RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-09-03_04:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.60 18.5454 0.644758 2 to 25 15.69 11.3712 0.163371 3 to 26 16.04 19.7514 0.712857 4 to 27 16.04 21.0151 0.774385 5 to 28 15.56 18.8761 0.664309 6 to 29 15.99 9.4715 0.075700 7 to 30 15.70 14.0731 0.338076 8 to 31 15.76 14.5678 0.373417 9 to 32 15.81 23.4287 0.864193 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.940022 Tough bday spacings test for dh-ranFile-2015-09-03_04:31: 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 73 95 99 75 57 30 14 9 1 (O-E)^2/E 0.4 0.0 0.0 0.1 0.0 0.1 0.5 0.0 0.1 0.9 2.3 Birthday Spacings: Sum(O-E)^2/E= 4.288, p= 0.067 RESULTS OF GCD FOR dh-ranFile-2015-09-03_04:31 Euclid's algorithm: p-value, steps to gcd: 0.781830 p-value, dist. of gcd's: 0.256042 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-09-03_04:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.868 0.228 0.146 0.202 0.705 0.375 0.755 0.835 Bits 8 to 15---> 0.775 0.982 0.916 0.948 0.900 0.910 0.296 0.772 Bits 16 to 23---> 0.448 0.918 0.943 0.769 0.857 0.929 0.443 0.527 Bits 24 to 31---> 0.514 0.358 0.544 0.741 0.152 0.758 0.976 0.585 KS test for the above 32 p values: 0.998 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-09-03_04:31, p-values for 5 runs: 0.3718, 0.9254, 0.0293, 0.8951, 0.5433 Rank test for binary matrices (31x31) for dh-ranFile-2015-09-03_04:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 204 211.4 0.260 0.260 r= 29 5158 5134.0 0.112 0.372 r= 30 23189 23103.0 0.320 0.692 r= 31 11449 11551.5 0.910 1.602 chi-square = 1.602 with df = 3; p-value = 0.341 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-09-03_04:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 220 211.4 0.348 0.348 r= 30 5047 5134.0 1.475 1.823 r= 31 23127 23103.0 0.025 1.848 r= 32 11606 11551.5 0.257 2.105 chi-square = 2.105 with df = 3; p-value = 0.449 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-09-03_04:31 b-rank test for bits 1 to 8, p=0.52327 b-rank test for bits 2 to 9, p=0.80783 b-rank test for bits 3 to 10, p=0.98077 b-rank test for bits 4 to 11, p=0.81551 b-rank test for bits 5 to 12, p=0.81182 b-rank test for bits 6 to 13, p=0.83891 b-rank test for bits 7 to 14, p=0.36846 b-rank test for bits 8 to 15, p=0.64350 b-rank test for bits 9 to 16, p=0.71793 b-rank test for bits 10 to 17, p=0.94225 b-rank test for bits 11 to 18, p=0.39609 b-rank test for bits 12 to 19, p=0.43841 b-rank test for bits 13 to 20, p=0.03209 b-rank test for bits 14 to 21, p=0.68395 b-rank test for bits 15 to 22, p=0.84611 b-rank test for bits 16 to 23, p=0.05757 b-rank test for bits 17 to 24, p=0.24296 b-rank test for bits 18 to 25, p=0.88008 b-rank test for bits 19 to 26, p=0.83136 b-rank test for bits 20 to 27, p=0.03991 b-rank test for bits 21 to 28, p=0.35658 b-rank test for bits 22 to 29, p=0.04079 b-rank test for bits 23 to 30, p=0.50662 b-rank test for bits 24 to 31, p=0.68724 b-rank test for bits 25 to 32, p=0.18111 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 = 0.431331 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-09-03_04:31 (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 142106 0.46 0.677066 2 141926 0.04 0.515534 3 142013 0.24 0.595695 4 142221 0.73 0.766755 5 141759 -0.35 0.362705 6 142312 0.94 0.826601 7 142263 0.83 0.795692 8 142281 0.87 0.807409 9 141689 -0.51 0.303350 10 141405 -1.18 0.119330 11 142088 0.42 0.661827 12 142302 0.92 0.820547 13 141460 -1.05 0.146897 14 141800 -0.26 0.399190 15 141691 -0.51 0.304985 16 142010 0.24 0.592977 17 141635 -0.64 0.260775 18 141828 -0.19 0.424645 19 141637 -0.64 0.262295 20 142201 0.68 0.752214 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-09-03_04:31 Bits used No. missing words z-score p-value 23 to 32 141728 -0.6253 0.265895 22 to 31 141919 0.0333 0.513300 21 to 30 142084 0.6023 0.726516 20 to 29 141633 -0.9529 0.170330 19 to 28 141634 -0.9494 0.171205 18 to 27 141932 0.0782 0.531155 17 to 26 141968 0.2023 0.580163 16 to 25 141825 -0.2908 0.385605 15 to 24 141565 -1.1873 0.117546 14 to 23 141833 -0.2632 0.396196 13 to 22 141441 -1.6149 0.053163 12 to 21 142396 1.6782 0.953343 11 to 20 142388 1.6506 0.950588 10 to 19 142094 0.6368 0.737870 9 to 18 142178 0.9264 0.822894 8 to 17 141758 -0.5218 0.300895 7 to 16 141999 0.3092 0.621418 6 to 15 141637 -0.9391 0.173848 5 to 14 142125 0.7437 0.771468 4 to 13 141452 -1.5770 0.057398 3 to 12 142007 0.3368 0.631864 2 to 11 141694 -0.7425 0.228887 1 to 10 141921 0.0402 0.516050 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-09-03_04:31 Bits used No. missing words z-score p-value 28 to 32 142437 1.7887 0.963169 27 to 31 141698 -0.7164 0.236881 26 to 30 142194 0.9650 0.832723 25 to 29 141817 -0.3130 0.377147 24 to 28 142091 0.6158 0.730997 23 to 27 141968 0.1989 0.578822 22 to 26 141509 -1.3571 0.087383 21 to 25 141893 -0.0554 0.477928 20 to 24 141858 -0.1740 0.430933 19 to 23 142527 2.0938 0.981861 18 to 22 141573 -1.1401 0.127122 17 to 21 141524 -1.3062 0.095742 16 to 20 141878 -0.1062 0.457711 15 to 19 141430 -1.6248 0.052098 14 to 18 142011 0.3446 0.634819 13 to 17 141500 -1.3876 0.082636 12 to 16 141587 -1.0926 0.137275 11 to 15 141545 -1.2350 0.108412 10 to 14 141451 -1.5537 0.060133 9 to 13 141873 -0.1232 0.450993 8 to 12 141766 -0.4859 0.313532 7 to 11 141925 0.0531 0.521181 6 to 10 141971 0.2091 0.582796 5 to 9 141638 -0.9198 0.178848 4 to 8 142328 1.4192 0.922083 3 to 7 142414 1.7107 0.956436 2 to 6 142833 3.1311 0.999129 1 to 5 141842 -0.2282 0.409731 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-09-03_04:31 Bits used No. missing words z-score p-value 31 to 32 141973 0.1878 0.574490 30 to 31 141645 -0.7797 0.217774 29 to 30 142074 0.4858 0.686429 28 to 29 141891 -0.0541 0.478439 27 to 28 141627 -0.8328 0.202470 26 to 27 142187 0.8191 0.793631 25 to 26 142276 1.0816 0.860290 24 to 25 141904 -0.0157 0.493728 23 to 24 141236 -1.9862 0.023504 22 to 23 142104 0.5742 0.717100 21 to 22 142076 0.4917 0.688517 20 to 21 142183 0.8073 0.790249 19 to 20 141532 -1.1131 0.132840 18 to 19 142167 0.7601 0.776399 17 to 18 141752 -0.4641 0.321288 16 to 17 141695 -0.6322 0.263614 15 to 16 141791 -0.3491 0.363524 14 to 15 141456 -1.3373 0.090569 13 to 14 141728 -0.5349 0.296361 12 to 13 142091 0.5359 0.703986 11 to 12 141829 -0.2370 0.406343 10 to 11 141921 0.0344 0.513731 9 to 10 141392 -1.5260 0.063499 8 to 9 141861 -0.1426 0.443316 7 to 8 142043 0.3943 0.653323 6 to 7 141780 -0.3815 0.351415 5 to 6 141928 0.0551 0.521960 4 to 5 142064 0.4563 0.675896 3 to 4 142440 1.5654 0.941255 2 to 3 141340 -1.6794 0.046533 1 to 2 142098 0.5565 0.711082 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-09-03_04:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2475.47 -0.347 0.364349 Test results for specific bytes for dh-ranFile-2015-09-03_04:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2507.21 0.102 0.540581 2 to 9 2515.49 0.219 0.586707 3 to 10 2386.62 -1.603 0.054427 4 to 11 2511.51 0.163 0.564646 5 to 12 2495.70 -0.061 0.475738 6 to 13 2461.56 -0.544 0.293368 7 to 14 2563.34 0.896 0.814799 8 to 15 2475.29 -0.349 0.363357 9 to 16 2593.11 1.317 0.906040 10 to 17 2466.97 -0.467 0.320198 11 to 18 2447.98 -0.736 0.230967 12 to 19 2532.69 0.462 0.678079 13 to 20 2480.44 -0.277 0.391032 14 to 21 2554.86 0.776 0.781088 15 to 22 2417.79 -1.163 0.122505 16 to 23 2450.06 -0.706 0.239995 17 to 24 2476.08 -0.338 0.367563 18 to 25 2415.46 -1.196 0.115933 19 to 26 2501.05 0.015 0.505943 20 to 27 2528.29 0.400 0.655451 21 to 28 2492.37 -0.108 0.457012 22 to 29 2474.16 -0.365 0.357381 23 to 30 2619.37 1.688 0.954311 24 to 31 2502.11 0.030 0.511925 25 to 32 2619.64 1.692 0.954679 CDPARK for dh-ranFile-2015-09-03_04:31: 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 3530 0.3196 0.625377 3500 -1.0502 0.146807 3560 1.6895 0.954438 3526 0.1370 0.554479 3511 -0.5479 0.291865 3501 -1.0046 0.157553 3535 0.5479 0.708135 3533 0.4566 0.676028 3545 1.0046 0.842447 3486 -1.6895 0.045562 Square side=100, avg. no. parked=3522.70 sample std.=21.63 p-value of the KSTEST for those 10 p-values: 0.980112 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-09-03_04:31 0.7555,0.6369,0.8416,0.5882,0.0163,0.8228,0.6117,0.9400,0.2425,0.2120, The KS test for those 10 p-values: 0.641158 The 3DSPHERES test for dh-ranFile-2015-09-03_04:31 sample no r^3 equiv. uni. 1 22.836 0.532901 2 5.364 0.163713 3 12.110 0.332123 4 63.046 0.877732 5 40.498 0.740740 6 71.682 0.908316 7 21.083 0.504781 8 13.435 0.360981 9 10.227 0.288868 10 46.763 0.789603 11 25.993 0.579548 12 7.523 0.221807 13 79.605 0.929595 14 71.711 0.908404 15 2.391 0.076601 16 15.558 0.404648 17 13.238 0.356774 18 69.015 0.899792 19 17.150 0.435422 20 53.226 0.830380 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.488918 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-09-03_04:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -0.3 0.3 -0.7 -0.2 -0.6 0.9 0.4 -0.4 -0.4 -1.2 0.7 -0.4 2.5 -0.9 -1.2 0.4 1.3 0.2 -0.9 -0.5 0.1 -0.5 -0.8 0.3 -0.5 1.2 -0.1 1.6 -1.2 -0.1 1.0 1.5 -0.8 1.5 -1.2 -0.5 -0.7 0.5 -0.1 0.1 -1.0 -0.1 Chi-square with 42 degrees of freedom:31.931490 z-score=-1.098565, p-value=0.129925 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-09-03_04:31 Test no p-value 1 0.000055 2 0.212901 3 0.147160 4 0.917654 5 0.031917 6 0.905511 7 0.784791 8 0.724336 9 0.180892 10 0.165505 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.073444 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-09-03_04:31: (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 66706 0.02 66577 0.12 3 25000.00 24944 0.13 25145 0.84 4 6666.67 6626 0.25 6616 0.39 5 1388.89 1426 0.99 1363 0.48 6 238.10 250 0.60 252 0.81 7 34.72 38 0.31 43 1.97 8 4.96 9 3.29 3 0.77 p=0.52864 p=0.50521 Number of rngs required: 688638, p-value: 0.607 RESULTS OF CRAPS TEST for dh-ranFile-2015-09-03_04:31 No. of wins: Observed Expected 98853 98585.9 z-score= 1.195, pvalue=0.88392 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66819 66666.7 0.348 0.348 2 37334 37654.3 2.725 3.073 3 27137 26954.7 1.232 4.306 4 19384 19313.5 0.258 4.563 5 13884 13851.4 0.077 4.640 6 9815 9943.5 1.662 6.301 7 7026 7145.0 1.983 8.284 8 5143 5139.1 0.003 8.287 9 3699 3699.9 0.000 8.287 10 2724 2666.3 1.249 9.536 11 1975 1923.3 1.388 10.924 12 1353 1388.7 0.920 11.844 13 1002 1003.7 0.003 11.847 14 747 726.1 0.599 12.446 15 503 525.8 0.992 13.438 16 387 381.2 0.090 13.528 17 290 276.5 0.655 14.183 18 211 200.8 0.515 14.698 19 135 146.0 0.827 15.525 20 121 106.2 2.058 17.583 21 311 287.1 1.987 19.570 Chisq= 19.57 for 20 degrees of freedom, p= 0.51488 SUMMARY of craptest p-value for no. of wins: 0.883920 p-value for throws/game: 0.514879 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-09-03_04:31 No. of wins: Observed Expected 98488 98585.9 z-score=-0.438, pvalue=0.33081 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66476 66666.7 0.545 0.545 2 37806 37654.3 0.611 1.156 3 26899 26954.7 0.115 1.272 4 19285 19313.5 0.042 1.313 5 13807 13851.4 0.142 1.456 6 9959 9943.5 0.024 1.480 7 7126 7145.0 0.051 1.531 8 5193 5139.1 0.566 2.097 9 3810 3699.9 3.278 5.375 10 2679 2666.3 0.061 5.435 11 1923 1923.3 0.000 5.436 12 1428 1388.7 1.110 6.545 13 985 1003.7 0.349 6.894 14 686 726.1 2.219 9.113 15 547 525.8 0.852 9.965 16 382 381.2 0.002 9.967 17 306 276.5 3.139 13.106 18 188 200.8 0.820 13.925 19 134 146.0 0.984 14.909 20 100 106.2 0.364 15.273 21 281 287.1 0.130 15.403 Chisq= 15.40 for 20 degrees of freedom, p= 0.24709 SUMMARY of craptest p-value for no. of wins: 0.330809 p-value for throws/game: 0.247091 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0001,0.0163,0.0235,0.0293,0.0319,0.0321,0.0399,0.0408,0.0456,0.0465, 0.0521,0.0532,0.0544,0.0574,0.0576,0.0601,0.0635,0.0666,0.0734,0.0757, 0.0766,0.0826,0.0874,0.0906,0.0957,0.1084,0.1159,0.1175,0.1193,0.1225, 0.1271,0.1299,0.1328,0.1373,0.1462,0.1468,0.1469,0.1472,0.1524,0.1576, 0.1634,0.1637,0.1655,0.1703,0.1712,0.1738,0.1788,0.1809,0.1811,0.2019, 0.2025,0.2120,0.2129,0.2178,0.2218,0.2285,0.2289,0.2310,0.2369,0.2400, 0.2425,0.2430,0.2471,0.2560,0.2608,0.2623,0.2636,0.2659,0.2889,0.2919, 0.2934,0.2956,0.2964,0.3009,0.3034,0.3050,0.3135,0.3202,0.3213,0.3308, 0.3321,0.3381,0.3411,0.3514,0.3566,0.3568,0.3574,0.3583,0.3610,0.3627, 0.3634,0.3635,0.3643,0.3676,0.3685,0.3718,0.3734,0.3754,0.3771,0.3856, 0.3910,0.3961,0.3962,0.3992,0.4046,0.4063,0.4097,0.4246,0.4309,0.4313, 0.4354,0.4384,0.4427,0.4433,0.4478,0.4490,0.4510,0.4570,0.4577,0.4757, 0.4779,0.4784,0.4889,0.4937,0.5048,0.5052,0.5059,0.5066,0.5119,0.5133, 0.5137,0.5144,0.5149,0.5155,0.5160,0.5212,0.5220,0.5233,0.5266,0.5286, 0.5312,0.5329,0.5406,0.5433,0.5445,0.5545,0.5646,0.5745,0.5788,0.5795, 0.5802,0.5828,0.5850,0.5867,0.5882,0.5930,0.5957,0.6066,0.6117,0.6214, 0.6254,0.6319,0.6348,0.6369,0.6412,0.6435,0.6448,0.6533,0.6555,0.6618, 0.6643,0.6759,0.6760,0.6771,0.6781,0.6839,0.6864,0.6872,0.6885,0.7040, 0.7054,0.7081,0.7111,0.7129,0.7171,0.7179,0.7243,0.7265,0.7310,0.7379, 0.7407,0.7411,0.7522,0.7552,0.7555,0.7585,0.7668,0.7688,0.7715,0.7715, 0.7744,0.7753,0.7764,0.7811,0.7818,0.7848,0.7896,0.7902,0.7936,0.7957, 0.8074,0.8078,0.8118,0.8148,0.8155,0.8205,0.8228,0.8229,0.8266,0.8304, 0.8314,0.8327,0.8355,0.8389,0.8416,0.8424,0.8461,0.8572,0.8603,0.8642, 0.8682,0.8777,0.8801,0.8839,0.8951,0.8998,0.9004,0.9055,0.9060,0.9083, 0.9084,0.9104,0.9162,0.9177,0.9185,0.9221,0.9254,0.9290,0.9296,0.9400, 0.9400,0.9413,0.9422,0.9427,0.9481,0.9506,0.9533,0.9543,0.9544,0.9547, 0.9564,0.9632,0.9763,0.9801,0.9808,0.9819,0.9821,0.9978,0.9991, Overall p-value after applying KStest on 269 p-values = 0.531887 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.