RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-04-07_02:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.72 14.8332 0.392503 2 to 25 15.63 17.7760 0.596899 3 to 26 15.74 25.0176 0.905684 4 to 27 15.46 23.1640 0.856012 5 to 28 15.63 21.7121 0.803954 6 to 29 15.59 16.6376 0.520835 7 to 30 15.78 20.1057 0.731143 8 to 31 15.94 14.2942 0.353824 9 to 32 15.82 23.6105 0.869591 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.112013 Tough bday spacings test for dh-ranFile-2016-04-07_02:31: 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 36 67 97 111 74 43 32 16 3 10 (O-E)^2/E 0.4 0.0 0.5 0.0 1.8 0.2 1.6 0.2 0.1 2.0 8.7 Birthday Spacings: Sum(O-E)^2/E= 15.432, p= 0.883 RESULTS OF GCD FOR dh-ranFile-2016-04-07_02:31 Euclid's algorithm: p-value, steps to gcd: 0.092322 p-value, dist. of gcd's: 0.759545 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-04-07_02:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.420 0.593 0.390 0.352 0.465 0.699 0.451 0.699 Bits 8 to 15---> 0.701 0.488 0.802 0.612 0.504 0.830 0.585 0.290 Bits 16 to 23---> 0.709 0.287 0.028 0.906 0.024 0.291 0.338 0.856 Bits 24 to 31---> 0.770 0.893 0.275 0.566 0.148 0.963 0.778 0.018 KS test for the above 32 p values: 0.328 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-04-07_02:31, p-values for 5 runs: 0.7426, 0.7139, 0.3852, 0.9967, 0.8355 Rank test for binary matrices (31x31) for dh-ranFile-2016-04-07_02:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 238 211.4 3.342 3.342 r= 29 5122 5134.0 0.028 3.370 r= 30 23187 23103.0 0.305 3.675 r= 31 11453 11551.5 0.840 4.516 chi-square = 4.516 with df = 3; p-value = 0.789 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-04-07_02:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 202 211.4 0.420 0.420 r= 30 5230 5134.0 1.795 2.214 r= 31 23091 23103.0 0.006 2.221 r= 32 11477 11551.5 0.481 2.701 chi-square = 2.701 with df = 3; p-value = 0.560 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-04-07_02:31 b-rank test for bits 1 to 8, p=0.03015 b-rank test for bits 2 to 9, p=0.84419 b-rank test for bits 3 to 10, p=0.98011 b-rank test for bits 4 to 11, p=0.68067 b-rank test for bits 5 to 12, p=0.02136 b-rank test for bits 6 to 13, p=0.63314 b-rank test for bits 7 to 14, p=0.61963 b-rank test for bits 8 to 15, p=0.88990 b-rank test for bits 9 to 16, p=0.20758 b-rank test for bits 10 to 17, p=0.49773 b-rank test for bits 11 to 18, p=0.84441 b-rank test for bits 12 to 19, p=0.48616 b-rank test for bits 13 to 20, p=0.12785 b-rank test for bits 14 to 21, p=0.41876 b-rank test for bits 15 to 22, p=0.32269 b-rank test for bits 16 to 23, p=0.62456 b-rank test for bits 17 to 24, p=0.08087 b-rank test for bits 18 to 25, p=0.17086 b-rank test for bits 19 to 26, p=0.89887 b-rank test for bits 20 to 27, p=0.77416 b-rank test for bits 21 to 28, p=0.26281 b-rank test for bits 22 to 29, p=0.78967 b-rank test for bits 23 to 30, p=0.61716 b-rank test for bits 24 to 31, p=0.20064 b-rank test for bits 25 to 32, p=0.55151 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 = 0.988787 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-04-07_02:31 (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 142575 1.56 0.940063 2 141998 0.21 0.582063 3 142221 0.73 0.766755 4 142544 1.48 0.930946 5 141724 -0.43 0.332502 6 141273 -1.49 0.068540 7 142079 0.40 0.654104 8 142523 1.43 0.924187 9 142598 1.61 0.946196 10 142271 0.85 0.800951 11 140930 -2.29 0.011064 12 141523 -0.90 0.183358 13 141619 -0.68 0.248778 14 141740 -0.40 0.346189 15 141748 -0.38 0.353109 16 142072 0.38 0.648053 17 142704 1.86 0.968323 18 142016 0.25 0.598408 19 141572 -0.79 0.215303 20 142758 1.98 0.976309 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-04-07_02:31 Bits used No. missing words z-score p-value 23 to 32 141631 -0.9598 0.168588 22 to 31 142427 1.7851 0.962875 21 to 30 141756 -0.5287 0.298498 20 to 29 142101 0.6609 0.745672 19 to 28 142216 1.0575 0.854854 18 to 27 142250 1.1747 0.879947 17 to 26 141531 -1.3046 0.096017 16 to 25 141631 -0.9598 0.168588 15 to 24 142193 0.9782 0.836006 14 to 23 141724 -0.6391 0.261389 13 to 22 142037 0.4402 0.670119 12 to 21 141786 -0.4253 0.335318 11 to 20 141997 0.3023 0.618792 10 to 19 141876 -0.1149 0.454250 9 to 18 141422 -1.6804 0.046435 8 to 17 141460 -1.5494 0.060641 7 to 16 141839 -0.2425 0.404190 6 to 15 141745 -0.5667 0.285474 5 to 14 142405 1.7092 0.956294 4 to 13 142035 0.4333 0.667618 3 to 12 141832 -0.2667 0.394867 2 to 11 141878 -0.1080 0.456984 1 to 10 142107 0.6816 0.752261 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-04-07_02:31 Bits used No. missing words z-score p-value 28 to 32 142423 1.7413 0.959181 27 to 31 141571 -1.1469 0.125715 26 to 30 141977 0.2294 0.590717 25 to 29 142195 0.9684 0.833571 24 to 28 141929 0.0667 0.526581 23 to 27 141727 -0.6181 0.268265 22 to 26 141294 -2.0859 0.018495 21 to 25 141933 0.0802 0.531976 20 to 24 142203 0.9955 0.840251 19 to 23 141361 -1.8587 0.031532 18 to 22 141602 -1.0418 0.148753 17 to 21 141674 -0.7977 0.212514 16 to 20 142107 0.6701 0.748593 15 to 19 142057 0.5006 0.691665 14 to 18 141690 -0.7435 0.228592 13 to 17 141201 -2.4011 0.008173 12 to 16 142124 0.7277 0.766600 11 to 15 141563 -1.1740 0.120198 10 to 14 141601 -1.0452 0.147968 9 to 13 141090 -2.7774 0.002740 8 to 12 142308 1.3514 0.911720 7 to 11 141689 -0.7469 0.227568 6 to 10 141921 0.0396 0.515778 5 to 9 142097 0.6362 0.737667 4 to 8 141778 -0.4452 0.328093 3 to 7 141625 -0.9638 0.167565 2 to 6 141691 -0.7401 0.229619 1 to 5 141853 -0.1909 0.424283 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-04-07_02:31 Bits used No. missing words z-score p-value 31 to 32 141452 -1.3491 0.088660 30 to 31 142112 0.5978 0.725029 29 to 30 142097 0.5536 0.710073 28 to 29 141639 -0.7974 0.212600 27 to 28 141669 -0.7089 0.239182 26 to 27 142122 0.6273 0.734784 25 to 26 142382 1.3943 0.918388 24 to 25 141974 0.1908 0.575646 23 to 24 142183 0.8073 0.790249 22 to 23 141046 -2.5467 0.005437 21 to 22 142180 0.7984 0.787691 20 to 21 142299 1.1495 0.874819 19 to 20 141751 -0.4671 0.320232 18 to 19 142446 1.5831 0.943300 17 to 18 142393 1.4268 0.923175 16 to 17 142042 0.3914 0.652233 15 to 16 142303 1.1613 0.877234 14 to 15 141812 -0.2871 0.387014 13 to 14 141599 -0.9154 0.179984 12 to 13 141486 -1.2488 0.105876 11 to 12 142367 1.3501 0.911501 10 to 11 141283 -1.8476 0.032331 9 to 10 141659 -0.7384 0.230125 8 to 9 142070 0.4740 0.682233 7 to 8 141921 0.0344 0.513731 6 to 7 142077 0.4946 0.689559 5 to 6 141858 -0.1514 0.439824 4 to 5 141684 -0.6647 0.253124 3 to 4 141666 -0.7178 0.236444 2 to 3 141550 -1.0600 0.144579 1 to 2 141724 -0.5467 0.292294 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-04-07_02:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2562.24 0.880 0.810638 Test results for specific bytes for dh-ranFile-2016-04-07_02:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2505.97 0.084 0.533647 2 to 9 2524.04 0.340 0.633082 3 to 10 2507.89 0.112 0.544439 4 to 11 2461.72 -0.541 0.294134 5 to 12 2486.63 -0.189 0.424995 6 to 13 2604.28 1.475 0.929851 7 to 14 2615.26 1.630 0.948450 8 to 15 2487.29 -0.180 0.428681 9 to 16 2491.70 -0.117 0.453285 10 to 17 2455.95 -0.623 0.266648 11 to 18 2492.61 -0.105 0.458359 12 to 19 2513.46 0.190 0.575481 13 to 20 2494.17 -0.082 0.467150 14 to 21 2422.97 -1.089 0.138011 15 to 22 2423.16 -1.087 0.138600 16 to 23 2531.33 0.443 0.671141 17 to 24 2603.21 1.460 0.927795 18 to 25 2538.23 0.541 0.705613 19 to 26 2439.66 -0.853 0.196731 20 to 27 2604.40 1.476 0.930089 21 to 28 2558.28 0.824 0.795086 22 to 29 2575.06 1.061 0.855761 23 to 30 2468.59 -0.444 0.328468 24 to 31 2577.67 1.098 0.863981 25 to 32 2359.02 -1.994 0.023093 CDPARK for dh-ranFile-2016-04-07_02:31: 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 3544 0.9589 0.831196 3522 -0.0457 0.481790 3520 -0.1370 0.445521 3524 0.0457 0.518210 3505 -0.8219 0.205562 3515 -0.3653 0.357445 3518 -0.2283 0.409702 3506 -0.7763 0.218799 3507 -0.7306 0.232514 3502 -0.9589 0.168804 Square side=100, avg. no. parked=3516.30 sample std.=11.84 p-value of the KSTEST for those 10 p-values: 0.173398 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-04-07_02:31 0.9048,0.7433,0.4659,0.2211,0.9864,0.0091,0.6020,0.2369,0.3427,0.9864, The KS test for those 10 p-values: 0.367148 The 3DSPHERES test for dh-ranFile-2016-04-07_02:31 sample no r^3 equiv. uni. 1 4.803 0.147952 2 16.191 0.417084 3 8.752 0.253043 4 17.495 0.441867 5 9.182 0.263653 6 28.771 0.616741 7 35.452 0.693251 8 72.631 0.911169 9 56.255 0.846669 10 21.302 0.508396 11 21.838 0.517093 12 0.206 0.006841 13 44.551 0.773506 14 12.287 0.336051 15 0.539 0.017795 16 34.149 0.679634 17 1.405 0.045742 18 6.447 0.193374 19 43.913 0.768639 20 41.447 0.748816 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.690302 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-04-07_02:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 1.8 0.6 0.6 -0.9 2.6 1.2 -0.8 0.1 0.8 -0.6 0.2 0.7 0.5 0.3 -0.7 -2.0 1.1 -2.3 -0.8 0.7 0.1 0.4 -0.2 -0.2 0.0 0.3 1.5 0.8 -0.5 0.4 1.4 1.9 0.7 1.9 1.9 -0.7 1.5 0.5 0.4 -1.3 0.0 -0.1 Chi-square with 42 degrees of freedom:49.570861 z-score=0.826049, p-value=0.803128 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-04-07_02:31 Test no p-value 1 0.775105 2 0.523017 3 0.022309 4 0.746589 5 0.171538 6 0.101612 7 0.401763 8 0.792082 9 0.998684 10 0.009651 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.263027 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-04-07_02:31: (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 66774 0.17 66772 0.17 3 25000.00 24969 0.04 24971 0.03 4 6666.67 6613 0.43 6581 1.10 5 1388.89 1334 2.17 1392 0.01 6 238.10 259 1.84 241 0.04 7 34.72 41 1.14 33 0.09 8 4.96 9 3.29 9 3.29 p=0.83057 p=0.41970 Number of rngs required: 687414, p-value: 0.125 RESULTS OF CRAPS TEST for dh-ranFile-2016-04-07_02:31 No. of wins: Observed Expected 98519 98585.9 z-score=-0.299, pvalue=0.38246 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66627 66666.7 0.024 0.024 2 37468 37654.3 0.922 0.946 3 27174 26954.7 1.784 2.729 4 19517 19313.5 2.145 4.874 5 13851 13851.4 0.000 4.874 6 9926 9943.5 0.031 4.905 7 7125 7145.0 0.056 4.961 8 5162 5139.1 0.102 5.064 9 3662 3699.9 0.388 5.451 10 2713 2666.3 0.818 6.269 11 1817 1923.3 5.878 12.147 12 1334 1388.7 2.158 14.305 13 962 1003.7 1.734 16.039 14 736 726.1 0.134 16.173 15 545 525.8 0.698 16.871 16 342 381.2 4.021 20.893 17 268 276.5 0.264 21.156 18 223 200.8 2.447 23.604 19 156 146.0 0.687 24.291 20 98 106.2 0.635 24.926 21 294 287.1 0.165 25.091 Chisq= 25.09 for 20 degrees of freedom, p= 0.80204 SUMMARY of craptest p-value for no. of wins: 0.382458 p-value for throws/game: 0.802044 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-04-07_02:31 No. of wins: Observed Expected 98413 98585.9 z-score=-0.773, pvalue=0.21972 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66359 66666.7 1.420 1.420 2 37822 37654.3 0.747 2.167 3 26989 26954.7 0.044 2.210 4 19335 19313.5 0.024 2.234 5 13674 13851.4 2.273 4.507 6 9892 9943.5 0.267 4.774 7 7272 7145.0 2.256 7.030 8 5082 5139.1 0.634 7.664 9 3659 3699.9 0.451 8.116 10 2741 2666.3 2.093 10.208 11 1986 1923.3 2.042 12.251 12 1439 1388.7 1.819 14.070 13 1063 1003.7 3.502 17.571 14 772 726.1 2.896 20.467 15 509 525.8 0.539 21.007 16 403 381.2 1.253 22.259 17 291 276.5 0.756 23.015 18 195 200.8 0.169 23.184 19 152 146.0 0.248 23.432 20 84 106.2 4.646 28.079 21 281 287.1 0.130 28.209 Chisq= 28.21 for 20 degrees of freedom, p= 0.89545 SUMMARY of craptest p-value for no. of wins: 0.219724 p-value for throws/game: 0.895454 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0027,0.0054,0.0068,0.0082,0.0091,0.0097,0.0111,0.0178,0.0178,0.0185, 0.0214,0.0223,0.0231,0.0236,0.0281,0.0301,0.0315,0.0323,0.0457,0.0464, 0.0606,0.0685,0.0809,0.0887,0.0923,0.0960,0.1016,0.1059,0.1120,0.1202, 0.1254,0.1257,0.1278,0.1380,0.1386,0.1446,0.1478,0.1480,0.1480,0.1488, 0.1676,0.1686,0.1686,0.1688,0.1709,0.1715,0.1734,0.1800,0.1834,0.1934, 0.1967,0.2006,0.2056,0.2076,0.2125,0.2126,0.2153,0.2188,0.2197,0.2211, 0.2276,0.2286,0.2296,0.2301,0.2325,0.2364,0.2369,0.2392,0.2488,0.2530, 0.2531,0.2614,0.2628,0.2630,0.2637,0.2666,0.2683,0.2747,0.2855,0.2874, 0.2902,0.2915,0.2923,0.2941,0.2985,0.3202,0.3227,0.3281,0.3284,0.3285, 0.3325,0.3353,0.3361,0.3383,0.3427,0.3462,0.3519,0.3531,0.3538,0.3574, 0.3671,0.3825,0.3852,0.3870,0.3900,0.3925,0.3949,0.4018,0.4042,0.4097, 0.4171,0.4188,0.4197,0.4203,0.4243,0.4250,0.4287,0.4398,0.4419,0.4455, 0.4513,0.4533,0.4542,0.4570,0.4584,0.4652,0.4659,0.4671,0.4818,0.4862, 0.4880,0.4977,0.5044,0.5084,0.5137,0.5158,0.5171,0.5182,0.5208,0.5230, 0.5266,0.5320,0.5336,0.5444,0.5515,0.5600,0.5655,0.5755,0.5756,0.5821, 0.5847,0.5907,0.5927,0.5969,0.5984,0.6020,0.6119,0.6167,0.6172,0.6188, 0.6196,0.6246,0.6331,0.6331,0.6481,0.6522,0.6541,0.6676,0.6701,0.6711, 0.6796,0.6807,0.6822,0.6896,0.6903,0.6917,0.6933,0.6988,0.6990,0.7009, 0.7056,0.7087,0.7101,0.7139,0.7250,0.7311,0.7348,0.7377,0.7426,0.7433, 0.7457,0.7466,0.7486,0.7488,0.7523,0.7595,0.7666,0.7668,0.7686,0.7701, 0.7735,0.7742,0.7751,0.7777,0.7877,0.7891,0.7897,0.7902,0.7921,0.7951, 0.8010,0.8020,0.8023,0.8031,0.8040,0.8106,0.8302,0.8306,0.8312,0.8336, 0.8355,0.8360,0.8403,0.8442,0.8444,0.8467,0.8549,0.8558,0.8559,0.8560, 0.8640,0.8696,0.8748,0.8772,0.8799,0.8829,0.8899,0.8927,0.8955,0.8989, 0.9048,0.9057,0.9064,0.9112,0.9115,0.9117,0.9184,0.9232,0.9242,0.9278, 0.9299,0.9301,0.9309,0.9401,0.9433,0.9462,0.9485,0.9563,0.9592,0.9628, 0.9629,0.9683,0.9763,0.9801,0.9864,0.9864,0.9888,0.9967,0.9987, Overall p-value after applying KStest on 269 p-values = 0.592667 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.