RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-08-11_12:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.77 14.0714 0.337958 2 to 25 16.10 23.7779 0.874405 3 to 26 16.00 13.6098 0.305496 4 to 27 15.55 27.8231 0.952952 5 to 28 15.70 15.4340 0.435748 6 to 29 15.76 18.5143 0.642886 7 to 30 15.89 23.3771 0.862628 8 to 31 15.49 21.3148 0.787475 9 to 32 15.43 27.6447 0.950735 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.077381 Tough bday spacings test for dh-ranFile-2015-08-11_12:31: 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 33 74 93 100 84 58 28 11 1 7 (O-E)^2/E 0.4 0.4 0.0 0.2 0.1 0.4 0.7 0.1 1.0 4.8 2.1 Birthday Spacings: Sum(O-E)^2/E= 10.127, p= 0.571 RESULTS OF GCD FOR dh-ranFile-2015-08-11_12:31 Euclid's algorithm: p-value, steps to gcd: 0.328454 p-value, dist. of gcd's: 0.938118 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-08-11_12:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.470 0.102 0.512 0.141 0.074 0.263 0.058 0.113 Bits 8 to 15---> 0.231 0.769 0.092 0.136 0.721 0.800 0.544 0.100 Bits 16 to 23---> 0.316 0.672 0.895 0.761 0.475 0.695 0.346 0.130 Bits 24 to 31---> 0.706 0.417 0.767 0.803 0.351 0.586 0.881 0.648 KS test for the above 32 p values: 0.598 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-08-11_12:31, p-values for 5 runs: 0.3000, 0.7881, 0.7645, 0.9379, 0.9961 Rank test for binary matrices (31x31) for dh-ranFile-2015-08-11_12:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 209 211.4 0.028 0.028 r= 29 5142 5134.0 0.012 0.040 r= 30 23114 23103.0 0.005 0.045 r= 31 11535 11551.5 0.024 0.069 chi-square = 0.069 with df = 3; p-value = 0.005 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-08-11_12:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 199 211.4 0.729 0.729 r= 30 5097 5134.0 0.267 0.996 r= 31 23192 23103.0 0.342 1.339 r= 32 11512 11551.5 0.135 1.474 chi-square = 1.474 with df = 3; p-value = 0.312 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-08-11_12:31 b-rank test for bits 1 to 8, p=0.29748 b-rank test for bits 2 to 9, p=0.12086 b-rank test for bits 3 to 10, p=0.05800 b-rank test for bits 4 to 11, p=0.96430 b-rank test for bits 5 to 12, p=0.88996 b-rank test for bits 6 to 13, p=0.23711 b-rank test for bits 7 to 14, p=0.46359 b-rank test for bits 8 to 15, p=0.29924 b-rank test for bits 9 to 16, p=0.46894 b-rank test for bits 10 to 17, p=0.88917 b-rank test for bits 11 to 18, p=0.49785 b-rank test for bits 12 to 19, p=0.24562 b-rank test for bits 13 to 20, p=0.79900 b-rank test for bits 14 to 21, p=0.44836 b-rank test for bits 15 to 22, p=0.81428 b-rank test for bits 16 to 23, p=0.26196 b-rank test for bits 17 to 24, p=0.61944 b-rank test for bits 18 to 25, p=0.86932 b-rank test for bits 19 to 26, p=0.03590 b-rank test for bits 20 to 27, p=0.35069 b-rank test for bits 21 to 28, p=0.64734 b-rank test for bits 22 to 29, p=0.69693 b-rank test for bits 23 to 30, p=0.34431 b-rank test for bits 24 to 31, p=0.50629 b-rank test for bits 25 to 32, p=0.42025 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 = 0.913688 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-08-11_12:31 (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 141824 -0.20 0.420987 2 141662 -0.58 0.281675 3 142211 0.70 0.759544 4 141954 0.10 0.541562 5 141789 -0.28 0.389300 6 142183 0.64 0.738724 7 142357 1.05 0.852210 8 141952 0.10 0.539707 9 141337 -1.34 0.090575 10 141979 0.16 0.564654 11 141499 -0.96 0.168851 12 142259 0.82 0.793032 13 141959 0.12 0.546194 14 142076 0.39 0.651516 15 141560 -0.82 0.207195 16 142848 2.19 0.985852 17 141807 -0.24 0.405518 18 141514 -0.92 0.177830 19 141850 -0.14 0.444875 20 142990 2.52 0.994214 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-08-11_12:31 Bits used No. missing words z-score p-value 23 to 32 141831 -0.2701 0.393540 22 to 31 141394 -1.7770 0.037784 21 to 30 141942 0.1127 0.544848 20 to 29 141675 -0.8080 0.209535 19 to 28 141751 -0.5460 0.292545 18 to 27 141923 0.0471 0.518798 17 to 26 141888 -0.0736 0.470684 16 to 25 141848 -0.2115 0.416255 15 to 24 141830 -0.2736 0.392215 14 to 23 142063 0.5299 0.701908 13 to 22 142182 0.9402 0.826453 12 to 21 142023 0.3920 0.652458 11 to 20 141752 -0.5425 0.293731 10 to 19 141670 -0.8253 0.204608 9 to 18 141631 -0.9598 0.168588 8 to 17 141926 0.0575 0.522920 7 to 16 142087 0.6127 0.729948 6 to 15 141430 -1.6529 0.049179 5 to 14 141840 -0.2391 0.405526 4 to 13 141843 -0.2287 0.409542 3 to 12 141375 -1.8425 0.032700 2 to 11 141970 0.2092 0.582857 1 to 10 142589 2.3437 0.990453 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-08-11_12:31 Bits used No. missing words z-score p-value 28 to 32 141968 0.1989 0.578822 27 to 31 141734 -0.5943 0.276143 26 to 30 141962 0.1785 0.570852 25 to 29 142048 0.4701 0.680847 24 to 28 141752 -0.5333 0.296905 23 to 27 141928 0.0633 0.525232 22 to 26 141857 -0.1774 0.429601 21 to 25 141624 -0.9672 0.166717 20 to 24 142110 0.6802 0.751823 19 to 23 141543 -1.2418 0.107156 18 to 22 142161 0.8531 0.803203 17 to 21 142080 0.5785 0.718551 16 to 20 142163 0.8599 0.805077 15 to 19 141836 -0.2486 0.401844 14 to 18 142232 1.0938 0.862978 13 to 17 141969 0.2023 0.580148 12 to 16 141879 -0.1028 0.459056 11 to 15 141870 -0.1333 0.446969 10 to 14 141753 -0.5299 0.298080 9 to 13 141722 -0.6350 0.262709 8 to 12 141728 -0.6147 0.269384 7 to 11 142136 0.7684 0.778867 6 to 10 142085 0.5955 0.724243 5 to 9 142004 0.3209 0.625863 4 to 8 142104 0.6599 0.745341 3 to 7 142258 1.1819 0.881384 2 to 6 141893 -0.0554 0.477928 1 to 5 141961 0.1752 0.569520 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-08-11_12:31 Bits used No. missing words z-score p-value 31 to 32 141681 -0.6735 0.250302 30 to 31 141881 -0.0836 0.466699 29 to 30 141874 -0.1042 0.458498 28 to 29 141894 -0.0452 0.481966 27 to 28 142123 0.6303 0.735749 26 to 27 141519 -1.1514 0.124781 25 to 26 141753 -0.4612 0.322345 24 to 25 141756 -0.4523 0.325526 23 to 24 142502 1.7483 0.959793 22 to 23 141538 -1.0954 0.136678 21 to 22 141231 -2.0010 0.022698 20 to 21 141715 -0.5732 0.283240 19 to 20 142725 2.4061 0.991938 18 to 19 141489 -1.2399 0.107504 17 to 18 142255 1.0197 0.846059 16 to 17 141795 -0.3373 0.367962 15 to 16 142062 0.4504 0.673772 14 to 15 142408 1.4710 0.929355 13 to 14 141465 -1.3107 0.094978 12 to 13 141870 -0.1160 0.453819 11 to 12 141978 0.2026 0.580263 10 to 11 141661 -0.7325 0.231921 9 to 10 141328 -1.7148 0.043188 8 to 9 141494 -1.2252 0.110257 7 to 8 142100 0.5624 0.713095 6 to 7 141715 -0.5732 0.283240 5 to 6 141607 -0.8918 0.186242 4 to 5 141782 -0.3756 0.353605 3 to 4 142211 0.8899 0.813235 2 to 3 141753 -0.4612 0.322345 1 to 2 142399 1.4445 0.925694 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-08-11_12:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2473.92 -0.369 0.356136 Test results for specific bytes for dh-ranFile-2015-08-11_12:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2513.85 0.196 0.577619 2 to 9 2519.76 0.279 0.610055 3 to 10 2581.20 1.148 0.874578 4 to 11 2416.68 -1.178 0.119346 5 to 12 2486.09 -0.197 0.422023 6 to 13 2703.94 2.884 0.998037 7 to 14 2420.67 -1.122 0.130955 8 to 15 2602.57 1.451 0.926556 9 to 16 2529.27 0.414 0.660548 10 to 17 2373.14 -1.794 0.036395 11 to 18 2574.50 1.054 0.853974 12 to 19 2472.05 -0.395 0.346327 13 to 20 2535.87 0.507 0.694019 14 to 21 2619.43 1.689 0.954391 15 to 22 2539.85 0.564 0.713470 16 to 23 2385.84 -1.614 0.053212 17 to 24 2514.00 0.198 0.578462 18 to 25 2656.87 2.218 0.986739 19 to 26 2578.60 1.112 0.866841 20 to 27 2441.97 -0.821 0.205903 21 to 28 2574.16 1.049 0.852872 22 to 29 2450.90 -0.694 0.243714 23 to 30 2506.50 0.092 0.536626 24 to 31 2522.83 0.323 0.626580 25 to 32 2421.36 -1.112 0.133049 CDPARK for dh-ranFile-2015-08-11_12:31: 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 3555 1.4612 0.928018 3500 -1.0502 0.146807 3514 -0.4110 0.340551 3534 0.5023 0.692266 3526 0.1370 0.554479 3559 1.6438 0.949895 3507 -0.7306 0.232514 3525 0.0913 0.536383 3526 0.1370 0.554479 3558 1.5982 0.944998 Square side=100, avg. no. parked=3530.40 sample std.=20.02 p-value of the KSTEST for those 10 p-values: 0.433030 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-08-11_12:31 0.3276,0.2525,0.5172,0.1802,0.7340,0.3857,0.8834,0.6664,0.6832,0.2372, The KS test for those 10 p-values: 0.795611 The 3DSPHERES test for dh-ranFile-2015-08-11_12:31 sample no r^3 equiv. uni. 1 3.465 0.109092 2 50.347 0.813297 3 40.882 0.744037 4 21.652 0.514089 5 25.224 0.568632 6 66.498 0.891021 7 10.051 0.284693 8 27.180 0.595862 9 37.638 0.714814 10 10.290 0.290356 11 27.483 0.599930 12 11.100 0.309268 13 31.779 0.653296 14 2.686 0.085629 15 51.590 0.820873 16 13.901 0.370843 17 26.015 0.579857 18 12.111 0.332157 19 33.390 0.671431 20 21.199 0.506694 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.450113 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-08-11_12:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -0.7 0.1 0.2 0.1 1.8 -1.1 -0.9 -1.3 1.0 0.3 0.8 0.1 -0.5 0.5 -0.4 2.0 0.7 1.7 -0.9 -0.9 -0.7 -1.8 0.2 -1.9 0.3 -0.4 0.5 0.8 -0.6 -0.4 -1.3 -1.1 1.7 1.0 -1.2 2.1 0.8 1.3 -0.7 0.1 0.0 -0.1 Chi-square with 42 degrees of freedom:43.540957 z-score=0.168132, p-value=0.594339 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-08-11_12:31 Test no p-value 1 0.380571 2 0.784205 3 0.514001 4 0.790738 5 0.007836 6 0.340288 7 0.371038 8 0.479657 9 0.204504 10 0.918714 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.849563 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-08-11_12:31: (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 66744 0.09 66840 0.45 3 25000.00 24960 0.06 24830 1.16 4 6666.67 6580 1.13 6626 0.25 5 1388.89 1419 0.65 1433 1.40 6 238.10 257 1.50 236 0.02 7 34.72 36 0.05 32 0.21 8 4.96 3 0.77 2 1.77 p=0.35792 p=0.48828 Number of rngs required: 688630, p-value: 0.603 RESULTS OF CRAPS TEST for dh-ranFile-2015-08-11_12:31 No. of wins: Observed Expected 98361 98585.9 z-score=-1.006, pvalue=0.15728 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66650 66666.7 0.004 0.004 2 37674 37654.3 0.010 0.014 3 27224 26954.7 2.690 2.704 4 19437 19313.5 0.790 3.495 5 13612 13851.4 4.138 7.633 6 9938 9943.5 0.003 7.636 7 6942 7145.0 5.769 13.405 8 5146 5139.1 0.009 13.414 9 3659 3699.9 0.451 13.866 10 2683 2666.3 0.105 13.970 11 1927 1923.3 0.007 13.977 12 1417 1388.7 0.575 14.552 13 1033 1003.7 0.854 15.407 14 714 726.1 0.203 15.610 15 514 525.8 0.266 15.876 16 383 381.2 0.009 15.885 17 266 276.5 0.402 16.287 18 183 200.8 1.583 17.870 19 165 146.0 2.477 20.347 20 112 106.2 0.315 20.662 21 321 287.1 3.999 24.661 Chisq= 24.66 for 20 degrees of freedom, p= 0.78529 SUMMARY of craptest p-value for no. of wins: 0.157280 p-value for throws/game: 0.785294 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-08-11_12:31 No. of wins: Observed Expected 98547 98585.9 z-score=-0.174, pvalue=0.43101 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66937 66666.7 1.096 1.096 2 37656 37654.3 0.000 1.096 3 27031 26954.7 0.216 1.312 4 19019 19313.5 4.490 5.802 5 13767 13851.4 0.515 6.316 6 10001 9943.5 0.332 6.648 7 7049 7145.0 1.291 7.939 8 5180 5139.1 0.326 8.265 9 3790 3699.9 2.196 10.460 10 2657 2666.3 0.032 10.493 11 1929 1923.3 0.017 10.510 12 1381 1388.7 0.043 10.553 13 1021 1003.7 0.298 10.850 14 700 726.1 0.941 11.791 15 529 525.8 0.019 11.810 16 389 381.2 0.162 11.972 17 255 276.5 1.678 13.650 18 190 200.8 0.584 14.234 19 159 146.0 1.160 15.394 20 83 106.2 5.074 20.468 21 277 287.1 0.356 20.825 Chisq= 20.82 for 20 degrees of freedom, p= 0.59248 SUMMARY of craptest p-value for no. of wins: 0.431012 p-value for throws/game: 0.592482 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0047,0.0078,0.0227,0.0327,0.0359,0.0364,0.0378,0.0432,0.0492,0.0532, 0.0577,0.0580,0.0735,0.0774,0.0856,0.0906,0.0917,0.0950,0.1002,0.1016, 0.1072,0.1075,0.1091,0.1103,0.1131,0.1193,0.1209,0.1248,0.1296,0.1310, 0.1330,0.1355,0.1367,0.1411,0.1468,0.1573,0.1667,0.1686,0.1689,0.1778, 0.1802,0.1862,0.2045,0.2046,0.2059,0.2072,0.2095,0.2310,0.2319,0.2325, 0.2371,0.2372,0.2437,0.2456,0.2503,0.2525,0.2620,0.2626,0.2627,0.2694, 0.2761,0.2817,0.2832,0.2832,0.2847,0.2904,0.2925,0.2937,0.2969,0.2975, 0.2981,0.2992,0.3000,0.3055,0.3093,0.3117,0.3159,0.3223,0.3223,0.3255, 0.3276,0.3285,0.3322,0.3380,0.3403,0.3406,0.3443,0.3459,0.3463,0.3507, 0.3511,0.3536,0.3561,0.3579,0.3680,0.3708,0.3710,0.3806,0.3857,0.3893, 0.3922,0.3935,0.4018,0.4055,0.4055,0.4095,0.4163,0.4166,0.4202,0.4210, 0.4220,0.4296,0.4310,0.4330,0.4357,0.4449,0.4470,0.4484,0.4501,0.4538, 0.4585,0.4591,0.4636,0.4667,0.4689,0.4697,0.4707,0.4750,0.4779,0.4797, 0.4820,0.4883,0.4979,0.5063,0.5067,0.5120,0.5140,0.5141,0.5172,0.5188, 0.5229,0.5252,0.5364,0.5366,0.5397,0.5416,0.5441,0.5448,0.5462,0.5545, 0.5545,0.5647,0.5686,0.5695,0.5706,0.5709,0.5776,0.5785,0.5788,0.5799, 0.5801,0.5803,0.5829,0.5864,0.5925,0.5943,0.5959,0.5979,0.5999,0.6030, 0.6101,0.6194,0.6259,0.6266,0.6429,0.6473,0.6481,0.6515,0.6525,0.6533, 0.6605,0.6664,0.6714,0.6719,0.6738,0.6808,0.6832,0.6923,0.6940,0.6948, 0.6969,0.7019,0.7059,0.7131,0.7135,0.7148,0.7186,0.7209,0.7242,0.7299, 0.7340,0.7357,0.7387,0.7440,0.7453,0.7518,0.7595,0.7615,0.7645,0.7670, 0.7688,0.7789,0.7842,0.7853,0.7875,0.7881,0.7907,0.7930,0.7956,0.7990, 0.7998,0.8029,0.8032,0.8051,0.8132,0.8133,0.8143,0.8209,0.8265,0.8461, 0.8496,0.8522,0.8529,0.8540,0.8626,0.8630,0.8668,0.8693,0.8744,0.8746, 0.8808,0.8814,0.8834,0.8892,0.8900,0.8910,0.8948,0.9137,0.9187,0.9257, 0.9266,0.9280,0.9294,0.9379,0.9381,0.9450,0.9499,0.9507,0.9530,0.9544, 0.9598,0.9643,0.9859,0.9867,0.9905,0.9919,0.9942,0.9961,0.9980, Overall p-value after applying KStest on 269 p-values = 0.397929 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.