RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-01-24_19:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.73 23.7876 0.874678 2 to 25 16.01 27.0308 0.942382 3 to 26 15.65 27.5501 0.949523 4 to 27 15.68 15.6058 0.448071 5 to 28 15.86 14.3713 0.359337 6 to 29 15.73 26.3964 0.932465 7 to 30 15.80 21.3035 0.786992 8 to 31 15.71 21.7120 0.803949 9 to 32 15.85 11.2498 0.156714 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.039133 Tough bday spacings test for dh-ranFile-2016-01-24_19:31: 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 5 32 80 88 105 86 50 29 18 4 3 (O-E)^2/E 1.9 0.6 0.6 1.0 0.5 0.8 0.1 0.0 0.7 1.0 0.3 Birthday Spacings: Sum(O-E)^2/E= 7.460, p= 0.319 RESULTS OF GCD FOR dh-ranFile-2016-01-24_19:31 Euclid's algorithm: p-value, steps to gcd: 0.345226 p-value, dist. of gcd's: 0.601897 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-01-24_19:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.963 0.395 0.617 0.204 0.644 0.529 0.328 0.522 Bits 8 to 15---> 0.791 0.130 0.650 0.584 0.059 0.612 0.205 0.623 Bits 16 to 23---> 0.712 0.903 0.935 0.530 0.034 0.766 0.490 0.818 Bits 24 to 31---> 0.898 0.524 0.233 0.018 0.000 0.616 0.290 0.744 KS test for the above 32 p values: 0.415 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-01-24_19:31, p-values for 5 runs: 0.9316, 0.7365, 0.6867, 0.9943, 0.7338 Rank test for binary matrices (31x31) for dh-ranFile-2016-01-24_19:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 196 211.4 1.124 1.124 r= 29 5198 5134.0 0.798 1.922 r= 30 23101 23103.0 0.000 1.922 r= 31 11505 11551.5 0.187 2.109 chi-square = 2.109 with df = 3; p-value = 0.450 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-01-24_19:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 208 211.4 0.055 0.055 r= 30 5153 5134.0 0.070 0.125 r= 31 22960 23103.0 0.886 1.011 r= 32 11679 11551.5 1.407 2.418 chi-square = 2.418 with df = 3; p-value = 0.510 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-01-24_19:31 b-rank test for bits 1 to 8, p=0.00297 b-rank test for bits 2 to 9, p=0.95288 b-rank test for bits 3 to 10, p=0.18393 b-rank test for bits 4 to 11, p=0.15679 b-rank test for bits 5 to 12, p=0.62008 b-rank test for bits 6 to 13, p=0.47732 b-rank test for bits 7 to 14, p=0.94023 b-rank test for bits 8 to 15, p=0.72436 b-rank test for bits 9 to 16, p=0.86010 b-rank test for bits 10 to 17, p=0.87979 b-rank test for bits 11 to 18, p=0.13342 b-rank test for bits 12 to 19, p=0.92614 b-rank test for bits 13 to 20, p=0.45177 b-rank test for bits 14 to 21, p=0.51361 b-rank test for bits 15 to 22, p=0.83931 b-rank test for bits 16 to 23, p=0.53100 b-rank test for bits 17 to 24, p=0.32219 b-rank test for bits 18 to 25, p=0.86642 b-rank test for bits 19 to 26, p=0.19751 b-rank test for bits 20 to 27, p=0.40941 b-rank test for bits 21 to 28, p=0.58622 b-rank test for bits 22 to 29, p=0.02111 b-rank test for bits 23 to 30, p=0.41625 b-rank test for bits 24 to 31, p=0.74918 b-rank test for bits 25 to 32, p=0.92864 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 = 0.493068 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-01-24_19:31 (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 141587 -0.75 0.225693 2 140955 -2.23 0.012882 3 142282 0.87 0.808048 4 141687 -0.52 0.301719 5 141414 -1.16 0.123572 6 141308 -1.40 0.080014 7 142156 0.58 0.717805 8 142643 1.71 0.956752 9 141818 -0.21 0.415512 10 142220 0.73 0.766039 11 141208 -1.64 0.050646 12 142473 1.32 0.906078 13 141580 -0.77 0.220809 14 142602 1.62 0.947210 15 141349 -1.31 0.095236 16 142064 0.36 0.641092 17 141612 -0.69 0.243623 18 141457 -1.06 0.145291 19 141989 0.19 0.573834 20 142283 0.87 0.808685 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-01-24_19:31 Bits used No. missing words z-score p-value 23 to 32 141962 0.1816 0.572060 22 to 31 142235 1.1230 0.869281 21 to 30 141971 0.2127 0.584202 20 to 29 142351 1.5230 0.936121 19 to 28 141651 -0.8908 0.186520 18 to 27 142305 1.3644 0.913776 17 to 26 141722 -0.6460 0.259151 16 to 25 141965 0.1920 0.576115 15 to 24 141925 0.0540 0.521546 14 to 23 141590 -1.1011 0.135418 13 to 22 141235 -2.3253 0.010029 12 to 21 142127 0.7506 0.773549 11 to 20 142054 0.4989 0.691062 10 to 19 141743 -0.5736 0.283136 9 to 18 142069 0.5506 0.709041 8 to 17 141676 -0.8046 0.210529 7 to 16 141793 -0.4011 0.344159 6 to 15 141921 0.0402 0.516050 5 to 14 141691 -0.7529 0.225766 4 to 13 142116 0.7127 0.761970 3 to 12 141774 -0.4667 0.320373 2 to 11 142161 0.8678 0.807256 1 to 10 142649 2.5506 0.994623 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-01-24_19:31 Bits used No. missing words z-score p-value 28 to 32 142083 0.5887 0.721973 27 to 31 141994 0.2870 0.612950 26 to 30 141910 0.0023 0.500906 25 to 29 141788 -0.4113 0.340431 24 to 28 141899 -0.0350 0.486033 23 to 27 142336 1.4463 0.925959 22 to 26 142162 0.8565 0.804142 21 to 25 141468 -1.4960 0.067322 20 to 24 141763 -0.4960 0.309935 19 to 23 141940 0.1040 0.541402 18 to 22 142222 1.0599 0.855405 17 to 21 142081 0.5819 0.719694 16 to 20 141936 0.0904 0.536018 15 to 19 141546 -1.2316 0.109044 14 to 18 141826 -0.2825 0.388790 13 to 17 141818 -0.3096 0.378435 12 to 16 142358 1.5209 0.935859 11 to 15 141953 0.1480 0.558842 10 to 14 142339 1.4565 0.927374 9 to 13 141826 -0.2825 0.388790 8 to 12 141843 -0.2248 0.411049 7 to 11 142069 0.5413 0.705834 6 to 10 141817 -0.3130 0.377147 5 to 9 142142 0.7887 0.784860 4 to 8 141975 0.2226 0.588081 3 to 7 141395 -1.7435 0.040624 2 to 6 141937 0.0938 0.537365 1 to 5 141995 0.2904 0.614248 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-01-24_19:31 Bits used No. missing words z-score p-value 31 to 32 142055 0.4297 0.666295 30 to 31 142031 0.3589 0.640168 29 to 30 141887 -0.0659 0.473741 28 to 29 141421 -1.4405 0.074863 27 to 28 141784 -0.3697 0.355801 26 to 27 141709 -0.5909 0.277279 25 to 26 142507 1.7630 0.961053 24 to 25 141782 -0.3756 0.353605 23 to 24 141569 -1.0039 0.157708 22 to 23 141822 -0.2576 0.398354 21 to 22 140971 -2.7679 0.002821 20 to 21 141990 0.2380 0.594046 19 to 20 142236 0.9636 0.832384 18 to 19 141173 -2.1721 0.014925 17 to 18 142541 1.8633 0.968792 16 to 17 142006 0.2852 0.612240 15 to 16 141663 -0.7266 0.233724 14 to 15 141376 -1.5732 0.057831 13 to 14 141877 -0.0954 0.462011 12 to 13 141810 -0.2930 0.384758 11 to 12 142901 2.9253 0.998279 10 to 11 141327 -1.7178 0.042918 9 to 10 142039 0.3825 0.648958 8 to 9 141399 -1.5054 0.066111 7 to 8 141758 -0.4464 0.327654 6 to 7 142314 1.1937 0.883706 5 to 6 141719 -0.5614 0.287247 4 to 5 141905 -0.0128 0.494905 3 to 4 141647 -0.7738 0.219514 2 to 3 142474 1.6657 0.952113 1 to 2 142033 0.3648 0.642373 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-01-24_19:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2601.23 1.432 0.923873 Test results for specific bytes for dh-ranFile-2016-01-24_19:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2583.45 1.180 0.881038 2 to 9 2535.54 0.503 0.692385 3 to 10 2566.85 0.945 0.827784 4 to 11 2533.24 0.470 0.680855 5 to 12 2515.48 0.219 0.586650 6 to 13 2611.19 1.572 0.942073 7 to 14 2550.92 0.720 0.764294 8 to 15 2539.66 0.561 0.712540 9 to 16 2533.14 0.469 0.680335 10 to 17 2483.01 -0.240 0.405075 11 to 18 2403.29 -1.368 0.085712 12 to 19 2370.89 -1.826 0.033936 13 to 20 2471.41 -0.404 0.342984 14 to 21 2621.37 1.716 0.956956 15 to 22 2495.47 -0.064 0.474441 16 to 23 2483.20 -0.238 0.406091 17 to 24 2480.74 -0.272 0.392676 18 to 25 2539.54 0.559 0.711964 19 to 26 2549.99 0.707 0.760185 20 to 27 2549.98 0.707 0.760147 21 to 28 2433.73 -0.937 0.174328 22 to 29 2518.59 0.263 0.603663 23 to 30 2564.98 0.919 0.820930 24 to 31 2505.09 0.072 0.528674 25 to 32 2545.36 0.641 0.739380 CDPARK for dh-ranFile-2016-01-24_19:31: 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 3526 0.1370 0.554479 3537 0.6393 0.738676 3529 0.2740 0.607947 3530 0.3196 0.625377 3563 1.8265 0.966111 3513 -0.4566 0.323972 3533 0.4566 0.676028 3489 -1.5525 0.060270 3510 -0.5936 0.276387 Square side=100, avg. no. parked=3522.70 sample std.=20.22 p-value of the KSTEST for those 10 p-values: 0.964791 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-01-24_19:31 0.2649,0.1256,0.9819,0.4478,0.3083,0.9328,0.7202,0.6642,0.7184,0.5057, The KS test for those 10 p-values: 0.755810 The 3DSPHERES test for dh-ranFile-2016-01-24_19:31 sample no r^3 equiv. uni. 1 26.032 0.580100 2 0.532 0.017574 3 5.434 0.165687 4 2.516 0.080457 5 10.885 0.304299 6 43.888 0.768441 7 8.562 0.248298 8 29.352 0.624093 9 6.081 0.183477 10 13.042 0.352558 11 80.016 0.930553 12 27.922 0.605739 13 71.465 0.907649 14 54.274 0.836204 15 0.674 0.022232 16 0.947 0.031080 17 2.374 0.076082 18 56.715 0.849005 19 49.793 0.809814 20 5.183 0.158654 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.171665 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-01-24_19:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 2.0 0.5 -1.1 -0.7 -0.2 -0.3 2.3 0.4 2.1 0.7 1.2 0.6 1.4 -0.1 -0.6 1.7 -0.4 -0.9 -0.5 -0.2 0.1 -0.9 -1.7 0.0 -0.8 -0.5 -0.4 0.2 0.8 -1.9 -0.9 0.2 0.0 -0.5 -0.5 1.3 0.5 -0.4 -0.4 0.4 -0.6 0.0 -0.1 Chi-square with 42 degrees of freedom:37.646001 z-score=-0.475060, p-value=0.337579 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-01-24_19:31 Test no p-value 1 0.560116 2 0.393864 3 0.377024 4 0.598847 5 0.650028 6 0.005107 7 0.037562 8 0.167269 9 0.009427 10 0.470839 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.035088 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-01-24_19:31: (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 66795 0.25 66570 0.14 3 25000.00 25050 0.10 25166 1.10 4 6666.67 6464 6.16 6582 1.08 5 1388.89 1379 0.07 1389 0.00 6 238.10 274 5.41 255 1.20 7 34.72 32 0.21 31 0.40 8 4.96 5 0.00 6 0.22 p=0.94248 p=0.34154 Number of rngs required: 689620, p-value: 0.922 RESULTS OF CRAPS TEST for dh-ranFile-2016-01-24_19:31 No. of wins: Observed Expected 98809 98585.9 z-score= 0.998, pvalue=0.84086 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66982 66666.7 1.492 1.492 2 37615 37654.3 0.041 1.533 3 26898 26954.7 0.119 1.652 4 19112 19313.5 2.101 3.753 5 13921 13851.4 0.350 4.103 6 9795 9943.5 2.219 6.322 7 7089 7145.0 0.439 6.761 8 5206 5139.1 0.872 7.633 9 3741 3699.9 0.457 8.090 10 2784 2666.3 5.196 13.286 11 1927 1923.3 0.007 13.293 12 1434 1388.7 1.475 14.768 13 931 1003.7 5.268 20.036 14 744 726.1 0.439 20.475 15 464 525.8 7.272 27.747 16 378 381.2 0.026 27.773 17 257 276.5 1.381 29.154 18 207 200.8 0.190 29.343 19 145 146.0 0.007 29.350 20 104 106.2 0.046 29.396 21 266 287.1 1.553 30.949 Chisq= 30.95 for 20 degrees of freedom, p= 0.94413 SUMMARY of craptest p-value for no. of wins: 0.840865 p-value for throws/game: 0.944130 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-01-24_19:31 No. of wins: Observed Expected 98937 98585.9 z-score= 1.571, pvalue=0.94185 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66927 66666.7 1.017 1.017 2 37667 37654.3 0.004 1.021 3 27125 26954.7 1.076 2.096 4 19097 19313.5 2.426 4.522 5 13909 13851.4 0.239 4.762 6 9874 9943.5 0.486 5.248 7 7112 7145.0 0.153 5.401 8 5137 5139.1 0.001 5.402 9 3581 3699.9 3.819 9.220 10 2702 2666.3 0.478 9.699 11 1881 1923.3 0.932 10.630 12 1383 1388.7 0.024 10.654 13 1013 1003.7 0.086 10.740 14 713 726.1 0.238 10.978 15 518 525.8 0.117 11.094 16 366 381.2 0.602 11.697 17 272 276.5 0.075 11.771 18 187 200.8 0.952 12.723 19 137 146.0 0.553 13.276 20 100 106.2 0.364 13.640 21 299 287.1 0.492 14.132 Chisq= 14.13 for 20 degrees of freedom, p= 0.17626 SUMMARY of craptest p-value for no. of wins: 0.941852 p-value for throws/game: 0.176265 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0000,0.0028,0.0030,0.0051,0.0094,0.0100,0.0129,0.0149,0.0176,0.0183, 0.0211,0.0222,0.0311,0.0337,0.0339,0.0351,0.0376,0.0391,0.0406,0.0429, 0.0506,0.0578,0.0591,0.0603,0.0661,0.0673,0.0749,0.0761,0.0800,0.0805, 0.0857,0.0952,0.1090,0.1176,0.1236,0.1256,0.1298,0.1334,0.1354,0.1453, 0.1567,0.1568,0.1577,0.1587,0.1657,0.1673,0.1717,0.1743,0.1763,0.1835, 0.1839,0.1865,0.1975,0.2045,0.2050,0.2105,0.2195,0.2208,0.2257,0.2258, 0.2326,0.2337,0.2436,0.2483,0.2592,0.2649,0.2764,0.2773,0.2831,0.2872, 0.2902,0.3017,0.3043,0.3083,0.3099,0.3186,0.3204,0.3222,0.3240,0.3277, 0.3279,0.3376,0.3404,0.3415,0.3430,0.3442,0.3452,0.3526,0.3536,0.3558, 0.3593,0.3770,0.3771,0.3784,0.3848,0.3888,0.3888,0.3927,0.3939,0.3953, 0.3984,0.4051,0.4061,0.4094,0.4110,0.4150,0.4155,0.4162,0.4478,0.4481, 0.4500,0.4518,0.4620,0.4708,0.4737,0.4744,0.4773,0.4860,0.4896,0.4931, 0.4949,0.5009,0.5057,0.5097,0.5136,0.5160,0.5215,0.5221,0.5244,0.5287, 0.5294,0.5301,0.5310,0.5360,0.5374,0.5414,0.5545,0.5588,0.5601,0.5721, 0.5738,0.5761,0.5801,0.5839,0.5842,0.5862,0.5866,0.5881,0.5940,0.5988, 0.6019,0.6037,0.6057,0.6079,0.6120,0.6122,0.6130,0.6142,0.6159,0.6168, 0.6201,0.6233,0.6241,0.6254,0.6402,0.6411,0.6424,0.6439,0.6490,0.6497, 0.6500,0.6642,0.6663,0.6760,0.6803,0.6809,0.6867,0.6911,0.6924,0.7058, 0.7090,0.7120,0.7122,0.7125,0.7178,0.7184,0.7197,0.7202,0.7220,0.7244, 0.7338,0.7365,0.7387,0.7394,0.7439,0.7492,0.7558,0.7601,0.7602,0.7620, 0.7643,0.7660,0.7663,0.7684,0.7735,0.7849,0.7870,0.7907,0.8039,0.8041, 0.8073,0.8080,0.8087,0.8098,0.8175,0.8209,0.8278,0.8324,0.8362,0.8393, 0.8409,0.8490,0.8554,0.8601,0.8664,0.8693,0.8747,0.8798,0.8810,0.8837, 0.8978,0.9035,0.9061,0.9076,0.9138,0.9221,0.9239,0.9260,0.9261,0.9274, 0.9286,0.9306,0.9316,0.9325,0.9328,0.9353,0.9359,0.9361,0.9402,0.9419, 0.9421,0.9424,0.9425,0.9441,0.9472,0.9495,0.9521,0.9529,0.9568,0.9570, 0.9611,0.9633,0.9648,0.9661,0.9688,0.9819,0.9943,0.9946,0.9983, Overall p-value after applying KStest on 269 p-values = 0.178255 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.