RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-10-19_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 15.84 13.4553 0.294784 2 to 25 15.82 7.5316 0.024436 3 to 26 15.69 19.1652 0.680868 4 to 27 15.71 18.0470 0.614117 5 to 28 15.87 26.1561 0.928338 6 to 29 16.10 16.3653 0.501901 7 to 30 16.04 14.9330 0.399691 8 to 31 16.00 8.5922 0.047806 9 to 32 15.83 13.3140 0.285074 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.635590 Tough bday spacings test for dh-ranFile-2016-10-19_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 4 48 81 87 72 75 55 39 24 10 5 (O-E)^2/E 2.9 3.5 0.8 1.2 6.8 0.1 0.2 2.9 5.6 1.7 0.2 Birthday Spacings: Sum(O-E)^2/E= 25.849, p= 0.996 RESULTS OF GCD FOR dh-ranFile-2016-10-19_19:31 Euclid's algorithm: p-value, steps to gcd: 0.601661 p-value, dist. of gcd's: 0.909278 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-10-19_19:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.838 0.243 0.904 0.713 0.176 0.739 0.354 0.444 Bits 8 to 15---> 0.491 0.544 0.214 0.574 0.053 0.615 0.527 0.755 Bits 16 to 23---> 0.787 0.283 0.964 0.726 0.719 0.138 0.338 0.771 Bits 24 to 31---> 0.185 0.460 0.041 0.547 0.422 0.130 0.679 0.218 KS test for the above 32 p values: 0.167 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-10-19_19:31, p-values for 5 runs: 0.6535, 0.9832, 0.5899, 0.7887, 0.7117 Rank test for binary matrices (31x31) for dh-ranFile-2016-10-19_19:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 189 211.4 2.377 2.377 r= 29 5139 5134.0 0.005 2.382 r= 30 23158 23103.0 0.131 2.513 r= 31 11514 11551.5 0.122 2.635 chi-square = 2.635 with df = 3; p-value = 0.549 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-10-19_19:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 220 211.4 0.348 0.348 r= 30 5115 5134.0 0.070 0.419 r= 31 23184 23103.0 0.284 0.702 r= 32 11481 11551.5 0.431 1.133 chi-square = 1.133 with df = 3; p-value = 0.231 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-10-19_19:31 b-rank test for bits 1 to 8, p=0.69191 b-rank test for bits 2 to 9, p=0.02628 b-rank test for bits 3 to 10, p=0.22484 b-rank test for bits 4 to 11, p=0.15517 b-rank test for bits 5 to 12, p=0.96845 b-rank test for bits 6 to 13, p=0.74502 b-rank test for bits 7 to 14, p=0.91231 b-rank test for bits 8 to 15, p=0.11892 b-rank test for bits 9 to 16, p=0.88345 b-rank test for bits 10 to 17, p=0.57595 b-rank test for bits 11 to 18, p=0.49509 b-rank test for bits 12 to 19, p=0.25425 b-rank test for bits 13 to 20, p=0.89826 b-rank test for bits 14 to 21, p=0.33916 b-rank test for bits 15 to 22, p=0.46703 b-rank test for bits 16 to 23, p=0.15116 b-rank test for bits 17 to 24, p=0.45241 b-rank test for bits 18 to 25, p=0.38651 b-rank test for bits 19 to 26, p=0.59973 b-rank test for bits 20 to 27, p=0.19108 b-rank test for bits 21 to 28, p=0.17693 b-rank test for bits 22 to 29, p=0.40541 b-rank test for bits 23 to 30, p=0.55179 b-rank test for bits 24 to 31, p=0.93941 b-rank test for bits 25 to 32, p=0.94968 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 = 0.881008 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-10-19_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 141912 0.01 0.502489 2 141996 0.20 0.580237 3 142094 0.43 0.666937 4 141552 -0.83 0.201892 5 141793 -0.27 0.392888 6 142436 1.23 0.890752 7 142798 2.08 0.981068 8 141860 -0.12 0.454121 9 141882 -0.06 0.474543 10 142141 0.54 0.705844 11 142474 1.32 0.906469 12 141071 -1.96 0.025073 13 142259 0.82 0.793032 14 141955 0.11 0.542489 15 141756 -0.36 0.360079 16 141922 0.03 0.511808 17 141101 -1.89 0.029471 18 142185 0.64 0.740241 19 142768 2.01 0.977585 20 141726 -0.43 0.334201 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-10-19_19:31 Bits used No. missing words z-score p-value 23 to 32 142284 1.2920 0.901815 22 to 31 141828 -0.2804 0.389567 21 to 30 141720 -0.6529 0.256923 20 to 29 141789 -0.4149 0.339096 19 to 28 142091 0.6264 0.734490 18 to 27 142047 0.4747 0.682508 17 to 26 141728 -0.6253 0.265895 16 to 25 141699 -0.7253 0.234141 15 to 24 142234 1.1196 0.868548 14 to 23 142335 1.4678 0.928924 13 to 22 141821 -0.3046 0.380341 12 to 21 141781 -0.4425 0.329058 11 to 20 141603 -1.0563 0.145413 10 to 19 141547 -1.2494 0.105757 9 to 18 141695 -0.7391 0.229933 8 to 17 142291 1.3161 0.905930 7 to 16 142555 2.2264 0.987008 6 to 15 141917 0.0264 0.510550 5 to 14 141684 -0.7770 0.218579 4 to 13 141602 -1.0598 0.144627 3 to 12 142195 0.9851 0.837705 2 to 11 142078 0.5816 0.719589 1 to 10 142224 1.0851 0.861054 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-10-19_19:31 Bits used No. missing words z-score p-value 28 to 32 142074 0.5582 0.711647 27 to 31 142010 0.3413 0.633544 26 to 30 142108 0.6735 0.749672 25 to 29 141943 0.1141 0.545435 24 to 28 141666 -0.8248 0.204729 23 to 27 141709 -0.6791 0.248542 22 to 26 141547 -1.2282 0.109679 21 to 25 142218 1.0463 0.852298 20 to 24 142260 1.1887 0.882723 19 to 23 142087 0.6023 0.726503 18 to 22 141687 -0.7537 0.225526 17 to 21 142403 1.6735 0.952881 16 to 20 141898 -0.0384 0.484682 15 to 19 141929 0.0667 0.526581 14 to 18 142206 1.0057 0.842711 13 to 17 141806 -0.3503 0.363068 12 to 16 141739 -0.5774 0.281838 11 to 15 141189 -2.4418 0.007307 10 to 14 142151 0.8192 0.793670 9 to 13 142025 0.3921 0.652509 8 to 12 141810 -0.3367 0.368167 7 to 11 142250 1.1548 0.875917 6 to 10 141704 -0.6960 0.243204 5 to 9 141975 0.2226 0.588081 4 to 8 141849 -0.2045 0.418978 3 to 7 142124 0.7277 0.766600 2 to 6 141911 0.0057 0.502258 1 to 5 142031 0.4124 0.659992 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-10-19_19:31 Bits used No. missing words z-score p-value 31 to 32 141593 -0.9331 0.175377 30 to 31 141640 -0.7945 0.213457 29 to 30 141769 -0.4140 0.339454 28 to 29 142328 1.2350 0.891588 27 to 28 141287 -1.8358 0.033195 26 to 27 141837 -0.2134 0.415522 25 to 26 141970 0.1790 0.571018 24 to 25 141767 -0.4199 0.337297 23 to 24 141436 -1.3963 0.081319 22 to 23 141136 -2.2812 0.011268 21 to 22 141893 -0.0482 0.480790 20 to 21 142214 0.8987 0.815602 19 to 20 141776 -0.3933 0.347048 18 to 19 142215 0.9017 0.816387 17 to 18 142116 0.6096 0.728952 16 to 17 141928 0.0551 0.521960 15 to 16 142245 0.9902 0.838956 14 to 15 141746 -0.4818 0.314974 13 to 14 141755 -0.4553 0.324464 12 to 13 141753 -0.4612 0.322345 11 to 12 142248 0.9990 0.841109 10 to 11 141862 -0.1396 0.444482 9 to 10 141958 0.1436 0.557080 8 to 9 141949 0.1170 0.546578 7 to 8 141450 -1.3550 0.087716 6 to 7 141591 -0.9390 0.173859 5 to 6 141885 -0.0718 0.471393 4 to 5 142221 0.9194 0.821052 3 to 4 141529 -1.1219 0.130949 2 to 3 142228 0.9400 0.826399 1 to 2 141901 -0.0246 0.490198 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-10-19_19:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2464.60 -0.501 0.308298 Test results for specific bytes for dh-ranFile-2016-10-19_19:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2475.90 -0.341 0.366603 2 to 9 2362.26 -1.948 0.025710 3 to 10 2608.35 1.532 0.937269 4 to 11 2567.80 0.959 0.831183 5 to 12 2462.32 -0.533 0.297064 6 to 13 2527.40 0.387 0.650792 7 to 14 2514.85 0.210 0.583186 8 to 15 2496.00 -0.057 0.477433 9 to 16 2610.73 1.566 0.941316 10 to 17 2494.98 -0.071 0.471717 11 to 18 2509.42 0.133 0.552983 12 to 19 2500.30 0.004 0.501702 13 to 20 2432.85 -0.950 0.171132 14 to 21 2545.81 0.648 0.741454 15 to 22 2536.95 0.523 0.699346 16 to 23 2514.95 0.211 0.583742 17 to 24 2464.17 -0.507 0.306182 18 to 25 2484.20 -0.223 0.411603 19 to 26 2438.29 -0.873 0.191405 20 to 27 2518.85 0.267 0.605117 21 to 28 2507.08 0.100 0.539863 22 to 29 2466.42 -0.475 0.317408 23 to 30 2543.01 0.608 0.728477 24 to 31 2459.25 -0.576 0.282224 25 to 32 2435.56 -0.911 0.181065 CDPARK for dh-ranFile-2016-10-19_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 3496 -1.2329 0.108811 3515 -0.3653 0.357445 3515 -0.3653 0.357445 3504 -0.8676 0.192812 3528 0.2283 0.590298 3541 0.8219 0.794438 3517 -0.2740 0.392053 3532 0.4110 0.659449 3512 -0.5023 0.307734 3508 -0.6849 0.246694 Square side=100, avg. no. parked=3516.80 sample std.=12.83 p-value of the KSTEST for those 10 p-values: 0.309847 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-10-19_19:31 0.7352,0.1824,0.2195,0.3727,0.0557,0.7718,0.5001,0.0208,0.3891,0.7747, The KS test for those 10 p-values: 0.452891 The 3DSPHERES test for dh-ranFile-2016-10-19_19:31 sample no r^3 equiv. uni. 1 56.849 0.849675 2 60.423 0.866562 3 25.206 0.568376 4 13.439 0.361082 5 20.565 0.496155 6 12.439 0.339423 7 12.697 0.345068 8 18.561 0.461355 9 39.460 0.731613 10 23.113 0.537189 11 44.032 0.769553 12 0.035 0.001161 13 15.109 0.395675 14 185.876 0.997962 15 62.036 0.873545 16 6.188 0.186376 17 4.399 0.136393 18 15.839 0.410188 19 85.055 0.941291 20 12.607 0.343113 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.616283 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-10-19_19:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 1.3 2.2 -0.8 -0.7 -0.1 0.7 -0.1 -0.3 0.5 -0.5 0.4 -0.8 0.3 -1.4 -1.9 1.1 1.2 0.8 0.7 -1.0 -0.1 0.0 0.5 1.0 -1.3 0.6 -0.1 -0.6 1.0 -1.0 0.7 0.7 -1.1 -0.1 -1.0 1.5 -0.5 0.5 -0.8 -0.1 -1.3 -1.0 0.8 Chi-square with 42 degrees of freedom:35.447105 z-score=-0.714979, p-value=0.247571 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-10-19_19:31 Test no p-value 1 0.953439 2 0.005422 3 0.554902 4 0.276463 5 0.024131 6 0.022625 7 0.970459 8 0.294404 9 0.392886 10 0.773116 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.125087 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-10-19_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 66706 0.02 66808 0.30 3 25000.00 24935 0.17 24839 1.04 4 6666.67 6676 0.01 6712 0.31 5 1388.89 1404 0.16 1384 0.02 6 238.10 252 0.81 218 1.70 7 34.72 24 3.31 33 0.09 8 4.96 2 1.77 5 0.00 p=0.60508 p=0.24852 Number of rngs required: 688070, p-value: 0.351 RESULTS OF CRAPS TEST for dh-ranFile-2016-10-19_19:31 No. of wins: Observed Expected 98473 98585.9 z-score=-0.505, pvalue=0.30686 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66617 66666.7 0.037 0.037 2 37489 37654.3 0.726 0.763 3 27011 26954.7 0.117 0.880 4 19393 19313.5 0.328 1.208 5 13895 13851.4 0.137 1.345 6 9933 9943.5 0.011 1.356 7 7118 7145.0 0.102 1.458 8 5272 5139.1 3.438 4.897 9 3650 3699.9 0.672 5.569 10 2644 2666.3 0.186 5.755 11 1946 1923.3 0.267 6.022 12 1424 1388.7 0.895 6.918 13 956 1003.7 2.268 9.186 14 719 726.1 0.070 9.256 15 524 525.8 0.006 9.263 16 372 381.2 0.220 9.482 17 290 276.5 0.655 10.137 18 202 200.8 0.007 10.144 19 157 146.0 0.831 10.976 20 110 106.2 0.135 11.110 21 278 287.1 0.289 11.400 Chisq= 11.40 for 20 degrees of freedom, p= 0.06481 SUMMARY of craptest p-value for no. of wins: 0.306860 p-value for throws/game: 0.064808 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-10-19_19:31 No. of wins: Observed Expected 98827 98585.9 z-score= 1.079, pvalue=0.85960 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66569 66666.7 0.143 0.143 2 37770 37654.3 0.355 0.498 3 26940 26954.7 0.008 0.507 4 19559 19313.5 3.122 3.628 5 13719 13851.4 1.266 4.894 6 9896 9943.5 0.227 5.121 7 7071 7145.0 0.767 5.888 8 5020 5139.1 2.759 8.647 9 3743 3699.9 0.503 9.150 10 2759 2666.3 3.223 12.373 11 1876 1923.3 1.165 13.538 12 1400 1388.7 0.091 13.629 13 996 1003.7 0.059 13.688 14 716 726.1 0.142 13.830 15 525 525.8 0.001 13.831 16 378 381.2 0.026 13.857 17 284 276.5 0.201 14.059 18 193 200.8 0.305 14.364 19 157 146.0 0.831 15.195 20 119 106.2 1.539 16.734 21 310 287.1 1.824 18.558 Chisq= 18.56 for 20 degrees of freedom, p= 0.44932 SUMMARY of craptest p-value for no. of wins: 0.859600 p-value for throws/game: 0.449321 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0012,0.0054,0.0073,0.0113,0.0208,0.0226,0.0241,0.0244,0.0251,0.0257, 0.0263,0.0295,0.0332,0.0407,0.0478,0.0532,0.0557,0.0648,0.0813,0.0877, 0.1058,0.1088,0.1097,0.1189,0.1251,0.1301,0.1309,0.1364,0.1380,0.1446, 0.1454,0.1512,0.1552,0.1673,0.1711,0.1739,0.1754,0.1757,0.1769,0.1811, 0.1824,0.1853,0.1864,0.1911,0.1914,0.1928,0.2019,0.2047,0.2135,0.2139, 0.2178,0.2186,0.2195,0.2248,0.2255,0.2299,0.2309,0.2341,0.2426,0.2432, 0.2467,0.2476,0.2485,0.2485,0.2542,0.2569,0.2659,0.2765,0.2818,0.2822, 0.2828,0.2851,0.2944,0.2948,0.2971,0.3062,0.3069,0.3077,0.3083,0.3098, 0.3150,0.3174,0.3223,0.3245,0.3291,0.3342,0.3373,0.3383,0.3391,0.3392, 0.3394,0.3395,0.3431,0.3451,0.3470,0.3507,0.3535,0.3574,0.3574,0.3601, 0.3611,0.3631,0.3666,0.3682,0.3727,0.3803,0.3865,0.3891,0.3896,0.3921, 0.3929,0.3929,0.3957,0.3997,0.4054,0.4102,0.4116,0.4155,0.4190,0.4220, 0.4440,0.4445,0.4493,0.4524,0.4529,0.4541,0.4604,0.4614,0.4670,0.4714, 0.4717,0.4745,0.4774,0.4808,0.4847,0.4902,0.4913,0.4951,0.4962,0.5001, 0.5017,0.5019,0.5023,0.5025,0.5106,0.5118,0.5220,0.5266,0.5271,0.5372, 0.5399,0.5425,0.5436,0.5454,0.5466,0.5466,0.5485,0.5518,0.5530,0.5549, 0.5571,0.5684,0.5710,0.5738,0.5759,0.5802,0.5832,0.5837,0.5881,0.5899, 0.5903,0.5997,0.6017,0.6051,0.6051,0.6141,0.6151,0.6163,0.6335,0.6356, 0.6508,0.6525,0.6535,0.6594,0.6600,0.6669,0.6788,0.6809,0.6825,0.6919, 0.6993,0.7058,0.7116,0.7117,0.7135,0.7191,0.7196,0.7260,0.7265,0.7285, 0.7290,0.7316,0.7345,0.7352,0.7392,0.7402,0.7415,0.7450,0.7497,0.7552, 0.7666,0.7696,0.7714,0.7718,0.7731,0.7747,0.7871,0.7887,0.7930,0.7937, 0.7944,0.8156,0.8164,0.8211,0.8264,0.8312,0.8377,0.8383,0.8390,0.8411, 0.8427,0.8497,0.8523,0.8596,0.8611,0.8666,0.8685,0.8735,0.8759,0.8810, 0.8827,0.8834,0.8908,0.8916,0.8983,0.9018,0.9043,0.9059,0.9065,0.9093, 0.9123,0.9283,0.9289,0.9373,0.9394,0.9413,0.9413,0.9497,0.9529,0.9534, 0.9640,0.9684,0.9705,0.9776,0.9811,0.9832,0.9870,0.9961,0.9980, Overall p-value after applying KStest on 269 p-values = 0.520007 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.