11_15:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2487.52 -0.176 0.429951 Test results for specific bytes for dh-ranFile-2016-03-11_15:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2467.07 -0.466 0.320710 2 to 9 2591.83 1.299 0.902971 3 to 10 2459.85 -0.568 0.285092 4 to 11 2521.25 0.301 0.618125 5 to 12 2329.50 -2.411 0.007950 6 to 13 2566.65 0.943 0.827046 7 to 14 2405.38 -1.338 0.090432 8 to 15 2377.96 -1.726 0.042188 9 to 16 2598.87 1.398 0.918973 10 to 17 2456.82 -0.611 0.270697 11 to 18 2617.14 1.657 0.951198 12 to 19 2566.19 0.936 0.825382 13 to 20 2576.23 1.078 0.859493 14 to 21 2354.31 -2.060 0.019682 15 to 22 2545.14 0.638 0.738380 16 to 23 2551.06 0.722 0.764868 17 to 24 2394.36 -1.494 0.067595 18 to 25 2563.27 0.895 0.814562 19 to 26 2461.82 -0.540 0.294629 20 to 27 2532.58 0.461 0.677511 21 to 28 2441.89 -0.822 0.205611 22 to 29 2498.48 -0.022 0.491411 23 to 30 2508.66 0.122 0.548711 24 to 31 2448.17 -0.733 0.231775 25 to 32 2504.93 0.070 0.527797 CDPARK for dh-ranFile-2016-03-11_15:31: 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 3559 1.6438 0.949895 3539 0.7306 0.767486 3526 0.1370 0.554479 3509 -0.6393 0.261324 3545 1.0046 0.842447 3537 0.6393 0.738676 3494 -1.3242 0.092718 3569 2.1005 0.982156 3496 -1.2329 0.108811 3557 1.5525 0.939730 Square side=100, avg. no. parked=3533.10 sample std.=25.02 p-value of the KSTEST for those 10 p-values: 0.141869 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-03-11_15:31 0.4710,0.7674,0.6497,0.8912,0.3443,0.6087,0.1752,0.1963,0.8062,0.9503, The KS test for those 10 p-values: 0.661735 The 3DSPHERES test for dh-ranFile-2016-03-11_15:31 sample no r^3 equiv. uni. 1 25.755 0.576202 2 0.379 0.012542 3 17.137 0.435168 4 56.885 0.849857 5 8.020 0.234570 6 52.894 0.828491 7 19.716 0.481691 8 1.011 0.033137 9 19.015 0.469448 10 145.279 0.992114 11 87.001 0.944978 12 5.418 0.165243 13 124.737 0.984360 14 3.331 0.105088 15 63.200 0.878357 16 25.059 0.566263 17 1.695 0.054930 18 148.866 0.993002 19 117.262 0.979934 20 1.631 0.052930 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.045779 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-03-11_15:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 1.3 -0.7 0.8 1.9 -0.9 -0.9 1.1 0.1 -1.8 0.5 -1.6 0.2 1.1 0.8 0.2 -0.4 -0.6 1.6 -0.2 0.1 0.7 -0.1 -0.9 -1.0 1.1 -0.1 0.9 -2.1 -0.9 0.5 0.6 -0.9 -1.3 -1.2 -0.5 1.1 -0.7 -0.4 0.1 1.0 0.1 -1.0 -1.1 Chi-square with 42 degrees of freedom:39.636549 z-score=-0.257874, p-value=0.424768 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-03-11_15:31 Test no p-value 1 0.470873 2 0.571554 3 0.452619 4 0.524608 5 0.936000 6 0.072070 7 0.187964 8 0.052464 9 0.296172 10 0.725653 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.743491 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-03-11_15:31: (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 66676 0.00 66689 0.01 3 25000.00 25033 0.04 24833 1.12 4 6666.67 6587 0.95 6791 2.32 5 1388.89 1423 0.84 1385 0.01 6 238.10 240 0.02 266 3.27 7 34.72 37 0.15 28 1.30 8 4.96 3 0.77 7 0.84 p=0.16339 p=0.81855 Number of rngs required: 688917, p-value: 0.723 RESULTS OF CRAPS TEST for dh-ranFile-2016-03-11_15:31 No. of wins: Observed Expected 98544 98585.9 z-score=-0.187, pvalue=0.42575 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66443 66666.7 0.750 0.750 2 37462 37654.3 0.982 1.733 3 27026 26954.7 0.188 1.921 4 19418 19313.5 0.566 2.487 5 13699 13851.4 1.677 4.164 6 10115 9943.5 2.956 7.121 7 7202 7145.0 0.454 7.575 8 5217 5139.1 1.182 8.757 9 3740 3699.9 0.435 9.192 10 2746 2666.3 2.383 11.574 11 1989 1923.3 2.242 13.817 12 1364 1388.7 0.441 14.258 13 997 1003.7 0.045 14.302 14 702 726.1 0.803 15.105 15 550 525.8 1.110 16.215 16 390 381.2 0.205 16.421 17 302 276.5 2.344 18.765 18 158 200.8 9.134 27.899 19 124 146.0 3.311 31.210 20 92 106.2 1.902 33.112 21 264 287.1 1.861 34.973 Chisq= 34.97 for 20 degrees of freedom, p= 0.97975 SUMMARY of craptest p-value for no. of wins: 0.425746 p-value for throws/game: 0.979752 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-03-11_15:31 No. of wins: Observed Expected 98635 98585.9 z-score= 0.220, pvalue=0.58698 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66459 66666.7 0.647 0.647 2 37658 37654.3 0.000 0.647 3 26759 26954.7 1.421 2.069 4 19361 19313.5 0.117 2.186 5 13933 13851.4 0.480 2.666 6 10011 9943.5 0.458 3.124 7 7099 7145.0 0.296 3.420 8 5131 5139.1 0.013 3.433 9 3726 3699.9 0.185 3.617 10 2736 2666.3 1.822 5.440 11 1924 1923.3 0.000 5.440 12 1410 1388.7 0.325 5.765 13 1049 1003.7 2.043 7.808 14 763 726.1 1.871 9.679 15 541 525.8 0.437 10.117 16 429 381.2 6.007 16.124 17 274 276.5 0.023 16.147 18 193 200.8 0.305 16.452 19 135 146.0 0.827 17.279 20 107 106.2 0.006 17.285 21 302 287.1 0.772 18.056 Chisq= 18.06 for 20 degrees of freedom, p= 0.41631 SUMMARY of craptest p-value for no. of wins: 0.586982 p-value for throws/game: 0.416309 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0023,0.0079,0.0125,0.0153,0.0197,0.0331,0.0350,0.0419,0.0422,0.0427, 0.0458,0.0525,0.0529,0.0539,0.0549,0.0551,0.0618,0.0676,0.0721,0.0723, 0.0761,0.0796,0.0835,0.0871,0.0904,0.0920,0.0925,0.0927,0.0968,0.1047, 0.1051,0.1084,0.1088,0.1102,0.1103,0.1142,0.1145,0.1155,0.1243,0.1297, 0.1417,0.1419,0.1575,0.1634,0.1652,0.1660,0.1718,0.1733,0.1752,0.1825, 0.1880,0.1888,0.1955,0.1963,0.2056,0.2170,0.2171,0.2190,0.2269,0.2286, 0.2310,0.2318,0.2322,0.2346,0.2352,0.2364,0.2366,0.2401,0.2435,0.2484, 0.2512,0.2591,0.2613,0.2614,0.2627,0.2704,0.2707,0.2723,0.2753,0.2826, 0.2851,0.2854,0.2911,0.2946,0.2962,0.2974,0.2974,0.3091,0.3118,0.3207, 0.3252,0.3266,0.3266,0.3318,0.3341,0.3376,0.3443,0.3497,0.3696,0.3728, 0.4163,0.4177,0.4185,0.4243,0.4248,0.4257,0.4288,0.4300,0.4311,0.4352, 0.4375,0.4456,0.4468,0.4526,0.4585,0.4694,0.4709,0.4710,0.4817,0.4831, 0.4866,0.4890,0.4914,0.4928,0.4982,0.5031,0.5034,0.5104,0.5184,0.5246, 0.5278,0.5314,0.5351,0.5407,0.5487,0.5512,0.5545,0.5621,0.5663,0.5680, 0.5716,0.5762,0.5870,0.5882,0.5911,0.5923,0.5929,0.5943,0.6087,0.6150, 0.6181,0.6227,0.6231,0.6298,0.6319,0.6486,0.6497,0.6523,0.6610,0.6614, 0.6617,0.6659,0.6706,0.6775,0.6911,0.6950,0.7043,0.7090,0.7220,0.7233, 0.7257,0.7280,0.7280,0.7283,0.7309,0.7326,0.7345,0.7350,0.7355,0.7384, 0.7387,0.7388,0.7415,0.7435,0.7439,0.7471,0.7500,0.7540,0.7577,0.7600, 0.7602,0.7649,0.7671,0.7674,0.7675,0.7689,0.7729,0.7775,0.7808,0.7819, 0.7855,0.7898,0.7908,0.7928,0.8032,0.8062,0.8074,0.8088,0.8106,0.8146, 0.8186,0.8241,0.8254,0.8270,0.8285,0.8339,0.8408,0.8423,0.8424,0.8446, 0.8467,0.8499,0.8578,0.8578,0.8595,0.8766,0.8772,0.8784,0.8827,0.8909, 0.8912,0.8980,0.9015,0.9030,0.9056,0.9056,0.9067,0.9101,0.9117,0.9167, 0.9186,0.9187,0.9190,0.9334,0.9360,0.9367,0.9397,0.9446,0.9450,0.9477, 0.9482,0.9499,0.9502,0.9503,0.9512,0.9585,0.9700,0.9713,0.9718,0.9747, 0.9798,0.9799,0.9822,0.9844,0.9921,0.9930,0.9989,0.9990,0.9993, Overall p-value after applying KStest on 269 p-values = 0.084172 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.