RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-10-18_08:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.66 13.6327 0.307092 2 to 25 15.62 26.1549 0.928316 3 to 26 15.64 12.1815 0.210977 4 to 27 15.53 17.7834 0.597373 5 to 28 16.05 20.4899 0.750057 6 to 29 15.99 11.1411 0.150864 7 to 30 15.75 24.2034 0.885987 8 to 31 15.88 21.2802 0.785994 9 to 32 15.86 14.1884 0.346273 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.867356 Tough bday spacings test for dh-ranFile-2015-10-18_08:31: 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 39 80 99 99 72 53 21 16 8 4 (O-E)^2/E 0.0 0.2 0.6 0.0 0.0 0.5 0.0 2.6 0.1 0.3 0.0 Birthday Spacings: Sum(O-E)^2/E= 4.268, p= 0.066 RESULTS OF GCD FOR dh-ranFile-2015-10-18_08:31 Euclid's algorithm: p-value, steps to gcd: 0.035663 p-value, dist. of gcd's: 0.462090 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-10-18_08:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.736 0.277 0.149 0.160 0.970 0.053 0.743 0.940 Bits 8 to 15---> 0.745 0.205 0.346 0.704 0.502 0.251 0.895 0.366 Bits 16 to 23---> 0.149 0.756 0.498 0.958 0.621 0.640 0.467 0.383 Bits 24 to 31---> 0.726 0.110 0.085 0.709 0.226 0.530 0.058 0.174 KS test for the above 32 p values: 0.183 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-10-18_08:31, p-values for 5 runs: 0.4290, 0.5408, 0.5736, 0.4321, 0.2962 Rank test for binary matrices (31x31) for dh-ranFile-2015-10-18_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 217 211.4 0.147 0.147 r= 29 5104 5134.0 0.175 0.323 r= 30 23238 23103.0 0.788 1.111 r= 31 11441 11551.5 1.057 2.169 chi-square = 2.169 with df = 3; p-value = 0.462 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-10-18_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 225 211.4 0.873 0.873 r= 30 5089 5134.0 0.395 1.267 r= 31 23074 23103.0 0.037 1.304 r= 32 11612 11551.5 0.317 1.620 chi-square = 1.620 with df = 3; p-value = 0.345 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-10-18_08:31 b-rank test for bits 1 to 8, p=0.23687 b-rank test for bits 2 to 9, p=0.62742 b-rank test for bits 3 to 10, p=0.34144 b-rank test for bits 4 to 11, p=0.30768 b-rank test for bits 5 to 12, p=0.07263 b-rank test for bits 6 to 13, p=0.12252 b-rank test for bits 7 to 14, p=0.04950 b-rank test for bits 8 to 15, p=0.66660 b-rank test for bits 9 to 16, p=0.22643 b-rank test for bits 10 to 17, p=0.20967 b-rank test for bits 11 to 18, p=0.04005 b-rank test for bits 12 to 19, p=0.28851 b-rank test for bits 13 to 20, p=0.74289 b-rank test for bits 14 to 21, p=0.08301 b-rank test for bits 15 to 22, p=0.66924 b-rank test for bits 16 to 23, p=0.81065 b-rank test for bits 17 to 24, p=0.63450 b-rank test for bits 18 to 25, p=0.15021 b-rank test for bits 19 to 26, p=0.07217 b-rank test for bits 20 to 27, p=0.42903 b-rank test for bits 21 to 28, p=0.03581 b-rank test for bits 22 to 29, p=0.59866 b-rank test for bits 23 to 30, p=0.24258 b-rank test for bits 24 to 31, p=0.64268 b-rank test for bits 25 to 32, p=0.01377 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 = 0.003980 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-10-18_08:31 (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 141654 -0.60 0.275399 2 142098 0.44 0.670328 3 142417 1.19 0.882217 4 142633 1.69 0.954564 5 142154 0.57 0.716223 6 142058 0.35 0.635840 7 141378 -1.24 0.107224 8 142075 0.39 0.650651 9 141929 0.05 0.518328 10 142349 1.03 0.847852 11 142388 1.12 0.868299 12 142056 0.34 0.634083 13 141852 -0.13 0.446722 14 141302 -1.42 0.077950 15 142922 2.37 0.991011 16 142057 0.35 0.634962 17 142363 1.06 0.855422 18 141779 -0.30 0.380370 19 142338 1.00 0.841723 20 141757 -0.36 0.360954 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-10-18_08:31 Bits used No. missing words z-score p-value 23 to 32 141469 -1.5184 0.064459 22 to 31 141733 -0.6080 0.271582 21 to 30 141715 -0.6701 0.251396 20 to 29 141669 -0.8287 0.203630 19 to 28 141883 -0.0908 0.463829 18 to 27 141945 0.1230 0.548947 17 to 26 141931 0.0747 0.529783 16 to 25 142026 0.4023 0.656272 15 to 24 141870 -0.1356 0.446061 14 to 23 142078 0.5816 0.719589 13 to 22 141947 0.1299 0.551676 12 to 21 141678 -0.7977 0.212525 11 to 20 142113 0.7023 0.758757 10 to 19 141794 -0.3977 0.345430 9 to 18 142017 0.3713 0.644784 8 to 17 142061 0.5230 0.699513 7 to 16 141507 -1.3873 0.082668 6 to 15 141848 -0.2115 0.416255 5 to 14 141871 -0.1322 0.447424 4 to 13 141784 -0.4322 0.332808 3 to 12 142113 0.7023 0.758757 2 to 11 142324 1.4299 0.923627 1 to 10 141983 0.2540 0.600266 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-10-18_08:31 Bits used No. missing words z-score p-value 28 to 32 141854 -0.1876 0.425611 27 to 31 141637 -0.9232 0.177964 26 to 30 142145 0.7989 0.787820 25 to 29 141868 -0.1401 0.444290 24 to 28 141808 -0.3435 0.365614 23 to 27 141368 -1.8350 0.033252 22 to 26 142252 1.1616 0.877300 21 to 25 141768 -0.4791 0.315939 20 to 24 141907 -0.0079 0.496849 19 to 23 141646 -0.8926 0.186024 18 to 22 141838 -0.2418 0.404469 17 to 21 141958 0.1650 0.565521 16 to 20 141525 -1.3028 0.096319 15 to 19 142057 0.5006 0.691665 14 to 18 141851 -0.1977 0.421629 13 to 17 141956 0.1582 0.562852 12 to 16 142415 1.7141 0.956748 11 to 15 142341 1.4633 0.928306 10 to 14 142075 0.5616 0.712803 9 to 13 141482 -1.4486 0.073728 8 to 12 142335 1.4429 0.925483 7 to 11 141821 -0.2994 0.382308 6 to 10 141568 -1.1571 0.123626 5 to 9 141820 -0.3028 0.381016 4 to 8 142030 0.4091 0.658749 3 to 7 141971 0.2091 0.582796 2 to 6 141670 -0.8113 0.208600 1 to 5 141825 -0.2859 0.387491 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-10-18_08:31 Bits used No. missing words z-score p-value 31 to 32 141959 0.1465 0.558244 30 to 31 142129 0.6480 0.741506 29 to 30 141899 -0.0305 0.487845 28 to 29 141771 -0.4081 0.341617 27 to 28 141749 -0.4729 0.318125 26 to 27 142214 0.8987 0.815602 25 to 26 141611 -0.8800 0.189422 24 to 25 141759 -0.4435 0.328720 23 to 24 141060 -2.5054 0.006116 22 to 23 141001 -2.6794 0.003687 21 to 22 142481 1.6863 0.954135 20 to 21 141826 -0.2458 0.402914 19 to 20 142339 1.2675 0.897505 18 to 19 142011 0.2999 0.617878 17 to 18 141585 -0.9567 0.169353 16 to 17 142275 1.0787 0.859633 15 to 16 142043 0.3943 0.653323 14 to 15 142568 1.9430 0.973991 13 to 14 142544 1.8722 0.969409 12 to 13 141649 -0.7679 0.221263 11 to 12 142445 1.5801 0.942963 10 to 11 142247 0.9961 0.840394 9 to 10 142184 0.8102 0.791098 8 to 9 142158 0.7335 0.768385 7 to 8 142203 0.8663 0.806833 6 to 7 141893 -0.0482 0.480790 5 to 6 141271 -1.8830 0.029852 4 to 5 141127 -2.3078 0.010506 3 to 4 141886 -0.0688 0.472566 2 to 3 142381 1.3914 0.917941 1 to 2 141888 -0.0629 0.474915 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-10-18_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2537.04 0.524 0.699790 Test results for specific bytes for dh-ranFile-2015-10-18_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2629.81 1.836 0.966807 2 to 9 2489.55 -0.148 0.441270 3 to 10 2464.38 -0.504 0.307239 4 to 11 2509.37 0.132 0.552684 5 to 12 2334.65 -2.338 0.009684 6 to 13 2501.09 0.015 0.506147 7 to 14 2489.80 -0.144 0.442631 8 to 15 2610.98 1.569 0.941729 9 to 16 2525.36 0.359 0.640043 10 to 17 2406.26 -1.326 0.092473 11 to 18 2485.18 -0.210 0.416998 12 to 19 2445.45 -0.771 0.220229 13 to 20 2454.03 -0.650 0.257819 14 to 21 2617.25 1.658 0.951359 15 to 22 2644.71 2.047 0.979647 16 to 23 2429.85 -0.992 0.160576 17 to 24 2438.03 -0.876 0.190406 18 to 25 2480.75 -0.272 0.392732 19 to 26 2544.42 0.628 0.735084 20 to 27 2458.07 -0.593 0.276610 21 to 28 2593.51 1.322 0.906989 22 to 29 2415.71 -1.192 0.116618 23 to 30 2535.20 0.498 0.690684 24 to 31 2455.89 -0.624 0.266388 25 to 32 2491.15 -0.125 0.450219 CDPARK for dh-ranFile-2015-10-18_08:31: 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 3512 -0.5023 0.307734 3484 -1.7808 0.037471 3537 0.6393 0.738676 3526 0.1370 0.554479 3553 1.3699 0.914635 3533 0.4566 0.676028 3534 0.5023 0.692266 3520 -0.1370 0.445521 3508 -0.6849 0.246694 3535 0.5479 0.708135 Square side=100, avg. no. parked=3524.20 sample std.=18.25 p-value of the KSTEST for those 10 p-values: 0.837928 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-10-18_08:31 0.6758,0.1892,0.5696,0.0022,0.0489,0.3393,0.2730,0.2940,0.8630,0.8378, The KS test for those 10 p-values: 0.400345 The 3DSPHERES test for dh-ranFile-2015-10-18_08:31 sample no r^3 equiv. uni. 1 102.406 0.967076 2 167.192 0.996201 3 2.954 0.093768 4 28.014 0.606938 5 8.784 0.253831 6 30.299 0.635766 7 13.220 0.356382 8 19.370 0.475687 9 26.892 0.591960 10 40.523 0.740957 11 35.087 0.689498 12 81.347 0.933568 13 19.431 0.476748 14 18.955 0.468381 15 11.773 0.324579 16 57.105 0.850953 17 10.402 0.293001 18 73.771 0.914481 19 7.552 0.222552 20 6.258 0.188279 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.565254 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-10-18_08:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.5 1.1 0.0 -0.7 -0.1 -0.3 1.8 -0.3 0.3 1.2 -0.4 -0.6 0.4 -0.6 -1.0 0.4 0.5 -1.1 1.3 -0.3 0.3 1.1 -1.4 -1.4 0.6 -0.0 0.8 -1.0 0.3 0.2 -0.5 1.7 0.4 1.3 -0.5 -1.2 -1.0 -0.4 2.1 0.1 4.1 -0.1 Chi-square with 42 degrees of freedom:48.425941 z-score=0.701128, p-value=0.770410 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-10-18_08:31 Test no p-value 1 0.070764 2 0.129102 3 0.140495 4 0.002990 5 0.604225 6 0.808981 7 0.178865 8 0.867177 9 0.132506 10 0.010848 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.006936 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-10-18_08:31: (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 66809 0.30 66555 0.19 3 25000.00 24921 0.25 24931 0.19 4 6666.67 6575 1.26 6830 4.00 5 1388.89 1407 0.24 1419 0.65 6 238.10 246 0.26 226 0.61 7 34.72 39 0.53 30 0.64 8 4.96 2 1.77 8 1.86 p=0.40484 p=0.77276 Number of rngs required: 688538, p-value: 0.562 RESULTS OF CRAPS TEST for dh-ranFile-2015-10-18_08:31 No. of wins: Observed Expected 98686 98585.9 z-score= 0.448, pvalue=0.67288 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66581 66666.7 0.110 0.110 2 37642 37654.3 0.004 0.114 3 26834 26954.7 0.541 0.655 4 19480 19313.5 1.436 2.091 5 13883 13851.4 0.072 2.163 6 9910 9943.5 0.113 2.276 7 7103 7145.0 0.247 2.523 8 5086 5139.1 0.548 3.071 9 3674 3699.9 0.181 3.252 10 2646 2666.3 0.155 3.407 11 2042 1923.3 7.322 10.729 12 1406 1388.7 0.215 10.943 13 1046 1003.7 1.781 12.725 14 687 726.1 2.110 14.834 15 546 525.8 0.773 15.608 16 384 381.2 0.021 15.629 17 326 276.5 8.846 24.475 18 196 200.8 0.116 24.591 19 135 146.0 0.827 25.418 20 97 106.2 0.800 26.217 21 296 287.1 0.275 26.492 Chisq= 26.49 for 20 degrees of freedom, p= 0.84984 SUMMARY of craptest p-value for no. of wins: 0.672884 p-value for throws/game: 0.849843 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-10-18_08:31 No. of wins: Observed Expected 98586 98585.9 z-score= 0.001, pvalue=0.50025 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66397 66666.7 1.091 1.091 2 37678 37654.3 0.015 1.106 3 27032 26954.7 0.221 1.327 4 19009 19313.5 4.800 6.127 5 13951 13851.4 0.716 6.843 6 10091 9943.5 2.187 9.029 7 7100 7145.0 0.284 9.313 8 5262 5139.1 2.940 12.254 9 3711 3699.9 0.034 12.287 10 2652 2666.3 0.077 12.364 11 1936 1923.3 0.083 12.447 12 1447 1388.7 2.444 14.891 13 1017 1003.7 0.176 15.067 14 725 726.1 0.002 15.069 15 560 525.8 2.220 17.289 16 375 381.2 0.099 17.388 17 276 276.5 0.001 17.389 18 199 200.8 0.017 17.406 19 145 146.0 0.007 17.412 20 122 106.2 2.346 19.758 21 315 287.1 2.708 22.466 Chisq= 22.47 for 20 degrees of freedom, p= 0.68426 SUMMARY of craptest p-value for no. of wins: 0.500252 p-value for throws/game: 0.684256 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0022,0.0030,0.0037,0.0040,0.0061,0.0069,0.0097,0.0105,0.0108,0.0138, 0.0299,0.0333,0.0357,0.0358,0.0375,0.0400,0.0489,0.0495,0.0529,0.0576, 0.0645,0.0656,0.0708,0.0722,0.0726,0.0737,0.0780,0.0827,0.0830,0.0851, 0.0925,0.0938,0.0963,0.1072,0.1104,0.1166,0.1225,0.1236,0.1291,0.1325, 0.1405,0.1485,0.1494,0.1502,0.1509,0.1598,0.1606,0.1694,0.1738,0.1780, 0.1789,0.1831,0.1860,0.1883,0.1892,0.1894,0.1904,0.2036,0.2054,0.2086, 0.2097,0.2110,0.2125,0.2202,0.2213,0.2226,0.2258,0.2264,0.2369,0.2426, 0.2467,0.2511,0.2514,0.2538,0.2578,0.2664,0.2716,0.2730,0.2754,0.2766, 0.2767,0.2885,0.2930,0.2940,0.2962,0.3071,0.3072,0.3077,0.3077,0.3159, 0.3181,0.3246,0.3287,0.3328,0.3393,0.3414,0.3416,0.3452,0.3454,0.3460, 0.3463,0.3564,0.3610,0.3656,0.3665,0.3804,0.3810,0.3823,0.3829,0.3875, 0.3927,0.4003,0.4029,0.4045,0.4048,0.4163,0.4170,0.4216,0.4256,0.4290, 0.4290,0.4321,0.4413,0.4426,0.4443,0.4455,0.4461,0.4467,0.4474,0.4502, 0.4618,0.4621,0.4638,0.4671,0.4684,0.4726,0.4749,0.4757,0.4767,0.4808, 0.4878,0.4968,0.4983,0.5003,0.5023,0.5061,0.5183,0.5298,0.5305,0.5408, 0.5489,0.5517,0.5527,0.5545,0.5582,0.5617,0.5629,0.5653,0.5655,0.5696, 0.5736,0.5828,0.5920,0.5974,0.5987,0.6003,0.6042,0.6069,0.6179,0.6210, 0.6274,0.6341,0.6345,0.6350,0.6358,0.6358,0.6400,0.6402,0.6427,0.6448, 0.6507,0.6533,0.6563,0.6587,0.6666,0.6692,0.6703,0.6729,0.6758,0.6760, 0.6843,0.6895,0.6907,0.6917,0.6923,0.6995,0.6998,0.7040,0.7081,0.7091, 0.7128,0.7162,0.7196,0.7263,0.7351,0.7356,0.7387,0.7410,0.7415,0.7429, 0.7430,0.7446,0.7501,0.7562,0.7588,0.7588,0.7684,0.7704,0.7728,0.7860, 0.7878,0.7911,0.8068,0.8090,0.8107,0.8156,0.8378,0.8379,0.8404,0.8417, 0.8479,0.8498,0.8510,0.8554,0.8596,0.8630,0.8672,0.8674,0.8683,0.8773, 0.8822,0.8860,0.8951,0.8975,0.9070,0.9145,0.9146,0.9179,0.9236,0.9255, 0.9283,0.9283,0.9336,0.9404,0.9417,0.9430,0.9514,0.9541,0.9546,0.9567, 0.9583,0.9668,0.9671,0.9694,0.9696,0.9740,0.9796,0.9910,0.9962, Overall p-value after applying KStest on 269 p-values = 0.493990 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.