RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-01-17_02:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.97 14.0007 0.332947 2 to 25 15.89 17.4301 0.574386 3 to 26 15.72 19.1219 0.678422 4 to 27 15.79 19.6254 0.706164 5 to 28 15.76 13.7023 0.311946 6 to 29 15.67 18.2539 0.627002 7 to 30 15.67 18.3485 0.632818 8 to 31 15.40 24.1260 0.883949 9 to 32 15.51 15.4505 0.436936 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.315692 Tough bday spacings test for dh-ranFile-2017-01-17_02:31: 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 13 36 86 99 92 73 37 31 18 11 4 (O-E)^2/E 1.6 0.0 2.2 0.0 0.3 0.3 4.4 0.1 0.7 2.9 0.0 Birthday Spacings: Sum(O-E)^2/E= 12.510, p= 0.748 RESULTS OF GCD FOR dh-ranFile-2017-01-17_02:31 Euclid's algorithm: p-value, steps to gcd: 0.904242 p-value, dist. of gcd's: 0.249667 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-01-17_02:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.157 0.973 0.366 0.363 0.615 0.447 0.717 0.124 Bits 8 to 15---> 0.948 0.123 0.520 0.599 0.737 0.435 0.643 0.071 Bits 16 to 23---> 0.710 0.173 0.803 0.395 0.471 0.828 0.910 0.538 Bits 24 to 31---> 0.090 0.580 0.038 0.899 0.781 0.533 0.616 0.709 KS test for the above 32 p values: 0.239 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-01-17_02:31, p-values for 5 runs: 0.8588, 0.6192, 0.9269, 0.2447, 0.0481 Rank test for binary matrices (31x31) for dh-ranFile-2017-01-17_02:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 202 211.4 0.420 0.420 r= 29 5117 5134.0 0.056 0.476 r= 30 23062 23103.0 0.073 0.549 r= 31 11619 11551.5 0.394 0.943 chi-square = 0.943 with df = 3; p-value = 0.185 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2017-01-17_02:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 221 211.4 0.434 0.434 r= 30 5153 5134.0 0.070 0.505 r= 31 23154 23103.0 0.112 0.617 r= 32 11472 11551.5 0.547 1.164 chi-square = 1.164 with df = 3; p-value = 0.238 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2017-01-17_02:31 b-rank test for bits 1 to 8, p=0.20308 b-rank test for bits 2 to 9, p=0.68365 b-rank test for bits 3 to 10, p=0.21536 b-rank test for bits 4 to 11, p=0.00431 b-rank test for bits 5 to 12, p=0.56929 b-rank test for bits 6 to 13, p=0.69718 b-rank test for bits 7 to 14, p=0.22602 b-rank test for bits 8 to 15, p=0.66096 b-rank test for bits 9 to 16, p=0.89202 b-rank test for bits 10 to 17, p=0.93238 b-rank test for bits 11 to 18, p=0.60384 b-rank test for bits 12 to 19, p=0.85496 b-rank test for bits 13 to 20, p=0.39103 b-rank test for bits 14 to 21, p=0.86972 b-rank test for bits 15 to 22, p=0.59387 b-rank test for bits 16 to 23, p=0.52267 b-rank test for bits 17 to 24, p=0.38742 b-rank test for bits 18 to 25, p=0.95463 b-rank test for bits 19 to 26, p=0.97165 b-rank test for bits 20 to 27, p=0.51203 b-rank test for bits 21 to 28, p=0.28026 b-rank test for bits 22 to 29, p=0.94625 b-rank test for bits 23 to 30, p=0.14167 b-rank test for bits 24 to 31, p=0.51077 b-rank test for bits 25 to 32, p=0.60738 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 = 0.338557 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-01-17_02:31 (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 141687 -0.52 0.301719 2 141461 -1.05 0.147435 3 141408 -1.17 0.120733 4 142681 1.80 0.964303 5 140844 -2.49 0.006404 6 142120 0.49 0.688718 7 141750 -0.37 0.354847 8 141405 -1.18 0.119330 9 142017 0.25 0.599312 10 141403 -1.18 0.118402 11 141757 -0.36 0.360954 12 141486 -0.99 0.161310 13 141658 -0.59 0.278528 14 141559 -0.82 0.206528 15 141763 -0.34 0.366216 16 141824 -0.20 0.420987 17 142515 1.42 0.921483 18 141403 -1.18 0.118402 19 142402 1.15 0.875154 20 142346 1.02 0.846197 ---------------------------------------------------------------- OPSO test for dh-ranFile-2017-01-17_02:31 Bits used No. missing words z-score p-value 23 to 32 141305 -2.0839 0.018585 22 to 31 142434 1.8092 0.964791 21 to 30 142016 0.3678 0.643499 20 to 29 142031 0.4196 0.662594 19 to 28 141987 0.2678 0.605584 18 to 27 141799 -0.3804 0.351806 17 to 26 141781 -0.4425 0.329058 16 to 25 142160 0.8644 0.806310 15 to 24 141886 -0.0804 0.467940 14 to 23 142316 1.4023 0.919589 13 to 22 141470 -1.5149 0.064895 12 to 21 141763 -0.5046 0.306925 11 to 20 142130 0.7609 0.776651 10 to 19 141985 0.2609 0.602927 9 to 18 141631 -0.9598 0.168588 8 to 17 142053 0.4954 0.689846 7 to 16 141753 -0.5391 0.294920 6 to 15 141613 -1.0218 0.153431 5 to 14 141992 0.2851 0.612204 4 to 13 141819 -0.3115 0.377717 3 to 12 142062 0.5264 0.700712 2 to 11 142403 1.7023 0.955651 1 to 10 141952 0.1471 0.558488 ----------------------------------------------------------------- OQSO test for dh-ranFile-2017-01-17_02:31 Bits used No. missing words z-score p-value 28 to 32 142009 0.3379 0.632267 27 to 31 142306 1.3446 0.910630 26 to 30 141613 -1.0045 0.157567 25 to 29 142306 1.3446 0.910630 24 to 28 141958 0.1650 0.565521 23 to 27 141726 -0.6215 0.267149 22 to 26 141916 0.0226 0.509019 21 to 25 142018 0.3684 0.643702 20 to 24 141957 0.1616 0.564187 19 to 23 142026 0.3955 0.653760 18 to 22 142012 0.3480 0.636093 17 to 21 141956 0.1582 0.562852 16 to 20 141581 -1.1130 0.132858 15 to 19 141867 -0.1435 0.442951 14 to 18 141865 -0.1503 0.440275 13 to 17 141229 -2.3062 0.010550 12 to 16 142137 0.7718 0.779873 11 to 15 141865 -0.1503 0.440275 10 to 14 141993 0.2836 0.611652 9 to 13 141745 -0.5571 0.288746 8 to 12 141807 -0.3469 0.364340 7 to 11 141788 -0.4113 0.340431 6 to 10 141463 -1.5130 0.065142 5 to 9 141805 -0.3537 0.361797 4 to 8 142230 1.0870 0.861485 3 to 7 142159 0.8463 0.801318 2 to 6 141843 -0.2248 0.411049 1 to 5 141547 -1.2282 0.109679 ----------------------------------------------------------------- DNA test for dh-ranFile-2017-01-17_02:31 Bits used No. missing words z-score p-value 31 to 32 142200 0.8574 0.804397 30 to 31 142217 0.9076 0.817950 29 to 30 141521 -1.1455 0.125998 28 to 29 141759 -0.4435 0.328720 27 to 28 142418 1.5005 0.933258 26 to 27 141942 0.0964 0.538387 25 to 26 141792 -0.3461 0.364632 24 to 25 142008 0.2911 0.614498 23 to 24 141738 -0.5054 0.306640 22 to 23 141511 -1.1750 0.119994 21 to 22 142039 0.3825 0.648958 20 to 21 141638 -0.8004 0.211744 19 to 20 142295 1.1377 0.872371 18 to 19 141365 -1.6057 0.054171 17 to 18 141168 -2.1868 0.014378 16 to 17 142117 0.6126 0.729928 15 to 16 141626 -0.8358 0.201639 14 to 15 141556 -1.0423 0.148643 13 to 14 141833 -0.2252 0.410927 12 to 13 142006 0.2852 0.612240 11 to 12 142285 1.1082 0.866106 10 to 11 142143 0.6893 0.754680 9 to 10 142329 1.2380 0.892135 8 to 9 142472 1.6598 0.951522 7 to 8 142148 0.7040 0.759297 6 to 7 141601 -0.9095 0.181536 5 to 6 141603 -0.9036 0.183096 4 to 5 141922 0.0374 0.514907 3 to 4 141910 0.0020 0.500789 2 to 3 142119 0.6185 0.731876 1 to 2 141899 -0.0305 0.487845 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2017-01-17_02:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2516.80 0.238 0.593901 Test results for specific bytes for dh-ranFile-2017-01-17_02:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2533.30 0.471 0.681165 2 to 9 2538.01 0.538 0.704569 3 to 10 2452.13 -0.677 0.249205 4 to 11 2445.55 -0.770 0.220653 5 to 12 2420.00 -1.131 0.128953 6 to 13 2449.67 -0.712 0.238293 7 to 14 2545.70 0.646 0.740953 8 to 15 2444.21 -0.789 0.215078 9 to 16 2543.65 0.617 0.731490 10 to 17 2593.91 1.328 0.907920 11 to 18 2489.37 -0.150 0.440263 12 to 19 2607.22 1.516 0.935280 13 to 20 2448.17 -0.733 0.231776 14 to 21 2396.70 -1.461 0.072032 15 to 22 2586.27 1.220 0.888782 16 to 23 2548.84 0.691 0.755140 17 to 24 2504.53 0.064 0.525560 18 to 25 2537.23 0.526 0.700727 19 to 26 2520.87 0.295 0.616081 20 to 27 2459.43 -0.574 0.283082 21 to 28 2501.53 0.022 0.508652 22 to 29 2658.52 2.242 0.987514 23 to 30 2483.88 -0.228 0.409831 24 to 31 2682.44 2.580 0.995061 25 to 32 2576.02 1.075 0.858834 CDPARK for dh-ranFile-2017-01-17_02:31: 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 3519 -0.1826 0.427537 3525 0.0913 0.536383 3501 -1.0046 0.157553 3477 -2.1005 0.017844 3544 0.9589 0.831196 3530 0.3196 0.625377 3556 1.5068 0.934075 3534 0.5023 0.692266 3504 -0.8676 0.192812 3498 -1.1416 0.126820 Square side=100, avg. no. parked=3518.80 sample std.=22.65 p-value of the KSTEST for those 10 p-values: 0.903573 Results for the MINIMUM DISTANCE test for dh-ranFile-2017-01-17_02:31 0.1500,0.7975,0.1555,0.4402,0.8072,0.8176,0.1496,0.4378,0.0706,0.2806, The KS test for those 10 p-values: 0.402732 The 3DSPHERES test for dh-ranFile-2017-01-17_02:31 sample no r^3 equiv. uni. 1 4.103 0.127829 2 17.935 0.449990 3 70.748 0.905416 4 41.837 0.752063 5 36.714 0.705894 6 31.905 0.654757 7 22.613 0.529410 8 24.912 0.564129 9 97.580 0.961329 10 0.310 0.010264 11 29.348 0.624036 12 1.897 0.061261 13 19.539 0.478624 14 45.117 0.777741 15 54.014 0.834780 16 128.496 0.986202 17 17.392 0.439955 18 6.222 0.187301 19 14.943 0.392312 20 4.674 0.144266 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.926078 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-01-17_02:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 1.3 1.3 0.8 1.5 -0.2 0.1 2.8 -0.1 0.5 -0.0 -0.2 -0.7 0.1 0.4 -0.0 0.4 -1.3 -1.0 -1.1 -1.6 0.7 -0.0 0.8 1.4 -1.4 1.4 3.2 0.7 1.1 -1.1 -1.1 0.8 1.1 -0.2 1.2 0.1 0.5 0.5 0.5 -0.1 0.1 0.0 0.8 Chi-square with 42 degrees of freedom:47.192327 z-score=0.566529, p-value=0.731329 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2017-01-17_02:31 Test no p-value 1 0.847974 2 0.400755 3 0.013425 4 0.845365 5 0.702713 6 0.905902 7 0.951768 8 0.799101 9 0.414444 10 0.123411 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.276201 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-01-17_02:31: (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 66696 0.01 66702 0.02 3 25000.00 25003 0.00 24967 0.04 4 6666.67 6674 0.01 6699 0.16 5 1388.89 1360 0.60 1357 0.73 6 238.10 225 0.72 230 0.28 7 34.72 36 0.05 40 0.80 8 4.96 5 0.00 4 0.19 p=0.03354 p=0.10113 Number of rngs required: 688495, p-value: 0.542 RESULTS OF CRAPS TEST for dh-ranFile-2017-01-17_02:31 No. of wins: Observed Expected 98172 98585.9 z-score=-1.851, pvalue=0.03208 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66690 66666.7 0.008 0.008 2 37488 37654.3 0.735 0.743 3 26773 26954.7 1.225 1.968 4 19418 19313.5 0.566 2.534 5 13836 13851.4 0.017 2.551 6 10027 9943.5 0.700 3.252 7 7247 7145.0 1.455 4.707 8 5195 5139.1 0.609 5.316 9 3680 3699.9 0.107 5.422 10 2697 2666.3 0.354 5.776 11 1860 1923.3 2.085 7.861 12 1428 1388.7 1.110 8.971 13 1012 1003.7 0.068 9.039 14 728 726.1 0.005 9.044 15 500 525.8 1.269 10.313 16 400 381.2 0.932 11.246 17 318 276.5 6.216 17.462 18 182 200.8 1.765 19.227 19 118 146.0 5.364 24.592 20 126 106.2 3.685 28.277 21 277 287.1 0.356 28.633 Chisq= 28.63 for 20 degrees of freedom, p= 0.90476 SUMMARY of craptest p-value for no. of wins: 0.032084 p-value for throws/game: 0.904762 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2017-01-17_02:31 No. of wins: Observed Expected 98938 98585.9 z-score= 1.575, pvalue=0.94237 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66881 66666.7 0.689 0.689 2 37506 37654.3 0.584 1.273 3 26826 26954.7 0.615 1.888 4 19257 19313.5 0.165 2.053 5 14010 13851.4 1.816 3.869 6 10046 9943.5 1.056 4.924 7 7107 7145.0 0.202 5.127 8 5029 5139.1 2.358 7.484 9 3599 3699.9 2.750 10.234 10 2667 2666.3 0.000 10.234 11 1947 1923.3 0.291 10.526 12 1457 1388.7 3.355 13.881 13 1015 1003.7 0.127 14.008 14 669 726.1 4.496 18.504 15 556 525.8 1.730 20.234 16 379 381.2 0.012 20.247 17 253 276.5 2.004 22.250 18 226 200.8 3.155 25.405 19 145 146.0 0.007 25.412 20 111 106.2 0.216 25.627 21 314 287.1 2.518 28.145 Chisq= 28.14 for 20 degrees of freedom, p= 0.89398 SUMMARY of craptest p-value for no. of wins: 0.942370 p-value for throws/game: 0.893982 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0043,0.0064,0.0103,0.0105,0.0134,0.0144,0.0178,0.0186,0.0321,0.0335, 0.0378,0.0481,0.0542,0.0613,0.0649,0.0651,0.0706,0.0707,0.0720,0.0899, 0.1011,0.1097,0.1184,0.1184,0.1193,0.1200,0.1207,0.1231,0.1234,0.1237, 0.1260,0.1268,0.1278,0.1290,0.1329,0.1417,0.1443,0.1474,0.1486,0.1496, 0.1500,0.1534,0.1555,0.1568,0.1576,0.1576,0.1613,0.1686,0.1725,0.1815, 0.1831,0.1850,0.1873,0.1928,0.2016,0.2031,0.2065,0.2117,0.2151,0.2154, 0.2207,0.2260,0.2318,0.2383,0.2384,0.2395,0.2447,0.2492,0.2497,0.2671, 0.2762,0.2785,0.2803,0.2806,0.2831,0.2887,0.2949,0.3017,0.3066,0.3069, 0.3119,0.3157,0.3287,0.3291,0.3329,0.3386,0.3404,0.3518,0.3548,0.3610, 0.3618,0.3630,0.3643,0.3646,0.3662,0.3664,0.3777,0.3874,0.3910,0.3923, 0.3950,0.4008,0.4027,0.4098,0.4109,0.4110,0.4144,0.4210,0.4275,0.4351, 0.4369,0.4378,0.4400,0.4402,0.4403,0.4403,0.4403,0.4430,0.4470,0.4500, 0.4679,0.4714,0.4786,0.4878,0.5008,0.5087,0.5090,0.5108,0.5120,0.5149, 0.5198,0.5227,0.5256,0.5294,0.5328,0.5364,0.5378,0.5384,0.5421,0.5585, 0.5629,0.5641,0.5642,0.5655,0.5693,0.5744,0.5805,0.5939,0.5939,0.5992, 0.5993,0.6029,0.6038,0.6056,0.6074,0.6117,0.6122,0.6122,0.6145,0.6152, 0.6157,0.6161,0.6192,0.6240,0.6254,0.6270,0.6323,0.6328,0.6361,0.6429, 0.6435,0.6437,0.6490,0.6538,0.6548,0.6610,0.6626,0.6784,0.6812,0.6837, 0.6887,0.6898,0.6923,0.6972,0.7007,0.7007,0.7027,0.7046,0.7059,0.7062, 0.7090,0.7095,0.7169,0.7299,0.7313,0.7315,0.7319,0.7374,0.7410,0.7476, 0.7521,0.7547,0.7551,0.7593,0.7767,0.7777,0.7799,0.7813,0.7975,0.7991, 0.8013,0.8025,0.8044,0.8063,0.8072,0.8176,0.8180,0.8284,0.8312,0.8348, 0.8454,0.8462,0.8480,0.8550,0.8588,0.8588,0.8615,0.8661,0.8697,0.8724, 0.8752,0.8839,0.8888,0.8920,0.8921,0.8940,0.8994,0.9036,0.9042,0.9048, 0.9054,0.9059,0.9079,0.9100,0.9106,0.9106,0.9196,0.9215,0.9261,0.9269, 0.9324,0.9333,0.9341,0.9353,0.9424,0.9462,0.9481,0.9515,0.9518,0.9546, 0.9557,0.9613,0.9643,0.9648,0.9717,0.9727,0.9862,0.9875,0.9951, Overall p-value after applying KStest on 269 p-values = 0.687549 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.