RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-09-17_14:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.68 22.4431 0.831727 2 to 25 15.93 16.7559 0.528979 3 to 26 15.73 25.6515 0.918951 4 to 27 15.84 23.1873 0.856749 5 to 28 15.67 16.9094 0.539476 6 to 29 15.67 15.1822 0.417642 7 to 30 15.49 16.0429 0.479207 8 to 31 15.71 9.6224 0.081305 9 to 32 15.71 16.5442 0.514361 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.534511 Tough bday spacings test for dh-ranFile-2016-09-17_14:31: 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 41 72 96 98 72 54 29 19 6 4 (O-E)^2/E 0.0 0.5 0.0 0.0 0.0 0.5 0.1 0.0 1.1 0.1 0.0 Birthday Spacings: Sum(O-E)^2/E= 2.344, p= 0.007 RESULTS OF GCD FOR dh-ranFile-2016-09-17_14:31 Euclid's algorithm: p-value, steps to gcd: 0.268208 p-value, dist. of gcd's: 0.813724 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-09-17_14:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.197 0.300 0.658 0.026 0.488 0.394 0.716 0.820 Bits 8 to 15---> 0.338 0.837 0.755 0.917 0.647 0.547 0.007 0.704 Bits 16 to 23---> 0.099 0.712 0.106 0.493 0.827 0.772 0.434 0.367 Bits 24 to 31---> 0.823 0.219 0.443 0.598 0.690 0.157 0.278 0.656 KS test for the above 32 p values: 0.299 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-09-17_14:31, p-values for 5 runs: 0.2180, 0.1039, 0.9074, 0.6277, 0.4829 Rank test for binary matrices (31x31) for dh-ranFile-2016-09-17_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 206 211.4 0.139 0.139 r= 29 5097 5134.0 0.267 0.406 r= 30 23100 23103.0 0.000 0.406 r= 31 11597 11551.5 0.179 0.585 chi-square = 0.585 with df = 3; p-value = 0.100 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-09-17_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 223 211.4 0.634 0.634 r= 30 5163 5134.0 0.164 0.798 r= 31 23165 23103.0 0.166 0.964 r= 32 11449 11551.5 0.910 1.874 chi-square = 1.874 with df = 3; p-value = 0.401 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-09-17_14:31 b-rank test for bits 1 to 8, p=0.92323 b-rank test for bits 2 to 9, p=0.59008 b-rank test for bits 3 to 10, p=0.47065 b-rank test for bits 4 to 11, p=0.49144 b-rank test for bits 5 to 12, p=0.27973 b-rank test for bits 6 to 13, p=0.20380 b-rank test for bits 7 to 14, p=0.96478 b-rank test for bits 8 to 15, p=0.09558 b-rank test for bits 9 to 16, p=0.60476 b-rank test for bits 10 to 17, p=0.14739 b-rank test for bits 11 to 18, p=0.92477 b-rank test for bits 12 to 19, p=0.23338 b-rank test for bits 13 to 20, p=0.20487 b-rank test for bits 14 to 21, p=0.56027 b-rank test for bits 15 to 22, p=0.60213 b-rank test for bits 16 to 23, p=0.36777 b-rank test for bits 17 to 24, p=0.88188 b-rank test for bits 18 to 25, p=0.57065 b-rank test for bits 19 to 26, p=0.02408 b-rank test for bits 20 to 27, p=0.20017 b-rank test for bits 21 to 28, p=0.43729 b-rank test for bits 22 to 29, p=0.11472 b-rank test for bits 23 to 30, p=0.56659 b-rank test for bits 24 to 31, p=0.55431 b-rank test for bits 25 to 32, p=0.28514 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 = 0.486225 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-09-17_14:31 (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 142164 0.60 0.724086 2 141888 -0.05 0.480126 3 142110 0.47 0.680413 4 142202 0.68 0.752952 5 142121 0.49 0.689543 6 142032 0.29 0.612795 7 141837 -0.17 0.432900 8 142168 0.60 0.727201 9 142269 0.84 0.799644 10 142553 1.50 0.933697 11 141677 -0.54 0.293624 12 141370 -1.26 0.103814 13 141033 -2.05 0.020305 14 142117 0.49 0.686236 15 142039 0.30 0.619043 16 141688 -0.52 0.302534 17 142309 0.93 0.824799 18 142150 0.56 0.713049 19 141557 -0.82 0.205197 20 142566 1.53 0.937519 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-09-17_14:31 Bits used No. missing words z-score p-value 23 to 32 141816 -0.3218 0.373792 22 to 31 142054 0.4989 0.691062 21 to 30 142235 1.1230 0.869281 20 to 29 141926 0.0575 0.522920 19 to 28 141273 -2.1942 0.014109 18 to 27 142108 0.6851 0.753350 17 to 26 141450 -1.5839 0.056609 16 to 25 141697 -0.7322 0.232032 15 to 24 142143 0.8058 0.789809 14 to 23 141671 -0.8218 0.205588 13 to 22 141723 -0.6425 0.260269 12 to 21 141974 0.2230 0.588232 11 to 20 141802 -0.3701 0.355653 10 to 19 141477 -1.4908 0.068008 9 to 18 141868 -0.1425 0.443336 8 to 17 141581 -1.1322 0.128781 7 to 16 142034 0.4299 0.666365 6 to 15 141838 -0.2460 0.402855 5 to 14 142404 1.7058 0.955973 4 to 13 142132 0.7678 0.778705 3 to 12 141664 -0.8460 0.198786 2 to 11 142226 1.0920 0.862576 1 to 10 142280 1.2782 0.899406 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-09-17_14:31 Bits used No. missing words z-score p-value 28 to 32 142264 1.2023 0.885371 27 to 31 141953 0.1480 0.558842 26 to 30 141506 -1.3672 0.085778 25 to 29 142420 1.7311 0.958282 24 to 28 142212 1.0260 0.847554 23 to 27 141859 -0.1706 0.432265 22 to 26 142245 1.1379 0.872411 21 to 25 142106 0.6667 0.747511 20 to 24 141722 -0.6350 0.262709 19 to 23 141452 -1.5503 0.060538 18 to 22 142091 0.6158 0.730997 17 to 21 141628 -0.9537 0.170128 16 to 20 141719 -0.6452 0.259403 15 to 19 142186 0.9379 0.825843 14 to 18 142156 0.8362 0.798470 13 to 17 141467 -1.4994 0.066882 12 to 16 141657 -0.8554 0.196177 11 to 15 141468 -1.4960 0.067322 10 to 14 141283 -2.1232 0.016871 9 to 13 141918 0.0294 0.511723 8 to 12 142114 0.6938 0.756095 7 to 11 141777 -0.4486 0.326869 6 to 10 141768 -0.4791 0.315939 5 to 9 142094 0.6260 0.734343 4 to 8 141707 -0.6859 0.246399 3 to 7 142012 0.3480 0.636093 2 to 6 142036 0.4294 0.666180 1 to 5 141828 -0.2757 0.391391 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-09-17_14:31 Bits used No. missing words z-score p-value 31 to 32 141973 0.1878 0.574490 30 to 31 142243 0.9843 0.837510 29 to 30 142492 1.7188 0.957174 28 to 29 141649 -0.7679 0.221263 27 to 28 142111 0.5949 0.724044 26 to 27 141613 -0.8741 0.191024 25 to 26 141678 -0.6824 0.247496 24 to 25 141569 -1.0039 0.157708 23 to 24 142039 0.3825 0.648958 22 to 23 142636 2.1436 0.983966 21 to 22 141620 -0.8535 0.196696 20 to 21 141768 -0.4169 0.338375 19 to 20 141392 -1.5260 0.063499 18 to 19 141659 -0.7384 0.230125 17 to 18 141617 -0.8623 0.194253 16 to 17 142212 0.8928 0.814026 15 to 16 141872 -0.1101 0.456158 14 to 15 141676 -0.6883 0.245635 13 to 14 142060 0.4445 0.671643 12 to 13 141949 0.1170 0.546578 11 to 12 141820 -0.2635 0.396079 10 to 11 141658 -0.7414 0.229230 9 to 10 142042 0.3914 0.652233 8 to 9 141470 -1.2960 0.097495 7 to 8 141507 -1.1868 0.117650 6 to 7 142013 0.3058 0.620126 5 to 6 142105 0.5772 0.718097 4 to 5 142295 1.1377 0.872371 3 to 4 142133 0.6598 0.745307 2 to 3 142140 0.6804 0.751888 1 to 2 141508 -1.1839 0.118233 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-09-17_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2492.94 -0.100 0.460226 Test results for specific bytes for dh-ranFile-2016-09-17_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2473.81 -0.370 0.355557 2 to 9 2438.73 -0.867 0.193093 3 to 10 2692.33 2.720 0.996735 4 to 11 2521.81 0.309 0.621151 5 to 12 2471.15 -0.408 0.341632 6 to 13 2429.48 -0.997 0.159292 7 to 14 2491.18 -0.125 0.450360 8 to 15 2487.88 -0.171 0.431938 9 to 16 2502.56 0.036 0.514459 10 to 17 2525.42 0.360 0.640404 11 to 18 2414.06 -1.215 0.112106 12 to 19 2476.63 -0.330 0.370533 13 to 20 2524.96 0.353 0.637961 14 to 21 2448.90 -0.723 0.234956 15 to 22 2518.77 0.265 0.604649 16 to 23 2480.44 -0.277 0.391037 17 to 24 2381.25 -1.679 0.046537 18 to 25 2454.23 -0.647 0.258703 19 to 26 2573.69 1.042 0.851336 20 to 27 2551.27 0.725 0.765807 21 to 28 2609.52 1.549 0.939285 22 to 29 2426.03 -1.046 0.147760 23 to 30 2393.76 -1.502 0.066495 24 to 31 2527.24 0.385 0.649975 25 to 32 2441.41 -0.829 0.203654 CDPARK for dh-ranFile-2016-09-17_14:31: 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 3559 1.6438 0.949895 3506 -0.7763 0.218799 3528 0.2283 0.590298 3514 -0.4110 0.340551 3526 0.1370 0.554479 3540 0.7763 0.781201 3510 -0.5936 0.276387 3565 1.9178 0.972432 3488 -1.5982 0.055002 3519 -0.1826 0.427537 Square side=100, avg. no. parked=3525.50 sample std.=22.58 p-value of the KSTEST for those 10 p-values: 0.946063 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-09-17_14:31 0.2076,0.9826,0.3669,0.5844,0.2771,0.1871,0.7151,0.5639,0.6733,0.5783, The KS test for those 10 p-values: 0.734697 The 3DSPHERES test for dh-ranFile-2016-09-17_14:31 sample no r^3 equiv. uni. 1 14.789 0.389181 2 103.383 0.968130 3 2.881 0.091553 4 135.869 0.989208 5 1.433 0.046658 6 7.289 0.215699 7 2.766 0.088072 8 3.473 0.109331 9 16.640 0.425741 10 24.713 0.561217 11 7.178 0.212783 12 13.034 0.352383 13 14.791 0.389232 14 44.087 0.769978 15 70.828 0.905668 16 9.520 0.271916 17 27.342 0.598036 18 70.260 0.903864 19 27.777 0.603832 20 20.107 0.488418 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.762351 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-09-17_14:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 0.9 0.1 0.9 -0.5 -2.2 0.9 0.2 -0.6 -0.1 -1.8 0.7 0.5 1.3 0.8 0.5 -1.2 -0.2 -0.8 0.4 0.2 1.0 0.7 -0.8 -0.1 -1.6 0.5 -0.8 -0.3 -0.1 -0.1 0.5 1.0 0.7 -1.0 -0.5 -0.7 0.5 0.5 -1.3 0.1 0.0 -0.1 Chi-square with 42 degrees of freedom:28.454163 z-score=-1.477972, p-value=0.054723 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-09-17_14:31 Test no p-value 1 0.145212 2 0.548822 3 0.681890 4 0.558226 5 0.482708 6 0.676253 7 0.103692 8 0.813003 9 0.015561 10 0.361192 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.647484 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-09-17_14:31: (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 66834 0.42 66784 0.21 3 25000.00 24937 0.16 24817 1.34 4 6666.67 6630 0.20 6723 0.48 5 1388.89 1343 1.52 1389 0.00 6 238.10 222 1.09 257 1.50 7 34.72 33 0.09 26 2.19 8 4.96 0 4.96 3 0.77 p=0.79173 p=0.62917 Number of rngs required: 688304, p-value: 0.455 RESULTS OF CRAPS TEST for dh-ranFile-2016-09-17_14:31 No. of wins: Observed Expected 98709 98585.9 z-score= 0.551, pvalue=0.70910 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66913 66666.7 0.910 0.910 2 37545 37654.3 0.317 1.228 3 26771 26954.7 1.252 2.480 4 19399 19313.5 0.379 2.859 5 13845 13851.4 0.003 2.862 6 9874 9943.5 0.486 3.348 7 7065 7145.0 0.896 4.244 8 5218 5139.1 1.212 5.457 9 3725 3699.9 0.171 5.627 10 2604 2666.3 1.456 7.083 11 1968 1923.3 1.038 8.121 12 1377 1388.7 0.099 8.220 13 975 1003.7 0.822 9.041 14 772 726.1 2.896 11.938 15 539 525.8 0.330 12.267 16 388 381.2 0.123 12.390 17 270 276.5 0.155 12.545 18 177 200.8 2.828 15.372 19 149 146.0 0.062 15.435 20 119 106.2 1.539 16.974 21 307 287.1 1.377 18.351 Chisq= 18.35 for 20 degrees of freedom, p= 0.43569 SUMMARY of craptest p-value for no. of wins: 0.709101 p-value for throws/game: 0.435693 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-09-17_14:31 No. of wins: Observed Expected 98155 98585.9 z-score=-1.927, pvalue=0.02699 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66630 66666.7 0.020 0.020 2 37674 37654.3 0.010 0.030 3 27133 26954.7 1.179 1.209 4 19286 19313.5 0.039 1.248 5 13957 13851.4 0.805 2.053 6 9807 9943.5 1.875 3.928 7 7061 7145.0 0.988 4.916 8 5081 5139.1 0.656 5.573 9 3796 3699.9 2.498 8.071 10 2550 2666.3 5.073 13.143 11 1909 1923.3 0.107 13.250 12 1421 1388.7 0.749 13.999 13 952 1003.7 2.665 16.664 14 734 726.1 0.085 16.749 15 548 525.8 0.934 17.683 16 389 381.2 0.162 17.845 17 301 276.5 2.164 20.008 18 211 200.8 0.515 20.523 19 160 146.0 1.346 21.869 20 115 106.2 0.727 22.596 21 285 287.1 0.016 22.611 Chisq= 22.61 for 20 degrees of freedom, p= 0.69171 SUMMARY of craptest p-value for no. of wins: 0.026987 p-value for throws/game: 0.691708 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0070,0.0074,0.0141,0.0156,0.0169,0.0203,0.0241,0.0259,0.0270,0.0465, 0.0467,0.0547,0.0550,0.0566,0.0605,0.0635,0.0665,0.0669,0.0673,0.0680, 0.0813,0.0858,0.0881,0.0916,0.0956,0.0975,0.0987,0.1002,0.1037,0.1038, 0.1039,0.1063,0.1093,0.1121,0.1147,0.1177,0.1182,0.1288,0.1452,0.1474, 0.1478,0.1566,0.1577,0.1593,0.1701,0.1871,0.1910,0.1931,0.1943,0.1962, 0.1967,0.1974,0.1988,0.2002,0.2037,0.2038,0.2049,0.2052,0.2056,0.2076, 0.2128,0.2157,0.2180,0.2187,0.2188,0.2213,0.2292,0.2301,0.2320,0.2334, 0.2350,0.2456,0.2464,0.2475,0.2587,0.2594,0.2603,0.2627,0.2682,0.2719, 0.2764,0.2771,0.2775,0.2797,0.2851,0.2936,0.2990,0.2997,0.3025,0.3159, 0.3269,0.3383,0.3384,0.3406,0.3416,0.3524,0.3556,0.3557,0.3612,0.3669, 0.3672,0.3678,0.3705,0.3738,0.3892,0.3892,0.3910,0.3914,0.3939,0.3961, 0.4011,0.4029,0.4176,0.4257,0.4275,0.4319,0.4323,0.4329,0.4338,0.4357, 0.4373,0.4431,0.4433,0.4504,0.4547,0.4562,0.4602,0.4706,0.4792,0.4801, 0.4827,0.4829,0.4862,0.4882,0.4884,0.4914,0.4927,0.5117,0.5144,0.5145, 0.5229,0.5290,0.5345,0.5395,0.5466,0.5471,0.5488,0.5543,0.5545,0.5582, 0.5588,0.5603,0.5612,0.5639,0.5666,0.5707,0.5745,0.5783,0.5844,0.5882, 0.5901,0.5903,0.5980,0.5982,0.6021,0.6038,0.6046,0.6048,0.6128,0.6190, 0.6201,0.6212,0.6277,0.6292,0.6361,0.6380,0.6404,0.6473,0.6475,0.6490, 0.6500,0.6522,0.6562,0.6582,0.6662,0.6664,0.6716,0.6733,0.6763,0.6804, 0.6819,0.6862,0.6895,0.6900,0.6911,0.6917,0.7044,0.7091,0.7125,0.7130, 0.7151,0.7160,0.7181,0.7240,0.7241,0.7272,0.7310,0.7343,0.7347,0.7453, 0.7475,0.7519,0.7530,0.7533,0.7555,0.7561,0.7624,0.7658,0.7700,0.7718, 0.7787,0.7812,0.7898,0.7917,0.7985,0.7996,0.8130,0.8137,0.8140,0.8203, 0.8231,0.8248,0.8258,0.8274,0.8317,0.8372,0.8375,0.8476,0.8513,0.8567, 0.8626,0.8693,0.8724,0.8724,0.8819,0.8854,0.8994,0.9039,0.9057,0.9074, 0.9175,0.9190,0.9232,0.9248,0.9337,0.9375,0.9393,0.9461,0.9499,0.9560, 0.9572,0.9583,0.9648,0.9681,0.9724,0.9826,0.9840,0.9892,0.9967, Overall p-value after applying KStest on 269 p-values = 0.551430 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.