RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-10-26_20:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.62 13.6067 0.305280 2 to 25 16.17 23.1377 0.855179 3 to 26 15.61 19.6163 0.705677 4 to 27 15.85 22.8835 0.846918 5 to 28 15.58 17.1463 0.555501 6 to 29 15.65 16.6485 0.521586 7 to 30 15.75 19.7276 0.711600 8 to 31 15.87 19.7411 0.712315 9 to 32 15.90 13.7885 0.317985 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.244329 Tough bday spacings test for dh-ranFile-2015-10-26_20:31: 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 10 30 85 114 93 69 51 23 21 2 2 (O-E)^2/E 0.1 1.2 1.9 2.7 0.2 1.1 0.0 1.5 2.5 3.2 1.0 Birthday Spacings: Sum(O-E)^2/E= 15.524, p= 0.886 RESULTS OF GCD FOR dh-ranFile-2015-10-26_20:31 Euclid's algorithm: p-value, steps to gcd: 0.127724 p-value, dist. of gcd's: 0.130668 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-10-26_20:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.897 0.169 0.511 0.473 0.622 0.880 0.981 0.723 Bits 8 to 15---> 0.843 0.291 0.965 0.539 0.071 0.327 0.029 0.190 Bits 16 to 23---> 0.655 0.914 0.280 0.632 0.635 0.315 0.866 0.977 Bits 24 to 31---> 0.206 0.629 0.511 0.847 0.210 0.615 0.870 0.122 KS test for the above 32 p values: 0.591 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-10-26_20:31, p-values for 5 runs: 0.3810, 0.0916, 0.0363, 0.8070, 0.1528 Rank test for binary matrices (31x31) for dh-ranFile-2015-10-26_20:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 211 211.4 0.001 0.001 r= 29 5153 5134.0 0.070 0.071 r= 30 23018 23103.0 0.313 0.384 r= 31 11618 11551.5 0.383 0.767 chi-square = 0.767 with df = 3; p-value = 0.143 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-10-26_20:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 199 211.4 0.729 0.729 r= 30 5104 5134.0 0.175 0.905 r= 31 22986 23103.0 0.593 1.498 r= 32 11711 11551.5 2.202 3.699 chi-square = 3.699 with df = 3; p-value = 0.704 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-10-26_20:31 b-rank test for bits 1 to 8, p=0.59527 b-rank test for bits 2 to 9, p=0.71340 b-rank test for bits 3 to 10, p=0.07393 b-rank test for bits 4 to 11, p=0.14802 b-rank test for bits 5 to 12, p=0.12748 b-rank test for bits 6 to 13, p=0.50994 b-rank test for bits 7 to 14, p=0.92894 b-rank test for bits 8 to 15, p=0.64950 b-rank test for bits 9 to 16, p=0.87416 b-rank test for bits 10 to 17, p=0.44807 b-rank test for bits 11 to 18, p=0.86094 b-rank test for bits 12 to 19, p=0.97352 b-rank test for bits 13 to 20, p=0.45833 b-rank test for bits 14 to 21, p=0.25238 b-rank test for bits 15 to 22, p=0.13670 b-rank test for bits 16 to 23, p=0.60467 b-rank test for bits 17 to 24, p=0.31705 b-rank test for bits 18 to 25, p=0.48880 b-rank test for bits 19 to 26, p=0.73668 b-rank test for bits 20 to 27, p=0.86285 b-rank test for bits 21 to 28, p=0.09088 b-rank test for bits 22 to 29, p=0.70811 b-rank test for bits 23 to 30, p=0.23499 b-rank test for bits 24 to 31, p=0.24168 b-rank test for bits 25 to 32, p=0.50122 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 = 0.986815 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-10-26_20:31 (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 142737 1.93 0.973432 2 142316 0.95 0.828985 3 141816 -0.22 0.413691 4 141735 -0.41 0.341889 5 142270 0.84 0.800298 6 141500 -0.96 0.169441 7 141695 -0.50 0.308266 8 142408 1.17 0.878014 9 141808 -0.24 0.406425 10 141608 -0.70 0.240703 11 142032 0.29 0.612795 12 143153 2.91 0.998168 13 142082 0.40 0.656686 14 141716 -0.45 0.325741 15 142285 0.88 0.809956 16 141635 -0.64 0.260775 17 141983 0.17 0.568331 18 141196 -1.67 0.047791 19 141831 -0.18 0.427394 20 142346 1.02 0.846197 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-10-26_20:31 Bits used No. missing words z-score p-value 23 to 32 142185 0.9506 0.829093 22 to 31 141868 -0.1425 0.443336 21 to 30 142031 0.4196 0.662594 20 to 29 142012 0.3540 0.638344 19 to 28 142398 1.6851 0.954012 18 to 27 142440 1.8299 0.966367 17 to 26 142309 1.3782 0.915925 16 to 25 141570 -1.1701 0.120980 15 to 24 141338 -1.9701 0.024413 14 to 23 141736 -0.5977 0.275024 13 to 22 141332 -1.9908 0.023252 12 to 21 142206 1.0230 0.846846 11 to 20 142265 1.2264 0.889985 10 to 19 142347 1.5092 0.934377 9 to 18 142075 0.5713 0.716094 8 to 17 142094 0.6368 0.737870 7 to 16 142332 1.4575 0.927508 6 to 15 141732 -0.6115 0.270440 5 to 14 141712 -0.6804 0.248110 4 to 13 142063 0.5299 0.701908 3 to 12 141585 -1.1184 0.131703 2 to 11 141344 -1.9494 0.025623 1 to 10 141501 -1.4080 0.079560 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-10-26_20:31 Bits used No. missing words z-score p-value 28 to 32 141396 -1.7401 0.040921 27 to 31 142331 1.4294 0.923554 26 to 30 142057 0.5006 0.691665 25 to 29 141851 -0.1977 0.421629 24 to 28 142003 0.3175 0.624578 23 to 27 141765 -0.4893 0.312331 22 to 26 142260 1.1887 0.882723 21 to 25 141887 -0.0757 0.469831 20 to 24 141823 -0.2926 0.384897 19 to 23 141900 -0.0316 0.487385 18 to 22 141913 0.0124 0.504963 17 to 21 142200 0.9853 0.837767 16 to 20 141874 -0.1198 0.452336 15 to 19 142206 1.0057 0.842711 14 to 18 142021 0.3785 0.647486 13 to 17 142227 1.0768 0.859226 12 to 16 142013 0.3514 0.637365 11 to 15 141950 0.1379 0.554826 10 to 14 142577 2.2633 0.988191 9 to 13 141905 -0.0147 0.494145 8 to 12 141541 -1.2486 0.105910 7 to 11 141685 -0.7604 0.223496 6 to 10 140725 -4.0147 0.000030 5 to 9 141456 -1.5367 0.062182 4 to 8 141902 -0.0248 0.490088 3 to 7 142134 0.7616 0.776849 2 to 6 141594 -1.0689 0.142554 1 to 5 142656 2.5311 0.994314 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-10-26_20:31 Bits used No. missing words z-score p-value 31 to 32 142721 2.3943 0.991674 30 to 31 141799 -0.3255 0.372418 29 to 30 142076 0.4917 0.688517 28 to 29 141932 0.0669 0.526659 27 to 28 141950 0.1200 0.547747 26 to 27 142044 0.3973 0.654411 25 to 26 142147 0.7011 0.758377 24 to 25 142438 1.5595 0.940561 23 to 24 142203 0.8663 0.806833 22 to 23 141963 0.1583 0.562897 21 to 22 141594 -0.9302 0.176140 20 to 21 141888 -0.0629 0.474915 19 to 20 142023 0.3353 0.631304 18 to 19 141958 0.1436 0.557080 17 to 18 141854 -0.1632 0.435174 16 to 17 142577 1.9695 0.975554 15 to 16 142059 0.4415 0.670576 14 to 15 142066 0.4622 0.678014 13 to 14 141935 0.0757 0.530180 12 to 13 141788 -0.3579 0.360207 11 to 12 141771 -0.4081 0.341617 10 to 11 141912 0.0079 0.503142 9 to 10 142016 0.3147 0.623490 8 to 9 141579 -0.9744 0.164923 7 to 8 142013 0.3058 0.620126 6 to 7 142029 0.3530 0.637959 5 to 6 141847 -0.1839 0.427060 4 to 5 141839 -0.2075 0.417824 3 to 4 141642 -0.7886 0.215178 2 to 3 141890 -0.0570 0.477264 1 to 2 141902 -0.0216 0.491375 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-10-26_20:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2456.56 -0.614 0.269514 Test results for specific bytes for dh-ranFile-2015-10-26_20:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2370.69 -1.829 0.033716 2 to 9 2513.21 0.187 0.574100 3 to 10 2439.09 -0.861 0.194516 4 to 11 2497.43 -0.036 0.485521 5 to 12 2450.66 -0.698 0.242674 6 to 13 2526.55 0.375 0.646342 7 to 14 2636.10 1.925 0.972867 8 to 15 2464.73 -0.499 0.308946 9 to 16 2410.68 -1.263 0.103258 10 to 17 2587.47 1.237 0.891960 11 to 18 2666.83 2.359 0.990846 12 to 19 2533.73 0.477 0.683304 13 to 20 2599.34 1.405 0.919973 14 to 21 2490.33 -0.137 0.445615 15 to 22 2524.89 0.352 0.637585 16 to 23 2428.67 -1.009 0.156554 17 to 24 2451.85 -0.681 0.247952 18 to 25 2358.27 -2.004 0.022519 19 to 26 2308.34 -2.710 0.003359 20 to 27 2427.01 -1.032 0.150990 21 to 28 2594.51 1.337 0.909323 22 to 29 2491.74 -0.117 0.453524 23 to 30 2546.85 0.663 0.746194 24 to 31 2463.22 -0.520 0.301458 25 to 32 2472.33 -0.391 0.347796 CDPARK for dh-ranFile-2015-10-26_20:31: 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 3532 0.4110 0.659449 3510 -0.5936 0.276387 3516 -0.3196 0.374623 3525 0.0913 0.536383 3533 0.4566 0.676028 3495 -1.2785 0.100530 3505 -0.8219 0.205562 3547 1.0959 0.863437 3487 -1.6438 0.050105 3568 2.0548 0.980051 Square side=100, avg. no. parked=3521.80 sample std.=23.22 p-value of the KSTEST for those 10 p-values: 0.982792 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-10-26_20:31 0.5395,0.0806,0.7437,0.6083,0.2522,0.1639,0.0606,0.6613,0.8200,0.1457, The KS test for those 10 p-values: 0.442520 The 3DSPHERES test for dh-ranFile-2015-10-26_20:31 sample no r^3 equiv. uni. 1 42.899 0.760684 2 39.873 0.735287 3 19.142 0.471678 4 45.118 0.777748 5 56.082 0.845785 6 15.453 0.402566 7 10.837 0.303176 8 0.230 0.007642 9 26.982 0.593185 10 13.791 0.368531 11 25.163 0.567760 12 132.450 0.987906 13 42.222 0.755222 14 8.663 0.250807 15 18.436 0.459110 16 61.560 0.871520 17 6.989 0.207817 18 11.112 0.309547 19 4.355 0.135109 20 90.455 0.950963 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.877605 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-10-26_20:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -0.3 -1.3 1.2 0.4 -0.3 -0.2 -0.7 -2.4 1.9 0.6 0.0 0.3 -0.0 -1.3 0.2 0.7 -0.2 0.2 1.6 0.7 0.1 -0.3 -2.1 -0.3 -0.6 -0.1 0.7 -1.4 1.5 -0.5 0.6 0.6 -0.8 -2.4 -1.2 -0.7 -1.3 -0.4 -1.3 0.9 0.0 -0.1 Chi-square with 42 degrees of freedom:42.674937 z-score=0.073642, p-value=0.558030 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-10-26_20:31 Test no p-value 1 0.120771 2 0.919163 3 0.396264 4 0.354135 5 0.217756 6 0.002956 7 0.074350 8 0.500722 9 0.638228 10 0.022141 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.053898 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-10-26_20:31: (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 66582 0.11 66687 0.01 3 25000.00 25053 0.11 25074 0.22 4 6666.67 6710 0.28 6610 0.48 5 1388.89 1356 0.78 1353 0.93 6 238.10 254 1.06 234 0.07 7 34.72 38 0.31 37 0.15 8 4.96 6 0.22 4 0.19 p=0.17511 p=0.08405 Number of rngs required: 687404, p-value: 0.123 RESULTS OF CRAPS TEST for dh-ranFile-2015-10-26_20:31 No. of wins: Observed Expected 98810 98585.9 z-score= 1.002, pvalue=0.84195 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66969 66666.7 1.371 1.371 2 37418 37654.3 1.483 2.854 3 26980 26954.7 0.024 2.878 4 19419 19313.5 0.577 3.455 5 13831 13851.4 0.030 3.485 6 9865 9943.5 0.620 4.105 7 7064 7145.0 0.919 5.024 8 5179 5139.1 0.310 5.334 9 3650 3699.9 0.672 6.006 10 2645 2666.3 0.170 6.176 11 1945 1923.3 0.244 6.421 12 1383 1388.7 0.024 6.444 13 998 1003.7 0.033 6.477 14 742 726.1 0.346 6.823 15 535 525.8 0.160 6.983 16 385 381.2 0.039 7.022 17 260 276.5 0.989 8.011 18 206 200.8 0.133 8.144 19 127 146.0 2.469 10.613 20 106 106.2 0.000 10.613 21 293 287.1 0.121 10.734 Chisq= 10.73 for 20 degrees of freedom, p= 0.04717 SUMMARY of craptest p-value for no. of wins: 0.841947 p-value for throws/game: 0.047169 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-10-26_20:31 No. of wins: Observed Expected 98679 98585.9 z-score= 0.417, pvalue=0.66151 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66752 66666.7 0.109 0.109 2 37696 37654.3 0.046 0.155 3 26794 26954.7 0.958 1.114 4 19360 19313.5 0.112 1.226 5 13899 13851.4 0.163 1.389 6 9954 9943.5 0.011 1.400 7 7127 7145.0 0.045 1.446 8 5094 5139.1 0.395 1.841 9 3797 3699.9 2.550 4.391 10 2706 2666.3 0.591 4.983 11 1889 1923.3 0.613 5.595 12 1326 1388.7 2.834 8.430 13 1059 1003.7 3.045 11.475 14 675 726.1 3.602 15.077 15 531 525.8 0.051 15.127 16 356 381.2 1.660 16.787 17 263 276.5 0.663 17.450 18 187 200.8 0.952 18.402 19 134 146.0 0.984 19.386 20 109 106.2 0.073 19.459 21 292 287.1 0.083 19.542 Chisq= 19.54 for 20 degrees of freedom, p= 0.51312 SUMMARY of craptest p-value for no. of wins: 0.661508 p-value for throws/game: 0.513122 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0000,0.0030,0.0034,0.0076,0.0221,0.0225,0.0233,0.0244,0.0256,0.0286, 0.0337,0.0363,0.0409,0.0472,0.0478,0.0501,0.0539,0.0606,0.0622,0.0710, 0.0739,0.0744,0.0796,0.0806,0.0841,0.0909,0.0916,0.1005,0.1033,0.1059, 0.1208,0.1210,0.1218,0.1230,0.1275,0.1277,0.1307,0.1317,0.1351,0.1367, 0.1426,0.1426,0.1457,0.1480,0.1510,0.1528,0.1566,0.1639,0.1649,0.1685, 0.1694,0.1751,0.1761,0.1900,0.1945,0.2056,0.2059,0.2078,0.2098,0.2152, 0.2178,0.2235,0.2350,0.2407,0.2417,0.2427,0.2443,0.2480,0.2481,0.2508, 0.2522,0.2524,0.2608,0.2695,0.2704,0.2750,0.2764,0.2802,0.2908,0.3015, 0.3032,0.3053,0.3083,0.3089,0.3095,0.3123,0.3152,0.3171,0.3180,0.3257, 0.3274,0.3416,0.3419,0.3478,0.3541,0.3602,0.3685,0.3724,0.3746,0.3810, 0.3849,0.3963,0.4026,0.4064,0.4137,0.4178,0.4216,0.4271,0.4274,0.4352, 0.4425,0.4433,0.4456,0.4481,0.4523,0.4535,0.4583,0.4591,0.4698,0.4717, 0.4731,0.4749,0.4773,0.4855,0.4874,0.4888,0.4901,0.4914,0.4941,0.5007, 0.5012,0.5031,0.5050,0.5099,0.5105,0.5106,0.5131,0.5216,0.5267,0.5302, 0.5364,0.5395,0.5395,0.5477,0.5548,0.5555,0.5571,0.5580,0.5629,0.5678, 0.5683,0.5741,0.5910,0.5932,0.5953,0.6047,0.6083,0.6128,0.6153,0.6201, 0.6216,0.6235,0.6246,0.6288,0.6313,0.6318,0.6352,0.6374,0.6376,0.6380, 0.6382,0.6383,0.6463,0.6475,0.6495,0.6544,0.6545,0.6567,0.6594,0.6613, 0.6615,0.6626,0.6706,0.6760,0.6780,0.6833,0.6885,0.6917,0.7019,0.7042, 0.7057,0.7081,0.7116,0.7123,0.7134,0.7161,0.7234,0.7353,0.7367,0.7379, 0.7437,0.7462,0.7552,0.7584,0.7607,0.7768,0.7777,0.8003,0.8068,0.8070, 0.8100,0.8200,0.8290,0.8291,0.8378,0.8419,0.8427,0.8427,0.8458,0.8462, 0.8466,0.8468,0.8469,0.8552,0.8592,0.8609,0.8628,0.8634,0.8664,0.8701, 0.8715,0.8742,0.8776,0.8780,0.8799,0.8827,0.8859,0.8900,0.8920,0.8972, 0.9093,0.9136,0.9159,0.9192,0.9200,0.9236,0.9275,0.9289,0.9344,0.9406, 0.9510,0.9540,0.9653,0.9664,0.9729,0.9734,0.9735,0.9756,0.9770,0.9801, 0.9814,0.9828,0.9868,0.9879,0.9882,0.9908,0.9917,0.9943,0.9982, Overall p-value after applying KStest on 269 p-values = 0.714207 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.