RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-11-28_06:31 (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 24.6520 0.897226 2 to 25 15.72 13.1673 0.275086 3 to 26 15.61 25.9410 0.924458 4 to 27 15.76 10.8664 0.136577 5 to 28 15.56 18.7126 0.654723 6 to 29 15.69 18.3908 0.635406 7 to 30 15.65 17.9129 0.605645 8 to 31 15.64 19.3110 0.689024 9 to 32 15.39 35.6055 0.994824 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.169011 Tough bday spacings test for dh-ranFile-2015-11-28_06:31: 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 7 30 77 87 104 86 56 28 16 5 4 (O-E)^2/E 0.5 1.2 0.2 1.2 0.4 0.8 0.3 0.1 0.1 0.4 0.0 Birthday Spacings: Sum(O-E)^2/E= 5.142, p= 0.119 RESULTS OF GCD FOR dh-ranFile-2015-11-28_06:31 Euclid's algorithm: p-value, steps to gcd: 0.321474 p-value, dist. of gcd's: 0.430187 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-11-28_06:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.054 0.085 0.559 0.327 0.584 0.845 0.460 0.204 Bits 8 to 15---> 0.208 0.160 0.716 0.631 0.862 0.967 0.370 0.565 Bits 16 to 23---> 0.451 0.304 0.159 0.319 0.456 0.812 0.721 0.644 Bits 24 to 31---> 0.993 0.560 0.862 0.596 0.916 0.282 0.284 0.579 KS test for the above 32 p values: 0.134 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-11-28_06:31, p-values for 5 runs: 0.2475, 0.6388, 0.6222, 0.5729, 0.5234 Rank test for binary matrices (31x31) for dh-ranFile-2015-11-28_06:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 220 211.4 0.348 0.348 r= 29 5226 5134.0 1.648 1.997 r= 30 23019 23103.0 0.306 2.302 r= 31 11535 11551.5 0.024 2.326 chi-square = 2.326 with df = 3; p-value = 0.492 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-11-28_06:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 190 211.4 2.170 2.170 r= 30 5132 5134.0 0.001 2.171 r= 31 23058 23103.0 0.088 2.258 r= 32 11620 11551.5 0.406 2.664 chi-square = 2.664 with df = 3; p-value = 0.554 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-11-28_06:31 b-rank test for bits 1 to 8, p=0.01534 b-rank test for bits 2 to 9, p=0.78100 b-rank test for bits 3 to 10, p=0.47117 b-rank test for bits 4 to 11, p=0.40618 b-rank test for bits 5 to 12, p=0.16802 b-rank test for bits 6 to 13, p=0.70343 b-rank test for bits 7 to 14, p=0.06118 b-rank test for bits 8 to 15, p=0.16279 b-rank test for bits 9 to 16, p=0.52697 b-rank test for bits 10 to 17, p=0.28360 b-rank test for bits 11 to 18, p=0.43352 b-rank test for bits 12 to 19, p=0.48108 b-rank test for bits 13 to 20, p=0.46122 b-rank test for bits 14 to 21, p=0.76458 b-rank test for bits 15 to 22, p=0.38896 b-rank test for bits 16 to 23, p=0.74572 b-rank test for bits 17 to 24, p=0.60830 b-rank test for bits 18 to 25, p=0.46397 b-rank test for bits 19 to 26, p=0.40227 b-rank test for bits 20 to 27, p=0.72035 b-rank test for bits 21 to 28, p=0.17753 b-rank test for bits 22 to 29, p=0.03650 b-rank test for bits 23 to 30, p=0.68304 b-rank test for bits 24 to 31, p=0.98008 b-rank test for bits 25 to 32, p=0.46430 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 = 0.412479 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-11-28_06:31 (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 141594 -0.74 0.230637 2 142300 0.91 0.819321 3 141714 -0.46 0.324059 4 141613 -0.69 0.244356 5 141885 -0.06 0.477334 6 141807 -0.24 0.405518 7 142278 0.86 0.805485 8 142062 0.36 0.639344 9 141790 -0.28 0.390196 10 141385 -1.23 0.110274 11 141421 -1.14 0.126944 12 142224 0.74 0.768894 13 141346 -1.32 0.094055 14 141723 -0.44 0.331654 15 141951 0.10 0.538780 16 142180 0.63 0.736439 17 141816 -0.22 0.413691 18 141891 -0.04 0.482920 19 142024 0.27 0.605620 20 142344 1.02 0.845086 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-11-28_06:31 Bits used No. missing words z-score p-value 23 to 32 141997 0.3023 0.618792 22 to 31 142120 0.7264 0.766218 21 to 30 141964 0.1885 0.574764 20 to 29 142028 0.4092 0.658806 19 to 28 142189 0.9644 0.832572 18 to 27 142463 1.9092 0.971882 17 to 26 141649 -0.8977 0.184676 16 to 25 141453 -1.5736 0.057796 15 to 24 141463 -1.5391 0.061894 14 to 23 142351 1.5230 0.936121 13 to 22 142153 0.8402 0.799614 12 to 21 141752 -0.5425 0.293731 11 to 20 142076 0.5747 0.717261 10 to 19 141586 -1.1149 0.132440 9 to 18 141763 -0.5046 0.306925 8 to 17 141351 -1.9253 0.027097 7 to 16 141834 -0.2598 0.397525 6 to 15 142335 1.4678 0.928924 5 to 14 142237 1.1299 0.870740 4 to 13 142312 1.3885 0.917510 3 to 12 141885 -0.0839 0.466569 2 to 11 141968 0.2023 0.580163 1 to 10 142136 0.7816 0.782781 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-11-28_06:31 Bits used No. missing words z-score p-value 28 to 32 142012 0.3480 0.636093 27 to 31 141724 -0.6282 0.264924 26 to 30 141961 0.1752 0.569520 25 to 29 141634 -0.9333 0.175327 24 to 28 141922 0.0429 0.517129 23 to 27 142151 0.8192 0.793670 22 to 26 142261 1.1921 0.883389 21 to 25 141680 -0.7774 0.218464 20 to 24 141515 -1.3367 0.090658 19 to 23 142404 1.6768 0.953214 18 to 22 141234 -2.2893 0.011032 17 to 21 141622 -0.9740 0.165028 16 to 20 142070 0.5446 0.707001 15 to 19 142153 0.8260 0.795598 14 to 18 141889 -0.0689 0.472529 13 to 17 142079 0.5752 0.717406 12 to 16 141445 -1.5740 0.057744 11 to 15 141857 -0.1774 0.429601 10 to 14 141672 -0.8045 0.210552 9 to 13 141698 -0.7164 0.236881 8 to 12 141902 -0.0248 0.490088 7 to 11 141622 -0.9740 0.165028 6 to 10 141752 -0.5333 0.296905 5 to 9 141989 0.2701 0.606446 4 to 8 141459 -1.5265 0.063437 3 to 7 142336 1.4463 0.925959 2 to 6 142149 0.8124 0.791731 1 to 5 141973 0.2158 0.585440 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-11-28_06:31 Bits used No. missing words z-score p-value 31 to 32 142321 1.2144 0.887696 30 to 31 142671 2.2468 0.987674 29 to 30 142000 0.2675 0.605444 28 to 29 142462 1.6303 0.948480 27 to 28 141609 -0.8859 0.187828 26 to 27 142245 0.9902 0.838956 25 to 26 141501 -1.2045 0.114196 24 to 25 142196 0.8456 0.801122 23 to 24 142346 1.2881 0.901147 22 to 23 141777 -0.3904 0.348137 21 to 22 141353 -1.6411 0.050389 20 to 21 142102 0.5683 0.715101 19 to 20 141457 -1.3343 0.091052 18 to 19 142321 1.2144 0.887696 17 to 18 141677 -0.6853 0.246565 16 to 17 141357 -1.6293 0.051626 15 to 16 142232 0.9518 0.829408 14 to 15 141253 -1.9361 0.026429 13 to 14 141978 0.2026 0.580263 12 to 13 142005 0.2822 0.611110 11 to 12 142201 0.8604 0.805211 10 to 11 141905 -0.0128 0.494905 9 to 10 141566 -1.0128 0.155584 8 to 9 141439 -1.3874 0.082659 7 to 8 141889 -0.0600 0.476090 6 to 7 142012 0.3029 0.619002 5 to 6 141513 -1.1691 0.121179 4 to 5 141693 -0.6381 0.261691 3 to 4 141655 -0.7502 0.226556 2 to 3 142074 0.4858 0.686429 1 to 2 142050 0.4150 0.660913 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-11-28_06:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2367.15 -1.879 0.030138 Test results for specific bytes for dh-ranFile-2015-11-28_06:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2472.45 -0.390 0.348386 2 to 9 2608.75 1.538 0.937978 3 to 10 2535.80 0.506 0.693691 4 to 11 2467.98 -0.453 0.325335 5 to 12 2528.67 0.405 0.657421 6 to 13 2423.72 -1.079 0.140360 7 to 14 2474.37 -0.362 0.358528 8 to 15 2367.17 -1.878 0.030160 9 to 16 2441.30 -0.830 0.203231 10 to 17 2543.46 0.615 0.730617 11 to 18 2557.73 0.816 0.792858 12 to 19 2400.65 -1.405 0.080015 13 to 20 2545.78 0.647 0.741340 14 to 21 2514.04 0.199 0.578674 15 to 22 2516.14 0.228 0.590276 16 to 23 2606.15 1.501 0.933342 17 to 24 2457.95 -0.595 0.276041 18 to 25 2509.52 0.135 0.553547 19 to 26 2347.00 -2.164 0.015240 20 to 27 2456.67 -0.613 0.269990 21 to 28 2457.46 -0.602 0.273727 22 to 29 2504.91 0.069 0.527687 23 to 30 2507.90 0.112 0.544456 24 to 31 2507.76 0.110 0.543699 25 to 32 2482.15 -0.252 0.400352 CDPARK for dh-ranFile-2015-11-28_06:31: 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 3501 -1.0046 0.157553 3505 -0.8219 0.205562 3504 -0.8676 0.192812 3521 -0.0913 0.463617 3532 0.4110 0.659449 3522 -0.0457 0.481790 3529 0.2740 0.607947 3551 1.2785 0.899470 3559 1.6438 0.949895 3534 0.5023 0.692266 Square side=100, avg. no. parked=3525.80 sample std.=18.48 p-value of the KSTEST for those 10 p-values: 0.917752 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-11-28_06:31 0.2681,0.9878,0.7277,0.5442,0.9602,0.8833,0.7993,0.5400,0.2063,0.9904, The KS test for those 10 p-values: 0.026874 The 3DSPHERES test for dh-ranFile-2015-11-28_06:31 sample no r^3 equiv. uni. 1 6.280 0.188869 2 52.810 0.828010 3 27.015 0.593633 4 4.960 0.152387 5 4.429 0.137258 6 36.734 0.706090 7 73.640 0.914107 8 17.446 0.440969 9 2.222 0.071386 10 0.233 0.007721 11 6.191 0.186459 12 0.121 0.004036 13 84.947 0.941080 14 101.287 0.965824 15 5.217 0.159617 16 5.016 0.153967 17 11.803 0.325264 18 46.357 0.786739 19 17.806 0.447624 20 1.247 0.040725 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.063803 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-11-28_06:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 2.2 1.3 -1.0 -0.7 1.3 1.0 -0.1 -0.5 0.0 -0.1 -1.0 0.2 -0.5 -0.0 -0.9 -0.8 1.7 1.4 -0.3 -1.6 0.6 0.1 0.8 -0.2 1.6 1.1 -1.2 -0.2 -1.1 -0.7 -0.7 -0.6 0.2 0.8 0.1 -0.2 -1.3 -1.2 -0.7 -0.6 0.0 -0.1 Chi-square with 42 degrees of freedom:35.112791 z-score=-0.751456, p-value=0.234807 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-11-28_06:31 Test no p-value 1 0.486918 2 0.968808 3 0.255663 4 0.849542 5 0.040732 6 0.107601 7 0.451508 8 0.782562 9 0.035613 10 0.243025 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.463837 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-11-28_06:31: (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 66526 0.30 66529 0.28 3 25000.00 25187 1.40 25101 0.41 4 6666.67 6621 0.31 6637 0.13 5 1388.89 1394 0.02 1445 2.27 6 238.10 229 0.35 251 0.70 7 34.72 37 0.15 27 1.72 8 4.96 5 0.00 9 3.29 p=0.13431 p=0.81473 Number of rngs required: 688607, p-value: 0.593 RESULTS OF CRAPS TEST for dh-ranFile-2015-11-28_06:31 No. of wins: Observed Expected 98317 98585.9 z-score=-1.202, pvalue=0.11459 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66455 66666.7 0.672 0.672 2 37804 37654.3 0.595 1.267 3 26769 26954.7 1.280 2.547 4 19395 19313.5 0.344 2.891 5 13807 13851.4 0.142 3.034 6 10133 9943.5 3.610 6.643 7 7040 7145.0 1.544 8.187 8 5201 5139.1 0.746 8.933 9 3736 3699.9 0.353 9.286 10 2705 2666.3 0.562 9.848 11 1898 1923.3 0.334 10.182 12 1392 1388.7 0.008 10.189 13 960 1003.7 1.904 12.093 14 758 726.1 1.398 13.491 15 514 525.8 0.266 13.757 16 391 381.2 0.255 14.012 17 301 276.5 2.164 16.176 18 202 200.8 0.007 16.182 19 155 146.0 0.557 16.739 20 101 106.2 0.256 16.995 21 283 287.1 0.059 17.054 Chisq= 17.05 for 20 degrees of freedom, p= 0.35055 SUMMARY of craptest p-value for no. of wins: 0.114586 p-value for throws/game: 0.350545 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-11-28_06:31 No. of wins: Observed Expected 98857 98585.9 z-score= 1.213, pvalue=0.88738 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67149 66666.7 3.490 3.490 2 37689 37654.3 0.032 3.522 3 26641 26954.7 3.652 7.173 4 19561 19313.5 3.173 10.346 5 13680 13851.4 2.121 12.467 6 10011 9943.5 0.458 12.925 7 6936 7145.0 6.115 19.040 8 4975 5139.1 5.238 24.278 9 3656 3699.9 0.520 24.798 10 2647 2666.3 0.140 24.938 11 2012 1923.3 4.088 29.026 12 1410 1388.7 0.325 29.351 13 1027 1003.7 0.540 29.892 14 708 726.1 0.453 30.345 15 519 525.8 0.089 30.434 16 417 381.2 3.372 33.805 17 262 276.5 0.764 34.570 18 179 200.8 2.373 36.943 19 138 146.0 0.437 37.379 20 101 106.2 0.256 37.635 21 282 287.1 0.091 37.727 Chisq= 37.73 for 20 degrees of freedom, p= 0.99044 SUMMARY of craptest p-value for no. of wins: 0.887378 p-value for throws/game: 0.990438 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0040,0.0077,0.0110,0.0152,0.0153,0.0264,0.0269,0.0271,0.0301,0.0302, 0.0356,0.0365,0.0407,0.0407,0.0504,0.0516,0.0538,0.0577,0.0578,0.0612, 0.0619,0.0634,0.0638,0.0714,0.0800,0.0827,0.0847,0.0907,0.0911,0.0941, 0.1076,0.1103,0.1142,0.1146,0.1185,0.1212,0.1269,0.1324,0.1340,0.1343, 0.1366,0.1373,0.1404,0.1524,0.1540,0.1556,0.1576,0.1587,0.1596,0.1603, 0.1628,0.1650,0.1650,0.1680,0.1690,0.1753,0.1775,0.1847,0.1865,0.1878, 0.1889,0.1928,0.2032,0.2039,0.2056,0.2063,0.2079,0.2106,0.2185,0.2266, 0.2306,0.2348,0.2369,0.2430,0.2444,0.2466,0.2475,0.2557,0.2617,0.2649, 0.2681,0.2700,0.2737,0.2751,0.2760,0.2815,0.2836,0.2839,0.2937,0.2969, 0.3040,0.3069,0.3188,0.3215,0.3241,0.3253,0.3253,0.3274,0.3317,0.3481, 0.3484,0.3505,0.3585,0.3703,0.3890,0.3902,0.3975,0.4004,0.4023,0.4055, 0.4062,0.4125,0.4137,0.4296,0.4302,0.4335,0.4410,0.4476,0.4509,0.4515, 0.4562,0.4604,0.4612,0.4636,0.4638,0.4640,0.4643,0.4666,0.4712,0.4725, 0.4761,0.4773,0.4811,0.4818,0.4829,0.4869,0.4901,0.4924,0.4949,0.5171, 0.5234,0.5270,0.5277,0.5388,0.5400,0.5437,0.5442,0.5445,0.5535,0.5537, 0.5595,0.5601,0.5650,0.5695,0.5729,0.5748,0.5787,0.5794,0.5802,0.5803, 0.5843,0.5854,0.5903,0.5928,0.5936,0.5962,0.6054,0.6056,0.6056,0.6064, 0.6079,0.6083,0.6111,0.6188,0.6190,0.6222,0.6312,0.6354,0.6361,0.6388, 0.6393,0.6445,0.6547,0.6574,0.6588,0.6594,0.6609,0.6830,0.6864,0.6890, 0.6923,0.6937,0.7034,0.7061,0.7070,0.7151,0.7157,0.7173,0.7174,0.7203, 0.7213,0.7277,0.7306,0.7364,0.7413,0.7457,0.7646,0.7662,0.7689,0.7810, 0.7826,0.7828,0.7867,0.7917,0.7929,0.7937,0.7956,0.7993,0.7996,0.8011, 0.8052,0.8055,0.8116,0.8147,0.8193,0.8280,0.8294,0.8326,0.8390,0.8451, 0.8452,0.8495,0.8619,0.8621,0.8707,0.8833,0.8834,0.8874,0.8877,0.8877, 0.8972,0.8995,0.9011,0.9141,0.9157,0.9175,0.9178,0.9245,0.9260,0.9289, 0.9333,0.9361,0.9380,0.9411,0.9485,0.9499,0.9532,0.9602,0.9658,0.9667, 0.9688,0.9719,0.9801,0.9877,0.9878,0.9904,0.9904,0.9928,0.9948, Overall p-value after applying KStest on 269 p-values = 0.713756 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.