RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-10-05_03:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.83 25.4220 0.914346 2 to 25 15.96 14.7672 0.387754 3 to 26 15.82 9.6708 0.083157 4 to 27 15.75 10.4893 0.118149 5 to 28 15.52 20.5381 0.752365 6 to 29 15.77 12.1090 0.206506 7 to 30 16.00 13.2848 0.283076 8 to 31 15.62 17.0601 0.549700 9 to 32 15.84 24.3967 0.890950 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.930269 Tough bday spacings test for dh-ranFile-2016-10-05_03:31: 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 8 33 69 105 88 94 52 24 13 9 5 (O-E)^2/E 0.1 0.4 0.2 0.5 1.0 3.2 0.0 1.1 0.2 0.9 0.2 Birthday Spacings: Sum(O-E)^2/E= 7.910, p= 0.362 RESULTS OF GCD FOR dh-ranFile-2016-10-05_03:31 Euclid's algorithm: p-value, steps to gcd: 0.845770 p-value, dist. of gcd's: 0.925115 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-10-05_03:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.820 0.610 0.693 0.185 0.339 0.715 0.447 0.414 Bits 8 to 15---> 0.657 0.414 0.912 0.421 0.392 0.425 0.628 0.938 Bits 16 to 23---> 0.168 0.398 0.696 0.200 0.110 0.515 0.788 0.352 Bits 24 to 31---> 0.215 0.314 0.338 0.379 0.545 0.850 0.295 0.244 KS test for the above 32 p values: 0.774 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-10-05_03:31, p-values for 5 runs: 0.8303, 0.3783, 0.8261, 0.5736, 0.3176 Rank test for binary matrices (31x31) for dh-ranFile-2016-10-05_03:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 218 211.4 0.205 0.205 r= 29 5213 5134.0 1.215 1.420 r= 30 23035 23103.0 0.200 1.621 r= 31 11534 11551.5 0.027 1.647 chi-square = 1.647 with df = 3; p-value = 0.351 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-10-05_03:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 187 211.4 2.820 2.820 r= 30 5022 5134.0 2.444 5.264 r= 31 23264 23103.0 1.121 6.385 r= 32 11527 11551.5 0.052 6.437 chi-square = 6.437 with df = 3; p-value = 0.908 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-10-05_03:31 b-rank test for bits 1 to 8, p=0.97816 b-rank test for bits 2 to 9, p=0.75542 b-rank test for bits 3 to 10, p=0.25242 b-rank test for bits 4 to 11, p=0.54810 b-rank test for bits 5 to 12, p=0.80576 b-rank test for bits 6 to 13, p=0.06937 b-rank test for bits 7 to 14, p=0.39638 b-rank test for bits 8 to 15, p=0.34388 b-rank test for bits 9 to 16, p=0.19361 b-rank test for bits 10 to 17, p=0.80424 b-rank test for bits 11 to 18, p=0.91243 b-rank test for bits 12 to 19, p=0.21968 b-rank test for bits 13 to 20, p=0.04472 b-rank test for bits 14 to 21, p=0.08926 b-rank test for bits 15 to 22, p=0.56394 b-rank test for bits 16 to 23, p=0.35412 b-rank test for bits 17 to 24, p=0.37148 b-rank test for bits 18 to 25, p=0.39646 b-rank test for bits 19 to 26, p=0.70694 b-rank test for bits 20 to 27, p=0.78421 b-rank test for bits 21 to 28, p=0.96534 b-rank test for bits 22 to 29, p=0.89528 b-rank test for bits 23 to 30, p=0.53300 b-rank test for bits 24 to 31, p=0.08331 b-rank test for bits 25 to 32, p=0.46581 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 = 0.986973 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-10-05_03:31 (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 141520 -0.91 0.181504 2 142035 0.29 0.615476 3 141183 -1.70 0.044845 4 141832 -0.18 0.428310 5 141914 0.01 0.504353 6 141616 -0.69 0.246561 7 142387 1.12 0.867800 8 141891 -0.04 0.482920 9 141611 -0.70 0.242891 10 142200 0.68 0.751474 11 141164 -1.74 0.040805 12 141459 -1.05 0.146360 13 141731 -0.42 0.338464 14 142283 0.87 0.808685 15 142316 0.95 0.828985 16 141926 0.04 0.515534 17 141740 -0.40 0.346189 18 141635 -0.64 0.260775 19 141819 -0.21 0.416424 20 142051 0.33 0.629680 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-10-05_03:31 Bits used No. missing words z-score p-value 23 to 32 141788 -0.4184 0.337835 22 to 31 141555 -1.2218 0.110886 21 to 30 141956 0.1609 0.563926 20 to 29 141627 -0.9736 0.165140 19 to 28 141320 -2.0322 0.021068 18 to 27 141900 -0.0322 0.487167 17 to 26 142180 0.9333 0.824679 16 to 25 142934 3.5333 0.999795 15 to 24 142068 0.5471 0.707858 14 to 23 141579 -1.1391 0.127337 13 to 22 142094 0.6368 0.737870 12 to 21 141602 -1.0598 0.144627 11 to 20 141366 -1.8736 0.030496 10 to 19 141586 -1.1149 0.132440 9 to 18 141453 -1.5736 0.057796 8 to 17 141620 -0.9977 0.159215 7 to 16 141787 -0.4218 0.336575 6 to 15 141364 -1.8804 0.030024 5 to 14 141606 -1.0460 0.147789 4 to 13 142024 0.3954 0.653731 3 to 12 141526 -1.3218 0.093113 2 to 11 141632 -0.9563 0.169458 1 to 10 141569 -1.1736 0.120287 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-10-05_03:31 Bits used No. missing words z-score p-value 28 to 32 141788 -0.4113 0.340431 27 to 31 141999 0.3040 0.619423 26 to 30 142210 1.0192 0.845951 25 to 29 141710 -0.6757 0.249617 24 to 28 141751 -0.5367 0.295733 23 to 27 141905 -0.0147 0.494145 22 to 26 141919 0.0328 0.513075 21 to 25 142432 1.7718 0.961783 20 to 24 141896 -0.0452 0.481979 19 to 23 141736 -0.5876 0.278414 18 to 22 141801 -0.3672 0.356727 17 to 21 142144 0.7955 0.786836 16 to 20 142342 1.4667 0.928768 15 to 19 141424 -1.6452 0.049966 14 to 18 141612 -1.0079 0.156752 13 to 17 141521 -1.3164 0.094024 12 to 16 141815 -0.3198 0.374574 11 to 15 142263 1.1989 0.884713 10 to 14 142031 0.4124 0.659992 9 to 13 141694 -0.7299 0.232716 8 to 12 141587 -1.0926 0.137275 7 to 11 141653 -0.8689 0.192447 6 to 10 141754 -0.5265 0.299256 5 to 9 142162 0.8565 0.804142 4 to 8 142200 0.9853 0.837767 3 to 7 141807 -0.3469 0.364340 2 to 6 142243 1.1311 0.870990 1 to 5 141582 -1.1096 0.133587 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-10-05_03:31 Bits used No. missing words z-score p-value 31 to 32 141647 -0.7738 0.219514 30 to 31 141671 -0.7030 0.241016 29 to 30 142380 1.3884 0.917493 28 to 29 142391 1.4209 0.922321 27 to 28 142071 0.4769 0.683284 26 to 27 142665 2.2291 0.987097 25 to 26 142230 0.9459 0.827908 24 to 25 141734 -0.5172 0.302509 23 to 24 142126 0.6391 0.738636 22 to 23 141872 -0.1101 0.456158 21 to 22 141968 0.1731 0.568701 20 to 21 142083 0.5123 0.695780 19 to 20 141893 -0.0482 0.480790 18 to 19 141974 0.1908 0.575646 17 to 18 142208 0.8810 0.810850 16 to 17 142037 0.3766 0.646767 15 to 16 141829 -0.2370 0.406343 14 to 15 142042 0.3914 0.652233 13 to 14 142045 0.4002 0.655498 12 to 13 142129 0.6480 0.741506 11 to 12 141390 -1.5319 0.062768 10 to 11 141144 -2.2576 0.011985 9 to 10 142111 0.5949 0.724044 8 to 9 141920 0.0315 0.512555 7 to 8 141631 -0.8210 0.205814 6 to 7 141527 -1.1278 0.129699 5 to 6 142305 1.1672 0.878429 4 to 5 142008 0.2911 0.614498 3 to 4 141677 -0.6853 0.246565 2 to 3 142314 1.1937 0.883706 1 to 2 141944 0.1023 0.540729 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-10-05_03:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2497.64 -0.033 0.486660 Test results for specific bytes for dh-ranFile-2016-10-05_03:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2432.57 -0.954 0.170145 2 to 9 2399.32 -1.424 0.077238 3 to 10 2494.81 -0.073 0.470765 4 to 11 2641.70 2.004 0.977463 5 to 12 2477.92 -0.312 0.377429 6 to 13 2410.85 -1.261 0.103686 7 to 14 2499.65 -0.005 0.498003 8 to 15 2394.50 -1.492 0.067846 9 to 16 2519.62 0.277 0.609286 10 to 17 2435.63 -0.910 0.181314 11 to 18 2508.29 0.117 0.546645 12 to 19 2407.17 -1.313 0.094615 13 to 20 2453.84 -0.653 0.256955 14 to 21 2566.57 0.941 0.826772 15 to 22 2349.27 -2.132 0.016517 16 to 23 2438.38 -0.871 0.191768 17 to 24 2541.85 0.592 0.723040 18 to 25 2523.25 0.329 0.628834 19 to 26 2513.35 0.189 0.574892 20 to 27 2550.66 0.716 0.763151 21 to 28 2479.21 -0.294 0.384381 22 to 29 2285.75 -3.030 0.001223 23 to 30 2601.41 1.434 0.924242 24 to 31 2463.79 -0.512 0.304281 25 to 32 2532.90 0.465 0.679146 CDPARK for dh-ranFile-2016-10-05_03:31: 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 3536 0.5936 0.723613 3553 1.3699 0.914635 3537 0.6393 0.738676 3513 -0.4566 0.323972 3547 1.0959 0.863437 3528 0.2283 0.590298 3551 1.2785 0.899470 3543 0.9132 0.819442 3500 -1.0502 0.146807 3527 0.1826 0.572463 Square side=100, avg. no. parked=3533.50 sample std.=16.10 p-value of the KSTEST for those 10 p-values: 0.120915 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-10-05_03:31 0.3212,0.2870,0.4130,0.2278,0.7044,0.2074,0.8388,0.6393,0.3475,0.7250, The KS test for those 10 p-values: 0.587537 The 3DSPHERES test for dh-ranFile-2016-10-05_03:31 sample no r^3 equiv. uni. 1 23.502 0.543147 2 1.256 0.041010 3 30.067 0.632944 4 24.090 0.552018 5 25.663 0.574901 6 105.630 0.970430 7 21.421 0.510342 8 10.136 0.286717 9 20.176 0.489592 10 19.677 0.481025 11 78.535 0.927040 12 0.248 0.008233 13 7.178 0.212783 14 5.370 0.163898 15 37.328 0.711844 16 10.679 0.299506 17 3.827 0.119764 18 22.885 0.533651 19 30.704 0.640658 20 46.030 0.784398 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.768395 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-10-05_03:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 2.7 0.9 -1.6 1.4 -0.1 -0.6 -0.6 2.0 -0.1 0.8 -0.1 1.5 0.5 0.7 -1.4 -0.5 -1.6 0.2 1.4 1.5 -1.7 -0.2 0.2 -0.8 0.2 -0.6 -0.5 0.2 2.5 -1.7 -1.9 -0.9 0.7 -0.4 0.2 0.2 -1.2 1.5 0.1 -1.3 4.6 2.0 -0.1 Chi-square with 42 degrees of freedom:78.918273 z-score=4.028114, p-value=0.999513 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-10-05_03:31 Test no p-value 1 0.417555 2 0.680583 3 0.006550 4 0.324029 5 0.052858 6 0.749985 7 0.012360 8 0.297408 9 0.122939 10 0.423038 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.031633 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-10-05_03:31: (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 66705 0.02 66685 0.01 3 25000.00 24866 0.72 25048 0.09 4 6666.67 6785 2.10 6604 0.59 5 1388.89 1358 0.69 1397 0.05 6 238.10 236 0.02 224 0.83 7 34.72 43 1.97 35 0.00 8 4.96 6 0.22 6 0.22 p=0.54691 p=0.06191 Number of rngs required: 689156, p-value: 0.808 RESULTS OF CRAPS TEST for dh-ranFile-2016-10-05_03:31 No. of wins: Observed Expected 98453 98585.9 z-score=-0.594, pvalue=0.27618 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66485 66666.7 0.495 0.495 2 37721 37654.3 0.118 0.613 3 26882 26954.7 0.196 0.809 4 19286 19313.5 0.039 0.848 5 13767 13851.4 0.515 1.363 6 10086 9943.5 2.041 3.404 7 7150 7145.0 0.003 3.407 8 5227 5139.1 1.504 4.912 9 3689 3699.9 0.032 4.944 10 2744 2666.3 2.264 7.208 11 1906 1923.3 0.156 7.364 12 1393 1388.7 0.013 7.377 13 1021 1003.7 0.298 7.675 14 754 726.1 1.069 8.744 15 517 525.8 0.148 8.892 16 388 381.2 0.123 9.015 17 280 276.5 0.043 9.059 18 180 200.8 2.160 11.219 19 122 146.0 3.940 15.160 20 104 106.2 0.046 15.206 21 298 287.1 0.413 15.619 Chisq= 15.62 for 20 degrees of freedom, p= 0.26001 SUMMARY of craptest p-value for no. of wins: 0.276182 p-value for throws/game: 0.260013 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-10-05_03:31 No. of wins: Observed Expected 98687 98585.9 z-score= 0.452, pvalue=0.67450 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66287 66666.7 2.162 2.162 2 37648 37654.3 0.001 2.163 3 27389 26954.7 6.996 9.160 4 19399 19313.5 0.379 9.539 5 13869 13851.4 0.022 9.561 6 9812 9943.5 1.740 11.301 7 7071 7145.0 0.767 12.068 8 5123 5139.1 0.050 12.118 9 3784 3699.9 1.913 14.032 10 2712 2666.3 0.783 14.815 11 1927 1923.3 0.007 14.822 12 1399 1388.7 0.076 14.898 13 1014 1003.7 0.105 15.003 14 708 726.1 0.453 15.456 15 531 525.8 0.051 15.507 16 392 381.2 0.309 15.816 17 238 276.5 5.371 21.187 18 182 200.8 1.765 22.952 19 148 146.0 0.028 22.980 20 96 106.2 0.982 23.963 21 271 287.1 0.904 24.867 Chisq= 24.87 for 20 degrees of freedom, p= 0.79343 SUMMARY of craptest p-value for no. of wins: 0.674496 p-value for throws/game: 0.793432 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0012,0.0066,0.0082,0.0120,0.0124,0.0165,0.0211,0.0300,0.0305,0.0316, 0.0408,0.0410,0.0447,0.0448,0.0500,0.0529,0.0578,0.0619,0.0628,0.0678, 0.0694,0.0772,0.0832,0.0833,0.0893,0.0931,0.0940,0.0946,0.1037,0.1096, 0.1109,0.1181,0.1198,0.1203,0.1209,0.1229,0.1273,0.1297,0.1324,0.1336, 0.1373,0.1446,0.1464,0.1468,0.1478,0.1568,0.1592,0.1639,0.1651,0.1675, 0.1695,0.1701,0.1813,0.1815,0.1853,0.1918,0.1924,0.1936,0.1998,0.2058, 0.2065,0.2074,0.2128,0.2151,0.2195,0.2197,0.2278,0.2327,0.2410,0.2429, 0.2439,0.2466,0.2466,0.2496,0.2524,0.2570,0.2600,0.2608,0.2762,0.2784, 0.2831,0.2867,0.2870,0.2945,0.2957,0.2974,0.2993,0.2995,0.3025,0.3043, 0.3138,0.3176,0.3212,0.3240,0.3240,0.3366,0.3376,0.3378,0.3385,0.3395, 0.3404,0.3439,0.3462,0.3475,0.3513,0.3521,0.3541,0.3567,0.3623,0.3643, 0.3715,0.3746,0.3774,0.3783,0.3794,0.3844,0.3878,0.3919,0.3964,0.3965, 0.3979,0.4063,0.4130,0.4135,0.4138,0.4164,0.4176,0.4205,0.4230,0.4250, 0.4283,0.4471,0.4562,0.4658,0.4708,0.4808,0.4810,0.4820,0.4829,0.4867, 0.4872,0.4896,0.4941,0.4980,0.5044,0.5103,0.5126,0.5131,0.5147,0.5155, 0.5330,0.5337,0.5407,0.5431,0.5448,0.5466,0.5469,0.5481,0.5497,0.5520, 0.5639,0.5639,0.5687,0.5725,0.5736,0.5749,0.5749,0.5756,0.5875,0.5903, 0.6093,0.6100,0.6145,0.6155,0.6194,0.6282,0.6288,0.6297,0.6329,0.6393, 0.6407,0.6468,0.6522,0.6537,0.6555,0.6574,0.6600,0.6745,0.6791,0.6806, 0.6833,0.6933,0.6958,0.6961,0.7044,0.7069,0.7079,0.7118,0.7153,0.7230, 0.7236,0.7240,0.7250,0.7379,0.7386,0.7387,0.7415,0.7500,0.7515,0.7524, 0.7554,0.7632,0.7684,0.7736,0.7842,0.7844,0.7868,0.7878,0.7934,0.8041, 0.8042,0.8058,0.8081,0.8087,0.8108,0.8194,0.8201,0.8247,0.8261,0.8268, 0.8279,0.8290,0.8303,0.8378,0.8388,0.8458,0.8460,0.8500,0.8634,0.8678, 0.8710,0.8784,0.8837,0.8847,0.8909,0.8953,0.8995,0.9078,0.9118,0.9124, 0.9143,0.9146,0.9175,0.9223,0.9242,0.9251,0.9270,0.9288,0.9303,0.9384, 0.9618,0.9653,0.9704,0.9775,0.9782,0.9870,0.9871,0.9995,0.9998, Overall p-value after applying KStest on 269 p-values = 0.354441 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.