RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-03-27_13:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.55 19.3206 0.689555 2 to 25 15.64 18.1527 0.620729 3 to 26 15.82 35.1657 0.994083 4 to 27 15.77 20.0781 0.729744 5 to 28 15.71 19.8132 0.716104 6 to 29 15.55 25.7722 0.921288 7 to 30 15.87 18.5117 0.642734 8 to 31 15.88 19.8142 0.716155 9 to 32 15.68 26.5522 0.935029 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.004604 Tough bday spacings test for dh-ranFile-2017-03-27_13:31: 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 35 71 101 79 83 53 40 18 7 4 (O-E)^2/E 0.0 0.1 0.1 0.1 3.6 0.3 0.0 3.5 0.7 0.0 0.0 Birthday Spacings: Sum(O-E)^2/E= 8.339, p= 0.404 RESULTS OF GCD FOR dh-ranFile-2017-03-27_13:31 Euclid's algorithm: p-value, steps to gcd: 0.953592 p-value, dist. of gcd's: 0.616774 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-03-27_13:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.074 0.366 0.831 0.099 0.073 0.607 0.279 0.171 Bits 8 to 15---> 0.914 0.771 0.933 0.801 0.552 0.223 0.633 0.275 Bits 16 to 23---> 0.711 0.954 0.644 0.192 0.183 0.308 0.356 0.698 Bits 24 to 31---> 0.123 0.436 0.885 0.543 0.756 0.962 0.943 0.636 KS test for the above 32 p values: 0.193 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-03-27_13:31, p-values for 5 runs: 0.4328, 0.1467, 0.5720, 0.4035, 0.6148 Rank test for binary matrices (31x31) for dh-ranFile-2017-03-27_13:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 203 211.4 0.335 0.335 r= 29 5085 5134.0 0.468 0.803 r= 30 23186 23103.0 0.298 1.101 r= 31 11526 11551.5 0.056 1.157 chi-square = 1.157 with df = 3; p-value = 0.237 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2017-03-27_13:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 199 211.4 0.729 0.729 r= 30 5065 5134.0 0.928 1.657 r= 31 23159 23103.0 0.136 1.793 r= 32 11577 11551.5 0.056 1.849 chi-square = 1.849 with df = 3; p-value = 0.396 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2017-03-27_13:31 b-rank test for bits 1 to 8, p=0.51581 b-rank test for bits 2 to 9, p=0.91377 b-rank test for bits 3 to 10, p=0.70693 b-rank test for bits 4 to 11, p=0.55219 b-rank test for bits 5 to 12, p=0.58891 b-rank test for bits 6 to 13, p=0.71458 b-rank test for bits 7 to 14, p=0.36852 b-rank test for bits 8 to 15, p=0.72078 b-rank test for bits 9 to 16, p=0.16885 b-rank test for bits 10 to 17, p=0.89334 b-rank test for bits 11 to 18, p=0.02014 b-rank test for bits 12 to 19, p=0.17053 b-rank test for bits 13 to 20, p=0.23080 b-rank test for bits 14 to 21, p=0.34585 b-rank test for bits 15 to 22, p=0.99902 b-rank test for bits 16 to 23, p=0.41936 b-rank test for bits 17 to 24, p=0.66207 b-rank test for bits 18 to 25, p=0.87169 b-rank test for bits 19 to 26, p=0.34195 b-rank test for bits 20 to 27, p=0.51876 b-rank test for bits 21 to 28, p=0.39267 b-rank test for bits 22 to 29, p=0.42054 b-rank test for bits 23 to 30, p=0.89305 b-rank test for bits 24 to 31, p=0.17302 b-rank test for bits 25 to 32, p=0.89938 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 = 0.645529 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-03-27_13:31 (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 141770 -0.33 0.372387 2 141768 -0.33 0.370621 3 141640 -0.63 0.264584 4 142188 0.65 0.742508 5 142295 0.90 0.816232 6 142059 0.35 0.636717 7 142073 0.38 0.648920 8 142803 2.09 0.981602 9 141947 0.09 0.535067 10 140942 -2.26 0.011907 11 142026 0.27 0.607417 12 142151 0.56 0.713844 13 142195 0.67 0.747759 14 141826 -0.19 0.422815 15 141918 0.02 0.508081 16 141743 -0.39 0.348778 17 141467 -1.03 0.150689 18 142048 0.32 0.627029 19 142040 0.31 0.619933 20 142103 0.45 0.674546 ---------------------------------------------------------------- OPSO test for dh-ranFile-2017-03-27_13:31 Bits used No. missing words z-score p-value 23 to 32 141968 0.2023 0.580163 22 to 31 142151 0.8333 0.797675 21 to 30 141637 -0.9391 0.173848 20 to 29 141663 -0.8494 0.197826 19 to 28 142061 0.5230 0.699513 18 to 27 141627 -0.9736 0.165140 17 to 26 141752 -0.5425 0.293731 16 to 25 141603 -1.0563 0.145413 15 to 24 141561 -1.2011 0.114849 14 to 23 141705 -0.7046 0.240534 13 to 22 141610 -1.0322 0.150996 12 to 21 141875 -0.1184 0.452884 11 to 20 141826 -0.2873 0.386924 10 to 19 141835 -0.2563 0.398856 9 to 18 142055 0.5023 0.692275 8 to 17 141690 -0.7563 0.224732 7 to 16 141485 -1.4632 0.071705 6 to 15 142005 0.3299 0.629261 5 to 14 141711 -0.6839 0.247020 4 to 13 141703 -0.7115 0.238393 3 to 12 141952 0.1471 0.558488 2 to 11 141641 -0.9253 0.177411 1 to 10 141746 -0.5632 0.286647 ----------------------------------------------------------------- OQSO test for dh-ranFile-2017-03-27_13:31 Bits used No. missing words z-score p-value 28 to 32 141863 -0.1571 0.437602 27 to 31 141836 -0.2486 0.401844 26 to 30 141841 -0.2316 0.408414 25 to 29 141934 0.0836 0.533324 24 to 28 141590 -1.0825 0.139521 23 to 27 141652 -0.8723 0.191521 22 to 26 141585 -1.0994 0.135792 21 to 25 141358 -1.8689 0.030817 20 to 24 141743 -0.5638 0.286435 19 to 23 142136 0.7684 0.778867 18 to 22 141361 -1.8587 0.031532 17 to 21 141740 -0.5740 0.282984 16 to 20 141715 -0.6587 0.255030 15 to 19 142101 0.6497 0.742066 14 to 18 142382 1.6023 0.945452 13 to 17 141718 -0.6486 0.258306 12 to 16 141393 -1.7503 0.040036 11 to 15 141580 -1.1164 0.132131 10 to 14 141893 -0.0554 0.477928 9 to 13 141753 -0.5299 0.298080 8 to 12 142407 1.6870 0.954200 7 to 11 141707 -0.6859 0.246399 6 to 10 141466 -1.5028 0.066444 5 to 9 142584 2.2870 0.988903 4 to 8 141960 0.1718 0.568188 3 to 7 141660 -0.8452 0.199003 2 to 6 142580 2.2735 0.988501 1 to 5 141671 -0.8079 0.209575 ----------------------------------------------------------------- DNA test for dh-ranFile-2017-03-27_13:31 Bits used No. missing words z-score p-value 31 to 32 141071 -2.4729 0.006700 30 to 31 142855 2.7896 0.997361 29 to 30 142058 0.4386 0.669508 28 to 29 141926 0.0492 0.519610 27 to 28 142692 2.3088 0.989522 26 to 27 141909 -0.0010 0.499612 25 to 26 141527 -1.1278 0.129699 24 to 25 141877 -0.0954 0.462011 23 to 24 141848 -0.1809 0.428217 22 to 23 141669 -0.7089 0.239182 21 to 22 141493 -1.2281 0.109702 20 to 21 142042 0.3914 0.652233 19 to 20 141463 -1.3166 0.093985 18 to 19 141549 -1.0629 0.143909 17 to 18 142168 0.7630 0.777280 16 to 17 142337 1.2616 0.896447 15 to 16 141458 -1.3314 0.091536 14 to 15 141942 0.0964 0.538387 13 to 14 141637 -0.8033 0.210891 12 to 13 142369 1.3560 0.912444 11 to 12 142193 0.8368 0.798643 10 to 11 141691 -0.6440 0.259774 9 to 10 141571 -0.9980 0.159134 8 to 9 142442 1.5713 0.941943 7 to 8 141425 -1.4287 0.076545 6 to 7 142238 0.9695 0.833859 5 to 6 141979 0.2055 0.581416 4 to 5 142070 0.4740 0.682233 3 to 4 141670 -0.7060 0.240098 2 to 3 141666 -0.7178 0.236444 1 to 2 141258 -1.9213 0.027345 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2017-03-27_13:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2512.08 0.171 0.567802 Test results for specific bytes for dh-ranFile-2017-03-27_13:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2573.27 1.036 0.849946 2 to 9 2514.75 0.209 0.582642 3 to 10 2514.67 0.208 0.582193 4 to 11 2367.64 -1.872 0.030616 5 to 12 2455.91 -0.623 0.266489 6 to 13 2369.67 -1.843 0.032649 7 to 14 2539.53 0.559 0.711932 8 to 15 2377.47 -1.733 0.041564 9 to 16 2518.34 0.259 0.602304 10 to 17 2505.19 0.073 0.529275 11 to 18 2575.21 1.064 0.856266 12 to 19 2510.29 0.145 0.557839 13 to 20 2536.32 0.514 0.696250 14 to 21 2577.60 1.097 0.863758 15 to 22 2472.61 -0.387 0.349269 16 to 23 2492.45 -0.107 0.457484 17 to 24 2434.21 -0.930 0.176082 18 to 25 2413.48 -1.224 0.110545 19 to 26 2493.60 -0.091 0.463938 20 to 27 2417.63 -1.165 0.122030 21 to 28 2520.40 0.289 0.613535 22 to 29 2459.95 -0.566 0.285540 23 to 30 2529.62 0.419 0.662374 24 to 31 2484.47 -0.220 0.413090 25 to 32 2486.66 -0.189 0.425176 CDPARK for dh-ranFile-2017-03-27_13:31: 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 3527 0.1826 0.572463 3514 -0.4110 0.340551 3496 -1.2329 0.108811 3542 0.8676 0.807188 3539 0.7306 0.767486 3524 0.0457 0.518210 3533 0.4566 0.676028 3522 -0.0457 0.481790 3504 -0.8676 0.192812 3544 0.9589 0.831196 Square side=100, avg. no. parked=3524.50 sample std.=15.25 p-value of the KSTEST for those 10 p-values: 0.836517 Results for the MINIMUM DISTANCE test for dh-ranFile-2017-03-27_13:31 0.1831,0.6764,0.7708,0.7189,0.2198,0.7394,0.8877,0.5965,0.8046,0.1691, The KS test for those 10 p-values: 0.403423 The 3DSPHERES test for dh-ranFile-2017-03-27_13:31 sample no r^3 equiv. uni. 1 58.619 0.858290 2 20.696 0.498355 3 53.431 0.831535 4 63.492 0.879536 5 13.232 0.356657 6 75.843 0.920189 7 9.109 0.261869 8 20.361 0.492729 9 50.481 0.814128 10 15.736 0.408165 11 17.092 0.434317 12 15.187 0.397238 13 17.178 0.435945 14 70.001 0.903030 15 39.429 0.731340 16 1.990 0.064184 17 14.641 0.386167 18 53.132 0.829847 19 3.433 0.108125 20 0.780 0.025660 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.637539 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-03-27_13:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 -0.7 0.3 -0.8 2.3 -0.4 0.3 -1.2 1.2 1.2 -1.4 -0.1 -0.7 -0.1 1.8 -1.0 0.0 1.3 -1.5 -0.0 -1.1 0.8 -0.2 -1.0 -0.2 1.3 1.2 0.8 0.1 0.7 0.3 -1.3 -0.6 -0.1 0.5 -0.3 -1.2 -0.4 -0.8 -0.7 -0.6 1.0 -1.1 Chi-square with 42 degrees of freedom:39.109926 z-score=-0.315333, p-value=0.401438 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2017-03-27_13:31 Test no p-value 1 0.518200 2 0.010248 3 0.429580 4 0.512504 5 0.503266 6 0.318308 7 0.749799 8 0.123295 9 0.554486 10 0.047645 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.192927 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-03-27_13:31: (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 66657 0.00 66454 0.68 3 25000.00 25105 0.44 25205 1.68 4 6666.67 6608 0.52 6667 0.00 5 1388.89 1357 0.73 1407 0.24 6 238.10 236 0.02 232 0.16 7 34.72 32 0.21 28 1.30 8 4.96 4 0.19 6 0.22 p=0.09052 p=0.35985 Number of rngs required: 688041, p-value: 0.338 RESULTS OF CRAPS TEST for dh-ranFile-2017-03-27_13:31 No. of wins: Observed Expected 98734 98585.9 z-score= 0.663, pvalue=0.74620 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66713 66666.7 0.032 0.032 2 37620 37654.3 0.031 0.063 3 27096 26954.7 0.740 0.804 4 19345 19313.5 0.051 0.855 5 13871 13851.4 0.028 0.883 6 9849 9943.5 0.899 1.782 7 7101 7145.0 0.271 2.053 8 5201 5139.1 0.746 2.799 9 3637 3699.9 1.068 3.868 10 2640 2666.3 0.259 4.127 11 1930 1923.3 0.023 4.150 12 1335 1388.7 2.080 6.230 13 1028 1003.7 0.588 6.817 14 694 726.1 1.423 8.240 15 502 525.8 1.080 9.320 16 403 381.2 1.253 10.573 17 282 276.5 0.108 10.681 18 210 200.8 0.419 11.099 19 136 146.0 0.683 11.782 20 106 106.2 0.000 11.783 21 301 287.1 0.672 12.454 Chisq= 12.45 for 20 degrees of freedom, p= 0.10045 SUMMARY of craptest p-value for no. of wins: 0.746199 p-value for throws/game: 0.100448 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2017-03-27_13:31 No. of wins: Observed Expected 98201 98585.9 z-score=-1.721, pvalue=0.04260 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66356 66666.7 1.448 1.448 2 37656 37654.3 0.000 1.448 3 27284 26954.7 4.022 5.470 4 19358 19313.5 0.103 5.573 5 13852 13851.4 0.000 5.573 6 9976 9943.5 0.106 5.679 7 7122 7145.0 0.074 5.753 8 5086 5139.1 0.548 6.301 9 3636 3699.9 1.102 7.403 10 2713 2666.3 0.818 8.221 11 1900 1923.3 0.283 8.504 12 1399 1388.7 0.076 8.580 13 1044 1003.7 1.617 10.197 14 734 726.1 0.085 10.282 15 537 525.8 0.237 10.519 16 381 381.2 0.000 10.519 17 260 276.5 0.989 11.508 18 182 200.8 1.765 13.274 19 134 146.0 0.984 14.258 20 112 106.2 0.315 14.573 21 278 287.1 0.289 14.862 Chisq= 14.86 for 20 degrees of freedom, p= 0.21576 SUMMARY of craptest p-value for no. of wins: 0.042597 p-value for throws/game: 0.215755 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0046,0.0067,0.0102,0.0119,0.0201,0.0257,0.0273,0.0306,0.0308,0.0315, 0.0326,0.0400,0.0416,0.0426,0.0476,0.0642,0.0664,0.0717,0.0735,0.0736, 0.0765,0.0905,0.0915,0.0940,0.0989,0.1004,0.1081,0.1088,0.1097,0.1105, 0.1148,0.1220,0.1231,0.1233,0.1297,0.1321,0.1358,0.1395,0.1439,0.1454, 0.1467,0.1507,0.1510,0.1591,0.1651,0.1688,0.1691,0.1705,0.1713,0.1730, 0.1738,0.1761,0.1774,0.1831,0.1832,0.1915,0.1917,0.1928,0.1929,0.1933, 0.1978,0.1990,0.2096,0.2109,0.2158,0.2198,0.2226,0.2247,0.2308,0.2364, 0.2367,0.2384,0.2392,0.2401,0.2405,0.2464,0.2470,0.2550,0.2583,0.2598, 0.2619,0.2646,0.2665,0.2745,0.2791,0.2830,0.2855,0.2864,0.2866,0.2937, 0.2981,0.3080,0.3183,0.3384,0.3406,0.3420,0.3459,0.3488,0.3493,0.3559, 0.3567,0.3599,0.3657,0.3685,0.3706,0.3724,0.3862,0.3869,0.3927,0.3956, 0.3972,0.3989,0.4014,0.4018,0.4034,0.4035,0.4042,0.4082,0.4084,0.4131, 0.4194,0.4205,0.4228,0.4252,0.4282,0.4296,0.4328,0.4343,0.4356,0.4359, 0.4376,0.4529,0.4575,0.4620,0.4639,0.4779,0.4818,0.4927,0.4984,0.4996, 0.5033,0.5081,0.5125,0.5158,0.5182,0.5182,0.5188,0.5196,0.5293,0.5333, 0.5351,0.5384,0.5431,0.5517,0.5522,0.5545,0.5578,0.5585,0.5678,0.5682, 0.5720,0.5725,0.5802,0.5814,0.5822,0.5826,0.5889,0.5965,0.6023,0.6065, 0.6074,0.6135,0.6148,0.6168,0.6199,0.6207,0.6270,0.6293,0.6333,0.6355, 0.6367,0.6375,0.6427,0.6439,0.6455,0.6489,0.6522,0.6621,0.6624,0.6695, 0.6745,0.6760,0.6764,0.6822,0.6896,0.6923,0.6963,0.6978,0.6995,0.7069, 0.7106,0.7119,0.7138,0.7146,0.7161,0.7162,0.7189,0.7208,0.7297,0.7313, 0.7394,0.7421,0.7425,0.7462,0.7478,0.7498,0.7560,0.7675,0.7708,0.7714, 0.7773,0.7789,0.7977,0.7986,0.8012,0.8046,0.8072,0.8141,0.8162,0.8298, 0.8307,0.8312,0.8315,0.8339,0.8365,0.8499,0.8563,0.8583,0.8638,0.8717, 0.8795,0.8849,0.8877,0.8930,0.8933,0.8964,0.8994,0.9030,0.9124,0.9135, 0.9138,0.9202,0.9213,0.9331,0.9350,0.9419,0.9431,0.9455,0.9536,0.9541, 0.9542,0.9618,0.9816,0.9885,0.9889,0.9895,0.9941,0.9974,0.9990, Overall p-value after applying KStest on 269 p-values = 0.346644 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.