RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-04_01:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.88 12.3286 0.220153 2 to 25 15.64 26.1020 0.927377 3 to 26 16.10 14.6778 0.381326 4 to 27 15.84 13.9466 0.329119 5 to 28 15.44 22.5909 0.836951 6 to 29 15.72 1653268998690766848.0000 1.000000 7 to 30 15.75 15.4422 0.436336 8 to 31 15.94 21.7332 0.804802 9 to 32 15.96 18.6549 0.651301 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.001700 Tough bday spacings test for dh-ranFile-2018-07-04_01:31: 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 3 35 62 110 102 80 47 32 19 9 1 (O-E)^2/E 4.1 0.1 1.7 1.6 0.2 0.0 0.5 0.2 1.1 0.9 2.3 Birthday Spacings: Sum(O-E)^2/E= 12.707, p= 0.759 RESULTS OF GCD FOR dh-ranFile-2018-07-04_01:31 Euclid's algorithm: p-value, steps to gcd: 0.111234 p-value, dist. of gcd's: 0.675509 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-04_01:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.409 0.536 0.560 0.474 0.334 0.201 0.116 0.549 Bits 8 to 15---> 0.908 0.479 0.282 0.370 0.529 0.707 0.187 0.326 Bits 16 to 23---> 0.242 0.539 0.877 0.724 0.591 0.674 0.037 0.748 Bits 24 to 31---> 0.292 0.198 0.676 0.115 0.008 0.962 0.700 0.111 KS test for the above 32 p values: 0.498 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-04_01:31, p-values for 5 runs: 0.6886, 0.5748, 0.8898, 0.0921, 0.5996 Rank test for binary matrices (31x31) for dh-ranFile-2018-07-04_01:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 229 211.4 1.462 1.462 r= 29 5088 5134.0 0.412 1.875 r= 30 23161 23103.0 0.145 2.020 r= 31 11522 11551.5 0.075 2.095 chi-square = 2.095 with df = 3; p-value = 0.447 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-07-04_01:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 204 211.4 0.260 0.260 r= 30 5051 5134.0 1.342 1.602 r= 31 23235 23103.0 0.754 2.356 r= 32 11510 11551.5 0.149 2.505 chi-square = 2.505 with df = 3; p-value = 0.526 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-07-04_01:31 b-rank test for bits 1 to 8, p=0.09129 b-rank test for bits 2 to 9, p=0.30546 b-rank test for bits 3 to 10, p=0.21260 b-rank test for bits 4 to 11, p=0.03577 b-rank test for bits 5 to 12, p=0.42062 b-rank test for bits 6 to 13, p=0.82905 b-rank test for bits 7 to 14, p=0.40024 b-rank test for bits 8 to 15, p=0.46893 b-rank test for bits 9 to 16, p=0.54901 b-rank test for bits 10 to 17, p=0.16762 b-rank test for bits 11 to 18, p=0.28360 b-rank test for bits 12 to 19, p=0.18178 b-rank test for bits 13 to 20, p=0.34399 b-rank test for bits 14 to 21, p=0.51549 b-rank test for bits 15 to 22, p=0.33048 b-rank test for bits 16 to 23, p=0.00506 b-rank test for bits 17 to 24, p=0.20251 b-rank test for bits 18 to 25, p=0.92468 b-rank test for bits 19 to 26, p=0.62699 b-rank test for bits 20 to 27, p=0.78062 b-rank test for bits 21 to 28, p=0.62540 b-rank test for bits 22 to 29, p=0.49947 b-rank test for bits 23 to 30, p=0.30095 b-rank test for bits 24 to 31, p=0.67035 b-rank test for bits 25 to 32, p=0.84175 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 = 0.298236 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-04_01:31 (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 141774 -0.32 0.375929 2 141922 0.03 0.511808 3 142266 0.83 0.797674 4 142090 0.42 0.663534 5 142007 0.23 0.590255 6 142849 2.20 0.985936 7 141631 -0.65 0.257748 8 141542 -0.86 0.195378 9 142262 0.82 0.795029 10 141711 -0.46 0.321543 11 142879 2.27 0.988262 12 141671 -0.56 0.288816 13 142204 0.69 0.754425 14 142068 0.37 0.644579 15 141699 -0.49 0.311563 16 142108 0.46 0.678741 17 141868 -0.10 0.461536 18 142075 0.39 0.650651 19 141680 -0.54 0.296042 20 141868 -0.10 0.461536 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-07-04_01:31 Bits used No. missing words z-score p-value 23 to 32 142095 0.6402 0.738992 22 to 31 141840 -0.2391 0.405526 21 to 30 142070 0.5540 0.710222 20 to 29 141965 0.1920 0.576115 19 to 28 142016 0.3678 0.643499 18 to 27 141661 -0.8563 0.195913 17 to 26 142007 0.3368 0.631864 16 to 25 141426 -1.6667 0.047792 15 to 24 142296 1.3333 0.908791 14 to 23 141886 -0.0804 0.467940 13 to 22 141504 -1.3977 0.081103 12 to 21 141821 -0.3046 0.380341 11 to 20 141855 -0.1873 0.425695 10 to 19 141455 -1.5667 0.058598 9 to 18 141733 -0.6080 0.271582 8 to 17 142144 0.8092 0.790802 7 to 16 141595 -1.0839 0.139205 6 to 15 141880 -0.1011 0.459721 5 to 14 142279 1.2747 0.898797 4 to 13 141694 -0.7425 0.228887 3 to 12 142221 1.0747 0.858751 2 to 11 141906 -0.0115 0.495419 1 to 10 141967 0.1989 0.578815 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-07-04_01:31 Bits used No. missing words z-score p-value 28 to 32 141986 0.2599 0.602529 27 to 31 141380 -1.7943 0.036380 26 to 30 141670 -0.8113 0.208600 25 to 29 142153 0.8260 0.795598 24 to 28 141971 0.2091 0.582796 23 to 27 141859 -0.1706 0.432265 22 to 26 141606 -1.0282 0.151919 21 to 25 142140 0.7819 0.782873 20 to 24 142115 0.6972 0.757157 19 to 23 141988 0.2667 0.605141 18 to 22 142072 0.5514 0.709328 17 to 21 142122 0.7209 0.764519 16 to 20 141591 -1.0791 0.140275 15 to 19 141975 0.2226 0.588081 14 to 18 141850 -0.2011 0.420303 13 to 17 142018 0.3684 0.643702 12 to 16 141682 -0.7706 0.220469 11 to 15 142128 0.7413 0.770730 10 to 14 142213 1.0294 0.848352 9 to 13 141394 -1.7469 0.040329 8 to 12 141754 -0.5265 0.299256 7 to 11 142080 0.5785 0.718551 6 to 10 141639 -0.9164 0.179736 5 to 9 141813 -0.3265 0.372007 4 to 8 142253 1.1650 0.877987 3 to 7 141886 -0.0791 0.468483 2 to 6 142243 1.1311 0.870990 1 to 5 142053 0.4870 0.686877 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-07-04_01:31 Bits used No. missing words z-score p-value 31 to 32 142037 0.3766 0.646767 30 to 31 142365 1.3442 0.910552 29 to 30 141812 -0.2871 0.387014 28 to 29 142069 0.4710 0.681181 27 to 28 141432 -1.4081 0.079558 26 to 27 141880 -0.0865 0.465527 25 to 26 141853 -0.1662 0.434014 24 to 25 141385 -1.5467 0.060968 23 to 24 141672 -0.7001 0.241936 22 to 23 141921 0.0344 0.513731 21 to 22 141420 -1.4435 0.074447 20 to 21 141373 -1.5821 0.056814 19 to 20 141758 -0.4464 0.327654 18 to 19 142099 0.5595 0.712089 17 to 18 141940 0.0905 0.536044 16 to 17 142283 1.1023 0.864828 15 to 16 141956 0.1377 0.554749 14 to 15 142156 0.7276 0.766583 13 to 14 141732 -0.5231 0.300453 12 to 13 141881 -0.0836 0.466699 11 to 12 141976 0.1967 0.577956 10 to 11 142432 1.5418 0.938439 9 to 10 141515 -1.1632 0.122371 8 to 9 141829 -0.2370 0.406343 7 to 8 141403 -1.4936 0.067640 6 to 7 141703 -0.6086 0.271381 5 to 6 141988 0.2321 0.591756 4 to 5 141887 -0.0659 0.473741 3 to 4 142397 1.4386 0.924862 2 to 3 141616 -0.8653 0.193443 1 to 2 141333 -1.7001 0.044557 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-04_01:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2588.13 1.246 0.893673 Test results for specific bytes for dh-ranFile-2018-07-04_01:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2382.04 -1.668 0.047631 2 to 9 2396.07 -1.470 0.070809 3 to 10 2447.04 -0.749 0.226922 4 to 11 2507.51 0.106 0.542291 5 to 12 2616.81 1.652 0.950721 6 to 13 2459.63 -0.571 0.284023 7 to 14 2364.00 -1.923 0.027218 8 to 15 2525.55 0.361 0.641056 9 to 16 2540.58 0.574 0.716971 10 to 17 2399.42 -1.422 0.077460 11 to 18 2570.12 0.992 0.839331 12 to 19 2452.21 -0.676 0.249576 13 to 20 2459.14 -0.578 0.281685 14 to 21 2610.41 1.561 0.940790 15 to 22 2477.67 -0.316 0.376067 16 to 23 2438.62 -0.868 0.192702 17 to 24 2597.57 1.380 0.916176 18 to 25 2543.76 0.619 0.732004 19 to 26 2315.30 -2.612 0.004500 20 to 27 2398.69 -1.433 0.075957 21 to 28 2496.89 -0.044 0.482464 22 to 29 2481.52 -0.261 0.396906 23 to 30 2473.39 -0.376 0.353352 24 to 31 2432.51 -0.954 0.169928 25 to 32 2468.97 -0.439 0.330405 CDPARK for dh-ranFile-2018-07-04_01:31: 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 3541 0.8219 0.794438 3518 -0.2283 0.409702 3516 -0.3196 0.374623 3491 -1.4612 0.071982 3516 -0.3196 0.374623 3560 1.6895 0.954438 3527 0.1826 0.572463 3509 -0.6393 0.261324 3527 0.1826 0.572463 3527 0.1826 0.572463 Square side=100, avg. no. parked=3523.20 sample std.=17.56 p-value of the KSTEST for those 10 p-values: 0.827469 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-04_01:31 0.7729,0.7665,0.8969,0.2036,0.2316,0.5793,0.7663,0.1930,0.4738,0.3996, The KS test for those 10 p-values: 0.815398 The 3DSPHERES test for dh-ranFile-2018-07-04_01:31 sample no r^3 equiv. uni. 1 16.033 0.413991 2 1.025 0.033579 3 11.784 0.324846 4 28.189 0.609230 5 60.504 0.866919 6 31.553 0.650685 7 6.087 0.183650 8 15.611 0.405694 9 12.218 0.334529 10 34.079 0.678887 11 30.236 0.635001 12 25.838 0.577370 13 28.600 0.614546 14 65.384 0.886898 15 13.194 0.355833 16 13.558 0.363603 17 16.737 0.427590 18 69.686 0.902009 19 0.268 0.008897 20 66.118 0.889634 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.689312 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-04_01:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.1 0.3 1.2 -0.6 0.3 -1.4 0.7 -0.1 0.0 -1.6 -0.5 -0.2 -0.3 -0.7 2.5 -1.0 -0.5 -1.2 -0.9 -0.5 2.5 -0.8 1.2 1.1 0.1 0.2 -0.1 1.5 0.4 0.8 1.2 -0.1 0.2 -1.3 1.9 -1.2 0.2 -0.8 -0.1 0.1 0.0 -0.1 Chi-square with 42 degrees of freedom:39.392473 z-score=-0.284505, p-value=0.413943 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-07-04_01:31 Test no p-value 1 0.450119 2 0.462629 3 0.417783 4 0.003613 5 0.485907 6 0.011608 7 0.091652 8 0.942872 9 0.545616 10 0.478290 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.110091 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-04_01:31: (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 66942 1.14 66560 0.17 3 25000.00 24907 0.35 25069 0.19 4 6666.67 6542 2.33 6749 1.02 5 1388.89 1353 0.93 1355 0.83 6 238.10 226 0.61 231 0.21 7 34.72 22 4.66 31 0.40 8 4.96 7 0.84 4 0.19 p=0.90705 p=0.19123 Number of rngs required: 688283, p-value: 0.445 RESULTS OF CRAPS TEST for dh-ranFile-2018-07-04_01:31 No. of wins: Observed Expected 98487 98585.9 z-score=-0.442, pvalue=0.32919 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67067 66666.7 2.404 2.404 2 37570 37654.3 0.189 2.593 3 26674 26954.7 2.924 5.517 4 19234 19313.5 0.327 5.844 5 13641 13851.4 3.197 9.040 6 9893 9943.5 0.257 9.297 7 7139 7145.0 0.005 9.302 8 5250 5139.1 2.394 11.697 9 3847 3699.9 5.851 17.548 10 2675 2666.3 0.028 17.576 11 1936 1923.3 0.083 17.660 12 1440 1388.7 1.892 19.552 13 969 1003.7 1.201 20.752 14 743 726.1 0.391 21.144 15 506 525.8 0.748 21.892 16 385 381.2 0.039 21.931 17 293 276.5 0.980 22.911 18 199 200.8 0.017 22.927 19 146 146.0 0.000 22.927 20 103 106.2 0.097 23.025 21 290 287.1 0.029 23.054 Chisq= 23.05 for 20 degrees of freedom, p= 0.71383 SUMMARY of craptest p-value for no. of wins: 0.329189 p-value for throws/game: 0.713834 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-04_01:31 No. of wins: Observed Expected 98278 98585.9 z-score=-1.377, pvalue=0.08427 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67119 66666.7 3.069 3.069 2 37458 37654.3 1.024 4.093 3 26973 26954.7 0.012 4.105 4 19088 19313.5 2.632 6.737 5 13869 13851.4 0.022 6.759 6 9989 9943.5 0.208 6.967 7 7155 7145.0 0.014 6.981 8 5070 5139.1 0.928 7.909 9 3665 3699.9 0.329 8.238 10 2593 2666.3 2.015 10.253 11 1886 1923.3 0.725 10.977 12 1439 1388.7 1.819 12.796 13 1009 1003.7 0.028 12.824 14 742 726.1 0.346 13.171 15 550 525.8 1.110 14.281 16 365 381.2 0.684 14.965 17 290 276.5 0.655 15.621 18 184 200.8 1.410 17.031 19 148 146.0 0.028 17.059 20 106 106.2 0.000 17.059 21 302 287.1 0.772 17.831 Chisq= 17.83 for 20 degrees of freedom, p= 0.40146 SUMMARY of craptest p-value for no. of wins: 0.084268 p-value for throws/game: 0.401462 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0017,0.0036,0.0045,0.0051,0.0081,0.0089,0.0116,0.0272,0.0336,0.0358, 0.0364,0.0369,0.0403,0.0446,0.0476,0.0478,0.0568,0.0586,0.0610,0.0676, 0.0708,0.0720,0.0744,0.0760,0.0775,0.0796,0.0811,0.0843,0.0913,0.0917, 0.0921,0.1101,0.1107,0.1112,0.1147,0.1163,0.1224,0.1392,0.1403,0.1519, 0.1676,0.1699,0.1797,0.1818,0.1837,0.1867,0.1912,0.1927,0.1930,0.1934, 0.1954,0.1959,0.1976,0.2013,0.2025,0.2036,0.2086,0.2126,0.2202,0.2205, 0.2269,0.2289,0.2316,0.2419,0.2421,0.2496,0.2577,0.2613,0.2714,0.2716, 0.2817,0.2819,0.2836,0.2840,0.2888,0.2919,0.2960,0.2982,0.2993,0.3005, 0.3010,0.3055,0.3116,0.3215,0.3248,0.3262,0.3277,0.3291,0.3292,0.3304, 0.3305,0.3345,0.3345,0.3440,0.3534,0.3558,0.3636,0.3699,0.3720,0.3746, 0.3746,0.3759,0.3761,0.3803,0.3813,0.3870,0.3969,0.3996,0.4002,0.4015, 0.4055,0.4057,0.4063,0.4090,0.4097,0.4139,0.4140,0.4178,0.4203,0.4206, 0.4257,0.4276,0.4323,0.4340,0.4363,0.4451,0.4471,0.4501,0.4597,0.4615, 0.4615,0.4626,0.4655,0.4667,0.4679,0.4685,0.4689,0.4737,0.4738,0.4745, 0.4783,0.4788,0.4825,0.4859,0.4954,0.4983,0.4995,0.5118,0.5137,0.5155, 0.5257,0.5293,0.5356,0.5360,0.5394,0.5423,0.5456,0.5490,0.5492,0.5547, 0.5601,0.5725,0.5725,0.5725,0.5748,0.5761,0.5774,0.5780,0.5788,0.5793, 0.5828,0.5881,0.5903,0.5910,0.5918,0.5996,0.6025,0.6051,0.6092,0.6145, 0.6254,0.6270,0.6319,0.6350,0.6411,0.6435,0.6437,0.6446,0.6468,0.6507, 0.6507,0.6513,0.6635,0.6704,0.6739,0.6755,0.6763,0.6787,0.6789,0.6812, 0.6869,0.6886,0.6893,0.7003,0.7066,0.7093,0.7102,0.7121,0.7138,0.7170, 0.7186,0.7240,0.7320,0.7390,0.7483,0.7544,0.7572,0.7595,0.7645,0.7663, 0.7665,0.7666,0.7707,0.7729,0.7806,0.7829,0.7908,0.7944,0.7950,0.7956, 0.7977,0.8048,0.8154,0.8275,0.8290,0.8370,0.8393,0.8417,0.8484,0.8588, 0.8648,0.8669,0.8710,0.8766,0.8780,0.8869,0.8896,0.8898,0.8937,0.8969, 0.8988,0.9020,0.9071,0.9084,0.9088,0.9106,0.9162,0.9247,0.9249,0.9274, 0.9384,0.9408,0.9429,0.9507,0.9544,0.9622,0.9859,0.9883,1.0000, Overall p-value after applying KStest on 269 p-values = 0.095231 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.