RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-02-18_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 15.77 11.5772 0.174966 2 to 25 15.77 8.0099 0.033666 3 to 26 15.43 21.2074 0.782849 4 to 27 15.50 20.5187 0.751438 5 to 28 16.03 22.8153 0.844640 6 to 29 15.48 20.7210 0.760979 7 to 30 15.45 38.1944 0.997689 8 to 31 15.69 22.6412 0.838700 9 to 32 15.53 28.5605 0.961199 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.027797 Tough bday spacings test for dh-ranFile-2016-02-18_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 9 34 80 107 93 68 56 27 16 6 4 (O-E)^2/E 0.0 0.2 0.6 0.9 0.2 1.3 0.3 0.3 0.1 0.1 0.0 Birthday Spacings: Sum(O-E)^2/E= 3.934, p= 0.050 RESULTS OF GCD FOR dh-ranFile-2016-02-18_10:31 Euclid's algorithm: p-value, steps to gcd: 0.989914 p-value, dist. of gcd's: 0.464604 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-02-18_10:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.564 0.759 0.467 0.589 0.629 0.472 0.134 0.547 Bits 8 to 15---> 0.784 0.679 0.675 0.117 0.367 0.481 0.349 0.697 Bits 16 to 23---> 0.156 0.314 0.298 0.125 0.705 0.455 0.479 0.078 Bits 24 to 31---> 0.180 0.056 0.964 0.737 0.288 0.996 0.207 0.153 KS test for the above 32 p values: 0.589 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-02-18_10:31, p-values for 5 runs: 0.9413, 0.9917, 0.8358, 0.7905, 0.8112 Rank test for binary matrices (31x31) for dh-ranFile-2016-02-18_10:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 215 211.4 0.061 0.061 r= 29 5052 5134.0 1.310 1.371 r= 30 23095 23103.0 0.003 1.374 r= 31 11638 11551.5 0.647 2.021 chi-square = 2.021 with df = 3; p-value = 0.432 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-02-18_10:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 207 211.4 0.092 0.092 r= 30 5266 5134.0 3.393 3.486 r= 31 23026 23103.0 0.257 3.743 r= 32 11501 11551.5 0.221 3.964 chi-square = 3.964 with df = 3; p-value = 0.735 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-02-18_10:31 b-rank test for bits 1 to 8, p=0.51390 b-rank test for bits 2 to 9, p=0.58774 b-rank test for bits 3 to 10, p=0.57649 b-rank test for bits 4 to 11, p=0.96765 b-rank test for bits 5 to 12, p=0.09335 b-rank test for bits 6 to 13, p=0.36455 b-rank test for bits 7 to 14, p=0.43792 b-rank test for bits 8 to 15, p=0.78037 b-rank test for bits 9 to 16, p=0.08012 b-rank test for bits 10 to 17, p=0.26165 b-rank test for bits 11 to 18, p=0.64497 b-rank test for bits 12 to 19, p=0.03169 b-rank test for bits 13 to 20, p=0.02359 b-rank test for bits 14 to 21, p=0.20874 b-rank test for bits 15 to 22, p=0.57681 b-rank test for bits 16 to 23, p=0.45389 b-rank test for bits 17 to 24, p=0.75788 b-rank test for bits 18 to 25, p=0.95173 b-rank test for bits 19 to 26, p=0.14694 b-rank test for bits 20 to 27, p=0.68956 b-rank test for bits 21 to 28, p=0.25068 b-rank test for bits 22 to 29, p=0.91588 b-rank test for bits 23 to 30, p=0.07784 b-rank test for bits 24 to 31, p=0.82385 b-rank test for bits 25 to 32, p=0.06583 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 = 0.543302 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-02-18_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 141365 -1.27 0.101722 2 142234 0.76 0.775947 3 142000 0.21 0.583886 4 141648 -0.61 0.270738 5 142411 1.17 0.879427 6 141935 0.06 0.523913 7 141532 -0.88 0.188993 8 142157 0.58 0.718594 9 142050 0.33 0.628797 10 142407 1.16 0.877541 11 142074 0.38 0.649786 12 142268 0.84 0.798989 13 140664 -2.91 0.001809 14 141075 -1.95 0.025626 15 141683 -0.53 0.298469 16 141638 -0.63 0.263057 17 141423 -1.14 0.127919 18 142015 0.25 0.597504 19 142674 1.79 0.963000 20 141587 -0.75 0.225693 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-02-18_10:31 Bits used No. missing words z-score p-value 23 to 32 141445 -1.6011 0.054673 22 to 31 141772 -0.4736 0.317910 21 to 30 142053 0.4954 0.689846 20 to 29 141773 -0.4701 0.319141 19 to 28 141809 -0.3460 0.364684 18 to 27 141288 -2.1425 0.016076 17 to 26 141981 0.2471 0.597599 16 to 25 142041 0.4540 0.675098 15 to 24 141675 -0.8080 0.209535 14 to 23 142188 0.9609 0.831707 13 to 22 142193 0.9782 0.836006 12 to 21 142036 0.4368 0.668869 11 to 20 142087 0.6127 0.729948 10 to 19 142165 0.8816 0.811009 9 to 18 141693 -0.7460 0.227844 8 to 17 141990 0.2782 0.609560 7 to 16 142020 0.3816 0.648629 6 to 15 142025 0.3989 0.655003 5 to 14 141796 -0.3908 0.347975 4 to 13 141877 -0.1115 0.455617 3 to 12 141620 -0.9977 0.159215 2 to 11 141851 -0.2011 0.420295 1 to 10 141670 -0.8253 0.204608 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-02-18_10:31 Bits used No. missing words z-score p-value 28 to 32 141959 0.1684 0.566855 27 to 31 142315 1.3752 0.915458 26 to 30 141890 -0.0655 0.473878 25 to 29 142032 0.4158 0.661233 24 to 28 142203 0.9955 0.840251 23 to 27 141868 -0.1401 0.444290 22 to 26 142317 1.3819 0.916504 21 to 25 142556 2.1921 0.985814 20 to 24 141331 -1.9604 0.024972 19 to 23 141880 -0.0994 0.460401 18 to 22 141953 0.1480 0.558842 17 to 21 141288 -2.1062 0.017593 16 to 20 141690 -0.7435 0.228592 15 to 19 142458 1.8599 0.968550 14 to 18 141843 -0.2248 0.411049 13 to 17 142150 0.8158 0.792702 12 to 16 141452 -1.5503 0.060538 11 to 15 141869 -0.1367 0.445629 10 to 14 142140 0.7819 0.782873 9 to 13 142189 0.9480 0.828444 8 to 12 141544 -1.2384 0.107783 7 to 11 142246 1.1413 0.873118 6 to 10 142328 1.4192 0.922083 5 to 9 141430 -1.6248 0.052098 4 to 8 141407 -1.7028 0.044301 3 to 7 142035 0.4260 0.664946 2 to 6 141372 -1.8215 0.034269 1 to 5 141756 -0.5198 0.301615 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-02-18_10:31 Bits used No. missing words z-score p-value 31 to 32 141557 -1.0393 0.149328 30 to 31 141508 -1.1839 0.118233 29 to 30 142278 1.0875 0.861597 28 to 29 141892 -0.0511 0.479615 27 to 28 141813 -0.2842 0.388144 26 to 27 141689 -0.6499 0.257865 25 to 26 142516 1.7896 0.963240 24 to 25 142144 0.6922 0.755607 23 to 24 141915 0.0167 0.506672 22 to 23 142003 0.2763 0.608846 21 to 22 141632 -0.8181 0.206655 20 to 21 141848 -0.1809 0.428217 19 to 20 141944 0.1023 0.540729 18 to 19 142138 0.6745 0.750017 17 to 18 141629 -0.8269 0.204138 16 to 17 142151 0.7129 0.762043 15 to 16 142172 0.7748 0.780782 14 to 15 141585 -0.9567 0.169353 13 to 14 142207 0.8781 0.810051 12 to 13 141865 -0.1308 0.447980 11 to 12 142242 0.9813 0.836784 10 to 11 141943 0.0993 0.539559 9 to 10 142404 1.4592 0.927745 8 to 9 141487 -1.2458 0.106417 7 to 8 141683 -0.6676 0.252182 6 to 7 141710 -0.5880 0.278268 5 to 6 142095 0.5477 0.708051 4 to 5 141763 -0.4317 0.332997 3 to 4 141890 -0.0570 0.477264 2 to 3 141945 0.1052 0.541900 1 to 2 142116 0.6096 0.728952 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-02-18_10:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2370.70 -1.829 0.033729 Test results for specific bytes for dh-ranFile-2016-02-18_10:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2407.66 -1.306 0.095798 2 to 9 2670.34 2.409 0.992000 3 to 10 2394.15 -1.497 0.067198 4 to 11 2423.00 -1.089 0.138081 5 to 12 2559.62 0.843 0.800446 6 to 13 2464.07 -0.508 0.305691 7 to 14 2519.35 0.274 0.607818 8 to 15 2554.78 0.775 0.780749 9 to 16 2545.48 0.643 0.739957 10 to 17 2524.80 0.351 0.637092 11 to 18 2520.76 0.294 0.615467 12 to 19 2446.84 -0.752 0.226104 13 to 20 2440.63 -0.840 0.200570 14 to 21 2548.46 0.685 0.753419 15 to 22 2475.93 -0.340 0.366764 16 to 23 2405.40 -1.338 0.090474 17 to 24 2443.00 -0.806 0.210074 18 to 25 2512.78 0.181 0.571737 19 to 26 2451.35 -0.688 0.245720 20 to 27 2431.44 -0.970 0.166114 21 to 28 2555.71 0.788 0.784602 22 to 29 2393.14 -1.511 0.065360 23 to 30 2547.20 0.668 0.747792 24 to 31 2509.27 0.131 0.552176 25 to 32 2525.85 0.366 0.642656 CDPARK for dh-ranFile-2016-02-18_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 3530 0.3196 0.625377 3531 0.3653 0.642555 3496 -1.2329 0.108811 3532 0.4110 0.659449 3527 0.1826 0.572463 3538 0.6849 0.753306 3534 0.5023 0.692266 3518 -0.2283 0.409702 3506 -0.7763 0.218799 3502 -0.9589 0.168804 Square side=100, avg. no. parked=3521.40 sample std.=14.19 p-value of the KSTEST for those 10 p-values: 0.575060 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-02-18_10:31 0.8750,0.8633,0.9559,0.3922,0.8201,0.7270,0.2796,0.4271,0.2869,0.2428, The KS test for those 10 p-values: 0.436925 The 3DSPHERES test for dh-ranFile-2016-02-18_10:31 sample no r^3 equiv. uni. 1 46.799 0.789856 2 15.231 0.398114 3 22.904 0.533948 4 49.863 0.810260 5 10.035 0.284297 6 16.931 0.431278 7 55.435 0.842420 8 21.576 0.512852 9 5.161 0.158051 10 5.853 0.177237 11 23.174 0.538134 12 37.889 0.717190 13 44.515 0.773232 14 69.742 0.902192 15 23.075 0.536604 16 8.273 0.241001 17 65.685 0.888027 18 10.823 0.302849 19 2.566 0.081982 20 24.102 0.552191 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.775726 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-02-18_10:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -0.7 0.6 -1.9 0.9 -2.1 0.6 0.9 1.4 -0.5 -0.6 -0.2 1.3 -1.0 0.3 0.3 0.9 1.0 0.4 -2.3 1.6 -0.3 0.9 -0.9 -2.1 0.2 -0.3 -0.8 0.1 -0.0 -1.3 0.2 -0.2 0.4 -1.3 -0.8 0.0 1.1 -0.4 0.4 0.1 -1.0 -0.1 Chi-square with 42 degrees of freedom:39.509421 z-score=-0.271744, p-value=0.419128 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-02-18_10:31 Test no p-value 1 0.182971 2 0.594026 3 0.866267 4 0.408647 5 0.347196 6 0.555046 7 0.058734 8 0.007279 9 0.072377 10 0.629660 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.220395 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-02-18_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 66499 0.42 66600 0.07 3 25000.00 24956 0.08 25104 0.43 4 6666.67 6828 3.90 6667 0.00 5 1388.89 1433 1.40 1347 1.26 6 238.10 258 1.66 240 0.02 7 34.72 21 5.42 32 0.21 8 4.96 4 0.19 9 3.29 p=0.95815 p=0.49178 Number of rngs required: 688925, p-value: 0.726 RESULTS OF CRAPS TEST for dh-ranFile-2016-02-18_10:31 No. of wins: Observed Expected 98567 98585.9 z-score=-0.084, pvalue=0.46639 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66444 66666.7 0.744 0.744 2 37763 37654.3 0.314 1.057 3 27027 26954.7 0.194 1.251 4 19227 19313.5 0.387 1.638 5 13914 13851.4 0.283 1.921 6 9912 9943.5 0.100 2.021 7 7207 7145.0 0.538 2.559 8 5049 5139.1 1.579 4.137 9 3762 3699.9 1.043 5.181 10 2665 2666.3 0.001 5.181 11 1954 1923.3 0.489 5.670 12 1402 1388.7 0.127 5.797 13 969 1003.7 1.201 6.998 14 768 726.1 2.413 9.411 15 533 525.8 0.098 9.508 16 389 381.2 0.162 9.670 17 279 276.5 0.022 9.692 18 189 200.8 0.697 10.389 19 149 146.0 0.062 10.451 20 98 106.2 0.635 11.086 21 300 287.1 0.578 11.665 Chisq= 11.66 for 20 degrees of freedom, p= 0.07287 SUMMARY of craptest p-value for no. of wins: 0.466390 p-value for throws/game: 0.072870 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-02-18_10:31 No. of wins: Observed Expected 98649 98585.9 z-score= 0.282, pvalue=0.61118 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66712 66666.7 0.031 0.031 2 37549 37654.3 0.295 0.325 3 26773 26954.7 1.225 1.551 4 19457 19313.5 1.067 2.617 5 13812 13851.4 0.112 2.730 6 10090 9943.5 2.157 4.887 7 7192 7145.0 0.309 5.196 8 5098 5139.1 0.328 5.524 9 3694 3699.9 0.009 5.533 10 2643 2666.3 0.204 5.737 11 1883 1923.3 0.846 6.582 12 1424 1388.7 0.895 7.478 13 1000 1003.7 0.014 7.491 14 745 726.1 0.490 7.981 15 563 525.8 2.627 10.608 16 387 381.2 0.090 10.698 17 273 276.5 0.045 10.743 18 192 200.8 0.388 11.131 19 118 146.0 5.364 16.496 20 110 106.2 0.135 16.630 21 285 287.1 0.016 16.646 Chisq= 16.65 for 20 degrees of freedom, p= 0.32417 SUMMARY of craptest p-value for no. of wins: 0.611184 p-value for throws/game: 0.324171 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0018,0.0073,0.0161,0.0176,0.0236,0.0250,0.0256,0.0278,0.0317,0.0337, 0.0337,0.0343,0.0443,0.0497,0.0521,0.0547,0.0561,0.0587,0.0605,0.0654, 0.0658,0.0672,0.0724,0.0729,0.0778,0.0782,0.0801,0.0820,0.0905,0.0934, 0.0958,0.1017,0.1064,0.1078,0.1088,0.1172,0.1182,0.1251,0.1279,0.1342, 0.1381,0.1469,0.1493,0.1530,0.1559,0.1581,0.1592,0.1661,0.1688,0.1694, 0.1750,0.1772,0.1799,0.1830,0.1890,0.2006,0.2041,0.2046,0.2065,0.2067, 0.2087,0.2095,0.2101,0.2188,0.2204,0.2257,0.2261,0.2278,0.2286,0.2410, 0.2428,0.2457,0.2507,0.2522,0.2579,0.2617,0.2631,0.2707,0.2783,0.2796, 0.2843,0.2869,0.2880,0.2982,0.2985,0.3016,0.3028,0.3057,0.3143,0.3179, 0.3191,0.3242,0.3330,0.3472,0.3480,0.3491,0.3645,0.3647,0.3667,0.3668, 0.3881,0.3922,0.3981,0.4086,0.4097,0.4110,0.4191,0.4203,0.4271,0.4282, 0.4313,0.4319,0.4369,0.4379,0.4443,0.4456,0.4480,0.4539,0.4552,0.4556, 0.4604,0.4646,0.4664,0.4665,0.4719,0.4739,0.4773,0.4789,0.4796,0.4812, 0.4918,0.5067,0.5129,0.5139,0.5239,0.5339,0.5366,0.5381,0.5396,0.5407, 0.5419,0.5433,0.5468,0.5522,0.5522,0.5550,0.5588,0.5635,0.5669,0.5717, 0.5725,0.5751,0.5765,0.5768,0.5839,0.5877,0.5893,0.5895,0.5940,0.5975, 0.5976,0.6078,0.6088,0.6096,0.6112,0.6155,0.6254,0.6288,0.6290,0.6297, 0.6371,0.6426,0.6427,0.6450,0.6486,0.6498,0.6550,0.6594,0.6612,0.6649, 0.6689,0.6751,0.6751,0.6787,0.6896,0.6898,0.6923,0.6972,0.7052,0.7081, 0.7172,0.7186,0.7264,0.7270,0.7290,0.7299,0.7346,0.7367,0.7400,0.7478, 0.7500,0.7514,0.7533,0.7534,0.7556,0.7579,0.7586,0.7610,0.7620,0.7732, 0.7757,0.7759,0.7804,0.7807,0.7808,0.7828,0.7829,0.7844,0.7846,0.7899, 0.7905,0.7927,0.7990,0.8004,0.8101,0.8103,0.8110,0.8112,0.8201,0.8239, 0.8284,0.8317,0.8358,0.8360,0.8368,0.8387,0.8403,0.8424,0.8446,0.8616, 0.8633,0.8663,0.8731,0.8750,0.8775,0.8794,0.8880,0.9022,0.9155,0.9159, 0.9165,0.9221,0.9277,0.9413,0.9517,0.9559,0.9581,0.9612,0.9630,0.9632, 0.9641,0.9676,0.9686,0.9858,0.9899,0.9917,0.9920,0.9959,0.9977, Overall p-value after applying KStest on 269 p-values = 0.756953 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.