RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-03-10_00:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.84 10.2685 0.108025 2 to 25 15.48 22.2278 0.823882 3 to 26 15.72 18.3762 0.634511 4 to 27 15.54 21.8644 0.810008 5 to 28 15.73 20.1225 0.731986 6 to 29 15.77 24.0689 0.882424 7 to 30 15.84 18.1929 0.623232 8 to 31 15.86 9.0361 0.060877 9 to 32 15.77 15.0824 0.410454 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.601549 Tough bday spacings test for dh-ranFile-2016-03-10_00:31: 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 14 27 72 105 88 84 54 38 12 4 2 (O-E)^2/E 2.6 2.5 0.0 0.5 1.0 0.4 0.1 2.3 0.6 1.0 1.0 Birthday Spacings: Sum(O-E)^2/E= 12.048, p= 0.718 RESULTS OF GCD FOR dh-ranFile-2016-03-10_00:31 Euclid's algorithm: p-value, steps to gcd: 0.097708 p-value, dist. of gcd's: 0.156517 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-03-10_00:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.187 0.647 0.641 0.398 0.795 0.331 0.889 0.573 Bits 8 to 15---> 0.614 0.444 0.015 0.554 0.398 0.681 0.273 0.413 Bits 16 to 23---> 0.497 0.287 0.444 0.451 0.743 0.751 0.167 0.411 Bits 24 to 31---> 0.136 0.363 0.817 0.283 0.279 0.906 0.356 0.709 KS test for the above 32 p values: 0.730 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-03-10_00:31, p-values for 5 runs: 0.1860, 0.0187, 0.0011, 0.7142, 0.9940 Rank test for binary matrices (31x31) for dh-ranFile-2016-03-10_00:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 211 211.4 0.001 0.001 r= 29 5115 5134.0 0.070 0.071 r= 30 23168 23103.0 0.183 0.254 r= 31 11506 11551.5 0.179 0.433 chi-square = 0.433 with df = 3; p-value = 0.067 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-03-10_00:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 217 211.4 0.147 0.147 r= 30 5132 5134.0 0.001 0.148 r= 31 23075 23103.0 0.034 0.182 r= 32 11576 11551.5 0.052 0.234 chi-square = 0.234 with df = 3; p-value = 0.028 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-03-10_00:31 b-rank test for bits 1 to 8, p=0.94540 b-rank test for bits 2 to 9, p=0.85331 b-rank test for bits 3 to 10, p=0.56310 b-rank test for bits 4 to 11, p=0.26034 b-rank test for bits 5 to 12, p=0.61883 b-rank test for bits 6 to 13, p=0.74305 b-rank test for bits 7 to 14, p=0.25641 b-rank test for bits 8 to 15, p=0.34801 b-rank test for bits 9 to 16, p=0.39936 b-rank test for bits 10 to 17, p=0.36331 b-rank test for bits 11 to 18, p=0.95786 b-rank test for bits 12 to 19, p=0.57252 b-rank test for bits 13 to 20, p=0.00319 b-rank test for bits 14 to 21, p=0.94304 b-rank test for bits 15 to 22, p=0.40155 b-rank test for bits 16 to 23, p=0.82940 b-rank test for bits 17 to 24, p=0.42873 b-rank test for bits 18 to 25, p=0.03247 b-rank test for bits 19 to 26, p=0.15697 b-rank test for bits 20 to 27, p=0.17213 b-rank test for bits 21 to 28, p=0.41067 b-rank test for bits 22 to 29, p=0.05053 b-rank test for bits 23 to 30, p=0.24851 b-rank test for bits 24 to 31, p=0.35107 b-rank test for bits 25 to 32, p=0.24927 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 = 0.441018 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-03-10_00:31 (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 141446 -1.08 0.139505 2 141398 -1.19 0.116103 3 140930 -2.29 0.011064 4 141192 -1.68 0.046869 5 142240 0.77 0.780119 6 141892 -0.04 0.483851 7 142060 0.35 0.637593 8 142355 1.04 0.851128 9 142126 0.51 0.693655 10 142252 0.80 0.788327 11 142071 0.38 0.647186 12 141800 -0.26 0.399190 13 141784 -0.29 0.384827 14 141341 -1.33 0.092110 15 141845 -0.15 0.440263 16 142018 0.25 0.600214 17 142362 1.06 0.854890 18 142025 0.27 0.606519 19 141865 -0.10 0.458753 20 141641 -0.63 0.265350 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-03-10_00:31 Bits used No. missing words z-score p-value 23 to 32 141964 0.1885 0.574764 22 to 31 141948 0.1333 0.553040 21 to 30 141918 0.0299 0.511925 20 to 29 142084 0.6023 0.726516 19 to 28 141948 0.1333 0.553040 18 to 27 142015 0.3644 0.642213 17 to 26 142420 1.7609 0.960875 16 to 25 142004 0.3264 0.627957 15 to 24 142346 1.5058 0.933935 14 to 23 142132 0.7678 0.778705 13 to 22 142189 0.9644 0.832572 12 to 21 142393 1.6678 0.952325 11 to 20 141323 -2.0218 0.021597 10 to 19 142181 0.9368 0.825568 9 to 18 142064 0.5333 0.703103 8 to 17 141851 -0.2011 0.420295 7 to 16 141714 -0.6736 0.250298 6 to 15 142079 0.5851 0.720749 5 to 14 141990 0.2782 0.609560 4 to 13 141767 -0.4908 0.311786 3 to 12 142093 0.6333 0.736746 2 to 11 141782 -0.4391 0.330306 1 to 10 141814 -0.3287 0.371182 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-03-10_00:31 Bits used No. missing words z-score p-value 28 to 32 142069 0.5413 0.705834 27 to 31 141603 -1.0384 0.149540 26 to 30 141538 -1.2587 0.104061 25 to 29 142165 0.8667 0.806941 24 to 28 141822 -0.2960 0.383602 23 to 27 142362 1.5345 0.937544 22 to 26 141973 0.2158 0.585440 21 to 25 141694 -0.7299 0.232716 20 to 24 142191 0.9548 0.830164 19 to 23 142174 0.8972 0.815190 18 to 22 142169 0.8802 0.810635 17 to 21 142173 0.8938 0.814285 16 to 20 141833 -0.2587 0.397916 15 to 19 142060 0.5107 0.695236 14 to 18 142061 0.5141 0.696421 13 to 17 141760 -0.5062 0.306357 12 to 16 142046 0.4633 0.678421 11 to 15 141551 -1.2147 0.112244 10 to 14 142226 1.0735 0.858467 9 to 13 141813 -0.3265 0.372007 8 to 12 141239 -2.2723 0.011534 7 to 11 141728 -0.6147 0.269384 6 to 10 141776 -0.4520 0.325647 5 to 9 141619 -0.9842 0.162516 4 to 8 141724 -0.6282 0.264924 3 to 7 142094 0.6260 0.734343 2 to 6 141055 -2.8960 0.001890 1 to 5 141892 -0.0587 0.476577 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-03-10_00:31 Bits used No. missing words z-score p-value 31 to 32 141902 -0.0216 0.491375 30 to 31 141876 -0.0983 0.460840 29 to 30 141718 -0.5644 0.286243 28 to 29 142671 2.2468 0.987674 27 to 28 141962 0.1554 0.561735 26 to 27 141433 -1.4051 0.079995 25 to 26 141995 0.2527 0.599755 24 to 25 142034 0.3678 0.643473 23 to 24 141529 -1.1219 0.130949 22 to 23 141483 -1.2576 0.104266 21 to 22 142230 0.9459 0.827908 20 to 21 141214 -2.0511 0.020128 19 to 20 141948 0.1141 0.545409 18 to 19 141517 -1.1573 0.123572 17 to 18 141662 -0.7296 0.232821 16 to 17 141928 0.0551 0.521960 15 to 16 141095 -2.4022 0.008149 14 to 15 141656 -0.7473 0.227445 13 to 14 141804 -0.3107 0.378011 12 to 13 141486 -1.2488 0.105876 11 to 12 141487 -1.2458 0.106417 10 to 11 141784 -0.3697 0.355801 9 to 10 141513 -1.1691 0.121179 8 to 9 141614 -0.8712 0.191828 7 to 8 141955 0.1347 0.553583 6 to 7 142547 1.8810 0.970016 5 to 6 141094 -2.4051 0.008084 4 to 5 142013 0.3058 0.620126 3 to 4 141852 -0.1691 0.432853 2 to 3 141911 0.0049 0.501965 1 to 2 142141 0.6834 0.752821 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-03-10_00:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2546.37 0.656 0.744017 Test results for specific bytes for dh-ranFile-2016-03-10_00:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2435.19 -0.917 0.179676 2 to 9 2398.00 -1.443 0.074573 3 to 10 2597.09 1.373 0.915125 4 to 11 2511.82 0.167 0.566354 5 to 12 2569.13 0.978 0.835872 6 to 13 2524.11 0.341 0.633450 7 to 14 2404.13 -1.356 0.087588 8 to 15 2623.68 1.749 0.959869 9 to 16 2495.10 -0.069 0.472386 10 to 17 2514.72 0.208 0.582438 11 to 18 2514.77 0.209 0.582708 12 to 19 2511.32 0.160 0.563585 13 to 20 2572.82 1.030 0.848471 14 to 21 2468.92 -0.440 0.330128 15 to 22 2630.90 1.851 0.967931 16 to 23 2453.27 -0.661 0.254368 17 to 24 2520.97 0.297 0.616619 18 to 25 2589.58 1.267 0.897405 19 to 26 2531.01 0.439 0.669511 20 to 27 2555.20 0.781 0.782502 21 to 28 2513.50 0.191 0.575712 22 to 29 2525.05 0.354 0.638433 23 to 30 2577.41 1.095 0.863193 24 to 31 2588.19 1.247 0.893836 25 to 32 2572.16 1.020 0.846241 CDPARK for dh-ranFile-2016-03-10_00:31: 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 3496 -1.2329 0.108811 3528 0.2283 0.590298 3553 1.3699 0.914635 3535 0.5479 0.708135 3553 1.3699 0.914635 3537 0.6393 0.738676 3519 -0.1826 0.427537 3543 0.9132 0.819442 3542 0.8676 0.807188 3517 -0.2740 0.392053 Square side=100, avg. no. parked=3532.30 sample std.=16.86 p-value of the KSTEST for those 10 p-values: 0.187436 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-03-10_00:31 0.7526,0.5177,0.5858,0.5976,0.2791,0.4998,0.6360,0.2904,0.3011,0.1769, The KS test for those 10 p-values: 0.368154 The 3DSPHERES test for dh-ranFile-2016-03-10_00:31 sample no r^3 equiv. uni. 1 21.944 0.518798 2 0.979 0.032093 3 27.523 0.600458 4 33.322 0.670682 5 14.471 0.382672 6 5.374 0.164003 7 1.198 0.039149 8 31.995 0.655784 9 1.452 0.047249 10 15.431 0.402113 11 12.281 0.335926 12 21.104 0.505137 13 88.609 0.947850 14 3.720 0.116632 15 10.678 0.299475 16 26.759 0.590152 17 1.208 0.039463 18 1.540 0.050032 19 12.463 0.339937 20 6.026 0.181977 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.019285 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-03-10_00:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 0.5 0.1 -1.1 0.1 0.3 1.1 -0.2 0.3 -1.5 -2.5 -0.1 0.7 0.1 -0.4 -0.7 1.3 0.4 -0.3 -1.0 1.0 1.0 -0.4 -0.5 0.7 0.5 1.1 0.5 -0.5 0.8 -0.4 -0.3 -1.4 0.3 0.1 -1.4 2.8 0.5 -2.0 0.4 -1.3 1.0 -1.1 Chi-square with 42 degrees of freedom:42.414804 z-score=0.045259, p-value=0.546915 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-03-10_00:31 Test no p-value 1 0.858923 2 0.761163 3 0.000280 4 0.188668 5 0.175067 6 0.961457 7 0.186491 8 0.396931 9 0.142389 10 0.064017 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.079123 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-03-10_00:31: (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 66422 0.90 66559 0.17 3 25000.00 25131 0.69 25197 1.55 4 6666.67 6752 1.09 6528 2.88 5 1388.89 1419 0.65 1424 0.89 6 238.10 227 0.52 247 0.33 7 34.72 41 1.14 39 0.53 8 4.96 7 0.84 5 0.00 p=0.55650 p=0.61582 Number of rngs required: 688361, p-value: 0.481 RESULTS OF CRAPS TEST for dh-ranFile-2016-03-10_00:31 No. of wins: Observed Expected 98494 98585.9 z-score=-0.411, pvalue=0.34059 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66288 66666.7 2.151 2.151 2 37647 37654.3 0.001 2.152 3 27198 26954.7 2.195 4.348 4 19284 19313.5 0.045 4.393 5 14000 13851.4 1.594 5.986 6 10002 9943.5 0.344 6.330 7 7119 7145.0 0.095 6.425 8 5128 5139.1 0.024 6.449 9 3655 3699.9 0.544 6.993 10 2666 2666.3 0.000 6.993 11 1953 1923.3 0.458 7.451 12 1385 1388.7 0.010 7.461 13 1046 1003.7 1.781 9.242 14 744 726.1 0.439 9.681 15 516 525.8 0.184 9.865 16 385 381.2 0.039 9.904 17 288 276.5 0.475 10.379 18 193 200.8 0.305 10.684 19 150 146.0 0.110 10.795 20 95 106.2 1.184 11.979 21 258 287.1 2.952 14.931 Chisq= 14.93 for 20 degrees of freedom, p= 0.21967 SUMMARY of craptest p-value for no. of wins: 0.340593 p-value for throws/game: 0.219674 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-03-10_00:31 No. of wins: Observed Expected 98814 98585.9 z-score= 1.020, pvalue=0.84623 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66854 66666.7 0.526 0.526 2 37486 37654.3 0.752 1.279 3 26697 26954.7 2.464 3.743 4 19367 19313.5 0.148 3.892 5 13901 13851.4 0.177 4.069 6 10025 9943.5 0.667 4.736 7 7082 7145.0 0.556 5.292 8 5229 5139.1 1.574 6.866 9 3663 3699.9 0.367 7.233 10 2642 2666.3 0.221 7.455 11 2043 1923.3 7.446 14.901 12 1350 1388.7 1.081 15.981 13 975 1003.7 0.822 16.803 14 747 726.1 0.599 17.402 15 527 525.8 0.003 17.405 16 385 381.2 0.039 17.444 17 286 276.5 0.324 17.767 18 207 200.8 0.190 17.957 19 145 146.0 0.007 17.963 20 100 106.2 0.364 18.327 21 289 287.1 0.012 18.339 Chisq= 18.34 for 20 degrees of freedom, p= 0.43494 SUMMARY of craptest p-value for no. of wins: 0.846226 p-value for throws/game: 0.434944 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0003,0.0011,0.0019,0.0032,0.0081,0.0081,0.0111,0.0115,0.0154,0.0187, 0.0193,0.0201,0.0216,0.0281,0.0321,0.0325,0.0391,0.0395,0.0469,0.0472, 0.0500,0.0505,0.0609,0.0640,0.0667,0.0746,0.0791,0.0800,0.0876,0.0921, 0.0977,0.1041,0.1043,0.1059,0.1064,0.1080,0.1088,0.1122,0.1161,0.1166, 0.1212,0.1236,0.1309,0.1360,0.1395,0.1424,0.1495,0.1565,0.1570,0.1625, 0.1640,0.1671,0.1721,0.1751,0.1769,0.1797,0.1820,0.1860,0.1865,0.1874, 0.1874,0.1887,0.1918,0.2197,0.2274,0.2327,0.2328,0.2485,0.2493,0.2503, 0.2544,0.2564,0.2603,0.2649,0.2653,0.2694,0.2731,0.2791,0.2794,0.2827, 0.2862,0.2870,0.2904,0.2995,0.3011,0.3064,0.3118,0.3256,0.3301,0.3303, 0.3310,0.3359,0.3399,0.3406,0.3480,0.3511,0.3556,0.3558,0.3633,0.3634, 0.3682,0.3712,0.3720,0.3780,0.3827,0.3836,0.3848,0.3921,0.3969,0.3975, 0.3979,0.3985,0.3992,0.3994,0.4016,0.4021,0.4105,0.4107,0.4113,0.4134, 0.4203,0.4275,0.4287,0.4329,0.4349,0.4403,0.4410,0.4436,0.4439,0.4514, 0.4588,0.4608,0.4724,0.4766,0.4807,0.4839,0.4914,0.4973,0.4998,0.5020, 0.5051,0.5119,0.5177,0.5188,0.5220,0.5454,0.5469,0.5530,0.5530,0.5535, 0.5536,0.5565,0.5617,0.5631,0.5636,0.5664,0.5725,0.5728,0.5748,0.5757, 0.5824,0.5827,0.5854,0.5858,0.5902,0.5903,0.5976,0.5998,0.6002,0.6005, 0.6015,0.6065,0.6096,0.6138,0.6158,0.6166,0.6188,0.6201,0.6232,0.6280, 0.6335,0.6345,0.6360,0.6376,0.6384,0.6406,0.6422,0.6435,0.6470,0.6472, 0.6558,0.6695,0.6707,0.6784,0.6812,0.6937,0.6952,0.6964,0.7031,0.7058, 0.7081,0.7093,0.7142,0.7182,0.7207,0.7265,0.7299,0.7320,0.7343,0.7367, 0.7387,0.7430,0.7433,0.7440,0.7509,0.7526,0.7528,0.7612,0.7787,0.7801, 0.7825,0.7883,0.7950,0.8069,0.8072,0.8100,0.8106,0.8143,0.8152,0.8167, 0.8194,0.8239,0.8256,0.8279,0.8294,0.8302,0.8326,0.8359,0.8462,0.8462, 0.8485,0.8511,0.8533,0.8549,0.8585,0.8589,0.8632,0.8824,0.8893,0.8938, 0.8974,0.9063,0.9146,0.9146,0.9151,0.9339,0.9375,0.9430,0.9454,0.9479, 0.9523,0.9579,0.9599,0.9609,0.9615,0.9679,0.9700,0.9877,0.9940, Overall p-value after applying KStest on 269 p-values = 0.143292 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.