RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-06-26_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 15.63 13.4329 0.293244 2 to 25 15.64 17.5571 0.582720 3 to 26 15.83 16.4174 0.505537 4 to 27 16.23 17.0431 0.548548 5 to 28 15.62 18.3587 0.633445 6 to 29 15.86 17.4358 0.574760 7 to 30 15.66 12.4622 0.228622 8 to 31 15.89 18.4522 0.639136 9 to 32 15.96 20.1657 0.734159 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.245844 Tough bday spacings test for dh-ranFile-2015-06-26_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 18 32 74 85 103 82 49 28 20 6 3 (O-E)^2/E 8.5 0.6 0.0 1.6 0.3 0.2 0.2 0.1 1.8 0.1 0.3 Birthday Spacings: Sum(O-E)^2/E= 13.640, p= 0.810 RESULTS OF GCD FOR dh-ranFile-2015-06-26_12:31 Euclid's algorithm: p-value, steps to gcd: 0.530827 p-value, dist. of gcd's: 0.821119 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-06-26_12:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.201 0.294 0.426 0.437 0.854 0.934 0.981 0.718 Bits 8 to 15---> 0.201 0.088 0.157 0.014 0.126 0.238 0.060 0.067 Bits 16 to 23---> 0.232 0.776 0.425 0.499 0.475 0.894 0.721 0.460 Bits 24 to 31---> 0.286 0.625 0.710 0.172 0.971 0.331 0.861 0.086 KS test for the above 32 p values: 0.562 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-06-26_12:31, p-values for 5 runs: 0.2530, 0.9205, 0.2546, 0.9542, 0.7293 Rank test for binary matrices (31x31) for dh-ranFile-2015-06-26_12:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 205 211.4 0.195 0.195 r= 29 4996 5134.0 3.710 3.905 r= 30 23152 23103.0 0.104 4.009 r= 31 11647 11551.5 0.789 4.798 chi-square = 4.798 with df = 3; p-value = 0.813 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-06-26_12:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 190 211.4 2.170 2.170 r= 30 5225 5134.0 1.613 3.782 r= 31 23063 23103.0 0.069 3.852 r= 32 11522 11551.5 0.075 3.927 chi-square = 3.927 with df = 3; p-value = 0.731 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-06-26_12:31 b-rank test for bits 1 to 8, p=0.64830 b-rank test for bits 2 to 9, p=0.00977 b-rank test for bits 3 to 10, p=0.98320 b-rank test for bits 4 to 11, p=0.83891 b-rank test for bits 5 to 12, p=0.52806 b-rank test for bits 6 to 13, p=0.89373 b-rank test for bits 7 to 14, p=0.73991 b-rank test for bits 8 to 15, p=0.62449 b-rank test for bits 9 to 16, p=0.86677 b-rank test for bits 10 to 17, p=0.80873 b-rank test for bits 11 to 18, p=0.65649 b-rank test for bits 12 to 19, p=0.17588 b-rank test for bits 13 to 20, p=0.28061 b-rank test for bits 14 to 21, p=0.82816 b-rank test for bits 15 to 22, p=0.24472 b-rank test for bits 16 to 23, p=0.19471 b-rank test for bits 17 to 24, p=0.99685 b-rank test for bits 18 to 25, p=0.32869 b-rank test for bits 19 to 26, p=0.86599 b-rank test for bits 20 to 27, p=0.23477 b-rank test for bits 21 to 28, p=0.01562 b-rank test for bits 22 to 29, p=0.74267 b-rank test for bits 23 to 30, p=0.64034 b-rank test for bits 24 to 31, p=0.81434 b-rank test for bits 25 to 32, p=0.32230 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 = 0.217811 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-06-26_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 141892 -0.04 0.483851 2 141824 -0.20 0.420987 3 141319 -1.38 0.083905 4 142312 0.94 0.826601 5 141687 -0.52 0.301719 6 141090 -1.91 0.027789 7 142042 0.31 0.621711 8 142149 0.56 0.712252 9 141350 -1.31 0.095633 10 142039 0.30 0.619043 11 142467 1.30 0.903707 12 142818 2.12 0.983126 13 141935 0.06 0.523913 14 140801 -2.59 0.004805 15 141485 -0.99 0.160739 16 142096 0.44 0.668634 17 142261 0.82 0.794364 18 141941 0.07 0.529493 19 142559 1.52 0.935483 20 141799 -0.26 0.398288 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-06-26_12:31 Bits used No. missing words z-score p-value 23 to 32 142120 0.7264 0.766218 22 to 31 141643 -0.9184 0.179210 21 to 30 141353 -1.9184 0.027531 20 to 29 141492 -1.4391 0.075066 19 to 28 141673 -0.8149 0.207556 18 to 27 141938 0.0989 0.539376 17 to 26 141704 -0.7080 0.239462 16 to 25 142158 0.8575 0.804411 15 to 24 142043 0.4609 0.677576 14 to 23 142012 0.3540 0.638344 13 to 22 142238 1.1333 0.871465 12 to 21 142171 0.9023 0.816554 11 to 20 142058 0.5127 0.695904 10 to 19 141640 -0.9287 0.176516 9 to 18 142072 0.5609 0.712578 8 to 17 141940 0.1058 0.542113 7 to 16 141924 0.0506 0.520172 6 to 15 141535 -1.2908 0.098388 5 to 14 141396 -1.7701 0.038355 4 to 13 142076 0.5747 0.717261 3 to 12 142333 1.4609 0.927983 2 to 11 142185 0.9506 0.829093 1 to 10 142010 0.3471 0.635756 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-06-26_12:31 Bits used No. missing words z-score p-value 28 to 32 141761 -0.5028 0.307548 27 to 31 142091 0.6158 0.730997 26 to 30 141704 -0.6960 0.243204 25 to 29 142289 1.2870 0.900956 24 to 28 141861 -0.1638 0.434932 23 to 27 141913 0.0124 0.504963 22 to 26 141608 -1.0215 0.153519 21 to 25 141947 0.1277 0.550805 20 to 24 141979 0.2362 0.593349 19 to 23 142023 0.3853 0.650001 18 to 22 141836 -0.2486 0.401844 17 to 21 141949 0.1345 0.553486 16 to 20 141723 -0.6316 0.263815 15 to 19 142010 0.3413 0.633544 14 to 18 141793 -0.3943 0.346665 13 to 17 142194 0.9650 0.832723 12 to 16 141850 -0.2011 0.420303 11 to 15 141963 0.1819 0.572182 10 to 14 142169 0.8802 0.810635 9 to 13 141954 0.1514 0.560179 8 to 12 141597 -1.0587 0.144858 7 to 11 141786 -0.4181 0.337949 6 to 10 141891 -0.0621 0.475227 5 to 9 142313 1.3684 0.914402 4 to 8 141414 -1.6791 0.046568 3 to 7 141878 -0.1062 0.457711 2 to 6 141741 -0.5706 0.284132 1 to 5 142056 0.4972 0.690471 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-06-26_12:31 Bits used No. missing words z-score p-value 31 to 32 141648 -0.7709 0.220388 30 to 31 141867 -0.1249 0.450314 29 to 30 141894 -0.0452 0.481966 28 to 29 141893 -0.0482 0.480790 27 to 28 142040 0.3855 0.650051 26 to 27 141740 -0.4995 0.308714 25 to 26 141815 -0.2783 0.390407 24 to 25 142412 1.4828 0.930937 23 to 24 141839 -0.2075 0.417824 22 to 23 142000 0.2675 0.605444 21 to 22 142252 1.0108 0.843950 20 to 21 141653 -0.7561 0.224784 19 to 20 141715 -0.5732 0.283240 18 to 19 142132 0.6568 0.744359 17 to 18 142734 2.4327 0.992506 16 to 17 141503 -1.1986 0.115339 15 to 16 142128 0.6450 0.740551 14 to 15 141906 -0.0098 0.496081 13 to 14 141470 -1.2960 0.097495 12 to 13 141995 0.2527 0.599755 11 to 12 141822 -0.2576 0.398354 10 to 11 142055 0.4297 0.666295 9 to 10 142185 0.8132 0.791944 8 to 9 142135 0.6657 0.747196 7 to 8 142308 1.1760 0.880206 6 to 7 142193 0.8368 0.798643 5 to 6 141885 -0.0718 0.471393 4 to 5 141905 -0.0128 0.494905 3 to 4 142115 0.6067 0.727974 2 to 3 142303 1.1613 0.877234 1 to 2 141807 -0.3019 0.381380 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-06-26_12:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2466.65 -0.472 0.318570 Test results for specific bytes for dh-ranFile-2015-06-26_12:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2477.03 -0.325 0.372649 2 to 9 2466.00 -0.481 0.315324 3 to 10 2453.93 -0.652 0.257346 4 to 11 2476.48 -0.333 0.369725 5 to 12 2519.42 0.275 0.608222 6 to 13 2537.36 0.528 0.701386 7 to 14 2506.50 0.092 0.536634 8 to 15 2586.84 1.228 0.890303 9 to 16 2550.92 0.720 0.764266 10 to 17 2460.73 -0.555 0.289329 11 to 18 2464.08 -0.508 0.305738 12 to 19 2565.88 0.932 0.824259 13 to 20 2536.53 0.517 0.697302 14 to 21 2582.88 1.172 0.879413 15 to 22 2541.10 0.581 0.719484 16 to 23 2452.25 -0.675 0.249729 17 to 24 2629.97 1.838 0.966975 18 to 25 2528.56 0.404 0.656861 19 to 26 2379.44 -1.705 0.044104 20 to 27 2511.79 0.167 0.566235 21 to 28 2477.48 -0.318 0.375063 22 to 29 2480.90 -0.270 0.393555 23 to 30 2520.10 0.284 0.611889 24 to 31 2594.52 1.337 0.909351 25 to 32 2392.06 -1.527 0.063438 CDPARK for dh-ranFile-2015-06-26_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 3497 -1.1872 0.117571 3489 -1.5525 0.060270 3516 -0.3196 0.374623 3516 -0.3196 0.374623 3540 0.7763 0.781201 3550 1.2329 0.891189 3490 -1.5068 0.065925 3511 -0.5479 0.291865 3520 -0.1370 0.445521 3498 -1.1416 0.126820 Square side=100, avg. no. parked=3512.70 sample std.=19.38 p-value of the KSTEST for those 10 p-values: 0.148151 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-06-26_12:31 0.6565,0.2461,0.5804,0.3658,0.7541,0.1084,0.7994,0.1989,0.4388,0.7716, The KS test for those 10 p-values: 0.878801 The 3DSPHERES test for dh-ranFile-2015-06-26_12:31 sample no r^3 equiv. uni. 1 19.193 0.472578 2 28.443 0.612519 3 40.775 0.743122 4 68.783 0.899013 5 15.362 0.400750 6 42.766 0.759617 7 10.002 0.283515 8 61.960 0.873224 9 79.392 0.929095 10 39.368 0.730791 11 69.821 0.902447 12 43.475 0.765235 13 5.421 0.165305 14 15.808 0.409589 15 2.522 0.080641 16 7.292 0.215775 17 8.549 0.247952 18 39.876 0.735314 19 7.240 0.214416 20 4.533 0.140230 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.761646 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-06-26_12:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 0.9 1.3 -1.0 0.6 0.6 -1.2 1.1 1.3 -0.4 -1.1 0.3 0.4 0.1 -0.1 1.6 0.6 -0.2 1.0 -1.0 -1.2 -1.5 -1.0 0.1 0.4 0.4 -1.0 2.0 -1.2 1.6 -0.1 -1.6 0.8 0.2 -0.5 -0.3 -0.2 -1.0 0.5 -0.1 0.9 -1.0 -1.1 Chi-square with 42 degrees of freedom:37.943558 z-score=-0.442594, p-value=0.350384 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-06-26_12:31 Test no p-value 1 0.567607 2 0.555172 3 0.002648 4 0.228886 5 0.699140 6 0.722413 7 0.237560 8 0.330690 9 0.908456 10 0.212628 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.658950 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-06-26_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 66490 0.47 66648 0.01 3 25000.00 25198 1.57 25051 0.10 4 6666.67 6658 0.01 6645 0.07 5 1388.89 1360 0.60 1401 0.11 6 238.10 248 0.41 211 3.08 7 34.72 41 1.14 37 0.15 8 4.96 4 0.19 6 0.22 p=0.37491 p=0.28772 Number of rngs required: 690405, p-value: 0.991 RESULTS OF CRAPS TEST for dh-ranFile-2015-06-26_12:31 No. of wins: Observed Expected 98646 98585.9 z-score= 0.269, pvalue=0.60603 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66741 66666.7 0.083 0.083 2 37815 37654.3 0.686 0.769 3 26933 26954.7 0.018 0.786 4 19240 19313.5 0.279 1.065 5 13793 13851.4 0.246 1.312 6 9910 9943.5 0.113 1.425 7 7011 7145.0 2.514 3.939 8 5233 5139.1 1.717 5.656 9 3748 3699.9 0.626 6.282 10 2610 2666.3 1.189 7.471 11 1898 1923.3 0.334 7.804 12 1391 1388.7 0.004 7.808 13 1049 1003.7 2.043 9.851 14 725 726.1 0.002 9.853 15 521 525.8 0.044 9.897 16 375 381.2 0.099 9.997 17 244 276.5 3.829 13.825 18 199 200.8 0.017 13.842 19 138 146.0 0.437 14.279 20 124 106.2 2.978 17.257 21 302 287.1 0.772 18.028 Chisq= 18.03 for 20 degrees of freedom, p= 0.41447 SUMMARY of craptest p-value for no. of wins: 0.606030 p-value for throws/game: 0.414469 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-06-26_12:31 No. of wins: Observed Expected 98257 98585.9 z-score=-1.471, pvalue=0.07067 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66725 66666.7 0.051 0.051 2 38063 37654.3 4.436 4.487 3 27029 26954.7 0.205 4.691 4 19235 19313.5 0.319 5.010 5 13776 13851.4 0.411 5.421 6 9756 9943.5 3.537 8.958 7 7128 7145.0 0.041 8.998 8 5154 5139.1 0.043 9.042 9 3659 3699.9 0.451 9.493 10 2605 2666.3 1.409 10.902 11 1926 1923.3 0.004 10.906 12 1304 1388.7 5.171 16.077 13 974 1003.7 0.880 16.957 14 769 726.1 2.530 19.486 15 524 525.8 0.006 19.493 16 359 381.2 1.287 20.780 17 253 276.5 2.004 22.784 18 215 200.8 1.000 23.784 19 164 146.0 2.223 26.007 20 107 106.2 0.006 26.013 21 275 287.1 0.511 26.524 Chisq= 26.52 for 20 degrees of freedom, p= 0.85080 SUMMARY of craptest p-value for no. of wins: 0.070666 p-value for throws/game: 0.850797 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0026,0.0048,0.0098,0.0144,0.0156,0.0275,0.0278,0.0384,0.0441,0.0466, 0.0599,0.0603,0.0634,0.0659,0.0674,0.0707,0.0751,0.0806,0.0839,0.0860, 0.0879,0.0956,0.0975,0.0984,0.1084,0.1153,0.1176,0.1255,0.1268,0.1402, 0.1449,0.1482,0.1535,0.1574,0.1607,0.1653,0.1716,0.1759,0.1765,0.1792, 0.1947,0.1989,0.2006,0.2012,0.2076,0.2126,0.2144,0.2158,0.2178,0.2204, 0.2248,0.2286,0.2289,0.2322,0.2348,0.2376,0.2379,0.2395,0.2432,0.2447, 0.2458,0.2461,0.2480,0.2497,0.2530,0.2546,0.2573,0.2638,0.2806,0.2832, 0.2835,0.2841,0.2860,0.2877,0.2893,0.2919,0.2932,0.2938,0.3017,0.3057, 0.3075,0.3087,0.3153,0.3186,0.3223,0.3287,0.3307,0.3314,0.3379,0.3467, 0.3504,0.3658,0.3697,0.3726,0.3746,0.3746,0.3749,0.3751,0.3814,0.3904, 0.3936,0.3983,0.3984,0.4008,0.4018,0.4096,0.4145,0.4178,0.4203,0.4210, 0.4250,0.4260,0.4349,0.4373,0.4388,0.4455,0.4503,0.4577,0.4598,0.4714, 0.4726,0.4752,0.4754,0.4808,0.4820,0.4839,0.4949,0.4961,0.4989,0.5050, 0.5055,0.5202,0.5239,0.5281,0.5295,0.5308,0.5366,0.5394,0.5421,0.5485, 0.5508,0.5535,0.5552,0.5602,0.5624,0.5662,0.5676,0.5722,0.5748,0.5804, 0.5827,0.5933,0.5998,0.6054,0.6060,0.6082,0.6119,0.6125,0.6190,0.6217, 0.6245,0.6250,0.6334,0.6335,0.6358,0.6383,0.6391,0.6403,0.6483,0.6500, 0.6501,0.6565,0.6565,0.6569,0.6590,0.6663,0.6686,0.6776,0.6905,0.6959, 0.6973,0.6991,0.7014,0.7104,0.7123,0.7126,0.7173,0.7178,0.7195,0.7207, 0.7224,0.7280,0.7293,0.7306,0.7308,0.7310,0.7342,0.7353,0.7399,0.7406, 0.7427,0.7431,0.7444,0.7472,0.7541,0.7596,0.7616,0.7643,0.7652,0.7662, 0.7716,0.7765,0.7812,0.7919,0.7944,0.7986,0.7994,0.8044,0.8087,0.8100, 0.8106,0.8128,0.8143,0.8166,0.8211,0.8243,0.8266,0.8282,0.8291,0.8327, 0.8389,0.8440,0.8508,0.8537,0.8607,0.8660,0.8668,0.8715,0.8732,0.8772, 0.8788,0.8794,0.8802,0.8903,0.8912,0.8937,0.8937,0.8990,0.9010,0.9024, 0.9037,0.9085,0.9094,0.9144,0.9205,0.9280,0.9291,0.9309,0.9342,0.9355, 0.9542,0.9670,0.9710,0.9813,0.9831,0.9832,0.9914,0.9925,0.9968, Overall p-value after applying KStest on 269 p-values = 0.473020 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.