RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-01-17_10:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.74 16.0106 0.476915 2 to 25 15.61 18.9230 0.667032 3 to 26 15.46 27.1272 0.943772 4 to 27 15.49 18.2462 0.626528 5 to 28 15.69 7.5190 0.024220 6 to 29 15.47 20.5275 0.751858 7 to 30 15.80 20.5585 0.753335 8 to 31 15.66 13.5101 0.298578 9 to 32 15.75 17.1293 0.554363 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.643686 Tough bday spacings test for dh-ranFile-2017-01-17_10:31: 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 11 46 55 104 93 80 57 28 16 7 3 (O-E)^2/E 0.4 2.4 4.6 0.4 0.2 0.0 0.5 0.1 0.1 0.0 0.3 Birthday Spacings: Sum(O-E)^2/E= 8.948, p= 0.463 RESULTS OF GCD FOR dh-ranFile-2017-01-17_10:31 Euclid's algorithm: p-value, steps to gcd: 0.771518 p-value, dist. of gcd's: 0.155704 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-01-17_10:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.687 0.690 0.299 0.272 0.722 0.621 0.099 0.440 Bits 8 to 15---> 0.641 0.116 0.715 0.707 0.081 0.245 0.975 0.430 Bits 16 to 23---> 0.357 0.844 0.251 0.414 0.249 0.189 0.577 0.239 Bits 24 to 31---> 0.689 0.349 0.042 0.261 0.872 0.893 0.093 0.043 KS test for the above 32 p values: 0.631 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-01-17_10:31, p-values for 5 runs: 0.8416, 0.0829, 0.8429, 0.1931, 0.5189 Rank test for binary matrices (31x31) for dh-ranFile-2017-01-17_10:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 199 211.4 0.729 0.729 r= 29 5195 5134.0 0.725 1.454 r= 30 22998 23103.0 0.478 1.932 r= 31 11608 11551.5 0.276 2.208 chi-square = 2.208 with df = 3; p-value = 0.470 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2017-01-17_10:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 230 211.4 1.633 1.633 r= 30 5096 5134.0 0.281 1.915 r= 31 23003 23103.0 0.433 2.348 r= 32 11671 11551.5 1.236 3.584 chi-square = 3.584 with df = 3; p-value = 0.690 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2017-01-17_10:31 b-rank test for bits 1 to 8, p=0.20996 b-rank test for bits 2 to 9, p=0.23943 b-rank test for bits 3 to 10, p=0.76112 b-rank test for bits 4 to 11, p=0.26908 b-rank test for bits 5 to 12, p=0.18307 b-rank test for bits 6 to 13, p=0.08585 b-rank test for bits 7 to 14, p=0.27439 b-rank test for bits 8 to 15, p=0.16489 b-rank test for bits 9 to 16, p=0.80311 b-rank test for bits 10 to 17, p=0.63779 b-rank test for bits 11 to 18, p=0.49999 b-rank test for bits 12 to 19, p=0.19815 b-rank test for bits 13 to 20, p=0.44348 b-rank test for bits 14 to 21, p=0.95125 b-rank test for bits 15 to 22, p=0.58309 b-rank test for bits 16 to 23, p=0.79574 b-rank test for bits 17 to 24, p=0.31067 b-rank test for bits 18 to 25, p=0.69107 b-rank test for bits 19 to 26, p=0.66064 b-rank test for bits 20 to 27, p=0.04914 b-rank test for bits 21 to 28, p=0.50358 b-rank test for bits 22 to 29, p=0.75511 b-rank test for bits 23 to 30, p=0.23576 b-rank test for bits 24 to 31, p=0.84090 b-rank test for bits 25 to 32, p=0.62262 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 = 0.710744 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-01-17_10:31 (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 141954 0.10 0.541562 2 141437 -1.10 0.134889 3 141915 0.01 0.505285 4 141295 -1.44 0.075594 5 142197 0.67 0.749248 6 141644 -0.62 0.267652 7 141416 -1.15 0.124529 8 141330 -1.35 0.087936 9 141568 -0.80 0.212580 10 141889 -0.05 0.481057 11 141691 -0.51 0.304985 12 142174 0.62 0.731840 13 141859 -0.12 0.453195 14 141355 -1.30 0.097632 15 142179 0.63 0.735676 16 142574 1.55 0.939785 17 142331 0.99 0.837740 18 141374 -1.25 0.105509 19 140993 -2.14 0.016139 20 141831 -0.18 0.427394 ---------------------------------------------------------------- OPSO test for dh-ranFile-2017-01-17_10:31 Bits used No. missing words z-score p-value 23 to 32 142168 0.8920 0.813794 22 to 31 141745 -0.5667 0.285474 21 to 30 142409 1.7230 0.957556 20 to 29 142212 1.0437 0.851686 19 to 28 142315 1.3989 0.919073 18 to 27 142011 0.3506 0.637051 17 to 26 141677 -0.8011 0.211526 16 to 25 141831 -0.2701 0.393540 15 to 24 142242 1.1471 0.874338 14 to 23 141888 -0.0736 0.470684 13 to 22 141097 -2.8011 0.002546 12 to 21 141844 -0.2253 0.410882 11 to 20 141148 -2.6253 0.004329 10 to 19 141695 -0.7391 0.229933 9 to 18 142024 0.3954 0.653731 8 to 17 142121 0.7299 0.767273 7 to 16 141621 -0.9942 0.160053 6 to 15 141968 0.2023 0.580163 5 to 14 142255 1.1920 0.883363 4 to 13 141616 -1.0115 0.155893 3 to 12 142156 0.8506 0.802500 2 to 11 142254 1.1885 0.882685 1 to 10 141550 -1.2391 0.107660 ----------------------------------------------------------------- OQSO test for dh-ranFile-2017-01-17_10:31 Bits used No. missing words z-score p-value 28 to 32 141824 -0.2893 0.386193 27 to 31 141932 0.0768 0.530628 26 to 30 141589 -1.0859 0.138770 25 to 29 141917 0.0260 0.510371 24 to 28 142204 0.9989 0.841074 23 to 27 142338 1.4531 0.926905 22 to 26 141945 0.1209 0.548121 21 to 25 141616 -0.9943 0.160029 20 to 24 141424 -1.6452 0.049966 19 to 23 142096 0.6328 0.736561 18 to 22 141863 -0.1571 0.437602 17 to 21 141804 -0.3571 0.360527 16 to 20 141610 -1.0147 0.155130 15 to 19 142106 0.6667 0.747511 14 to 18 141792 -0.3977 0.345415 13 to 17 142119 0.7107 0.761379 12 to 16 141909 -0.0011 0.499554 11 to 15 141798 -0.3774 0.352942 10 to 14 142409 1.6938 0.954848 9 to 13 141976 0.2260 0.589399 8 to 12 141775 -0.4554 0.324427 7 to 11 141892 -0.0587 0.476577 6 to 10 141845 -0.2181 0.413688 5 to 9 142007 0.3311 0.629710 4 to 8 141929 0.0667 0.526581 3 to 7 141637 -0.9232 0.177964 2 to 6 142112 0.6870 0.753964 1 to 5 141623 -0.9706 0.165871 ----------------------------------------------------------------- DNA test for dh-ranFile-2017-01-17_10:31 Bits used No. missing words z-score p-value 31 to 32 141595 -0.9272 0.176904 30 to 31 142103 0.5713 0.716101 29 to 30 142126 0.6391 0.738636 28 to 29 141627 -0.8328 0.202470 27 to 28 141822 -0.2576 0.398354 26 to 27 142086 0.5212 0.698869 25 to 26 141729 -0.5319 0.297381 24 to 25 141851 -0.1721 0.431693 23 to 24 142536 1.8486 0.967741 22 to 23 141543 -1.0806 0.139933 21 to 22 141693 -0.6381 0.261691 20 to 21 141675 -0.6912 0.244708 19 to 20 141881 -0.0836 0.466699 18 to 19 141794 -0.3402 0.366851 17 to 18 141469 -1.2989 0.096988 16 to 17 141969 0.1760 0.569860 15 to 16 141438 -1.3904 0.082211 14 to 15 142000 0.2675 0.605444 13 to 14 141699 -0.6204 0.267483 12 to 13 142054 0.4268 0.665221 11 to 12 141850 -0.1750 0.430534 10 to 11 142070 0.4740 0.682233 9 to 10 141526 -1.1308 0.129077 8 to 9 141732 -0.5231 0.300453 7 to 8 141873 -0.1072 0.457328 6 to 7 141692 -0.6411 0.260732 5 to 6 141865 -0.1308 0.447980 4 to 5 141809 -0.2960 0.383631 3 to 4 141785 -0.3668 0.356901 2 to 3 142540 1.8604 0.968584 1 to 2 141829 -0.2370 0.406343 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2017-01-17_10:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2511.29 0.160 0.563404 Test results for specific bytes for dh-ranFile-2017-01-17_10:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2481.70 -0.259 0.397902 2 to 9 2606.94 1.512 0.934780 3 to 10 2461.10 -0.550 0.291104 4 to 11 2399.09 -1.427 0.076780 5 to 12 2467.42 -0.461 0.322499 6 to 13 2460.25 -0.562 0.287000 7 to 14 2538.02 0.538 0.704624 8 to 15 2536.67 0.519 0.697971 9 to 16 2510.37 0.147 0.558312 10 to 17 2570.53 0.997 0.840710 11 to 18 2459.12 -0.578 0.281609 12 to 19 2602.38 1.448 0.926178 13 to 20 2594.52 1.337 0.909348 14 to 21 2440.71 -0.838 0.200877 15 to 22 2498.88 -0.016 0.493682 16 to 23 2530.76 0.435 0.668216 17 to 24 2653.35 2.169 0.984947 18 to 25 2575.21 1.064 0.856238 19 to 26 2584.20 1.191 0.883117 20 to 27 2491.47 -0.121 0.451975 21 to 28 2547.67 0.674 0.749889 22 to 29 2648.79 2.104 0.982322 23 to 30 2485.65 -0.203 0.419616 24 to 31 2533.03 0.467 0.679815 25 to 32 2516.89 0.239 0.594395 CDPARK for dh-ranFile-2017-01-17_10:31: 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 3515 -0.3653 0.357445 3511 -0.5479 0.291865 3541 0.8219 0.794438 3549 1.1872 0.882429 3538 0.6849 0.753306 3551 1.2785 0.899470 3501 -1.0046 0.157553 3490 -1.5068 0.065925 3502 -0.9589 0.168804 3537 0.6393 0.738676 Square side=100, avg. no. parked=3523.50 sample std.=21.03 p-value of the KSTEST for those 10 p-values: 0.799759 Results for the MINIMUM DISTANCE test for dh-ranFile-2017-01-17_10:31 0.4640,0.7414,0.5518,0.8399,0.5595,0.0183,0.3347,0.3663,0.4915,0.1090, The KS test for those 10 p-values: 0.683905 The 3DSPHERES test for dh-ranFile-2017-01-17_10:31 sample no r^3 equiv. uni. 1 3.590 0.112782 2 8.100 0.236613 3 84.764 0.940719 4 16.995 0.432495 5 31.468 0.649691 6 41.329 0.747828 7 75.114 0.918225 8 39.882 0.735361 9 6.227 0.187442 10 33.354 0.671037 11 10.572 0.296995 12 168.705 0.996388 13 6.137 0.185004 14 3.650 0.114571 15 15.186 0.397218 16 13.134 0.354549 17 37.196 0.710581 18 0.201 0.006689 19 29.167 0.621766 20 39.865 0.735217 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.917885 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-01-17_10:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -1.2 -0.6 0.2 -0.2 -0.2 0.3 -0.4 0.3 -1.4 -0.2 1.2 0.8 -0.1 -0.3 -0.8 -0.4 -0.0 0.7 -0.0 -0.2 1.2 -0.6 0.7 0.3 -0.0 -1.0 -0.6 0.2 -0.2 -0.6 -0.8 2.1 -0.1 0.2 -0.5 -1.2 -2.3 -0.8 0.4 0.9 -1.0 -1.1 Chi-square with 42 degrees of freedom:27.387645 z-score=-1.594339, p-value=0.039716 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2017-01-17_10:31 Test no p-value 1 0.886499 2 0.602344 3 0.167772 4 0.121659 5 0.304182 6 0.016997 7 0.995102 8 0.004010 9 0.407727 10 0.301838 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.117001 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-01-17_10:31: (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 66421 0.91 66768 0.15 3 25000.00 25138 0.76 25085 0.29 4 6666.67 6764 1.42 6506 3.87 5 1388.89 1390 0.00 1391 0.00 6 238.10 241 0.04 216 2.05 7 34.72 38 0.31 26 2.19 8 4.96 7 0.84 7 0.84 p=0.36025 p=0.84760 Number of rngs required: 687898, p-value: 0.280 RESULTS OF CRAPS TEST for dh-ranFile-2017-01-17_10:31 No. of wins: Observed Expected 98457 98585.9 z-score=-0.576, pvalue=0.28220 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66821 66666.7 0.357 0.357 2 37696 37654.3 0.046 0.403 3 27026 26954.7 0.188 0.592 4 19335 19313.5 0.024 0.616 5 13552 13851.4 6.472 7.088 6 10019 9943.5 0.573 7.661 7 7150 7145.0 0.003 7.664 8 5100 5139.1 0.297 7.961 9 3738 3699.9 0.393 8.354 10 2661 2666.3 0.011 8.365 11 1901 1923.3 0.259 8.624 12 1421 1388.7 0.749 9.374 13 953 1003.7 2.562 11.936 14 744 726.1 0.439 12.375 15 498 525.8 1.474 13.849 16 357 381.2 1.530 15.379 17 271 276.5 0.111 15.490 18 185 200.8 1.248 16.738 19 162 146.0 1.757 18.495 20 93 106.2 1.644 20.139 21 317 287.1 3.111 23.250 Chisq= 23.25 for 20 degrees of freedom, p= 0.72331 SUMMARY of craptest p-value for no. of wins: 0.282196 p-value for throws/game: 0.723313 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2017-01-17_10:31 No. of wins: Observed Expected 98400 98585.9 z-score=-0.831, pvalue=0.20291 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66910 66666.7 0.888 0.888 2 37622 37654.3 0.028 0.916 3 26758 26954.7 1.436 2.352 4 19316 19313.5 0.000 2.352 5 13917 13851.4 0.310 2.663 6 9777 9943.5 2.789 5.452 7 7069 7145.0 0.809 6.261 8 5149 5139.1 0.019 6.280 9 3726 3699.9 0.185 6.465 10 2608 2666.3 1.275 7.739 11 1964 1923.3 0.860 8.599 12 1448 1388.7 2.529 11.128 13 1039 1003.7 1.240 12.369 14 740 726.1 0.265 12.633 15 530 525.8 0.033 12.666 16 397 381.2 0.659 13.325 17 275 276.5 0.009 13.334 18 171 200.8 4.431 17.764 19 162 146.0 1.757 19.521 20 115 106.2 0.727 20.248 21 307 287.1 1.377 21.625 Chisq= 21.63 for 20 degrees of freedom, p= 0.63882 SUMMARY of craptest p-value for no. of wins: 0.202911 p-value for throws/game: 0.638819 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0025,0.0040,0.0043,0.0067,0.0161,0.0170,0.0183,0.0242,0.0397,0.0419, 0.0435,0.0491,0.0500,0.0659,0.0756,0.0768,0.0810,0.0822,0.0829,0.0858, 0.0879,0.0934,0.0970,0.0976,0.0989,0.1055,0.1077,0.1090,0.1128,0.1146, 0.1161,0.1170,0.1217,0.1245,0.1291,0.1349,0.1388,0.1399,0.1551,0.1557, 0.1559,0.1576,0.1600,0.1601,0.1649,0.1659,0.1678,0.1688,0.1769,0.1780, 0.1831,0.1850,0.1874,0.1888,0.1931,0.1982,0.2009,0.2025,0.2029,0.2100, 0.2115,0.2126,0.2299,0.2358,0.2366,0.2394,0.2394,0.2446,0.2447,0.2491, 0.2507,0.2607,0.2610,0.2617,0.2675,0.2677,0.2691,0.2718,0.2744,0.2802, 0.2816,0.2822,0.2855,0.2870,0.2911,0.2919,0.2970,0.2974,0.2986,0.2992, 0.3005,0.3018,0.3042,0.3050,0.3107,0.3225,0.3244,0.3347,0.3454,0.3494, 0.3529,0.3545,0.3569,0.3571,0.3574,0.3602,0.3605,0.3663,0.3669,0.3836, 0.3862,0.3935,0.3972,0.3979,0.3984,0.4063,0.4077,0.4109,0.4136,0.4137, 0.4196,0.4274,0.4300,0.4305,0.4317,0.4325,0.4376,0.4396,0.4435,0.4480, 0.4520,0.4532,0.4573,0.4630,0.4640,0.4667,0.4696,0.4707,0.4766,0.4769, 0.4811,0.4915,0.4937,0.4996,0.5000,0.5036,0.5053,0.5104,0.5189,0.5266, 0.5306,0.5416,0.5481,0.5518,0.5544,0.5583,0.5595,0.5634,0.5699,0.5767, 0.5802,0.5831,0.5894,0.5944,0.6023,0.6054,0.6213,0.6218,0.6226,0.6265, 0.6297,0.6311,0.6371,0.6378,0.6388,0.6407,0.6437,0.6497,0.6537,0.6606, 0.6652,0.6670,0.6682,0.6710,0.6798,0.6822,0.6839,0.6868,0.6889,0.6898, 0.6899,0.6911,0.6980,0.6989,0.7046,0.7071,0.7106,0.7107,0.7148,0.7161, 0.7224,0.7233,0.7318,0.7352,0.7354,0.7357,0.7366,0.7386,0.7387,0.7414, 0.7475,0.7478,0.7492,0.7499,0.7519,0.7533,0.7533,0.7540,0.7551,0.7611, 0.7614,0.7673,0.7715,0.7944,0.7957,0.7998,0.8025,0.8031,0.8138,0.8377, 0.8399,0.8407,0.8409,0.8411,0.8416,0.8429,0.8435,0.8476,0.8517,0.8562, 0.8724,0.8743,0.8824,0.8827,0.8831,0.8834,0.8865,0.8928,0.8995,0.9093, 0.9179,0.9182,0.9191,0.9262,0.9269,0.9348,0.9398,0.9407,0.9438,0.9512, 0.9548,0.9576,0.9677,0.9686,0.9753,0.9823,0.9849,0.9951,0.9964, Overall p-value after applying KStest on 269 p-values = 0.396910 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.