RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-03-15_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 15.52 38.0079 0.997548 2 to 25 15.60 16.1276 0.485194 3 to 26 15.71 17.7339 0.594187 4 to 27 15.62 24.1662 0.885012 5 to 28 15.66 30.3164 0.975849 6 to 29 15.63 33.1491 0.989209 7 to 30 16.09 16.6741 0.523355 8 to 31 15.86 12.8492 0.253781 9 to 32 16.03 15.8938 0.468623 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.018451 Tough bday spacings test for dh-ranFile-2018-03-15_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 3 37 74 98 106 77 49 23 20 7 6 (O-E)^2/E 4.1 0.0 0.0 0.0 0.7 0.0 0.2 1.5 1.8 0.0 0.9 Birthday Spacings: Sum(O-E)^2/E= 9.301, p= 0.496 RESULTS OF GCD FOR dh-ranFile-2018-03-15_15:31 Euclid's algorithm: p-value, steps to gcd: 0.210989 p-value, dist. of gcd's: 0.467627 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-03-15_15:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.389 0.884 0.699 0.873 0.574 0.324 0.001 0.361 Bits 8 to 15---> 0.023 0.206 0.136 0.565 0.290 0.439 0.173 0.394 Bits 16 to 23---> 0.611 0.886 0.390 0.582 0.987 0.093 0.842 0.654 Bits 24 to 31---> 0.738 0.700 0.002 0.346 0.812 0.873 0.389 0.873 KS test for the above 32 p values: 0.362 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-03-15_15:31, p-values for 5 runs: 0.3514, 0.7875, 0.5908, 0.6077, 0.0541 Rank test for binary matrices (31x31) for dh-ranFile-2018-03-15_15:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 210 211.4 0.010 0.010 r= 29 5204 5134.0 0.954 0.964 r= 30 23085 23103.0 0.014 0.978 r= 31 11501 11551.5 0.221 1.199 chi-square = 1.199 with df = 3; p-value = 0.247 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-03-15_15:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 242 211.4 4.424 4.424 r= 30 5139 5134.0 0.005 4.429 r= 31 22985 23103.0 0.603 5.032 r= 32 11634 11551.5 0.589 5.621 chi-square = 5.621 with df = 3; p-value = 0.868 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-03-15_15:31 b-rank test for bits 1 to 8, p=0.11533 b-rank test for bits 2 to 9, p=0.75629 b-rank test for bits 3 to 10, p=0.43465 b-rank test for bits 4 to 11, p=0.18269 b-rank test for bits 5 to 12, p=0.08001 b-rank test for bits 6 to 13, p=0.02899 b-rank test for bits 7 to 14, p=0.97415 b-rank test for bits 8 to 15, p=0.37488 b-rank test for bits 9 to 16, p=0.81122 b-rank test for bits 10 to 17, p=0.41360 b-rank test for bits 11 to 18, p=0.80389 b-rank test for bits 12 to 19, p=0.74167 b-rank test for bits 13 to 20, p=0.80085 b-rank test for bits 14 to 21, p=0.53074 b-rank test for bits 15 to 22, p=0.41819 b-rank test for bits 16 to 23, p=0.59296 b-rank test for bits 17 to 24, p=0.31814 b-rank test for bits 18 to 25, p=0.37618 b-rank test for bits 19 to 26, p=0.73295 b-rank test for bits 20 to 27, p=0.72234 b-rank test for bits 21 to 28, p=0.68518 b-rank test for bits 22 to 29, p=0.79555 b-rank test for bits 23 to 30, p=0.00809 b-rank test for bits 24 to 31, p=0.18738 b-rank test for bits 25 to 32, p=0.58613 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 = 0.804870 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-03-15_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 141829 -0.19 0.425561 2 141767 -0.33 0.369738 3 141571 -0.79 0.214621 4 141752 -0.37 0.356588 5 141444 -1.09 0.138470 6 142119 0.49 0.687892 7 141609 -0.70 0.241431 8 141498 -0.96 0.168263 9 141581 -0.77 0.221503 10 141401 -1.19 0.117478 11 142135 0.53 0.700996 12 141652 -0.60 0.273841 13 142377 1.09 0.862734 14 142066 0.37 0.642837 15 143031 2.62 0.995613 16 142328 0.98 0.836013 17 141640 -0.63 0.264584 18 142625 1.67 0.952750 19 141845 -0.15 0.440263 20 142223 0.73 0.768182 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-03-15_15:31 Bits used No. missing words z-score p-value 23 to 32 141748 -0.5563 0.288999 22 to 31 141258 -2.2460 0.012353 21 to 30 141726 -0.6322 0.263637 20 to 29 141753 -0.5391 0.294920 19 to 28 141830 -0.2736 0.392215 18 to 27 142071 0.5575 0.711401 17 to 26 141766 -0.4942 0.310568 16 to 25 142174 0.9127 0.819288 15 to 24 142407 1.7161 0.956928 14 to 23 142087 0.6127 0.729948 13 to 22 141244 -2.2942 0.010888 12 to 21 142378 1.6161 0.946964 11 to 20 141886 -0.0804 0.467940 10 to 19 141246 -2.2873 0.011088 9 to 18 141723 -0.6425 0.260269 8 to 17 141991 0.2816 0.610883 7 to 16 142015 0.3644 0.642213 6 to 15 141519 -1.3460 0.089157 5 to 14 141363 -1.8839 0.029789 4 to 13 141390 -1.7908 0.036663 3 to 12 141558 -1.2115 0.112855 2 to 11 142125 0.7437 0.771468 1 to 10 142251 1.1782 0.880636 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-03-15_15:31 Bits used No. missing words z-score p-value 28 to 32 142230 1.0870 0.861485 27 to 31 141830 -0.2689 0.393998 26 to 30 142165 0.8667 0.806941 25 to 29 142288 1.2836 0.900364 24 to 28 141855 -0.1842 0.426940 23 to 27 142192 0.9582 0.831020 22 to 26 141667 -0.8215 0.205693 21 to 25 142344 1.4735 0.929686 20 to 24 141835 -0.2520 0.400534 19 to 23 141850 -0.2011 0.420303 18 to 22 142229 1.0836 0.860735 17 to 21 142093 0.6226 0.733230 16 to 20 142528 2.0972 0.982011 15 to 19 141810 -0.3367 0.368167 14 to 18 142214 1.0328 0.849147 13 to 17 141958 0.1650 0.565521 12 to 16 141979 0.2362 0.593349 11 to 15 142119 0.7107 0.761379 10 to 14 142098 0.6396 0.738770 9 to 13 141831 -0.2655 0.395302 8 to 12 141969 0.2023 0.580148 7 to 11 141752 -0.5333 0.296905 6 to 10 141894 -0.0520 0.479278 5 to 9 142045 0.4599 0.677205 4 to 8 141300 -2.0655 0.019437 3 to 7 142115 0.6972 0.757157 2 to 6 142317 1.3819 0.916504 1 to 5 141827 -0.2791 0.390090 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-03-15_15:31 Bits used No. missing words z-score p-value 31 to 32 141469 -1.2989 0.096988 30 to 31 141867 -0.1249 0.450314 29 to 30 141957 0.1406 0.555915 28 to 29 142043 0.3943 0.653323 27 to 28 142081 0.5064 0.693713 26 to 27 141709 -0.5909 0.277279 25 to 26 141622 -0.8476 0.198336 24 to 25 141699 -0.6204 0.267483 23 to 24 141910 0.0020 0.500789 22 to 23 142379 1.3855 0.917044 21 to 22 141699 -0.6204 0.267483 20 to 21 141799 -0.3255 0.372418 19 to 20 142053 0.4238 0.664146 18 to 19 141592 -0.9361 0.174617 17 to 18 141951 0.1229 0.548915 16 to 17 142007 0.2881 0.613370 15 to 16 141211 -2.0600 0.019701 14 to 15 142010 0.2970 0.616752 13 to 14 142109 0.5890 0.722068 12 to 13 141938 0.0846 0.533699 11 to 12 141747 -0.4788 0.316023 10 to 11 142490 1.7129 0.956634 9 to 10 141941 0.0934 0.537216 8 to 9 141705 -0.6027 0.273340 7 to 8 142369 1.3560 0.912444 6 to 7 142252 1.0108 0.843950 5 to 6 142146 0.6981 0.757456 4 to 5 142069 0.4710 0.681181 3 to 4 141961 0.1524 0.560572 2 to 3 141684 -0.6647 0.253124 1 to 2 142118 0.6155 0.730903 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-03-15_15:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2405.24 -1.340 0.090113 Test results for specific bytes for dh-ranFile-2018-03-15_15:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2660.98 2.277 0.988593 2 to 9 2437.38 -0.886 0.187918 3 to 10 2541.76 0.591 0.722597 4 to 11 2498.44 -0.022 0.491188 5 to 12 2575.08 1.062 0.855834 6 to 13 2449.04 -0.721 0.235538 7 to 14 2519.34 0.273 0.607745 8 to 15 2500.01 0.000 0.500064 9 to 16 2503.57 0.050 0.520127 10 to 17 2540.85 0.578 0.718247 11 to 18 2611.84 1.582 0.943138 12 to 19 2647.37 2.084 0.981424 13 to 20 2484.06 -0.225 0.410844 14 to 21 2478.68 -0.302 0.381493 15 to 22 2543.77 0.619 0.732063 16 to 23 2456.82 -0.611 0.270731 17 to 24 2530.34 0.429 0.666049 18 to 25 2434.76 -0.923 0.178086 19 to 26 2485.33 -0.207 0.417847 20 to 27 2537.81 0.535 0.703558 21 to 28 2443.37 -0.801 0.211596 22 to 29 2488.59 -0.161 0.435922 23 to 30 2450.67 -0.698 0.242699 24 to 31 2627.60 1.804 0.964422 25 to 32 2557.88 0.819 0.793470 CDPARK for dh-ranFile-2018-03-15_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 3508 -0.6849 0.246694 3528 0.2283 0.590298 3531 0.3653 0.642555 3518 -0.2283 0.409702 3528 0.2283 0.590298 3529 0.2740 0.607947 3503 -0.9132 0.180558 3515 -0.3653 0.357445 3469 -2.4658 0.006836 3538 0.6849 0.753306 Square side=100, avg. no. parked=3516.70 sample std.=18.99 p-value of the KSTEST for those 10 p-values: 0.471902 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-03-15_15:31 0.4748,0.1177,0.9516,0.3864,0.3252,0.2577,0.1746,0.2319,0.6103,0.4615, The KS test for those 10 p-values: 0.312669 The 3DSPHERES test for dh-ranFile-2018-03-15_15:31 sample no r^3 equiv. uni. 1 45.592 0.781230 2 53.783 0.833503 3 5.020 0.154080 4 9.796 0.278578 5 39.751 0.734203 6 1.561 0.050691 7 27.528 0.600517 8 81.384 0.933648 9 9.693 0.276088 10 25.317 0.569968 11 19.870 0.484351 12 7.132 0.211598 13 9.423 0.269549 14 17.119 0.434832 15 24.942 0.564562 16 2.818 0.089647 17 134.790 0.988813 18 11.846 0.326236 19 22.485 0.527394 20 58.239 0.856481 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.997072 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-03-15_15:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -1.6 0.6 -0.3 -0.2 -2.1 0.7 -1.1 -0.6 -1.1 0.2 0.0 0.5 -0.4 -0.9 -1.5 1.5 -0.5 0.4 -0.1 1.4 0.0 0.9 0.2 0.2 0.3 0.1 -0.0 -0.5 0.7 -0.3 -1.5 2.0 0.2 1.2 -0.3 -1.9 -1.7 0.1 -1.3 2.4 0.0 0.8 Chi-square with 42 degrees of freedom:43.214470 z-score=0.132510, p-value=0.580785 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-03-15_15:31 Test no p-value 1 0.549399 2 0.795244 3 0.121865 4 0.403666 5 0.561065 6 0.120593 7 0.083608 8 0.004144 9 0.006581 10 0.796188 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.040527 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-03-15_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 66726 0.05 66606 0.06 3 25000.00 24992 0.00 24937 0.16 4 6666.67 6541 2.37 6764 1.42 5 1388.89 1456 3.24 1408 0.26 6 238.10 243 0.10 238 0.00 7 34.72 39 0.53 39 0.53 8 4.96 2 1.77 7 0.84 p=0.76641 p=0.22502 Number of rngs required: 687586, p-value: 0.172 RESULTS OF CRAPS TEST for dh-ranFile-2018-03-15_15:31 No. of wins: Observed Expected 98542 98585.9 z-score=-0.196, pvalue=0.42224 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66890 66666.7 0.748 0.748 2 37413 37654.3 1.547 2.295 3 27351 26954.7 5.826 8.120 4 19277 19313.5 0.069 8.189 5 13806 13851.4 0.149 8.338 6 9722 9943.5 4.936 13.274 7 7115 7145.0 0.126 13.400 8 5131 5139.1 0.013 13.413 9 3657 3699.9 0.497 13.910 10 2710 2666.3 0.716 14.626 11 1954 1923.3 0.489 15.115 12 1365 1388.7 0.406 15.521 13 972 1003.7 1.002 16.523 14 716 726.1 0.142 16.665 15 529 525.8 0.019 16.684 16 373 381.2 0.174 16.858 17 283 276.5 0.151 17.009 18 196 200.8 0.116 17.125 19 137 146.0 0.553 17.678 20 109 106.2 0.073 17.751 21 294 287.1 0.165 17.916 Chisq= 17.92 for 20 degrees of freedom, p= 0.40707 SUMMARY of craptest p-value for no. of wins: 0.422242 p-value for throws/game: 0.407067 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-03-15_15:31 No. of wins: Observed Expected 98600 98585.9 z-score= 0.063, pvalue=0.52522 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66802 66666.7 0.275 0.275 2 37343 37654.3 2.574 2.849 3 27100 26954.7 0.783 3.632 4 19519 19313.5 2.187 5.819 5 13623 13851.4 3.767 9.586 6 10076 9943.5 1.764 11.350 7 7053 7145.0 1.185 12.535 8 5161 5139.1 0.094 12.629 9 3698 3699.9 0.001 12.630 10 2808 2666.3 7.531 20.161 11 1906 1923.3 0.156 20.317 12 1356 1388.7 0.772 21.089 13 957 1003.7 2.174 23.263 14 720 726.1 0.052 23.315 15 487 525.8 2.868 26.183 16 426 381.2 5.277 31.461 17 251 276.5 2.359 33.819 18 194 200.8 0.232 34.052 19 138 146.0 0.437 34.488 20 95 106.2 1.184 35.672 21 287 287.1 0.000 35.673 Chisq= 35.67 for 20 degrees of freedom, p= 0.98320 SUMMARY of craptest p-value for no. of wins: 0.525216 p-value for throws/game: 0.983199 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0007,0.0020,0.0041,0.0066,0.0068,0.0081,0.0109,0.0111,0.0124,0.0185, 0.0194,0.0197,0.0227,0.0290,0.0298,0.0367,0.0405,0.0507,0.0541,0.0800, 0.0836,0.0892,0.0896,0.0901,0.0934,0.0970,0.1129,0.1153,0.1175,0.1177, 0.1206,0.1219,0.1362,0.1385,0.1541,0.1683,0.1721,0.1731,0.1746,0.1746, 0.1781,0.1806,0.1827,0.1874,0.1879,0.1983,0.2057,0.2057,0.2110,0.2116, 0.2116,0.2146,0.2215,0.2250,0.2319,0.2355,0.2414,0.2427,0.2467,0.2467, 0.2531,0.2538,0.2577,0.2603,0.2636,0.2646,0.2675,0.2675,0.2695,0.2707, 0.2733,0.2738,0.2761,0.2773,0.2786,0.2890,0.2897,0.2949,0.2969,0.3106, 0.3127,0.3160,0.3181,0.3240,0.3252,0.3262,0.3459,0.3514,0.3566,0.3574, 0.3609,0.3624,0.3682,0.3697,0.3724,0.3749,0.3762,0.3815,0.3864,0.3885, 0.3891,0.3899,0.3901,0.3922,0.3939,0.3940,0.3953,0.4005,0.4037,0.4071, 0.4097,0.4108,0.4136,0.4178,0.4182,0.4203,0.4222,0.4256,0.4269,0.4347, 0.4348,0.4359,0.4390,0.4403,0.4503,0.4615,0.4676,0.4679,0.4686,0.4719, 0.4748,0.4793,0.4844,0.4852,0.4912,0.4962,0.5001,0.5008,0.5201,0.5234, 0.5252,0.5274,0.5307,0.5337,0.5372,0.5489,0.5494,0.5559,0.5606,0.5611, 0.5646,0.5651,0.5655,0.5700,0.5744,0.5801,0.5808,0.5816,0.5861,0.5903, 0.5903,0.5908,0.5930,0.5933,0.5942,0.6005,0.6077,0.6077,0.6079,0.6103, 0.6108,0.6109,0.6134,0.6168,0.6422,0.6426,0.6428,0.6533,0.6542,0.6641, 0.6660,0.6772,0.6812,0.6852,0.6879,0.6937,0.6986,0.7001,0.7010,0.7036, 0.7114,0.7182,0.7221,0.7223,0.7226,0.7299,0.7309,0.7321,0.7329,0.7332, 0.7342,0.7377,0.7388,0.7417,0.7533,0.7563,0.7572,0.7575,0.7614,0.7664, 0.7682,0.7715,0.7812,0.7875,0.7935,0.7952,0.7955,0.7962,0.8009,0.8039, 0.8049,0.8069,0.8112,0.8122,0.8193,0.8310,0.8335,0.8360,0.8424,0.8440, 0.8491,0.8558,0.8565,0.8607,0.8615,0.8627,0.8684,0.8732,0.8732,0.8733, 0.8806,0.8838,0.8850,0.8863,0.9004,0.9124,0.9165,0.9170,0.9297,0.9336, 0.9431,0.9470,0.9516,0.9528,0.9566,0.9569,0.9644,0.9742,0.9758,0.9814, 0.9820,0.9832,0.9870,0.9886,0.9888,0.9892,0.9956,0.9971,0.9975, Overall p-value after applying KStest on 269 p-values = 0.637147 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.