RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-09-14_06:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.57 11.9321 0.195771 2 to 25 15.54 17.6786 0.590620 3 to 26 15.70 19.8005 0.715438 4 to 27 15.71 27.0891 0.943226 5 to 28 15.51 23.8854 0.877416 6 to 29 15.69 24.0650 0.882321 7 to 30 15.77 19.0407 0.673800 8 to 31 15.77 15.8803 0.467661 9 to 32 15.60 30.6861 0.978199 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.053951 Tough bday spacings test for dh-ranFile-2015-09-14_06:31: 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 40 88 83 102 68 44 38 15 8 5 (O-E)^2/E 0.0 0.3 3.0 2.2 0.2 1.3 1.3 2.3 0.0 0.3 0.2 Birthday Spacings: Sum(O-E)^2/E= 11.031, p= 0.645 RESULTS OF GCD FOR dh-ranFile-2015-09-14_06:31 Euclid's algorithm: p-value, steps to gcd: 0.562569 p-value, dist. of gcd's: 0.934217 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-09-14_06:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.993 0.603 0.394 0.265 0.797 0.594 0.097 0.655 Bits 8 to 15---> 0.087 0.385 0.121 0.714 0.790 0.595 0.203 0.834 Bits 16 to 23---> 0.242 0.247 0.220 0.962 0.066 0.632 0.749 0.985 Bits 24 to 31---> 0.297 0.240 0.224 0.620 0.647 0.961 0.207 0.525 KS test for the above 32 p values: 0.314 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-09-14_06:31, p-values for 5 runs: 0.4049, 0.5827, 0.0815, 0.9177, 0.0637 Rank test for binary matrices (31x31) for dh-ranFile-2015-09-14_06:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 218 211.4 0.205 0.205 r= 29 5129 5134.0 0.005 0.210 r= 30 22997 23103.0 0.487 0.697 r= 31 11656 11551.5 0.945 1.642 chi-square = 1.642 with df = 3; p-value = 0.350 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-09-14_06:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 215 211.4 0.061 0.061 r= 30 5135 5134.0 0.000 0.061 r= 31 23147 23103.0 0.084 0.144 r= 32 11503 11551.5 0.204 0.348 chi-square = 0.348 with df = 3; p-value = 0.049 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-09-14_06:31 b-rank test for bits 1 to 8, p=0.45010 b-rank test for bits 2 to 9, p=0.43305 b-rank test for bits 3 to 10, p=0.04796 b-rank test for bits 4 to 11, p=0.80860 b-rank test for bits 5 to 12, p=0.15422 b-rank test for bits 6 to 13, p=0.36136 b-rank test for bits 7 to 14, p=0.22470 b-rank test for bits 8 to 15, p=0.35356 b-rank test for bits 9 to 16, p=0.84948 b-rank test for bits 10 to 17, p=0.80160 b-rank test for bits 11 to 18, p=0.84134 b-rank test for bits 12 to 19, p=0.91614 b-rank test for bits 13 to 20, p=0.02674 b-rank test for bits 14 to 21, p=0.15470 b-rank test for bits 15 to 22, p=0.50851 b-rank test for bits 16 to 23, p=0.89464 b-rank test for bits 17 to 24, p=0.96421 b-rank test for bits 18 to 25, p=0.55797 b-rank test for bits 19 to 26, p=0.22378 b-rank test for bits 20 to 27, p=0.20942 b-rank test for bits 21 to 28, p=0.16222 b-rank test for bits 22 to 29, p=0.68067 b-rank test for bits 23 to 30, p=0.85938 b-rank test for bits 24 to 31, p=0.23276 b-rank test for bits 25 to 32, p=0.50296 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 = 0.870194 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-09-14_06:31 (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 141415 -1.15 0.124050 2 142126 0.51 0.693655 3 142013 0.24 0.595695 4 141750 -0.37 0.354847 5 142314 0.95 0.827796 6 141502 -0.95 0.170623 7 141899 -0.02 0.490372 8 142401 1.15 0.874673 9 141683 -0.53 0.298469 10 142064 0.36 0.641092 11 142054 0.34 0.632324 12 142144 0.55 0.708255 13 142184 0.64 0.739483 14 142645 1.72 0.957180 15 142786 2.05 0.979734 16 142254 0.81 0.789678 17 141293 -1.44 0.074930 18 141441 -1.09 0.136927 19 142529 1.45 0.926167 20 141480 -1.00 0.157905 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-09-14_06:31 Bits used No. missing words z-score p-value 23 to 32 141799 -0.3804 0.351806 22 to 31 141521 -1.3391 0.090274 21 to 30 141792 -0.4046 0.342891 20 to 29 142141 0.7989 0.787815 19 to 28 142076 0.5747 0.717261 18 to 27 141719 -0.6563 0.255812 17 to 26 141988 0.2713 0.606911 16 to 25 142240 1.1402 0.872907 15 to 24 141942 0.1127 0.544848 14 to 23 142074 0.5678 0.714924 13 to 22 142129 0.7575 0.775620 12 to 21 141872 -0.1287 0.448788 11 to 20 141621 -0.9942 0.160053 10 to 19 142517 2.0954 0.981933 9 to 18 141946 0.1264 0.550312 8 to 17 141961 0.1782 0.570706 7 to 16 141645 -0.9115 0.181021 6 to 15 142339 1.4816 0.930779 5 to 14 142025 0.3989 0.655003 4 to 13 142078 0.5816 0.719589 3 to 12 141470 -1.5149 0.064895 2 to 11 141751 -0.5460 0.292545 1 to 10 141783 -0.4356 0.331556 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-09-14_06:31 Bits used No. missing words z-score p-value 28 to 32 141812 -0.3299 0.370726 27 to 31 142273 1.2328 0.891171 26 to 30 141945 0.1209 0.548121 25 to 29 142147 0.8057 0.789781 24 to 28 142210 1.0192 0.845951 23 to 27 142214 1.0328 0.849147 22 to 26 142593 2.3175 0.989762 21 to 25 142123 0.7243 0.765561 20 to 24 141448 -1.5638 0.058929 19 to 23 141654 -0.8655 0.193375 18 to 22 141626 -0.9604 0.168417 17 to 21 142205 1.0023 0.841894 16 to 20 142142 0.7887 0.784860 15 to 19 141700 -0.7096 0.238978 14 to 18 141652 -0.8723 0.191521 13 to 17 142229 1.0836 0.860735 12 to 16 141619 -0.9842 0.162516 11 to 15 141752 -0.5333 0.296905 10 to 14 141805 -0.3537 0.361797 9 to 13 142783 2.9616 0.998470 8 to 12 142235 1.1040 0.865196 7 to 11 142285 1.2735 0.898572 6 to 10 142108 0.6735 0.749672 5 to 9 141773 -0.4621 0.321992 4 to 8 142164 0.8633 0.806011 3 to 7 141838 -0.2418 0.404469 2 to 6 142346 1.4802 0.930595 1 to 5 141407 -1.7028 0.044301 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-09-14_06:31 Bits used No. missing words z-score p-value 31 to 32 141883 -0.0777 0.469045 30 to 31 142820 2.6863 0.996388 29 to 30 142074 0.4858 0.686429 28 to 29 141525 -1.1337 0.128457 27 to 28 142172 0.7748 0.780782 26 to 27 141998 0.2616 0.603171 25 to 26 141773 -0.4022 0.343786 24 to 25 141777 -0.3904 0.348137 23 to 24 141549 -1.0629 0.143909 22 to 23 141994 0.2498 0.598615 21 to 22 142459 1.6214 0.947539 20 to 21 141798 -0.3284 0.371302 19 to 20 141780 -0.3815 0.351415 18 to 19 141853 -0.1662 0.434014 17 to 18 141472 -1.2901 0.098515 16 to 17 141654 -0.7532 0.225669 15 to 16 141953 0.1288 0.551250 14 to 15 142041 0.3884 0.651143 13 to 14 141858 -0.1514 0.439824 12 to 13 141699 -0.6204 0.267483 11 to 12 141837 -0.2134 0.415522 10 to 11 142043 0.3943 0.653323 9 to 10 141765 -0.4258 0.335144 8 to 9 141699 -0.6204 0.267483 7 to 8 142251 1.0079 0.843243 6 to 7 142003 0.2763 0.608846 5 to 6 142643 2.1642 0.984776 4 to 5 141739 -0.5024 0.307676 3 to 4 141361 -1.6175 0.052886 2 to 3 141951 0.1229 0.548915 1 to 2 141408 -1.4788 0.069590 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-09-14_06:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2447.49 -0.743 0.228846 Test results for specific bytes for dh-ranFile-2015-09-14_06:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2509.91 0.140 0.555736 2 to 9 2454.14 -0.649 0.258324 3 to 10 2491.44 -0.121 0.451833 4 to 11 2438.31 -0.872 0.191484 5 to 12 2561.36 0.868 0.807248 6 to 13 2489.36 -0.150 0.440190 7 to 14 2497.81 -0.031 0.487658 8 to 15 2529.92 0.423 0.663875 9 to 16 2466.05 -0.480 0.315586 10 to 17 2598.85 1.398 0.918929 11 to 18 2362.50 -1.944 0.025919 12 to 19 2414.29 -1.212 0.112729 13 to 20 2522.06 0.312 0.622471 14 to 21 2439.07 -0.862 0.194417 15 to 22 2466.69 -0.471 0.318783 16 to 23 2509.51 0.135 0.553512 17 to 24 2635.78 1.920 0.972585 18 to 25 2456.19 -0.620 0.267749 19 to 26 2547.22 0.668 0.747879 20 to 27 2370.24 -1.835 0.033252 21 to 28 2533.81 0.478 0.683703 22 to 29 2482.87 -0.242 0.404286 23 to 30 2497.65 -0.033 0.486743 24 to 31 2583.91 1.187 0.882334 25 to 32 2454.12 -0.649 0.258202 CDPARK for dh-ranFile-2015-09-14_06:31: 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 3507 -0.7306 0.232514 3526 0.1370 0.554479 3556 1.5068 0.934075 3535 0.5479 0.708135 3534 0.5023 0.692266 3544 0.9589 0.831196 3526 0.1370 0.554479 3555 1.4612 0.928018 3505 -0.8219 0.205562 3553 1.3699 0.914635 Square side=100, avg. no. parked=3534.10 sample std.=17.56 p-value of the KSTEST for those 10 p-values: 0.128499 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-09-14_06:31 0.8167,0.0955,0.9788,0.0766,0.2957,0.4913,0.3448,0.1821,0.8154,0.5325, The KS test for those 10 p-values: 0.905091 The 3DSPHERES test for dh-ranFile-2015-09-14_06:31 sample no r^3 equiv. uni. 1 32.036 0.656255 2 4.179 0.130029 3 34.397 0.682276 4 6.255 0.188189 5 0.834 0.027408 6 30.212 0.634711 7 20.852 0.500958 8 5.235 0.160133 9 60.541 0.867083 10 10.655 0.298943 11 92.080 0.953548 12 49.508 0.808002 13 14.896 0.391364 14 69.513 0.901442 15 17.979 0.450812 16 95.156 0.958074 17 32.799 0.664896 18 5.865 0.177573 19 4.024 0.125534 20 100.561 0.964987 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.738580 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-09-14_06:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 2.7 0.1 -0.4 1.1 1.9 0.0 1.2 0.6 -0.9 -0.1 2.1 0.5 -0.3 0.5 0.9 0.2 -0.5 -1.8 0.3 -1.7 0.2 0.6 1.4 0.5 -1.3 0.1 -0.1 -0.7 0.5 -1.9 -0.6 -1.3 -0.2 0.7 -0.5 0.6 -0.2 0.5 0.1 -1.8 0.9 -1.0 0.8 Chi-square with 42 degrees of freedom:45.138600 z-score=0.342449, p-value=0.657869 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-09-14_06:31 Test no p-value 1 0.057893 2 0.017792 3 0.646568 4 0.016344 5 0.383948 6 0.194516 7 0.295140 8 0.993944 9 0.086041 10 0.273478 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.014674 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-09-14_06:31: (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 66847 0.49 66556 0.18 3 25000.00 24844 0.97 25159 1.01 4 6666.67 6590 0.88 6640 0.11 5 1388.89 1419 0.65 1380 0.06 6 238.10 253 0.93 232 0.16 7 34.72 43 1.97 29 0.94 8 4.96 3 0.77 3 0.77 p=0.64834 p=0.22071 Number of rngs required: 688126, p-value: 0.375 RESULTS OF CRAPS TEST for dh-ranFile-2015-09-14_06:31 No. of wins: Observed Expected 98284 98585.9 z-score=-1.350, pvalue=0.08849 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66482 66666.7 0.512 0.512 2 37521 37654.3 0.472 0.984 3 27130 26954.7 1.140 2.123 4 19351 19313.5 0.073 2.196 5 14117 13851.4 5.092 7.288 6 9982 9943.5 0.149 7.437 7 7070 7145.0 0.788 8.225 8 5088 5139.1 0.508 8.732 9 3747 3699.9 0.600 9.333 10 2615 2666.3 0.987 10.320 11 1949 1923.3 0.343 10.662 12 1377 1388.7 0.099 10.762 13 970 1003.7 1.132 11.894 14 696 726.1 1.251 13.145 15 552 525.8 1.302 14.447 16 382 381.2 0.002 14.449 17 258 276.5 1.243 15.692 18 180 200.8 2.160 17.852 19 156 146.0 0.687 18.539 20 103 106.2 0.097 18.637 21 274 287.1 0.599 19.236 Chisq= 19.24 for 20 degrees of freedom, p= 0.49345 SUMMARY of craptest p-value for no. of wins: 0.088494 p-value for throws/game: 0.493449 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-09-14_06:31 No. of wins: Observed Expected 98518 98585.9 z-score=-0.304, pvalue=0.38075 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66583 66666.7 0.105 0.105 2 37662 37654.3 0.002 0.107 3 26867 26954.7 0.286 0.392 4 19390 19313.5 0.303 0.695 5 13954 13851.4 0.760 1.455 6 10030 9943.5 0.752 2.207 7 7122 7145.0 0.074 2.281 8 5115 5139.1 0.113 2.394 9 3633 3699.9 1.208 3.602 10 2650 2666.3 0.100 3.702 11 1943 1923.3 0.201 3.903 12 1398 1388.7 0.062 3.965 13 1024 1003.7 0.410 4.375 14 747 726.1 0.599 4.974 15 507 525.8 0.675 5.649 16 378 381.2 0.026 5.675 17 292 276.5 0.864 6.539 18 186 200.8 1.095 7.634 19 133 146.0 1.155 8.789 20 106 106.2 0.000 8.789 21 280 287.1 0.176 8.966 Chisq= 8.97 for 20 degrees of freedom, p= 0.01670 SUMMARY of craptest p-value for no. of wins: 0.380753 p-value for throws/game: 0.016699 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0147,0.0163,0.0167,0.0178,0.0259,0.0267,0.0274,0.0333,0.0443,0.0480, 0.0493,0.0529,0.0540,0.0579,0.0589,0.0637,0.0649,0.0659,0.0696,0.0749, 0.0766,0.0815,0.0860,0.0866,0.0885,0.0903,0.0955,0.0969,0.0985,0.1127, 0.1215,0.1241,0.1255,0.1285,0.1285,0.1300,0.1369,0.1439,0.1542,0.1547, 0.1579,0.1601,0.1601,0.1622,0.1625,0.1684,0.1706,0.1776,0.1810,0.1821, 0.1882,0.1915,0.1915,0.1934,0.1944,0.1945,0.1958,0.2031,0.2056,0.2068, 0.2094,0.2199,0.2207,0.2238,0.2240,0.2247,0.2257,0.2288,0.2325,0.2328, 0.2390,0.2402,0.2425,0.2469,0.2558,0.2582,0.2583,0.2654,0.2675,0.2675, 0.2677,0.2735,0.2925,0.2951,0.2957,0.2969,0.2970,0.2985,0.2989,0.3077, 0.3139,0.3156,0.3188,0.3220,0.3316,0.3351,0.3429,0.3438,0.3448,0.3481, 0.3500,0.3514,0.3518,0.3536,0.3548,0.3614,0.3618,0.3707,0.3713,0.3749, 0.3808,0.3839,0.3855,0.3914,0.3939,0.4043,0.4045,0.4049,0.4155,0.4331, 0.4340,0.4398,0.4402,0.4488,0.4501,0.4508,0.4518,0.4677,0.4690,0.4867, 0.4877,0.4904,0.4913,0.4934,0.5010,0.5030,0.5085,0.5249,0.5325,0.5448, 0.5481,0.5489,0.5503,0.5513,0.5535,0.5545,0.5545,0.5557,0.5580,0.5626, 0.5707,0.5827,0.5906,0.5945,0.5948,0.5957,0.5986,0.6026,0.6032,0.6069, 0.6088,0.6196,0.6225,0.6315,0.6323,0.6347,0.6411,0.6449,0.6466,0.6474, 0.6483,0.6511,0.6533,0.6550,0.6552,0.6563,0.6579,0.6639,0.6649,0.6738, 0.6807,0.6823,0.6837,0.6864,0.6923,0.6937,0.7081,0.7083,0.7140,0.7149, 0.7154,0.7173,0.7196,0.7386,0.7395,0.7479,0.7486,0.7497,0.7656,0.7756, 0.7808,0.7849,0.7878,0.7897,0.7898,0.7899,0.7973,0.8016,0.8060,0.8072, 0.8080,0.8086,0.8154,0.8167,0.8278,0.8312,0.8343,0.8413,0.8419,0.8432, 0.8460,0.8491,0.8495,0.8594,0.8607,0.8652,0.8671,0.8702,0.8729,0.8747, 0.8774,0.8823,0.8823,0.8912,0.8946,0.8986,0.9014,0.9051,0.9146,0.9161, 0.9177,0.9189,0.9262,0.9280,0.9306,0.9308,0.9341,0.9342,0.9432,0.9475, 0.9535,0.9572,0.9581,0.9612,0.9621,0.9642,0.9650,0.9726,0.9782,0.9788, 0.9797,0.9819,0.9848,0.9851,0.9898,0.9932,0.9939,0.9964,0.9985, Overall p-value after applying KStest on 269 p-values = 0.552626 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.