RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-08-16_01:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.83 19.1596 0.680554 2 to 25 15.72 31.6368 0.983311 3 to 26 15.78 24.9597 0.904384 4 to 27 15.88 19.3867 0.693210 5 to 28 15.83 33.1910 0.989341 6 to 29 16.00 13.9827 0.331671 7 to 30 15.75 16.0695 0.481088 8 to 31 15.86 8.3708 0.042038 9 to 32 15.93 19.5260 0.700813 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.117140 Tough bday spacings test for dh-ranFile-2016-08-16_01:31: 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 8 42 71 100 91 86 48 34 12 4 4 (O-E)^2/E 0.1 0.8 0.1 0.1 0.5 0.8 0.3 0.6 0.6 1.0 0.0 Birthday Spacings: Sum(O-E)^2/E= 4.822, p= 0.097 RESULTS OF GCD FOR dh-ranFile-2016-08-16_01:31 Euclid's algorithm: p-value, steps to gcd: 0.978203 p-value, dist. of gcd's: 0.842347 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-08-16_01:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.901 0.243 0.731 0.270 0.366 0.798 0.777 0.271 Bits 8 to 15---> 0.090 0.159 0.445 0.027 0.704 0.300 0.104 0.260 Bits 16 to 23---> 0.724 0.155 0.649 0.010 0.664 0.324 0.619 0.818 Bits 24 to 31---> 0.851 0.598 0.121 0.179 0.242 0.898 0.784 0.663 KS test for the above 32 p values: 0.496 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-08-16_01:31, p-values for 5 runs: 0.6190, 0.6207, 0.6325, 0.6627, 0.7925 Rank test for binary matrices (31x31) for dh-ranFile-2016-08-16_01:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 210 211.4 0.010 0.010 r= 29 5283 5134.0 4.324 4.333 r= 30 22948 23103.0 1.041 5.374 r= 31 11559 11551.5 0.005 5.379 chi-square = 5.379 with df = 3; p-value = 0.854 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-08-16_01:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 220 211.4 0.348 0.348 r= 30 5204 5134.0 0.954 1.302 r= 31 22990 23103.0 0.553 1.856 r= 32 11586 11551.5 0.103 1.959 chi-square = 1.959 with df = 3; p-value = 0.419 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-08-16_01:31 b-rank test for bits 1 to 8, p=0.60636 b-rank test for bits 2 to 9, p=0.81991 b-rank test for bits 3 to 10, p=0.09119 b-rank test for bits 4 to 11, p=0.63867 b-rank test for bits 5 to 12, p=0.31457 b-rank test for bits 6 to 13, p=0.56906 b-rank test for bits 7 to 14, p=0.40881 b-rank test for bits 8 to 15, p=0.51144 b-rank test for bits 9 to 16, p=0.55340 b-rank test for bits 10 to 17, p=0.02402 b-rank test for bits 11 to 18, p=0.18412 b-rank test for bits 12 to 19, p=0.37065 b-rank test for bits 13 to 20, p=0.32876 b-rank test for bits 14 to 21, p=0.77522 b-rank test for bits 15 to 22, p=0.39583 b-rank test for bits 16 to 23, p=0.71739 b-rank test for bits 17 to 24, p=0.31030 b-rank test for bits 18 to 25, p=0.76561 b-rank test for bits 19 to 26, p=0.61642 b-rank test for bits 20 to 27, p=0.56967 b-rank test for bits 21 to 28, p=0.20166 b-rank test for bits 22 to 29, p=0.41396 b-rank test for bits 23 to 30, p=0.50948 b-rank test for bits 24 to 31, p=0.05971 b-rank test for bits 25 to 32, p=0.29854 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 = 0.215642 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-08-16_01:31 (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 141928 0.04 0.517397 2 141911 0.00 0.501557 3 141885 -0.06 0.477334 4 141757 -0.36 0.360954 5 141237 -1.57 0.058107 6 141858 -0.12 0.452269 7 142578 1.56 0.940893 8 142668 1.77 0.961852 9 142177 0.63 0.734145 10 142303 0.92 0.821159 11 141805 -0.24 0.403708 12 141791 -0.28 0.391093 13 141111 -1.87 0.031073 14 141796 -0.26 0.395586 15 141661 -0.58 0.280886 16 141727 -0.43 0.335052 17 141919 0.02 0.509013 18 142770 2.01 0.977833 19 142298 0.91 0.818089 20 142210 0.70 0.758816 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-08-16_01:31 Bits used No. missing words z-score p-value 23 to 32 142612 2.4230 0.992304 22 to 31 142270 1.2437 0.893193 21 to 30 141540 -1.2736 0.101411 20 to 29 141947 0.1299 0.551676 19 to 28 142604 2.3954 0.991699 18 to 27 142160 0.8644 0.806310 17 to 26 142055 0.5023 0.692275 16 to 25 142350 1.5196 0.935688 15 to 24 142028 0.4092 0.658806 14 to 23 141286 -2.1494 0.015801 13 to 22 141847 -0.2149 0.414911 12 to 21 142139 0.7920 0.785810 11 to 20 141490 -1.4460 0.074093 10 to 19 141847 -0.2149 0.414911 9 to 18 141709 -0.6908 0.244848 8 to 17 142405 1.7092 0.956294 7 to 16 142262 1.2161 0.888027 6 to 15 142206 1.0230 0.846846 5 to 14 141384 -1.8115 0.035033 4 to 13 141752 -0.5425 0.293731 3 to 12 141747 -0.5598 0.287822 2 to 11 141821 -0.3046 0.380341 1 to 10 141967 0.1989 0.578815 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-08-16_01:31 Bits used No. missing words z-score p-value 28 to 32 142689 2.6429 0.995891 27 to 31 141558 -1.1909 0.116837 26 to 30 141779 -0.4418 0.329318 25 to 29 141747 -0.5503 0.291067 24 to 28 141748 -0.5469 0.292230 23 to 27 142282 1.2633 0.896757 22 to 26 141799 -0.3740 0.354202 21 to 25 141762 -0.4994 0.308741 20 to 24 141859 -0.1706 0.432265 19 to 23 142035 0.4260 0.664946 18 to 22 142264 1.2023 0.885371 17 to 21 141891 -0.0621 0.475227 16 to 20 141401 -1.7232 0.042430 15 to 19 141780 -0.4384 0.330546 14 to 18 141967 0.1955 0.577496 13 to 17 142214 1.0328 0.849147 12 to 16 142259 1.1853 0.882055 11 to 15 141757 -0.5164 0.302797 10 to 14 141667 -0.8215 0.205693 9 to 13 141626 -0.9604 0.168417 8 to 12 141820 -0.3028 0.381016 7 to 11 141768 -0.4791 0.315939 6 to 10 142170 0.8836 0.811551 5 to 9 142241 1.1243 0.869558 4 to 8 142388 1.6226 0.947664 3 to 7 142244 1.1345 0.871702 2 to 6 142191 0.9548 0.830164 1 to 5 142693 2.6565 0.996052 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-08-16_01:31 Bits used No. missing words z-score p-value 31 to 32 142488 1.7070 0.956088 30 to 31 142042 0.3914 0.652233 29 to 30 142530 1.8309 0.966441 28 to 29 141640 -0.7945 0.213457 27 to 28 141920 0.0315 0.512555 26 to 27 142306 1.1701 0.879023 25 to 26 142237 0.9666 0.833123 24 to 25 141505 -1.1927 0.116491 23 to 24 141795 -0.3373 0.367962 22 to 23 141875 -0.1013 0.459669 21 to 22 142137 0.6716 0.749079 20 to 21 141951 0.1229 0.548915 19 to 20 141754 -0.4582 0.323404 18 to 19 141662 -0.7296 0.232821 17 to 18 141785 -0.3668 0.356901 16 to 17 141824 -0.2517 0.400632 15 to 16 141640 -0.7945 0.213457 14 to 15 141549 -1.0629 0.143909 13 to 14 142035 0.3707 0.644573 12 to 13 141818 -0.2694 0.393807 11 to 12 141617 -0.8623 0.194253 10 to 11 142411 1.4799 0.930544 9 to 10 141430 -1.4140 0.078688 8 to 9 141678 -0.6824 0.247496 7 to 8 142147 0.7011 0.758377 6 to 7 141900 -0.0275 0.489022 5 to 6 141520 -1.1485 0.125388 4 to 5 141927 0.0521 0.520785 3 to 4 142039 0.3825 0.648958 2 to 3 142051 0.4179 0.661992 1 to 2 141914 0.0138 0.505496 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-08-16_01:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2438.84 -0.865 0.193524 Test results for specific bytes for dh-ranFile-2016-08-16_01:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2425.76 -1.050 0.146888 2 to 9 2503.07 0.043 0.517340 3 to 10 2572.50 1.025 0.847404 4 to 11 2533.68 0.476 0.683073 5 to 12 2590.92 1.286 0.900739 6 to 13 2590.59 1.281 0.899936 7 to 14 2470.82 -0.413 0.339925 8 to 15 2492.55 -0.105 0.458058 9 to 16 2562.93 0.890 0.813275 10 to 17 2523.96 0.339 0.632651 11 to 18 2421.53 -1.110 0.133550 12 to 19 2504.93 0.070 0.527778 13 to 20 2532.74 0.463 0.678346 14 to 21 2526.34 0.372 0.645224 15 to 22 2464.05 -0.508 0.305563 16 to 23 2494.13 -0.083 0.466936 17 to 24 2495.46 -0.064 0.474399 18 to 25 2463.86 -0.511 0.304634 19 to 26 2509.83 0.139 0.555272 20 to 27 2464.35 -0.504 0.307071 21 to 28 2434.40 -0.928 0.176774 22 to 29 2508.39 0.119 0.547210 23 to 30 2411.75 -1.248 0.106010 24 to 31 2526.53 0.375 0.646252 25 to 32 2452.24 -0.675 0.249696 CDPARK for dh-ranFile-2016-08-16_01:31: 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 3520 -0.1370 0.445521 3487 -1.6438 0.050105 3470 -2.4201 0.007758 3531 0.3653 0.642555 3523 0.0000 0.500000 3563 1.8265 0.966111 3530 0.3196 0.625377 3554 1.4155 0.921543 3512 -0.5023 0.307734 3491 -1.4612 0.071982 Square side=100, avg. no. parked=3518.10 sample std.=27.74 p-value of the KSTEST for those 10 p-values: 0.509622 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-08-16_01:31 0.9113,0.9627,0.4698,0.2519,0.0457,0.5309,0.5106,0.7760,0.2154,0.1815, The KS test for those 10 p-values: 0.969698 The 3DSPHERES test for dh-ranFile-2016-08-16_01:31 sample no r^3 equiv. uni. 1 10.820 0.302798 2 41.054 0.745505 3 4.594 0.141998 4 43.511 0.765513 5 27.087 0.594606 6 16.321 0.419591 7 126.922 0.985458 8 154.256 0.994153 9 62.735 0.876456 10 34.189 0.680064 11 43.124 0.762472 12 50.340 0.813251 13 18.701 0.463867 14 2.513 0.080353 15 88.395 0.947476 16 9.108 0.261853 17 5.957 0.180097 18 25.148 0.567547 19 54.294 0.836313 20 29.243 0.622724 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.182250 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-08-16_01:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 0.1 0.3 0.5 -0.4 0.8 0.0 2.2 1.4 -0.6 -1.9 1.5 0.2 -0.8 1.1 -1.0 0.6 -0.6 -0.2 0.7 0.4 -1.1 -1.6 -0.5 0.8 -1.3 0.3 1.2 -1.2 1.5 1.0 0.6 2.4 1.8 1.2 -1.0 -0.9 -0.1 -2.0 -0.1 1.6 -1.0 0.8 Chi-square with 42 degrees of freedom:52.869494 z-score=1.185959, p-value=0.878625 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-08-16_01:31 Test no p-value 1 0.720102 2 0.145710 3 0.865921 4 0.563773 5 0.578508 6 0.112736 7 0.381682 8 0.207789 9 0.039428 10 0.002403 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.148975 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-08-16_01:31: (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 66349 1.51 3 25000.00 24904 0.37 25309 3.82 4 6666.67 6583 1.05 6660 0.01 5 1388.89 1389 0.00 1418 0.61 6 238.10 239 0.00 218 1.70 7 34.72 31 0.40 40 0.80 8 4.96 6 0.22 5 0.00 p=0.13452 p=0.79299 Number of rngs required: 688534, p-value: 0.560 RESULTS OF CRAPS TEST for dh-ranFile-2016-08-16_01:31 No. of wins: Observed Expected 98128 98585.9 z-score=-2.048, pvalue=0.02029 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66475 66666.7 0.551 0.551 2 37786 37654.3 0.460 1.012 3 27256 26954.7 3.367 4.379 4 19168 19313.5 1.096 5.474 5 13785 13851.4 0.318 5.793 6 9834 9943.5 1.207 7.000 7 7072 7145.0 0.746 7.746 8 5082 5139.1 0.634 8.380 9 3777 3699.9 1.608 9.988 10 2660 2666.3 0.015 10.003 11 1897 1923.3 0.360 10.363 12 1433 1388.7 1.411 11.774 13 1061 1003.7 3.269 15.043 14 751 726.1 0.851 15.894 15 543 525.8 0.560 16.454 16 386 381.2 0.062 16.516 17 288 276.5 0.475 16.991 18 191 200.8 0.481 17.472 19 152 146.0 0.248 17.720 20 107 106.2 0.006 17.726 21 296 287.1 0.275 18.001 Chisq= 18.00 for 20 degrees of freedom, p= 0.41266 SUMMARY of craptest p-value for no. of wins: 0.020289 p-value for throws/game: 0.412656 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-08-16_01:31 No. of wins: Observed Expected 98484 98585.9 z-score=-0.456, pvalue=0.32435 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67204 66666.7 4.331 4.331 2 37601 37654.3 0.076 4.406 3 26549 26954.7 6.107 10.514 4 19514 19313.5 2.082 12.596 5 13829 13851.4 0.036 12.632 6 9875 9943.5 0.472 13.105 7 7075 7145.0 0.686 13.791 8 5129 5139.1 0.020 13.811 9 3667 3699.9 0.292 14.103 10 2649 2666.3 0.112 14.215 11 1932 1923.3 0.039 14.254 12 1427 1388.7 1.054 15.308 13 958 1003.7 2.082 17.390 14 663 726.1 5.490 22.880 15 560 525.8 2.220 25.100 16 368 381.2 0.454 25.554 17 255 276.5 1.678 27.232 18 206 200.8 0.133 27.365 19 144 146.0 0.027 27.392 20 96 106.2 0.982 28.374 21 299 287.1 0.492 28.866 Chisq= 28.87 for 20 degrees of freedom, p= 0.90957 SUMMARY of craptest p-value for no. of wins: 0.324349 p-value for throws/game: 0.909571 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0024,0.0078,0.0103,0.0158,0.0203,0.0240,0.0270,0.0311,0.0350,0.0394, 0.0420,0.0424,0.0457,0.0501,0.0581,0.0597,0.0720,0.0741,0.0787,0.0804, 0.0896,0.0912,0.0973,0.1014,0.1039,0.1060,0.1127,0.1165,0.1168,0.1171, 0.1206,0.1254,0.1335,0.1345,0.1420,0.1439,0.1457,0.1469,0.1490,0.1553, 0.1593,0.1684,0.1768,0.1786,0.1801,0.1815,0.1822,0.1841,0.1935,0.1943, 0.2017,0.2057,0.2078,0.2135,0.2135,0.2154,0.2156,0.2328,0.2423,0.2432, 0.2448,0.2475,0.2497,0.2519,0.2600,0.2619,0.2703,0.2713,0.2809,0.2878, 0.2911,0.2922,0.2937,0.2985,0.3002,0.3028,0.3028,0.3046,0.3056,0.3071, 0.3077,0.3087,0.3103,0.3146,0.3159,0.3234,0.3236,0.3243,0.3288,0.3293, 0.3305,0.3317,0.3351,0.3399,0.3542,0.3569,0.3610,0.3665,0.3680,0.3706, 0.3803,0.3810,0.3817,0.3911,0.3938,0.3956,0.3958,0.4006,0.4037,0.4088, 0.4127,0.4140,0.4149,0.4149,0.4189,0.4196,0.4323,0.4452,0.4455,0.4523, 0.4581,0.4597,0.4639,0.4669,0.4698,0.4744,0.4752,0.4773,0.4811,0.4890, 0.4963,0.5000,0.5016,0.5055,0.5090,0.5095,0.5096,0.5106,0.5114,0.5126, 0.5173,0.5174,0.5208,0.5278,0.5309,0.5472,0.5489,0.5517,0.5534,0.5553, 0.5599,0.5638,0.5675,0.5691,0.5697,0.5775,0.5785,0.5788,0.5946,0.5983, 0.6064,0.6164,0.6190,0.6193,0.6207,0.6227,0.6254,0.6325,0.6327,0.6387, 0.6426,0.6446,0.6452,0.6463,0.6490,0.6490,0.6522,0.6588,0.6620,0.6627, 0.6633,0.6636,0.6649,0.6783,0.6801,0.6806,0.6831,0.6923,0.6932,0.7008, 0.7043,0.7174,0.7201,0.7243,0.7313,0.7341,0.7455,0.7491,0.7584,0.7588, 0.7625,0.7655,0.7656,0.7752,0.7760,0.7775,0.7839,0.7858,0.7925,0.7930, 0.7977,0.8063,0.8116,0.8133,0.8133,0.8180,0.8181,0.8199,0.8212,0.8302, 0.8331,0.8363,0.8423,0.8468,0.8474,0.8491,0.8505,0.8539,0.8659,0.8696, 0.8717,0.8765,0.8786,0.8790,0.8821,0.8854,0.8880,0.8932,0.8968,0.8976, 0.8999,0.9007,0.9007,0.9044,0.9096,0.9113,0.9215,0.9305,0.9357,0.9409, 0.9475,0.9477,0.9561,0.9563,0.9619,0.9627,0.9661,0.9664,0.9697,0.9778, 0.9782,0.9833,0.9855,0.9893,0.9917,0.9923,0.9942,0.9959,0.9961, Overall p-value after applying KStest on 269 p-values = 0.948154 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.