RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-08-01_12:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.83 21.2354 0.784062 2 to 25 15.55 17.6195 0.586784 3 to 26 15.41 19.8592 0.718503 4 to 27 15.52 18.4671 0.640039 5 to 28 15.71 14.6320 0.378028 6 to 29 15.68 22.5190 0.834424 7 to 30 15.86 12.9760 0.262208 8 to 31 15.84 18.8767 0.664345 9 to 32 15.56 21.6021 0.799492 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.164555 Tough bday spacings test for dh-ranFile-2016-08-01_12:31: 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 40 67 93 102 86 46 33 18 5 3 (O-E)^2/E 0.5 0.3 0.5 0.2 0.2 0.8 0.7 0.4 0.7 0.4 0.3 Birthday Spacings: Sum(O-E)^2/E= 4.948, p= 0.105 RESULTS OF GCD FOR dh-ranFile-2016-08-01_12:31 Euclid's algorithm: p-value, steps to gcd: 0.246987 p-value, dist. of gcd's: 0.817716 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-08-01_12:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.462 0.424 0.477 0.166 0.297 0.882 0.344 0.560 Bits 8 to 15---> 0.393 0.817 0.597 0.841 0.656 0.739 0.684 0.066 Bits 16 to 23---> 0.327 0.722 0.585 0.852 0.897 0.047 0.282 0.895 Bits 24 to 31---> 0.549 0.093 0.845 0.911 0.475 0.578 0.243 0.065 KS test for the above 32 p values: 0.224 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-08-01_12:31, p-values for 5 runs: 0.1087, 0.7245, 0.4286, 0.8902, 0.9053 Rank test for binary matrices (31x31) for dh-ranFile-2016-08-01_12:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 218 211.4 0.205 0.205 r= 29 5222 5134.0 1.508 1.713 r= 30 23050 23103.0 0.122 1.835 r= 31 11510 11551.5 0.149 1.984 chi-square = 1.984 with df = 3; p-value = 0.424 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-08-01_12:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 209 211.4 0.028 0.028 r= 30 5174 5134.0 0.311 0.339 r= 31 23089 23103.0 0.009 0.348 r= 32 11528 11551.5 0.048 0.396 chi-square = 0.396 with df = 3; p-value = 0.059 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-08-01_12:31 b-rank test for bits 1 to 8, p=0.44258 b-rank test for bits 2 to 9, p=0.33019 b-rank test for bits 3 to 10, p=0.59218 b-rank test for bits 4 to 11, p=0.04061 b-rank test for bits 5 to 12, p=0.46774 b-rank test for bits 6 to 13, p=0.58348 b-rank test for bits 7 to 14, p=0.58053 b-rank test for bits 8 to 15, p=0.05106 b-rank test for bits 9 to 16, p=0.60076 b-rank test for bits 10 to 17, p=0.59281 b-rank test for bits 11 to 18, p=0.74173 b-rank test for bits 12 to 19, p=0.34464 b-rank test for bits 13 to 20, p=0.80191 b-rank test for bits 14 to 21, p=0.50681 b-rank test for bits 15 to 22, p=0.14920 b-rank test for bits 16 to 23, p=0.23445 b-rank test for bits 17 to 24, p=0.33026 b-rank test for bits 18 to 25, p=0.13238 b-rank test for bits 19 to 26, p=0.48955 b-rank test for bits 20 to 27, p=0.75575 b-rank test for bits 21 to 28, p=0.14711 b-rank test for bits 22 to 29, p=0.35321 b-rank test for bits 23 to 30, p=0.39069 b-rank test for bits 24 to 31, p=0.81206 b-rank test for bits 25 to 32, p=0.29514 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 = 0.186733 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-08-01_12:31 (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 141628 -0.66 0.255490 2 141688 -0.52 0.302534 3 142381 1.10 0.864776 4 141858 -0.12 0.452269 5 141460 -1.05 0.146897 6 141061 -1.98 0.023735 7 141836 -0.17 0.431981 8 142105 0.46 0.676227 9 141529 -0.89 0.187103 10 141856 -0.12 0.450419 11 141520 -0.91 0.181504 12 141630 -0.65 0.256994 13 141713 -0.46 0.323219 14 141845 -0.15 0.440263 15 141869 -0.09 0.462464 16 141755 -0.36 0.359205 17 142392 1.13 0.870284 18 142076 0.39 0.651516 19 141992 0.19 0.576581 20 141721 -0.44 0.329960 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-08-01_12:31 Bits used No. missing words z-score p-value 23 to 32 141724 -0.6391 0.261389 22 to 31 141335 -1.9804 0.023827 21 to 30 141631 -0.9598 0.168588 20 to 29 141815 -0.3253 0.372486 19 to 28 142076 0.5747 0.717261 18 to 27 142127 0.7506 0.773549 17 to 26 141707 -0.6977 0.242686 16 to 25 141894 -0.0529 0.478921 15 to 24 141716 -0.6667 0.252496 14 to 23 141892 -0.0598 0.476174 13 to 22 141872 -0.1287 0.448788 12 to 21 141744 -0.5701 0.284304 11 to 20 141619 -1.0011 0.158380 10 to 19 141986 0.2644 0.604256 9 to 18 141956 0.1609 0.563926 8 to 17 142154 0.8437 0.800579 7 to 16 141899 -0.0356 0.485792 6 to 15 141812 -0.3356 0.368579 5 to 14 142242 1.1471 0.874338 4 to 13 141830 -0.2736 0.392215 3 to 12 142044 0.4644 0.678812 2 to 11 141385 -1.8080 0.035301 1 to 10 141378 -1.8322 0.033463 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-08-01_12:31 Bits used No. missing words z-score p-value 28 to 32 142447 1.8226 0.965819 27 to 31 141839 -0.2384 0.405783 26 to 30 142463 1.8768 0.969731 25 to 29 141815 -0.3198 0.374574 24 to 28 141637 -0.9232 0.177964 23 to 27 141701 -0.7062 0.240031 22 to 26 141986 0.2599 0.602529 21 to 25 141637 -0.9232 0.177964 20 to 24 141058 -2.8859 0.001952 19 to 23 141879 -0.1028 0.459056 18 to 22 142038 0.4362 0.668643 17 to 21 141882 -0.0926 0.463093 16 to 20 142249 1.1514 0.875221 15 to 19 142162 0.8565 0.804142 14 to 18 141523 -1.3096 0.095167 13 to 17 142052 0.4836 0.685675 12 to 16 141314 -2.0181 0.021792 11 to 15 141491 -1.4181 0.078086 10 to 14 141672 -0.8045 0.210552 9 to 13 141875 -0.1164 0.453679 8 to 12 141720 -0.6418 0.260503 7 to 11 141982 0.2463 0.597290 6 to 10 141948 0.1311 0.552146 5 to 9 142028 0.4023 0.656258 4 to 8 142073 0.5548 0.710489 3 to 7 141529 -1.2893 0.098655 2 to 6 141842 -0.2282 0.409731 1 to 5 141542 -1.2452 0.106532 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-08-01_12:31 Bits used No. missing words z-score p-value 31 to 32 142082 0.5094 0.694747 30 to 31 142181 0.8014 0.788546 29 to 30 142132 0.6568 0.744359 28 to 29 141707 -0.5968 0.275306 27 to 28 142193 0.8368 0.798643 26 to 27 142374 1.3707 0.914767 25 to 26 142182 0.8043 0.789399 24 to 25 141749 -0.4729 0.318125 23 to 24 141588 -0.9479 0.171596 22 to 23 141751 -0.4671 0.320232 21 to 22 142383 1.3973 0.918832 20 to 21 141597 -0.9213 0.178440 19 to 20 142100 0.5624 0.713095 18 to 19 141650 -0.7650 0.222140 17 to 18 141853 -0.1662 0.434014 16 to 17 141539 -1.0924 0.137325 15 to 16 141472 -1.2901 0.098515 14 to 15 141776 -0.3933 0.347048 13 to 14 141661 -0.7325 0.231921 12 to 13 141770 -0.4110 0.340535 11 to 12 142061 0.4474 0.672708 10 to 11 142377 1.3796 0.916139 9 to 10 141885 -0.0718 0.471393 8 to 9 141601 -0.9095 0.181536 7 to 8 142522 1.8073 0.964641 6 to 7 142084 0.5153 0.696811 5 to 6 141995 0.2527 0.599755 4 to 5 141723 -0.5496 0.291281 3 to 4 141523 -1.1396 0.127223 2 to 3 141651 -0.7620 0.223019 1 to 2 141534 -1.1072 0.134111 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-08-01_12:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2533.71 0.477 0.683230 Test results for specific bytes for dh-ranFile-2016-08-01_12:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2434.68 -0.924 0.177811 2 to 9 2555.59 0.786 0.784096 3 to 10 2505.89 0.083 0.533178 4 to 11 2636.39 1.929 0.973126 5 to 12 2482.45 -0.248 0.402006 6 to 13 2457.61 -0.599 0.274443 7 to 14 2477.73 -0.315 0.376391 8 to 15 2468.77 -0.442 0.329389 9 to 16 2649.84 2.119 0.982956 10 to 17 2523.39 0.331 0.629570 11 to 18 2458.93 -0.581 0.280664 12 to 19 2571.74 1.015 0.844850 13 to 20 2524.35 0.344 0.634700 14 to 21 2538.79 0.549 0.708364 15 to 22 2453.08 -0.664 0.253488 16 to 23 2472.74 -0.385 0.349952 17 to 24 2512.29 0.174 0.568985 18 to 25 2578.07 1.104 0.865208 19 to 26 2496.64 -0.048 0.481043 20 to 27 2578.35 1.108 0.866088 21 to 28 2425.91 -1.048 0.147352 22 to 29 2552.75 0.746 0.772156 23 to 30 2395.29 -1.481 0.069333 24 to 31 2456.01 -0.622 0.266917 25 to 32 2518.96 0.268 0.605699 CDPARK for dh-ranFile-2016-08-01_12:31: 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 3524 0.0457 0.518210 3559 1.6438 0.949895 3513 -0.4566 0.323972 3507 -0.7306 0.232514 3507 -0.7306 0.232514 3493 -1.3699 0.085365 3539 0.7306 0.767486 3563 1.8265 0.966111 3484 -1.7808 0.037471 3484 -1.7808 0.037471 Square side=100, avg. no. parked=3517.30 sample std.=27.17 p-value of the KSTEST for those 10 p-values: 0.246238 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-08-01_12:31 0.5822,0.3946,0.0260,0.4105,0.2268,0.0775,0.1827,0.0164,0.9321,0.6309, The KS test for those 10 p-values: 0.120451 The 3DSPHERES test for dh-ranFile-2016-08-01_12:31 sample no r^3 equiv. uni. 1 1.017 0.033342 2 18.552 0.461188 3 4.418 0.136930 4 38.121 0.719365 5 0.072 0.002398 6 24.746 0.561710 7 0.524 0.017329 8 16.372 0.420579 9 52.002 0.823315 10 20.343 0.492425 11 123.735 0.983828 12 5.040 0.154641 13 36.858 0.707295 14 24.057 0.551527 15 1.035 0.033915 16 87.897 0.946597 17 26.117 0.581282 18 2.117 0.068143 19 60.231 0.865701 20 10.519 0.295757 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.208849 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-08-01_12:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -0.3 1.1 0.0 2.4 -1.5 -0.1 1.5 -2.3 0.7 1.5 1.7 -1.4 -0.7 0.9 -0.2 0.0 0.0 -0.4 0.4 0.4 -0.1 0.3 -1.7 0.8 -1.3 0.1 -0.0 0.7 -0.8 -0.1 0.6 0.8 -2.7 0.9 1.1 -1.9 0.5 -2.0 -0.7 0.1 -1.0 -1.1 Chi-square with 42 degrees of freedom:54.326617 z-score=1.344944, p-value=0.903768 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-08-01_12:31 Test no p-value 1 0.852809 2 0.463759 3 0.116561 4 0.538543 5 0.100424 6 0.514355 7 0.654648 8 0.979138 9 0.523820 10 0.173866 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.893663 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-08-01_12:31: (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 66310 1.91 66607 0.05 3 25000.00 25374 5.60 24899 0.41 4 6666.67 6675 0.01 6814 3.26 5 1388.89 1372 0.21 1415 0.49 6 238.10 223 0.96 228 0.43 7 34.72 33 0.09 29 0.94 8 4.96 12 9.99 7 0.84 p=0.99540 p=0.62193 Number of rngs required: 688113, p-value: 0.369 RESULTS OF CRAPS TEST for dh-ranFile-2016-08-01_12:31 No. of wins: Observed Expected 98258 98585.9 z-score=-1.466, pvalue=0.07127 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66623 66666.7 0.029 0.029 2 37594 37654.3 0.097 0.125 3 27078 26954.7 0.564 0.689 4 19140 19313.5 1.558 2.247 5 13859 13851.4 0.004 2.251 6 9957 9943.5 0.018 2.269 7 7285 7145.0 2.742 5.011 8 5249 5139.1 2.351 7.363 9 3629 3699.9 1.357 8.720 10 2664 2666.3 0.002 8.722 11 1845 1923.3 3.190 11.912 12 1446 1388.7 2.361 14.273 13 1038 1003.7 1.171 15.444 14 692 726.1 1.605 17.049 15 484 525.8 3.328 20.378 16 395 381.2 0.503 20.881 17 292 276.5 0.864 21.745 18 194 200.8 0.232 21.978 19 162 146.0 1.757 23.735 20 105 106.2 0.014 23.749 21 269 287.1 1.143 24.891 Chisq= 24.89 for 20 degrees of freedom, p= 0.79438 SUMMARY of craptest p-value for no. of wins: 0.071273 p-value for throws/game: 0.794382 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-08-01_12:31 No. of wins: Observed Expected 98437 98585.9 z-score=-0.666, pvalue=0.25278 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66568 66666.7 0.146 0.146 2 37902 37654.3 1.629 1.775 3 26828 26954.7 0.596 2.371 4 19109 19313.5 2.165 4.536 5 13968 13851.4 0.981 5.517 6 9912 9943.5 0.100 5.617 7 7193 7145.0 0.322 5.939 8 5172 5139.1 0.211 6.150 9 3772 3699.9 1.406 7.556 10 2703 2666.3 0.505 8.062 11 1970 1923.3 1.133 9.194 12 1359 1388.7 0.637 9.831 13 956 1003.7 2.268 12.099 14 686 726.1 2.219 14.318 15 572 525.8 4.053 18.371 16 365 381.2 0.684 19.055 17 262 276.5 0.764 19.820 18 189 200.8 0.697 20.517 19 147 146.0 0.007 20.524 20 94 106.2 1.405 21.929 21 273 287.1 0.694 22.622 Chisq= 22.62 for 20 degrees of freedom, p= 0.69228 SUMMARY of craptest p-value for no. of wins: 0.252775 p-value for throws/game: 0.692285 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0020,0.0024,0.0164,0.0173,0.0218,0.0237,0.0238,0.0260,0.0333,0.0335, 0.0339,0.0353,0.0375,0.0375,0.0406,0.0468,0.0511,0.0588,0.0646,0.0655, 0.0681,0.0693,0.0713,0.0775,0.0781,0.0854,0.0933,0.0952,0.0985,0.0987, 0.1004,0.1054,0.1065,0.1087,0.1166,0.1205,0.1272,0.1324,0.1341,0.1369, 0.1373,0.1469,0.1471,0.1474,0.1492,0.1546,0.1584,0.1646,0.1664,0.1686, 0.1716,0.1739,0.1778,0.1780,0.1780,0.1784,0.1815,0.1815,0.1827,0.1867, 0.1871,0.2088,0.2106,0.2221,0.2230,0.2242,0.2268,0.2319,0.2325,0.2325, 0.2344,0.2400,0.2427,0.2434,0.2462,0.2470,0.2525,0.2528,0.2535,0.2555, 0.2570,0.2605,0.2614,0.2622,0.2669,0.2744,0.2753,0.2807,0.2823,0.2843, 0.2913,0.2951,0.2958,0.2966,0.3025,0.3181,0.3202,0.3232,0.3240,0.3266, 0.3294,0.3300,0.3302,0.3303,0.3405,0.3441,0.3446,0.3470,0.3500,0.3532, 0.3592,0.3686,0.3692,0.3725,0.3746,0.3764,0.3780,0.3907,0.3922,0.3926, 0.3946,0.4020,0.4058,0.4097,0.4105,0.4206,0.4239,0.4243,0.4286,0.4320, 0.4340,0.4403,0.4426,0.4488,0.4504,0.4523,0.4537,0.4591,0.4612,0.4618, 0.4625,0.4631,0.4638,0.4677,0.4714,0.4751,0.4762,0.4768,0.4789,0.4810, 0.4858,0.4895,0.4924,0.5068,0.5144,0.5182,0.5238,0.5332,0.5385,0.5491, 0.5515,0.5521,0.5601,0.5617,0.5639,0.5690,0.5766,0.5782,0.5805,0.5813, 0.5822,0.5835,0.5848,0.5868,0.5922,0.5928,0.5969,0.5973,0.5998,0.6008, 0.6025,0.6043,0.6057,0.6219,0.6296,0.6309,0.6347,0.6400,0.6515,0.6546, 0.6559,0.6563,0.6643,0.6686,0.6727,0.6762,0.6788,0.6832,0.6839,0.6857, 0.6923,0.6947,0.6968,0.7073,0.7084,0.7105,0.7131,0.7173,0.7185,0.7194, 0.7222,0.7245,0.7385,0.7417,0.7444,0.7558,0.7675,0.7722,0.7735,0.7841, 0.7841,0.7885,0.7894,0.7944,0.7986,0.7995,0.8006,0.8019,0.8041,0.8121, 0.8172,0.8177,0.8233,0.8344,0.8412,0.8448,0.8450,0.8524,0.8528,0.8648, 0.8652,0.8657,0.8661,0.8703,0.8743,0.8752,0.8821,0.8902,0.8937,0.8955, 0.8968,0.9038,0.9053,0.9107,0.9148,0.9161,0.9188,0.9321,0.9466,0.9499, 0.9646,0.9658,0.9661,0.9697,0.9731,0.9791,0.9830,0.9838,0.9954, Overall p-value after applying KStest on 269 p-values = 0.054819 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.