RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-04-12_09:31 (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 16.3920 0.503761 2 to 25 15.74 16.1656 0.487871 3 to 26 15.71 19.6231 0.706041 4 to 27 15.57 28.3178 0.958640 5 to 28 15.57 35.3627 0.994427 6 to 29 15.73 22.2391 0.824303 7 to 30 15.87 18.3239 0.631315 8 to 31 15.69 15.3047 0.426455 9 to 32 16.12 19.1229 0.678474 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.060597 Tough bday spacings test for dh-ranFile-2018-04-12_09:31: 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 68 83 111 100 46 25 17 4 2 (O-E)^2/E 0.0 0.1 0.4 2.2 1.8 6.1 0.7 0.8 0.3 1.0 1.0 Birthday Spacings: Sum(O-E)^2/E= 14.450, p= 0.847 RESULTS OF GCD FOR dh-ranFile-2018-04-12_09:31 Euclid's algorithm: p-value, steps to gcd: 0.600838 p-value, dist. of gcd's: 0.558073 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-04-12_09:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.215 0.618 0.039 0.365 0.498 0.191 0.567 0.611 Bits 8 to 15---> 0.156 0.462 0.238 0.825 0.290 0.588 0.758 0.889 Bits 16 to 23---> 0.595 0.486 0.150 0.151 0.674 0.683 0.968 0.252 Bits 24 to 31---> 0.058 0.881 0.732 0.438 0.030 0.781 0.434 0.615 KS test for the above 32 p values: 0.160 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-04-12_09:31, p-values for 5 runs: 0.4545, 0.0641, 0.3634, 0.9053, 0.1343 Rank test for binary matrices (31x31) for dh-ranFile-2018-04-12_09:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 175 211.4 6.273 6.273 r= 29 5019 5134.0 2.576 8.850 r= 30 23170 23103.0 0.194 9.044 r= 31 11636 11551.5 0.618 9.661 chi-square = 9.661 with df = 3; p-value = 0.978 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-04-12_09:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 210 211.4 0.010 0.010 r= 30 5090 5134.0 0.377 0.387 r= 31 23142 23103.0 0.066 0.452 r= 32 11558 11551.5 0.004 0.456 chi-square = 0.456 with df = 3; p-value = 0.072 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-04-12_09:31 b-rank test for bits 1 to 8, p=0.84394 b-rank test for bits 2 to 9, p=0.57870 b-rank test for bits 3 to 10, p=0.74722 b-rank test for bits 4 to 11, p=0.13191 b-rank test for bits 5 to 12, p=0.53820 b-rank test for bits 6 to 13, p=0.46588 b-rank test for bits 7 to 14, p=0.47333 b-rank test for bits 8 to 15, p=0.43503 b-rank test for bits 9 to 16, p=0.24584 b-rank test for bits 10 to 17, p=0.19470 b-rank test for bits 11 to 18, p=0.43729 b-rank test for bits 12 to 19, p=0.49101 b-rank test for bits 13 to 20, p=0.44674 b-rank test for bits 14 to 21, p=0.11375 b-rank test for bits 15 to 22, p=0.57932 b-rank test for bits 16 to 23, p=0.57903 b-rank test for bits 17 to 24, p=0.01776 b-rank test for bits 18 to 25, p=0.32565 b-rank test for bits 19 to 26, p=0.32941 b-rank test for bits 20 to 27, p=0.83433 b-rank test for bits 21 to 28, p=0.02341 b-rank test for bits 22 to 29, p=0.42210 b-rank test for bits 23 to 30, p=0.75864 b-rank test for bits 24 to 31, p=0.75301 b-rank test for bits 25 to 32, p=0.19759 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 = 0.265375 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-04-12_09:31 (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 141664 -0.57 0.283254 2 142158 0.58 0.719381 3 142379 1.10 0.863758 4 142204 0.69 0.754425 5 141983 0.17 0.568331 6 142461 1.29 0.901292 7 142133 0.52 0.699371 8 141795 -0.27 0.394686 9 141709 -0.47 0.319871 10 141709 -0.47 0.319871 11 141556 -0.83 0.204533 12 142534 1.46 0.927788 13 141296 -1.43 0.075927 14 141784 -0.29 0.384827 15 141641 -0.63 0.265350 16 143166 2.94 0.998338 17 142189 0.65 0.743262 18 141943 0.08 0.531352 19 141316 -1.39 0.082830 20 142371 1.08 0.859632 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-04-12_09:31 Bits used No. missing words z-score p-value 23 to 32 141549 -1.2425 0.107023 22 to 31 142050 0.4851 0.686186 21 to 30 141945 0.1230 0.548947 20 to 29 141774 -0.4667 0.320373 19 to 28 141794 -0.3977 0.345430 18 to 27 142096 0.6437 0.740112 17 to 26 142033 0.4264 0.665109 16 to 25 142330 1.4506 0.926552 15 to 24 141715 -0.6701 0.251396 14 to 23 141972 0.2161 0.585547 13 to 22 141766 -0.4942 0.310568 12 to 21 141667 -0.8356 0.201684 11 to 20 142056 0.5058 0.693487 10 to 19 142065 0.5368 0.704295 9 to 18 141863 -0.1598 0.436536 8 to 17 142030 0.4161 0.661333 7 to 16 141746 -0.5632 0.286647 6 to 15 142155 0.8471 0.801541 5 to 14 141813 -0.3322 0.369880 4 to 13 141663 -0.8494 0.197826 3 to 12 141770 -0.4804 0.315454 2 to 11 141676 -0.8046 0.210529 1 to 10 142335 1.4678 0.928924 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-04-12_09:31 Bits used No. missing words z-score p-value 28 to 32 142103 0.6565 0.744252 27 to 31 141832 -0.2621 0.396609 26 to 30 142267 1.2124 0.887328 25 to 29 141993 0.2836 0.611652 24 to 28 141290 -2.0994 0.017890 23 to 27 142041 0.4463 0.672324 22 to 26 141288 -2.1062 0.017593 21 to 25 141658 -0.8520 0.197116 20 to 24 141880 -0.0994 0.460401 19 to 23 142236 1.1074 0.865930 18 to 22 141612 -1.0079 0.156752 17 to 21 142048 0.4701 0.680847 16 to 20 141630 -0.9469 0.171850 15 to 19 141898 -0.0384 0.484682 14 to 18 141906 -0.0113 0.495497 13 to 17 142048 0.4701 0.680847 12 to 16 142335 1.4429 0.925483 11 to 15 141933 0.0802 0.531976 10 to 14 141647 -0.8893 0.186933 9 to 13 141482 -1.4486 0.073728 8 to 12 141890 -0.0655 0.473878 7 to 11 142099 0.6429 0.739872 6 to 10 141944 0.1175 0.546778 5 to 9 141753 -0.5299 0.298080 4 to 8 141113 -2.6994 0.003473 3 to 7 142428 1.7582 0.960644 2 to 6 141763 -0.4960 0.309935 1 to 5 141446 -1.5706 0.058137 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-04-12_09:31 Bits used No. missing words z-score p-value 31 to 32 142241 0.9784 0.836056 30 to 31 141760 -0.4405 0.329787 29 to 30 141578 -0.9774 0.164192 28 to 29 142618 2.0905 0.981712 27 to 28 141764 -0.4287 0.334070 26 to 27 141678 -0.6824 0.247496 25 to 26 141521 -1.1455 0.125998 24 to 25 141843 -0.1957 0.422437 23 to 24 141656 -0.7473 0.227445 22 to 23 142585 1.9931 0.976876 21 to 22 142350 1.2999 0.903184 20 to 21 142045 0.4002 0.655498 19 to 20 142021 0.3294 0.629077 18 to 19 141661 -0.7325 0.231921 17 to 18 142052 0.4209 0.663070 16 to 17 141561 -1.0275 0.152087 15 to 16 141418 -1.4494 0.073620 14 to 15 142476 1.6716 0.952698 13 to 14 141841 -0.2016 0.420129 12 to 13 141655 -0.7502 0.226556 11 to 12 141804 -0.3107 0.378011 10 to 11 142678 2.2675 0.988319 9 to 10 142268 1.0580 0.854978 8 to 9 142127 0.6421 0.739594 7 to 8 142374 1.3707 0.914767 6 to 7 142070 0.4740 0.682233 5 to 6 142285 1.1082 0.866106 4 to 5 142232 0.9518 0.829408 3 to 4 141332 -1.7030 0.044280 2 to 3 141929 0.0580 0.523135 1 to 2 141791 -0.3491 0.363524 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-04-12_09:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2531.47 0.445 0.671850 Test results for specific bytes for dh-ranFile-2018-04-12_09:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2580.19 1.134 0.871611 2 to 9 2520.22 0.286 0.612530 3 to 10 2510.37 0.147 0.558270 4 to 11 2545.85 0.648 0.741656 5 to 12 2440.94 -0.835 0.201805 6 to 13 2500.49 0.007 0.502769 7 to 14 2455.95 -0.623 0.266675 8 to 15 2533.88 0.479 0.684078 9 to 16 2426.44 -1.040 0.149105 10 to 17 2498.71 -0.018 0.492719 11 to 18 2518.14 0.257 0.601237 12 to 19 2477.39 -0.320 0.374575 13 to 20 2486.46 -0.192 0.424046 14 to 21 2661.31 2.281 0.988734 15 to 22 2362.13 -1.950 0.025598 16 to 23 2589.69 1.268 0.897673 17 to 24 2579.79 1.128 0.870435 18 to 25 2477.07 -0.324 0.372865 19 to 26 2465.19 -0.492 0.311251 20 to 27 2508.34 0.118 0.546964 21 to 28 2386.03 -1.612 0.053508 22 to 29 2699.38 2.820 0.997596 23 to 30 2594.39 1.335 0.909040 24 to 31 2523.97 0.339 0.632696 25 to 32 2549.72 0.703 0.758999 CDPARK for dh-ranFile-2018-04-12_09:31: 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 3515 -0.3653 0.357445 3527 0.1826 0.572463 3525 0.0913 0.536383 3517 -0.2740 0.392053 3513 -0.4566 0.323972 3530 0.3196 0.625377 3509 -0.6393 0.261324 3553 1.3699 0.914635 3541 0.8219 0.794438 3515 -0.3653 0.357445 Square side=100, avg. no. parked=3524.50 sample std.=13.15 p-value of the KSTEST for those 10 p-values: 0.518453 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-04-12_09:31 0.4017,0.4145,0.1580,0.1454,0.8089,0.6146,0.6917,0.7436,0.3365,0.6844, The KS test for those 10 p-values: 0.746534 The 3DSPHERES test for dh-ranFile-2018-04-12_09:31 sample no r^3 equiv. uni. 1 9.283 0.266127 2 6.393 0.191927 3 2.202 0.070771 4 3.307 0.104369 5 4.455 0.137994 6 27.567 0.601036 7 64.906 0.885080 8 39.754 0.734233 9 8.249 0.240397 10 8.038 0.235044 11 25.865 0.577757 12 25.202 0.568314 13 11.297 0.313786 14 27.625 0.601817 15 32.128 0.657315 16 48.900 0.804068 17 49.975 0.810970 18 105.815 0.970612 19 5.519 0.168024 20 68.029 0.896442 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.912536 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-04-12_09:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 1.8 -0.4 -0.8 1.3 -2.0 0.4 -1.0 0.3 -0.4 0.4 0.9 -0.2 0.5 -1.0 1.7 -0.4 -1.6 0.2 2.2 0.6 -0.4 -1.7 0.8 -1.8 -0.8 1.8 -0.1 -0.0 -0.8 0.1 -0.3 -0.1 -0.5 -0.9 -0.1 1.9 -1.0 -0.8 0.4 -1.3 0.0 0.8 Chi-square with 42 degrees of freedom:45.207990 z-score=0.350020, p-value=0.660510 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-04-12_09:31 Test no p-value 1 0.043844 2 0.590327 3 0.459993 4 0.160398 5 0.106466 6 0.016467 7 0.740386 8 0.337996 9 0.274905 10 0.028001 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.015380 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-04-12_09:31: (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 66762 0.14 66368 1.34 3 25000.00 24890 0.48 25384 5.90 4 6666.67 6762 1.36 6615 0.40 5 1388.89 1327 2.76 1365 0.41 6 238.10 224 0.83 230 0.28 7 34.72 31 0.40 31 0.40 8 4.96 3 0.77 6 0.22 p=0.65530 p=0.82299 Number of rngs required: 688445, p-value: 0.519 RESULTS OF CRAPS TEST for dh-ranFile-2018-04-12_09:31 No. of wins: Observed Expected 98139 98585.9 z-score=-1.999, pvalue=0.02283 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66683 66666.7 0.004 0.004 2 37646 37654.3 0.002 0.006 3 27349 26954.7 5.767 5.773 4 19140 19313.5 1.558 7.331 5 13818 13851.4 0.081 7.411 6 9955 9943.5 0.013 7.425 7 6967 7145.0 4.436 11.860 8 5166 5139.1 0.141 12.001 9 3687 3699.9 0.045 12.046 10 2658 2666.3 0.026 12.072 11 1915 1923.3 0.036 12.108 12 1434 1388.7 1.475 13.583 13 960 1003.7 1.904 15.487 14 746 726.1 0.543 16.030 15 520 525.8 0.065 16.095 16 371 381.2 0.270 16.365 17 267 276.5 0.329 16.694 18 199 200.8 0.017 16.711 19 143 146.0 0.061 16.772 20 94 106.2 1.405 18.177 21 282 287.1 0.091 18.268 Chisq= 18.27 for 20 degrees of freedom, p= 0.43023 SUMMARY of craptest p-value for no. of wins: 0.022825 p-value for throws/game: 0.430230 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-04-12_09:31 No. of wins: Observed Expected 98341 98585.9 z-score=-1.095, pvalue=0.13673 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66761 66666.7 0.133 0.133 2 37592 37654.3 0.103 0.237 3 27217 26954.7 2.552 2.788 4 19146 19313.5 1.452 4.240 5 13830 13851.4 0.033 4.274 6 10011 9943.5 0.458 4.731 7 7103 7145.0 0.247 4.978 8 5001 5139.1 3.710 8.688 9 3684 3699.9 0.068 8.756 10 2602 2666.3 1.551 10.307 11 1949 1923.3 0.343 10.649 12 1393 1388.7 0.013 10.662 13 985 1003.7 0.349 11.011 14 745 726.1 0.490 11.501 15 542 525.8 0.497 11.998 16 390 381.2 0.205 12.203 17 285 276.5 0.259 12.462 18 193 200.8 0.305 12.768 19 136 146.0 0.683 13.450 20 102 106.2 0.167 13.618 21 333 287.1 7.333 20.951 Chisq= 20.95 for 20 degrees of freedom, p= 0.59998 SUMMARY of craptest p-value for no. of wins: 0.136725 p-value for throws/game: 0.599983 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0035,0.0154,0.0165,0.0176,0.0178,0.0179,0.0228,0.0234,0.0256,0.0280, 0.0302,0.0389,0.0438,0.0443,0.0535,0.0580,0.0581,0.0606,0.0641,0.0708, 0.0716,0.0736,0.0737,0.0759,0.0828,0.1044,0.1065,0.1070,0.1137,0.1260, 0.1319,0.1343,0.1367,0.1380,0.1454,0.1491,0.1499,0.1506,0.1521,0.1561, 0.1568,0.1580,0.1595,0.1604,0.1642,0.1680,0.1718,0.1869,0.1912,0.1919, 0.1947,0.1971,0.1976,0.1978,0.2017,0.2018,0.2045,0.2105,0.2153,0.2266, 0.2274,0.2319,0.2350,0.2378,0.2404,0.2458,0.2475,0.2514,0.2518,0.2613, 0.2653,0.2654,0.2661,0.2667,0.2749,0.2833,0.2866,0.2900,0.2981,0.3099, 0.3106,0.3113,0.3138,0.3155,0.3199,0.3199,0.3204,0.3240,0.3257,0.3294, 0.3298,0.3341,0.3365,0.3380,0.3454,0.3574,0.3574,0.3634,0.3635,0.3653, 0.3699,0.3729,0.3746,0.3780,0.3848,0.3921,0.3947,0.3966,0.4017,0.4145, 0.4201,0.4221,0.4224,0.4240,0.4265,0.4302,0.4336,0.4350,0.4365,0.4373, 0.4382,0.4467,0.4545,0.4600,0.4604,0.4623,0.4659,0.4733,0.4739,0.4847, 0.4859,0.4879,0.4910,0.4927,0.4955,0.4981,0.5028,0.5038,0.5185,0.5193, 0.5231,0.5314,0.5320,0.5364,0.5382,0.5468,0.5470,0.5489,0.5581,0.5583, 0.5670,0.5683,0.5683,0.5725,0.5778,0.5787,0.5790,0.5793,0.5855,0.5876, 0.5903,0.5952,0.6000,0.6008,0.6010,0.6012,0.6018,0.6107,0.6117,0.6125, 0.6146,0.6154,0.6178,0.6254,0.6291,0.6313,0.6327,0.6553,0.6555,0.6573, 0.6605,0.6613,0.6631,0.6651,0.6718,0.6723,0.6735,0.6785,0.6808,0.6808, 0.6822,0.6830,0.6841,0.6844,0.6862,0.6917,0.6935,0.6994,0.7043,0.7060, 0.7194,0.7317,0.7342,0.7396,0.7399,0.7401,0.7404,0.7417,0.7433,0.7436, 0.7443,0.7465,0.7472,0.7530,0.7544,0.7583,0.7586,0.7590,0.7807,0.7944, 0.8015,0.8041,0.8089,0.8110,0.8230,0.8243,0.8253,0.8294,0.8343,0.8361, 0.8439,0.8465,0.8550,0.8596,0.8638,0.8659,0.8661,0.8704,0.8716,0.8810, 0.8851,0.8873,0.8890,0.8964,0.8977,0.9013,0.9032,0.9053,0.9090,0.9125, 0.9146,0.9148,0.9255,0.9266,0.9278,0.9289,0.9527,0.9586,0.9606,0.9678, 0.9706,0.9769,0.9783,0.9817,0.9883,0.9887,0.9944,0.9976,0.9983, Overall p-value after applying KStest on 269 p-values = 0.876674 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.