RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-01-27_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 15.97 10.3671 0.112487 2 to 25 15.64 17.6361 0.587859 3 to 26 15.85 14.3350 0.356734 4 to 27 15.99 14.5360 0.371133 5 to 28 15.79 36.6292 0.996223 6 to 29 15.70 28.6832 0.962438 7 to 30 15.80 17.1597 0.556399 8 to 31 15.80 20.3202 0.741818 9 to 32 15.73 20.7907 0.764208 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.342366 Tough bday spacings test for dh-ranFile-2016-01-27_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 10 36 57 118 89 78 46 32 25 4 5 (O-E)^2/E 0.1 0.0 3.6 4.2 0.8 0.0 0.7 0.2 6.9 1.0 0.2 Birthday Spacings: Sum(O-E)^2/E= 17.699, p= 0.940 RESULTS OF GCD FOR dh-ranFile-2016-01-27_11:31 Euclid's algorithm: p-value, steps to gcd: 0.330140 p-value, dist. of gcd's: 0.919735 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-01-27_11:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.064 0.417 0.649 0.411 0.583 0.461 0.192 0.638 Bits 8 to 15---> 0.893 0.505 0.544 0.987 0.042 0.507 0.575 0.648 Bits 16 to 23---> 0.021 0.875 0.101 0.602 0.601 0.405 0.535 0.514 Bits 24 to 31---> 0.237 0.058 0.149 0.415 0.216 0.104 0.951 0.241 KS test for the above 32 p values: 0.716 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-01-27_11:31, p-values for 5 runs: 0.7612, 0.3486, 0.6042, 0.7143, 0.5607 Rank test for binary matrices (31x31) for dh-ranFile-2016-01-27_11:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 216 211.4 0.099 0.099 r= 29 4955 5134.0 6.242 6.341 r= 30 23223 23103.0 0.623 6.964 r= 31 11606 11551.5 0.257 7.221 chi-square = 7.221 with df = 3; p-value = 0.935 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-01-27_11:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 207 211.4 0.092 0.092 r= 30 5204 5134.0 0.954 1.046 r= 31 23019 23103.0 0.306 1.352 r= 32 11570 11551.5 0.030 1.382 chi-square = 1.382 with df = 3; p-value = 0.290 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-01-27_11:31 b-rank test for bits 1 to 8, p=0.40812 b-rank test for bits 2 to 9, p=0.49108 b-rank test for bits 3 to 10, p=0.18012 b-rank test for bits 4 to 11, p=0.56521 b-rank test for bits 5 to 12, p=0.48857 b-rank test for bits 6 to 13, p=0.32729 b-rank test for bits 7 to 14, p=0.31107 b-rank test for bits 8 to 15, p=0.44193 b-rank test for bits 9 to 16, p=0.75960 b-rank test for bits 10 to 17, p=0.57776 b-rank test for bits 11 to 18, p=0.77433 b-rank test for bits 12 to 19, p=0.21193 b-rank test for bits 13 to 20, p=0.26984 b-rank test for bits 14 to 21, p=0.60969 b-rank test for bits 15 to 22, p=0.26052 b-rank test for bits 16 to 23, p=0.08664 b-rank test for bits 17 to 24, p=0.76966 b-rank test for bits 18 to 25, p=0.07236 b-rank test for bits 19 to 26, p=0.37147 b-rank test for bits 20 to 27, p=0.30470 b-rank test for bits 21 to 28, p=0.79403 b-rank test for bits 22 to 29, p=0.70991 b-rank test for bits 23 to 30, p=0.96618 b-rank test for bits 24 to 31, p=0.36997 b-rank test for bits 25 to 32, p=0.19560 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 = 0.366993 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-01-27_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 141987 0.18 0.572001 2 141864 -0.11 0.457826 3 141687 -0.52 0.301719 4 141764 -0.34 0.367095 5 141486 -0.99 0.161310 6 141932 0.05 0.521121 7 141548 -0.84 0.199271 8 141492 -0.98 0.164763 9 141054 -2.00 0.022835 10 142199 0.68 0.750733 11 142299 0.91 0.818706 12 142038 0.30 0.618152 13 142833 2.16 0.984540 14 141428 -1.12 0.130379 15 142622 1.67 0.952055 16 141857 -0.12 0.451344 17 141509 -0.94 0.174804 18 141042 -2.03 0.021358 19 142736 1.93 0.973288 20 141659 -0.58 0.279313 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-01-27_11:31 Bits used No. missing words z-score p-value 23 to 32 141885 -0.0839 0.466569 22 to 31 141679 -0.7942 0.213528 21 to 30 141691 -0.7529 0.225766 20 to 29 141838 -0.2460 0.402855 19 to 28 141529 -1.3115 0.094847 18 to 27 141333 -1.9873 0.023442 17 to 26 142023 0.3920 0.652458 16 to 25 141671 -0.8218 0.205588 15 to 24 141827 -0.2839 0.388245 14 to 23 141666 -0.8391 0.200715 13 to 22 142029 0.4127 0.660070 12 to 21 142069 0.5506 0.709041 11 to 20 142062 0.5264 0.700712 10 to 19 142103 0.6678 0.747878 9 to 18 142264 1.2230 0.889335 8 to 17 142618 2.4437 0.992731 7 to 16 141945 0.1230 0.548947 6 to 15 142235 1.1230 0.869281 5 to 14 141696 -0.7356 0.230981 4 to 13 141822 -0.3011 0.381655 3 to 12 142144 0.8092 0.790802 2 to 11 142348 1.5127 0.934816 1 to 10 141734 -0.6046 0.272727 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-01-27_11:31 Bits used No. missing words z-score p-value 28 to 32 142339 1.4565 0.927374 27 to 31 142300 1.3243 0.907299 26 to 30 142033 0.4192 0.662473 25 to 29 141926 0.0565 0.522532 24 to 28 141389 -1.7638 0.038880 23 to 27 142226 1.0735 0.858467 22 to 26 141978 0.2328 0.592034 21 to 25 141886 -0.0791 0.468483 20 to 24 142038 0.4362 0.668643 19 to 23 141903 -0.0215 0.491440 18 to 22 141439 -1.5943 0.055430 17 to 21 141288 -2.1062 0.017593 16 to 20 142159 0.8463 0.801318 15 to 19 142095 0.6294 0.735453 14 to 18 142129 0.7446 0.771757 13 to 17 141873 -0.1232 0.450993 12 to 16 141954 0.1514 0.560179 11 to 15 141466 -1.5028 0.066444 10 to 14 142525 2.0870 0.981557 9 to 13 141694 -0.7299 0.232716 8 to 12 142026 0.3955 0.653760 7 to 11 141936 0.0904 0.536018 6 to 10 141834 -0.2554 0.399224 5 to 9 141971 0.2091 0.582796 4 to 8 141780 -0.4384 0.330546 3 to 7 141812 -0.3299 0.370726 2 to 6 141528 -1.2926 0.098067 1 to 5 141355 -1.8791 0.030116 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-01-27_11:31 Bits used No. missing words z-score p-value 31 to 32 142448 1.5890 0.943969 30 to 31 141478 -1.2724 0.101623 29 to 30 141088 -2.4228 0.007701 28 to 29 141573 -0.9921 0.160569 27 to 28 142104 0.5742 0.717100 26 to 27 142157 0.7306 0.767485 25 to 26 142049 0.4120 0.659832 24 to 25 141459 -1.3284 0.092022 23 to 24 141431 -1.4110 0.079122 22 to 23 141838 -0.2104 0.416673 21 to 22 142271 1.0669 0.856985 20 to 21 141865 -0.1308 0.447980 19 to 20 142226 0.9341 0.824882 18 to 19 142215 0.9017 0.816387 17 to 18 141794 -0.3402 0.366851 16 to 17 141040 -2.5644 0.005168 15 to 16 141961 0.1524 0.560572 14 to 15 141387 -1.5408 0.061683 13 to 14 141869 -0.1190 0.452651 12 to 13 141896 -0.0393 0.484317 11 to 12 141843 -0.1957 0.422437 10 to 11 141653 -0.7561 0.224784 9 to 10 141960 0.1495 0.559408 8 to 9 141301 -1.7945 0.036368 7 to 8 142044 0.3973 0.654411 6 to 7 142470 1.6539 0.950925 5 to 6 142346 1.2881 0.901147 4 to 5 141778 -0.3874 0.349229 3 to 4 141502 -1.2016 0.114766 2 to 3 142283 1.1023 0.864828 1 to 2 141879 -0.0895 0.464355 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-01-27_11:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2390.56 -1.548 0.060844 Test results for specific bytes for dh-ranFile-2016-01-27_11:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2618.82 1.680 0.953558 2 to 9 2705.00 2.899 0.998129 3 to 10 2598.48 1.393 0.918144 4 to 11 2448.28 -0.731 0.232276 5 to 12 2430.34 -0.985 0.162282 6 to 13 2434.35 -0.928 0.176592 7 to 14 2525.97 0.367 0.643280 8 to 15 2579.70 1.127 0.870153 9 to 16 2450.67 -0.698 0.242706 10 to 17 2519.90 0.281 0.610834 11 to 18 2389.86 -1.558 0.059669 12 to 19 2565.00 0.919 0.821019 13 to 20 2508.72 0.123 0.549056 14 to 21 2463.02 -0.523 0.300482 15 to 22 2279.34 -3.121 0.000903 16 to 23 2447.56 -0.742 0.229177 17 to 24 2430.20 -0.987 0.161794 18 to 25 2485.62 -0.203 0.419431 19 to 26 2380.67 -1.688 0.045741 20 to 27 2414.85 -1.204 0.114258 21 to 28 2350.44 -2.115 0.017213 22 to 29 2449.71 -0.711 0.238496 23 to 30 2382.12 -1.667 0.047748 24 to 31 2483.73 -0.230 0.408991 25 to 32 2565.51 0.927 0.822912 CDPARK for dh-ranFile-2016-01-27_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 3521 -0.0913 0.463617 3518 -0.2283 0.409702 3515 -0.3653 0.357445 3536 0.5936 0.723613 3533 0.4566 0.676028 3515 -0.3653 0.357445 3511 -0.5479 0.291865 3527 0.1826 0.572463 3519 -0.1826 0.427537 3572 2.2374 0.987371 Square side=100, avg. no. parked=3526.70 sample std.=16.93 p-value of the KSTEST for those 10 p-values: 0.368127 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-01-27_11:31 0.6694,0.0298,0.3219,0.3901,0.0007,0.7257,0.9917,0.3024,0.1098,0.3023, The KS test for those 10 p-values: 0.146991 The 3DSPHERES test for dh-ranFile-2016-01-27_11:31 sample no r^3 equiv. uni. 1 7.690 0.226110 2 4.335 0.134546 3 1.289 0.042053 4 23.406 0.541689 5 3.717 0.116526 6 1.669 0.054101 7 102.280 0.966937 8 47.550 0.795050 9 6.820 0.203333 10 11.559 0.319748 11 5.568 0.169390 12 55.686 0.843736 13 3.164 0.100090 14 4.759 0.146704 15 38.967 0.727167 16 23.537 0.543683 17 27.531 0.600570 18 2.964 0.094091 19 22.048 0.520457 20 4.241 0.131840 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.031247 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-01-27_11:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 0.9 -1.6 0.0 -0.4 0.6 0.7 0.9 0.8 -0.9 -0.1 1.1 0.5 0.3 -0.1 1.8 -1.0 0.0 -1.6 -1.3 -1.7 2.5 -1.1 0.3 0.9 -0.4 0.9 -0.0 -0.3 -1.4 0.9 -0.3 0.1 0.4 0.2 0.2 1.2 0.8 0.1 -0.1 0.9 0.0 -1.1 Chi-square with 42 degrees of freedom:36.599322 z-score=-0.589262, p-value=0.293574 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-01-27_11:31 Test no p-value 1 0.277829 2 0.387383 3 0.601516 4 0.481557 5 0.061729 6 0.014504 7 0.544461 8 0.379975 9 0.755299 10 0.351265 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.256924 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-01-27_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 66808 0.30 66468 0.59 3 25000.00 24776 2.01 25059 0.14 4 6666.67 6691 0.09 6704 0.21 5 1388.89 1434 1.47 1468 4.51 6 238.10 254 1.06 259 1.84 7 34.72 28 1.30 33 0.09 8 4.96 8 1.86 8 1.86 p=0.76819 p=0.83896 Number of rngs required: 688653, p-value: 0.613 RESULTS OF CRAPS TEST for dh-ranFile-2016-01-27_11:31 No. of wins: Observed Expected 98736 98585.9 z-score= 0.672, pvalue=0.74906 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67190 66666.7 4.108 4.108 2 37556 37654.3 0.257 4.365 3 26836 26954.7 0.523 4.888 4 19461 19313.5 1.127 6.015 5 13647 13851.4 3.017 9.032 6 9758 9943.5 3.462 12.494 7 7200 7145.0 0.423 12.917 8 5137 5139.1 0.001 12.918 9 3575 3699.9 4.214 17.132 10 2612 2666.3 1.106 18.238 11 1870 1923.3 1.479 19.716 12 1459 1388.7 3.555 23.271 13 1038 1003.7 1.171 24.442 14 730 726.1 0.021 24.462 15 512 525.8 0.364 24.826 16 380 381.2 0.003 24.830 17 290 276.5 0.655 25.485 18 191 200.8 0.481 25.966 19 177 146.0 6.590 32.556 20 98 106.2 0.635 33.191 21 283 287.1 0.059 33.250 Chisq= 33.25 for 20 degrees of freedom, p= 0.96833 SUMMARY of craptest p-value for no. of wins: 0.749055 p-value for throws/game: 0.968332 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-01-27_11:31 No. of wins: Observed Expected 98279 98585.9 z-score=-1.372, pvalue=0.08496 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66458 66666.7 0.653 0.653 2 37591 37654.3 0.106 0.760 3 27000 26954.7 0.076 0.836 4 19165 19313.5 1.141 1.977 5 13787 13851.4 0.300 2.276 6 10139 9943.5 3.842 6.118 7 7278 7145.0 2.475 8.593 8 5186 5139.1 0.429 9.022 9 3730 3699.9 0.245 9.267 10 2701 2666.3 0.452 9.719 11 1911 1923.3 0.079 9.798 12 1359 1388.7 0.637 10.435 13 954 1003.7 2.462 12.897 14 751 726.1 0.851 13.748 15 511 525.8 0.419 14.167 16 395 381.2 0.503 14.670 17 295 276.5 1.232 15.902 18 216 200.8 1.146 17.048 19 156 146.0 0.687 17.736 20 119 106.2 1.539 19.274 21 298 287.1 0.413 19.687 Chisq= 19.69 for 20 degrees of freedom, p= 0.52235 SUMMARY of craptest p-value for no. of wins: 0.084962 p-value for throws/game: 0.522352 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0007,0.0009,0.0052,0.0077,0.0145,0.0172,0.0176,0.0213,0.0214,0.0228, 0.0234,0.0298,0.0301,0.0312,0.0364,0.0389,0.0415,0.0421,0.0457,0.0477, 0.0541,0.0554,0.0577,0.0597,0.0608,0.0617,0.0617,0.0641,0.0664,0.0724, 0.0791,0.0850,0.0866,0.0920,0.0941,0.0948,0.0981,0.1001,0.1014,0.1016, 0.1039,0.1098,0.1125,0.1143,0.1148,0.1165,0.1304,0.1318,0.1345,0.1467, 0.1470,0.1494,0.1606,0.1613,0.1618,0.1623,0.1648,0.1694,0.1748,0.1766, 0.1801,0.1925,0.1956,0.1993,0.2007,0.2033,0.2056,0.2119,0.2135,0.2164, 0.2248,0.2258,0.2261,0.2292,0.2310,0.2323,0.2327,0.2371,0.2385,0.2408, 0.2427,0.2569,0.2605,0.2698,0.2727,0.2778,0.2793,0.2902,0.2919,0.2936, 0.3005,0.3017,0.3023,0.3024,0.3047,0.3111,0.3197,0.3219,0.3273,0.3301, 0.3305,0.3424,0.3486,0.3492,0.3513,0.3567,0.3574,0.3574,0.3669,0.3670, 0.3671,0.3681,0.3700,0.3707,0.3711,0.3715,0.3800,0.3817,0.3874,0.3882, 0.3901,0.3992,0.4029,0.4054,0.4081,0.4090,0.4097,0.4110,0.4155,0.4167, 0.4167,0.4194,0.4224,0.4275,0.4419,0.4480,0.4510,0.4513,0.4527,0.4578, 0.4606,0.4636,0.4644,0.4666,0.4685,0.4816,0.4843,0.4886,0.4911,0.4914, 0.5046,0.5069,0.5137,0.5205,0.5211,0.5224,0.5225,0.5348,0.5360,0.5417, 0.5437,0.5437,0.5445,0.5489,0.5491,0.5564,0.5594,0.5602,0.5606,0.5607, 0.5652,0.5720,0.5725,0.5749,0.5778,0.5828,0.5832,0.5879,0.5920,0.6005, 0.6006,0.6015,0.6025,0.6042,0.6097,0.6108,0.6132,0.6182,0.6376,0.6433, 0.6478,0.6488,0.6525,0.6538,0.6544,0.6598,0.6601,0.6625,0.6686,0.6694, 0.6760,0.7007,0.7090,0.7099,0.7143,0.7155,0.7171,0.7236,0.7257,0.7272, 0.7355,0.7418,0.7479,0.7491,0.7507,0.7553,0.7596,0.7612,0.7642,0.7675, 0.7682,0.7697,0.7718,0.7743,0.7908,0.7940,0.7950,0.8013,0.8164,0.8187, 0.8210,0.8229,0.8249,0.8390,0.8437,0.8570,0.8585,0.8648,0.8693,0.8702, 0.8749,0.8893,0.8933,0.9011,0.9073,0.9181,0.9197,0.9274,0.9348,0.9348, 0.9397,0.9440,0.9509,0.9513,0.9521,0.9536,0.9624,0.9662,0.9669,0.9683, 0.9733,0.9816,0.9845,0.9871,0.9874,0.9917,0.9927,0.9962,0.9981, Overall p-value after applying KStest on 269 p-values = 0.022939 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.