RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-03-22_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 15.73 16.4334 0.506658 2 to 25 15.57 27.1729 0.944419 3 to 26 15.83 24.3484 0.889726 4 to 27 15.87 15.3937 0.432857 5 to 28 15.78 16.6915 0.524551 6 to 29 15.85 16.3999 0.504320 7 to 30 15.78 29.0654 0.966072 8 to 31 15.84 15.6311 0.449880 9 to 32 15.68 22.6520 0.839074 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.077973 Tough bday spacings test for dh-ranFile-2018-03-22_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 14 32 71 99 96 80 51 31 16 8 2 (O-E)^2/E 2.6 0.6 0.1 0.0 0.0 0.0 0.0 0.1 0.1 0.3 1.0 Birthday Spacings: Sum(O-E)^2/E= 4.803, p= 0.096 RESULTS OF GCD FOR dh-ranFile-2018-03-22_15:31 Euclid's algorithm: p-value, steps to gcd: 0.890402 p-value, dist. of gcd's: 0.025987 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-03-22_15:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.812 0.926 0.018 0.659 0.074 0.747 0.496 0.963 Bits 8 to 15---> 0.034 0.657 0.092 0.847 0.266 0.924 0.823 0.492 Bits 16 to 23---> 0.547 0.049 0.631 0.725 0.586 0.481 0.687 0.213 Bits 24 to 31---> 0.903 0.917 0.148 0.897 0.299 0.289 0.529 0.006 KS test for the above 32 p values: 0.505 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-03-22_15:31, p-values for 5 runs: 0.6822, 0.3112, 0.8042, 0.3730, 0.7695 Rank test for binary matrices (31x31) for dh-ranFile-2018-03-22_15:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 220 211.4 0.348 0.348 r= 29 5090 5134.0 0.377 0.726 r= 30 23259 23103.0 1.053 1.778 r= 31 11431 11551.5 1.257 3.036 chi-square = 3.036 with df = 3; p-value = 0.614 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-03-22_15:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 216 211.4 0.099 0.099 r= 30 5018 5134.0 2.621 2.721 r= 31 23133 23103.0 0.039 2.760 r= 32 11633 11551.5 0.575 3.334 chi-square = 3.334 with df = 3; p-value = 0.657 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-03-22_15:31 b-rank test for bits 1 to 8, p=0.20326 b-rank test for bits 2 to 9, p=0.13672 b-rank test for bits 3 to 10, p=0.26336 b-rank test for bits 4 to 11, p=0.00581 b-rank test for bits 5 to 12, p=0.04798 b-rank test for bits 6 to 13, p=0.93968 b-rank test for bits 7 to 14, p=0.05744 b-rank test for bits 8 to 15, p=0.21193 b-rank test for bits 9 to 16, p=0.59947 b-rank test for bits 10 to 17, p=0.13372 b-rank test for bits 11 to 18, p=0.36853 b-rank test for bits 12 to 19, p=0.36147 b-rank test for bits 13 to 20, p=0.00919 b-rank test for bits 14 to 21, p=0.18249 b-rank test for bits 15 to 22, p=0.06244 b-rank test for bits 16 to 23, p=0.22570 b-rank test for bits 17 to 24, p=0.56824 b-rank test for bits 18 to 25, p=0.27515 b-rank test for bits 19 to 26, p=0.44696 b-rank test for bits 20 to 27, p=0.36747 b-rank test for bits 21 to 28, p=0.07328 b-rank test for bits 22 to 29, p=0.82233 b-rank test for bits 23 to 30, p=0.40607 b-rank test for bits 24 to 31, p=0.51305 b-rank test for bits 25 to 32, p=0.37998 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 = 0.001065 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-03-22_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 141978 0.16 0.563734 2 142316 0.95 0.828985 3 142238 0.77 0.778733 4 142545 1.49 0.931256 5 142096 0.44 0.668634 6 141238 -1.57 0.058379 7 143063 2.70 0.996486 8 141667 -0.57 0.285632 9 142375 1.09 0.861706 10 141463 -1.04 0.148514 11 141280 -1.47 0.070727 12 142153 0.57 0.715431 13 141864 -0.11 0.457826 14 142114 0.48 0.683746 15 141092 -1.91 0.028089 16 141542 -0.86 0.195378 17 141738 -0.40 0.344466 18 141855 -0.13 0.449494 19 141568 -0.80 0.212580 20 142094 0.43 0.666937 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-03-22_15:31 Bits used No. missing words z-score p-value 23 to 32 142150 0.8299 0.796701 22 to 31 142016 0.3678 0.643499 21 to 30 141837 -0.2494 0.401520 20 to 29 141629 -0.9667 0.166858 19 to 28 141963 0.1851 0.573413 18 to 27 141424 -1.6736 0.047109 17 to 26 141675 -0.8080 0.209535 16 to 25 142239 1.1368 0.872188 15 to 24 142466 1.9196 0.972543 14 to 23 141916 0.0230 0.509175 13 to 22 141543 -1.2632 0.103257 12 to 21 142051 0.4885 0.687408 11 to 20 142379 1.6196 0.947336 10 to 19 141945 0.1230 0.548947 9 to 18 141904 -0.0184 0.492668 8 to 17 141938 0.0989 0.539376 7 to 16 141921 0.0402 0.516050 6 to 15 142260 1.2092 0.886708 5 to 14 141812 -0.3356 0.368579 4 to 13 141921 0.0402 0.516050 3 to 12 142255 1.1920 0.883363 2 to 11 142444 1.8437 0.967386 1 to 10 142221 1.0747 0.858751 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-03-22_15:31 Bits used No. missing words z-score p-value 28 to 32 142040 0.4429 0.671099 27 to 31 142491 1.9718 0.975682 26 to 30 142116 0.7006 0.758216 25 to 29 142372 1.5684 0.941603 24 to 28 142157 0.8396 0.799422 23 to 27 141935 0.0870 0.534671 22 to 26 141369 -1.8316 0.033504 21 to 25 141671 -0.8079 0.209575 20 to 24 141901 -0.0282 0.488737 19 to 23 142345 1.4768 0.930142 18 to 22 142429 1.7616 0.960931 17 to 21 142009 0.3379 0.632267 16 to 20 141884 -0.0859 0.465787 15 to 19 142391 1.6328 0.948742 14 to 18 142238 1.1141 0.867390 13 to 17 141788 -0.4113 0.340431 12 to 16 142245 1.1379 0.872411 11 to 15 141860 -0.1672 0.433598 10 to 14 141788 -0.4113 0.340431 9 to 13 141952 0.1446 0.557504 8 to 12 141807 -0.3469 0.364340 7 to 11 141804 -0.3571 0.360527 6 to 10 141220 -2.3367 0.009727 5 to 9 142313 1.3684 0.914402 4 to 8 142012 0.3480 0.636093 3 to 7 142492 1.9752 0.975875 2 to 6 141774 -0.4587 0.323208 1 to 5 142033 0.4192 0.662473 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-03-22_15:31 Bits used No. missing words z-score p-value 31 to 32 142600 2.0374 0.979194 30 to 31 142263 1.0433 0.851589 29 to 30 141737 -0.5083 0.305605 28 to 29 141575 -0.9862 0.162012 27 to 28 141847 -0.1839 0.427060 26 to 27 142243 0.9843 0.837510 25 to 26 142924 2.9931 0.998619 24 to 25 142758 2.5035 0.993851 23 to 24 141826 -0.2458 0.402914 22 to 23 142041 0.3884 0.651143 21 to 22 142354 1.3117 0.905191 20 to 21 141547 -1.0688 0.142575 19 to 20 141344 -1.6676 0.047694 18 to 19 141841 -0.2016 0.420129 17 to 18 141633 -0.8151 0.207498 16 to 17 141894 -0.0452 0.481966 15 to 16 141379 -1.5644 0.058862 14 to 15 141648 -0.7709 0.220388 13 to 14 141151 -2.2370 0.012644 12 to 13 142071 0.4769 0.683284 11 to 12 141752 -0.4641 0.321288 10 to 11 141117 -2.3373 0.009713 9 to 10 142140 0.6804 0.751888 8 to 9 141961 0.1524 0.560572 7 to 8 141876 -0.0983 0.460840 6 to 7 141822 -0.2576 0.398354 5 to 6 142375 1.3737 0.915226 4 to 5 141838 -0.2104 0.416673 3 to 4 141839 -0.2075 0.417824 2 to 3 141997 0.2586 0.602033 1 to 2 142096 0.5506 0.709063 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-03-22_15:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2644.23 2.040 0.979308 Test results for specific bytes for dh-ranFile-2018-03-22_15:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2603.74 1.467 0.928819 2 to 9 2484.88 -0.214 0.415356 3 to 10 2352.08 -2.092 0.018226 4 to 11 2419.43 -1.139 0.127257 5 to 12 2471.17 -0.408 0.341762 6 to 13 2478.08 -0.310 0.378258 7 to 14 2499.67 -0.005 0.498145 8 to 15 2500.51 0.007 0.502868 9 to 16 2467.00 -0.467 0.320346 10 to 17 2379.61 -1.703 0.044323 11 to 18 2484.46 -0.220 0.413007 12 to 19 2370.08 -1.837 0.033080 13 to 20 2508.27 0.117 0.546543 14 to 21 2535.79 0.506 0.693638 15 to 22 2501.34 0.019 0.507565 16 to 23 2477.49 -0.318 0.375099 17 to 24 2499.47 -0.007 0.497024 18 to 25 2508.77 0.124 0.549334 19 to 26 2545.99 0.650 0.742280 20 to 27 2612.04 1.585 0.943461 21 to 28 2446.31 -0.759 0.223850 22 to 29 2539.03 0.552 0.709528 23 to 30 2343.95 -2.207 0.013662 24 to 31 2625.10 1.769 0.961574 25 to 32 2619.44 1.689 0.954397 CDPARK for dh-ranFile-2018-03-22_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 3522 -0.0457 0.481790 3548 1.1416 0.873180 3492 -1.4155 0.078457 3550 1.2329 0.891189 3515 -0.3653 0.357445 3582 2.6941 0.996471 3542 0.8676 0.807188 3507 -0.7306 0.232514 3510 -0.5936 0.276387 3568 2.0548 0.980051 Square side=100, avg. no. parked=3533.60 sample std.=27.47 p-value of the KSTEST for those 10 p-values: 0.175955 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-03-22_15:31 0.7133,0.3072,0.6036,0.4298,0.6114,0.0676,0.3026,0.9112,0.4803,0.0188, The KS test for those 10 p-values: 0.789490 The 3DSPHERES test for dh-ranFile-2018-03-22_15:31 sample no r^3 equiv. uni. 1 36.683 0.705585 2 7.664 0.225433 3 5.284 0.161497 4 77.265 0.923884 5 0.607 0.020040 6 9.452 0.270260 7 5.744 0.174264 8 41.272 0.747343 9 10.886 0.304319 10 40.326 0.739255 11 30.266 0.635365 12 6.644 0.198657 13 8.691 0.251511 14 0.181 0.006026 15 206.008 0.998958 16 30.885 0.642813 17 6.562 0.196471 18 51.592 0.820888 19 91.186 0.952142 20 32.660 0.663334 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.464450 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-03-22_15:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -1.2 -1.1 -0.3 1.9 1.0 2.0 0.1 -0.9 -0.0 -0.1 1.0 0.0 -0.6 1.0 -0.8 -0.7 0.3 0.3 -0.4 -0.2 0.8 0.1 -0.1 0.6 -0.7 -1.0 0.8 -1.3 0.6 -1.0 -0.5 -0.6 2.0 -0.4 -0.8 1.0 -0.4 -2.0 -1.3 0.1 -1.0 -0.1 Chi-square with 42 degrees of freedom:35.567636 z-score=-0.701828, p-value=0.252241 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-03-22_15:31 Test no p-value 1 0.114691 2 0.317901 3 0.975389 4 0.652873 5 0.788062 6 0.220908 7 0.934481 8 0.006742 9 0.243476 10 0.324362 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.581899 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-03-22_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 66759 0.13 66839 0.45 3 25000.00 24764 2.23 24759 2.32 4 6666.67 6776 1.79 6716 0.37 5 1388.89 1403 0.14 1434 1.47 6 238.10 249 0.50 214 2.44 7 34.72 42 1.53 31 0.40 8 4.96 6 0.22 6 0.22 p=0.63410 p=0.73543 Number of rngs required: 690185, p-value: 0.982 RESULTS OF CRAPS TEST for dh-ranFile-2018-03-22_15:31 No. of wins: Observed Expected 98701 98585.9 z-score= 0.515, pvalue=0.69672 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66843 66666.7 0.466 0.466 2 37670 37654.3 0.007 0.473 3 26912 26954.7 0.068 0.541 4 19341 19313.5 0.039 0.580 5 13835 13851.4 0.019 0.599 6 9931 9943.5 0.016 0.615 7 6850 7145.0 12.182 12.797 8 5150 5139.1 0.023 12.820 9 3719 3699.9 0.099 12.919 10 2714 2666.3 0.853 13.773 11 1962 1923.3 0.778 14.550 12 1426 1388.7 1.000 15.550 13 1014 1003.7 0.105 15.655 14 700 726.1 0.941 16.596 15 562 525.8 2.487 19.084 16 393 381.2 0.368 19.452 17 289 276.5 0.561 20.013 18 170 200.8 4.733 24.746 19 146 146.0 0.000 24.746 20 103 106.2 0.097 24.844 21 270 287.1 1.020 25.864 Chisq= 25.86 for 20 degrees of freedom, p= 0.82964 SUMMARY of craptest p-value for no. of wins: 0.696716 p-value for throws/game: 0.829638 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-03-22_15:31 No. of wins: Observed Expected 98502 98585.9 z-score=-0.375, pvalue=0.35381 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66814 66666.7 0.326 0.326 2 37743 37654.3 0.209 0.534 3 26840 26954.7 0.488 1.023 4 19571 19313.5 3.434 4.457 5 13648 13851.4 2.987 7.444 6 9997 9943.5 0.287 7.732 7 7077 7145.0 0.648 8.379 8 5041 5139.1 1.872 10.251 9 3672 3699.9 0.210 10.461 10 2657 2666.3 0.032 10.493 11 1913 1923.3 0.055 10.549 12 1397 1388.7 0.049 10.598 13 985 1003.7 0.349 10.947 14 687 726.1 2.110 13.057 15 522 525.8 0.028 13.085 16 405 381.2 1.492 14.577 17 292 276.5 0.864 15.441 18 199 200.8 0.017 15.458 19 145 146.0 0.007 15.465 20 103 106.2 0.097 15.562 21 292 287.1 0.083 15.645 Chisq= 15.65 for 20 degrees of freedom, p= 0.26161 SUMMARY of craptest p-value for no. of wins: 0.353806 p-value for throws/game: 0.261612 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0011,0.0058,0.0059,0.0060,0.0067,0.0092,0.0097,0.0097,0.0126,0.0137, 0.0177,0.0182,0.0188,0.0200,0.0260,0.0281,0.0331,0.0335,0.0343,0.0443, 0.0471,0.0477,0.0480,0.0494,0.0574,0.0584,0.0589,0.0624,0.0676,0.0707, 0.0733,0.0738,0.0780,0.0785,0.0921,0.0961,0.1033,0.1147,0.1273,0.1337, 0.1367,0.1426,0.1485,0.1485,0.1615,0.1620,0.1669,0.1743,0.1760,0.1825, 0.1954,0.1965,0.1987,0.2033,0.2075,0.2095,0.2096,0.2119,0.2126,0.2133, 0.2204,0.2209,0.2239,0.2254,0.2257,0.2325,0.2435,0.2515,0.2522,0.2616, 0.2634,0.2664,0.2703,0.2751,0.2764,0.2856,0.2892,0.2988,0.3026,0.3043, 0.3056,0.3072,0.3112,0.3179,0.3203,0.3213,0.3232,0.3244,0.3404,0.3404, 0.3418,0.3445,0.3538,0.3574,0.3605,0.3615,0.3643,0.3675,0.3685,0.3686, 0.3730,0.3751,0.3783,0.3800,0.3984,0.4015,0.4029,0.4061,0.4130,0.4154, 0.4167,0.4178,0.4201,0.4271,0.4298,0.4329,0.4336,0.4470,0.4495,0.4499, 0.4578,0.4608,0.4644,0.4658,0.4803,0.4808,0.4818,0.4820,0.4887,0.4922, 0.4927,0.4962,0.4970,0.4981,0.5029,0.5043,0.5047,0.5067,0.5076,0.5092, 0.5131,0.5160,0.5160,0.5246,0.5286,0.5347,0.5394,0.5465,0.5474,0.5489, 0.5493,0.5575,0.5606,0.5637,0.5682,0.5734,0.5819,0.5861,0.5995,0.6020, 0.6036,0.6114,0.6139,0.6312,0.6323,0.6341,0.6354,0.6361,0.6428,0.6435, 0.6511,0.6529,0.6570,0.6571,0.6592,0.6625,0.6633,0.6669,0.6686,0.6711, 0.6822,0.6833,0.6837,0.6869,0.6874,0.6936,0.6967,0.7056,0.7091,0.7095, 0.7133,0.7154,0.7253,0.7354,0.7393,0.7423,0.7466,0.7473,0.7519,0.7582, 0.7695,0.7787,0.7881,0.7895,0.7967,0.7994,0.8042,0.8072,0.8123,0.8209, 0.8223,0.8231,0.8290,0.8296,0.8375,0.8391,0.8474,0.8516,0.8588,0.8617, 0.8674,0.8722,0.8724,0.8732,0.8834,0.8867,0.8897,0.8904,0.8912,0.8973, 0.9033,0.9052,0.9112,0.9144,0.9152,0.9172,0.9235,0.9239,0.9257,0.9288, 0.9301,0.9313,0.9345,0.9397,0.9416,0.9435,0.9444,0.9473,0.9487,0.9521, 0.9544,0.9609,0.9616,0.9627,0.9661,0.9674,0.9725,0.9754,0.9757,0.9759, 0.9792,0.9793,0.9801,0.9825,0.9939,0.9965,0.9965,0.9986,0.9990, Overall p-value after applying KStest on 269 p-values = 0.143155 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.