RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-07-25_12:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.72 11.2422 0.156299 2 to 25 15.63 17.4960 0.578718 3 to 26 15.74 17.9520 0.608124 4 to 27 15.75 17.2051 0.559446 5 to 28 15.77 15.6844 0.453694 6 to 29 15.86 14.9265 0.399226 7 to 30 15.87 21.2993 0.786811 8 to 31 15.89 20.3406 0.742823 9 to 32 15.84 22.8719 0.846534 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.468093 Tough bday spacings test for dh-ranFile-2015-07-25_12:31: 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 34 90 94 93 75 48 33 17 6 6 (O-E)^2/E 2.9 0.2 3.8 0.1 0.2 0.1 0.3 0.4 0.3 0.1 0.9 Birthday Spacings: Sum(O-E)^2/E= 9.358, p= 0.502 RESULTS OF GCD FOR dh-ranFile-2015-07-25_12:31 Euclid's algorithm: p-value, steps to gcd: 0.671972 p-value, dist. of gcd's: 0.207830 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-07-25_12:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.860 0.680 0.173 0.150 0.275 0.397 0.780 0.409 Bits 8 to 15---> 0.273 0.390 0.066 0.533 0.818 0.310 0.837 0.225 Bits 16 to 23---> 0.334 0.602 0.864 0.235 0.751 0.047 0.071 0.408 Bits 24 to 31---> 0.031 0.106 0.362 0.927 0.764 0.404 0.214 0.534 KS test for the above 32 p values: 0.716 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-07-25_12:31, p-values for 5 runs: 0.5659, 0.4330, 0.7868, 0.1455, 0.8880 Rank test for binary matrices (31x31) for dh-ranFile-2015-07-25_12:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 220 211.4 0.348 0.348 r= 29 5095 5134.0 0.296 0.645 r= 30 23256 23103.0 1.013 1.657 r= 31 11429 11551.5 1.300 2.957 chi-square = 2.957 with df = 3; p-value = 0.602 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-07-25_12:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 214 211.4 0.032 0.032 r= 30 5066 5134.0 0.901 0.932 r= 31 23173 23103.0 0.212 1.144 r= 32 11547 11551.5 0.002 1.146 chi-square = 1.146 with df = 3; p-value = 0.234 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-07-25_12:31 b-rank test for bits 1 to 8, p=0.60463 b-rank test for bits 2 to 9, p=0.01838 b-rank test for bits 3 to 10, p=0.90235 b-rank test for bits 4 to 11, p=0.15996 b-rank test for bits 5 to 12, p=0.71300 b-rank test for bits 6 to 13, p=0.35123 b-rank test for bits 7 to 14, p=0.68535 b-rank test for bits 8 to 15, p=0.69186 b-rank test for bits 9 to 16, p=0.42959 b-rank test for bits 10 to 17, p=0.89784 b-rank test for bits 11 to 18, p=0.91165 b-rank test for bits 12 to 19, p=0.98269 b-rank test for bits 13 to 20, p=0.84772 b-rank test for bits 14 to 21, p=0.33048 b-rank test for bits 15 to 22, p=0.12501 b-rank test for bits 16 to 23, p=0.67475 b-rank test for bits 17 to 24, p=0.14104 b-rank test for bits 18 to 25, p=0.12154 b-rank test for bits 19 to 26, p=0.94633 b-rank test for bits 20 to 27, p=0.99366 b-rank test for bits 21 to 28, p=0.68832 b-rank test for bits 22 to 29, p=0.35383 b-rank test for bits 23 to 30, p=0.73947 b-rank test for bits 24 to 31, p=0.84869 b-rank test for bits 25 to 32, p=0.28030 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 = 0.201225 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-07-25_12:31 (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 141831 -0.18 0.427394 2 141944 0.08 0.532281 3 141798 -0.26 0.397387 4 141510 -0.93 0.175406 5 141574 -0.78 0.216672 6 141952 0.10 0.539707 7 141840 -0.16 0.435658 8 141328 -1.36 0.087193 9 141474 -1.02 0.154547 10 141710 -0.47 0.320706 11 141642 -0.62 0.266116 12 141477 -1.01 0.156220 13 142591 1.59 0.944385 14 141819 -0.21 0.416424 15 142817 2.12 0.983027 16 141992 0.19 0.576581 17 142468 1.31 0.904105 18 141930 0.05 0.519259 19 141877 -0.08 0.469894 20 141856 -0.12 0.450419 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-07-25_12:31 Bits used No. missing words z-score p-value 23 to 32 141773 -0.4701 0.319141 22 to 31 142045 0.4678 0.680046 21 to 30 141754 -0.5356 0.296110 20 to 29 142130 0.7609 0.776651 19 to 28 141834 -0.2598 0.397525 18 to 27 141765 -0.4977 0.309351 17 to 26 141998 0.3058 0.620106 16 to 25 142244 1.1540 0.875757 15 to 24 142291 1.3161 0.905930 14 to 23 141968 0.2023 0.580163 13 to 22 141766 -0.4942 0.310568 12 to 21 141522 -1.3356 0.090837 11 to 20 141979 0.2402 0.594928 10 to 19 141784 -0.4322 0.332808 9 to 18 141838 -0.2460 0.402855 8 to 17 141927 0.0609 0.524293 7 to 16 142349 1.5161 0.935253 6 to 15 142175 0.9161 0.820194 5 to 14 141514 -1.3632 0.086409 4 to 13 141602 -1.0598 0.144627 3 to 12 141985 0.2609 0.602927 2 to 11 141686 -0.7701 0.220619 1 to 10 141550 -1.2391 0.107660 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-07-25_12:31 Bits used No. missing words z-score p-value 28 to 32 141952 0.1446 0.557504 27 to 31 141724 -0.6282 0.264924 26 to 30 142428 1.7582 0.960644 25 to 29 142419 1.7277 0.957979 24 to 28 142262 1.1955 0.884053 23 to 27 141963 0.1819 0.572182 22 to 26 141667 -0.8215 0.205693 21 to 25 141377 -1.8045 0.035576 20 to 24 141682 -0.7706 0.220469 19 to 23 141662 -0.8384 0.200901 18 to 22 141766 -0.4859 0.313532 17 to 21 142350 1.4938 0.932386 16 to 20 141401 -1.7232 0.042430 15 to 19 142144 0.7955 0.786836 14 to 18 142008 0.3345 0.630989 13 to 17 142012 0.3480 0.636093 12 to 16 141674 -0.7977 0.212514 11 to 15 142560 2.2057 0.986296 10 to 14 142165 0.8667 0.806941 9 to 13 141986 0.2599 0.602529 8 to 12 141675 -0.7943 0.213499 7 to 11 141664 -0.8316 0.202810 6 to 10 141914 0.0158 0.506315 5 to 9 142001 0.3107 0.622003 4 to 8 141929 0.0667 0.526581 3 to 7 141933 0.0802 0.531976 2 to 6 142007 0.3311 0.629710 1 to 5 142108 0.6735 0.749672 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-07-25_12:31 Bits used No. missing words z-score p-value 31 to 32 142173 0.7778 0.781653 30 to 31 141564 -1.0187 0.154179 29 to 30 141416 -1.4553 0.072800 28 to 29 142377 1.3796 0.916139 27 to 28 141764 -0.4287 0.334070 26 to 27 141853 -0.1662 0.434014 25 to 26 141707 -0.5968 0.275306 24 to 25 141989 0.2350 0.592901 23 to 24 141774 -0.3992 0.344872 22 to 23 141841 -0.2016 0.420129 21 to 22 142575 1.9636 0.975213 20 to 21 142009 0.2940 0.615626 19 to 20 141853 -0.1662 0.434014 18 to 19 141844 -0.1927 0.423592 17 to 18 142314 1.1937 0.883706 16 to 17 142075 0.4887 0.687474 15 to 16 141588 -0.9479 0.171596 14 to 15 141548 -1.0659 0.143241 13 to 14 141868 -0.1219 0.451482 12 to 13 141639 -0.7974 0.212600 11 to 12 141998 0.2616 0.603171 10 to 11 141661 -0.7325 0.231921 9 to 10 141615 -0.8682 0.192634 8 to 9 141946 0.1082 0.543070 7 to 8 141605 -0.8977 0.184665 6 to 7 142086 0.5212 0.698869 5 to 6 141793 -0.3432 0.365740 4 to 5 141998 0.2616 0.603171 3 to 4 142058 0.4386 0.669508 2 to 3 141957 0.1406 0.555915 1 to 2 141868 -0.1219 0.451482 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-07-25_12:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2648.59 2.101 0.982195 Test results for specific bytes for dh-ranFile-2015-07-25_12:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2419.20 -1.143 0.126594 2 to 9 2602.50 1.450 0.926419 3 to 10 2443.23 -0.803 0.211041 4 to 11 2421.83 -1.105 0.134484 5 to 12 2521.62 0.306 0.620109 6 to 13 2574.99 1.061 0.855561 7 to 14 2573.22 1.035 0.849765 8 to 15 2392.27 -1.524 0.063810 9 to 16 2439.96 -0.849 0.197924 10 to 17 2493.60 -0.090 0.463966 11 to 18 2392.33 -1.523 0.063927 12 to 19 2559.40 0.840 0.799577 13 to 20 2402.70 -1.376 0.084406 14 to 21 2526.15 0.370 0.644255 15 to 22 2482.26 -0.251 0.400970 16 to 23 2403.82 -1.360 0.086882 17 to 24 2488.78 -0.159 0.436941 18 to 25 2490.47 -0.135 0.446378 19 to 26 2525.24 0.357 0.639426 20 to 27 2579.20 1.120 0.868650 21 to 28 2485.24 -0.209 0.417353 22 to 29 2447.24 -0.746 0.227809 23 to 30 2656.39 2.212 0.986508 24 to 31 2455.15 -0.634 0.262938 25 to 32 2518.47 0.261 0.603052 CDPARK for dh-ranFile-2015-07-25_12:31: 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 3539 0.7306 0.767486 3506 -0.7763 0.218799 3498 -1.1416 0.126820 3507 -0.7306 0.232514 3498 -1.1416 0.126820 3521 -0.0913 0.463617 3497 -1.1872 0.117571 3499 -1.0959 0.136563 3513 -0.4566 0.323972 3499 -1.0959 0.136563 Square side=100, avg. no. parked=3507.70 sample std.=12.81 p-value of the KSTEST for those 10 p-values: 0.007972 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-07-25_12:31 0.9584,0.8946,0.7055,0.1738,0.3589,0.6007,0.5965,0.0346,0.7702,0.5375, The KS test for those 10 p-values: 0.830293 The 3DSPHERES test for dh-ranFile-2015-07-25_12:31 sample no r^3 equiv. uni. 1 61.345 0.870599 2 25.673 0.575046 3 1.082 0.035412 4 48.627 0.802278 5 94.208 0.956729 6 40.310 0.739113 7 35.543 0.694182 8 31.980 0.655620 9 4.662 0.143935 10 63.710 0.880407 11 6.802 0.202858 12 20.012 0.486786 13 7.004 0.208209 14 1.260 0.041129 15 38.777 0.725439 16 5.171 0.158341 17 23.190 0.538371 18 80.228 0.931042 19 17.670 0.445124 20 8.892 0.256503 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.949466 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-07-25_12:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 2.6 0.6 -0.5 -0.2 -1.5 0.4 -1.1 -0.6 0.9 1.2 -1.7 1.0 1.2 0.0 -0.8 1.1 -0.3 0.3 -0.5 -1.8 -0.4 -0.0 2.0 -0.2 1.1 -0.9 -0.2 -0.5 -0.4 0.5 -1.0 -0.9 0.0 0.3 -0.5 0.7 0.5 0.1 0.4 0.9 0.0 -0.1 Chi-square with 42 degrees of freedom:35.216855 z-score=-0.740102, p-value=0.238749 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-07-25_12:31 Test no p-value 1 0.876135 2 0.487910 3 0.398561 4 0.367505 5 0.024018 6 0.757231 7 0.019473 8 0.003592 9 0.438834 10 0.074148 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.037834 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-07-25_12:31: (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 66674 0.00 66997 1.64 3 25000.00 25064 0.16 24884 0.54 4 6666.67 6642 0.09 6514 3.50 5 1388.89 1351 1.03 1325 2.94 6 238.10 232 0.16 242 0.06 7 34.72 29 0.94 35 0.00 8 4.96 7 0.84 2 1.77 p=0.22014 p=0.89281 Number of rngs required: 687309, p-value: 0.102 RESULTS OF CRAPS TEST for dh-ranFile-2015-07-25_12:31 No. of wins: Observed Expected 98621 98585.9 z-score= 0.157, pvalue=0.56245 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67049 66666.7 2.193 2.193 2 37653 37654.3 0.000 2.193 3 27001 26954.7 0.079 2.272 4 18966 19313.5 6.251 8.523 5 13840 13851.4 0.009 8.533 6 9914 9943.5 0.088 8.620 7 7142 7145.0 0.001 8.622 8 5130 5139.1 0.016 8.638 9 3752 3699.9 0.735 9.372 10 2621 2666.3 0.770 10.142 11 1945 1923.3 0.244 10.386 12 1363 1388.7 0.477 10.863 13 982 1003.7 0.470 11.333 14 709 726.1 0.405 11.738 15 539 525.8 0.330 12.067 16 368 381.2 0.454 12.521 17 260 276.5 0.989 13.510 18 205 200.8 0.087 13.597 19 169 146.0 3.629 17.225 20 104 106.2 0.046 17.271 21 288 287.1 0.003 17.274 Chisq= 17.27 for 20 degrees of freedom, p= 0.36490 SUMMARY of craptest p-value for no. of wins: 0.562446 p-value for throws/game: 0.364896 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-07-25_12:31 No. of wins: Observed Expected 98441 98585.9 z-score=-0.648, pvalue=0.25853 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66647 66666.7 0.006 0.006 2 37716 37654.3 0.101 0.107 3 27228 26954.7 2.770 2.877 4 19063 19313.5 3.248 6.125 5 13943 13851.4 0.605 6.731 6 9980 9943.5 0.134 6.864 7 7155 7145.0 0.014 6.878 8 4985 5139.1 4.619 11.498 9 3714 3699.9 0.054 11.552 10 2657 2666.3 0.032 11.584 11 1857 1923.3 2.287 13.871 12 1404 1388.7 0.168 14.039 13 984 1003.7 0.387 14.426 14 698 726.1 1.091 15.517 15 518 525.8 0.117 15.634 16 411 381.2 2.338 17.971 17 316 276.5 5.631 23.602 18 185 200.8 1.248 24.850 19 156 146.0 0.687 25.537 20 88 106.2 3.124 28.661 21 295 287.1 0.217 28.877 Chisq= 28.88 for 20 degrees of freedom, p= 0.90980 SUMMARY of craptest p-value for no. of wins: 0.258527 p-value for throws/game: 0.909797 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0036,0.0080,0.0184,0.0195,0.0240,0.0310,0.0346,0.0354,0.0356,0.0378, 0.0411,0.0424,0.0465,0.0638,0.0639,0.0657,0.0709,0.0728,0.0741,0.0844, 0.0864,0.0869,0.0872,0.0908,0.1015,0.1057,0.1077,0.1176,0.1215,0.1250, 0.1266,0.1268,0.1268,0.1345,0.1366,0.1366,0.1410,0.1432,0.1439,0.1446, 0.1455,0.1499,0.1542,0.1545,0.1562,0.1563,0.1583,0.1600,0.1716,0.1730, 0.1738,0.1754,0.1847,0.1926,0.1979,0.2009,0.2012,0.2028,0.2029,0.2057, 0.2078,0.2082,0.2110,0.2125,0.2126,0.2135,0.2140,0.2167,0.2188,0.2201, 0.2205,0.2206,0.2246,0.2278,0.2319,0.2325,0.2340,0.2354,0.2387,0.2565, 0.2585,0.2629,0.2649,0.2661,0.2727,0.2748,0.2753,0.2803,0.2961,0.3094, 0.3101,0.3106,0.3135,0.3191,0.3207,0.3240,0.3305,0.3328,0.3341,0.3341, 0.3449,0.3512,0.3538,0.3589,0.3620,0.3649,0.3657,0.3675,0.3903,0.3974, 0.3974,0.3975,0.3986,0.3992,0.4010,0.4029,0.4038,0.4084,0.4094,0.4164, 0.4174,0.4201,0.4236,0.4274,0.4296,0.4330,0.4340,0.4340,0.4357,0.4369, 0.4388,0.4451,0.4464,0.4504,0.4515,0.4515,0.4537,0.4636,0.4640,0.4681, 0.4699,0.4868,0.4879,0.5015,0.5063,0.5193,0.5243,0.5266,0.5320,0.5323, 0.5326,0.5338,0.5375,0.5384,0.5397,0.5431,0.5559,0.5575,0.5594,0.5624, 0.5659,0.5722,0.5750,0.5766,0.5787,0.5802,0.5929,0.5949,0.5965,0.6007, 0.6017,0.6018,0.6025,0.6029,0.6031,0.6032,0.6032,0.6046,0.6081,0.6156, 0.6201,0.6201,0.6220,0.6297,0.6310,0.6361,0.6394,0.6443,0.6556,0.6695, 0.6720,0.6748,0.6800,0.6803,0.6854,0.6875,0.6883,0.6919,0.6942,0.6989, 0.7055,0.7130,0.7162,0.7254,0.7391,0.7395,0.7428,0.7497,0.7509,0.7572, 0.7641,0.7675,0.7702,0.7767,0.7802,0.7817,0.7868,0.7868,0.7868,0.7996, 0.8023,0.8069,0.8183,0.8202,0.8303,0.8373,0.8465,0.8477,0.8487,0.8498, 0.8556,0.8596,0.8645,0.8687,0.8706,0.8758,0.8761,0.8804,0.8837,0.8841, 0.8880,0.8928,0.8946,0.8978,0.9024,0.9041,0.9059,0.9098,0.9116,0.9161, 0.9264,0.9271,0.9310,0.9324,0.9353,0.9444,0.9463,0.9495,0.9567,0.9580, 0.9584,0.9606,0.9752,0.9822,0.9827,0.9830,0.9863,0.9865,0.9937, Overall p-value after applying KStest on 269 p-values = 0.321931 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.