RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-01-13_14:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.91 7.7428 0.028258 2 to 25 15.68 7.8892 0.031142 3 to 26 15.74 16.4689 0.509129 4 to 27 15.95 18.1543 0.620832 5 to 28 15.75 20.6300 0.756722 6 to 29 15.91 20.8565 0.767224 7 to 30 15.97 10.9455 0.140617 8 to 31 16.02 22.2459 0.824553 9 to 32 16.21 20.7528 0.762458 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.398915 Tough bday spacings test for dh-ranFile-2016-01-13_14:31: 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 9 35 63 87 113 89 49 26 14 9 6 (O-E)^2/E 0.0 0.1 1.4 1.2 2.4 1.5 0.2 0.5 0.1 0.9 0.9 Birthday Spacings: Sum(O-E)^2/E= 9.084, p= 0.476 RESULTS OF GCD FOR dh-ranFile-2016-01-13_14:31 Euclid's algorithm: p-value, steps to gcd: 0.732252 p-value, dist. of gcd's: 0.207836 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-01-13_14:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.289 0.633 0.903 0.402 0.281 0.201 0.415 0.508 Bits 8 to 15---> 0.776 0.200 0.177 0.323 0.513 0.230 0.004 0.135 Bits 16 to 23---> 0.798 0.680 0.230 0.962 0.309 0.912 0.066 0.472 Bits 24 to 31---> 0.329 0.297 0.214 0.023 0.351 0.744 0.835 0.223 KS test for the above 32 p values: 0.863 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-01-13_14:31, p-values for 5 runs: 0.7577, 0.5306, 0.5736, 0.3430, 0.5974 Rank test for binary matrices (31x31) for dh-ranFile-2016-01-13_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 218 211.4 0.205 0.205 r= 29 5147 5134.0 0.033 0.238 r= 30 23064 23103.0 0.066 0.304 r= 31 11571 11551.5 0.033 0.337 chi-square = 0.337 with df = 3; p-value = 0.047 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-01-13_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 229 211.4 1.462 1.462 r= 30 5100 5134.0 0.225 1.687 r= 31 23133 23103.0 0.039 1.726 r= 32 11538 11551.5 0.016 1.742 chi-square = 1.742 with df = 3; p-value = 0.372 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-01-13_14:31 b-rank test for bits 1 to 8, p=0.80502 b-rank test for bits 2 to 9, p=0.72011 b-rank test for bits 3 to 10, p=0.42701 b-rank test for bits 4 to 11, p=0.14016 b-rank test for bits 5 to 12, p=0.03423 b-rank test for bits 6 to 13, p=0.26431 b-rank test for bits 7 to 14, p=0.88603 b-rank test for bits 8 to 15, p=0.81717 b-rank test for bits 9 to 16, p=0.79138 b-rank test for bits 10 to 17, p=0.85777 b-rank test for bits 11 to 18, p=0.59026 b-rank test for bits 12 to 19, p=0.34379 b-rank test for bits 13 to 20, p=0.23558 b-rank test for bits 14 to 21, p=0.57128 b-rank test for bits 15 to 22, p=0.08740 b-rank test for bits 16 to 23, p=0.51443 b-rank test for bits 17 to 24, p=0.09810 b-rank test for bits 18 to 25, p=0.60747 b-rank test for bits 19 to 26, p=0.89864 b-rank test for bits 20 to 27, p=0.21379 b-rank test for bits 21 to 28, p=0.15579 b-rank test for bits 22 to 29, p=0.72999 b-rank test for bits 23 to 30, p=0.17859 b-rank test for bits 24 to 31, p=0.40466 b-rank test for bits 25 to 32, p=0.75831 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 = 0.903013 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-01-13_14:31 (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 142112 0.47 0.682082 2 141801 -0.25 0.400093 3 142059 0.35 0.636717 4 142581 1.57 0.941714 5 141424 -1.13 0.128408 6 141862 -0.11 0.455973 7 141622 -0.67 0.251005 8 142252 0.80 0.788327 9 142294 0.90 0.815610 10 141493 -0.97 0.165343 11 141981 0.17 0.566493 12 142207 0.70 0.756626 13 141950 0.10 0.537852 14 142637 1.70 0.955450 15 142083 0.41 0.657545 16 142481 1.34 0.909173 17 142054 0.34 0.632324 18 141650 -0.61 0.272287 19 141765 -0.34 0.367976 20 141345 -1.32 0.093663 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-01-13_14:31 Bits used No. missing words z-score p-value 23 to 32 141882 -0.0942 0.462459 22 to 31 141906 -0.0115 0.495419 21 to 30 141970 0.2092 0.582857 20 to 29 141673 -0.8149 0.207556 19 to 28 142087 0.6127 0.729948 18 to 27 142057 0.5092 0.694696 17 to 26 141610 -1.0322 0.150996 16 to 25 142142 0.8023 0.788813 15 to 24 141629 -0.9667 0.166858 14 to 23 141769 -0.4839 0.314230 13 to 22 141770 -0.4804 0.315454 12 to 21 141480 -1.4804 0.069377 11 to 20 142216 1.0575 0.854854 10 to 19 141756 -0.5287 0.298498 9 to 18 141966 0.1954 0.577466 8 to 17 141977 0.2333 0.592253 7 to 16 141734 -0.6046 0.272727 6 to 15 141662 -0.8529 0.196868 5 to 14 141635 -0.9460 0.172083 4 to 13 141809 -0.3460 0.364684 3 to 12 142023 0.3920 0.652458 2 to 11 141728 -0.6253 0.265895 1 to 10 142251 1.1782 0.880636 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-01-13_14:31 Bits used No. missing words z-score p-value 28 to 32 142225 1.0701 0.857706 27 to 31 141551 -1.2147 0.112244 26 to 30 141720 -0.6418 0.260503 25 to 29 141931 0.0735 0.529279 24 to 28 142039 0.4396 0.669872 23 to 27 142025 0.3921 0.652509 22 to 26 141874 -0.1198 0.452336 21 to 25 141783 -0.4282 0.334239 20 to 24 142162 0.8565 0.804142 19 to 23 141731 -0.6045 0.272753 18 to 22 141821 -0.2994 0.382308 17 to 21 142070 0.5446 0.707001 16 to 20 141962 0.1785 0.570852 15 to 19 141464 -1.5096 0.065574 14 to 18 142040 0.4429 0.671099 13 to 17 142416 1.7175 0.957058 12 to 16 142076 0.5650 0.713957 11 to 15 141222 -2.3299 0.009905 10 to 14 141605 -1.0316 0.151123 9 to 13 141841 -0.2316 0.408414 8 to 12 142168 0.8768 0.809715 7 to 11 142144 0.7955 0.786836 6 to 10 141669 -0.8147 0.207628 5 to 9 141477 -1.4655 0.071389 4 to 8 142386 1.6158 0.946935 3 to 7 141684 -0.7638 0.222484 2 to 6 141708 -0.6825 0.247470 1 to 5 141627 -0.9571 0.169271 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-01-13_14:31 Bits used No. missing words z-score p-value 31 to 32 142041 0.3884 0.651143 30 to 31 142123 0.6303 0.735749 29 to 30 141519 -1.1514 0.124781 28 to 29 142313 1.1908 0.883127 27 to 28 142218 0.9105 0.818729 26 to 27 141808 -0.2989 0.382505 25 to 26 141886 -0.0688 0.472566 24 to 25 141905 -0.0128 0.494905 23 to 24 141864 -0.1337 0.446813 22 to 23 141853 -0.1662 0.434014 21 to 22 141528 -1.1249 0.130323 20 to 21 142158 0.7335 0.768385 19 to 20 141973 0.1878 0.574490 18 to 19 142262 1.0403 0.850905 17 to 18 141867 -0.1249 0.450314 16 to 17 142328 1.2350 0.891588 15 to 16 142248 0.9990 0.841109 14 to 15 141930 0.0610 0.524310 13 to 14 141942 0.0964 0.538387 12 to 13 142091 0.5359 0.703986 11 to 12 141664 -0.7237 0.234629 10 to 11 141762 -0.4346 0.331926 9 to 10 142223 0.9253 0.822590 8 to 9 141784 -0.3697 0.355801 7 to 8 140967 -2.7797 0.002720 6 to 7 141883 -0.0777 0.469045 5 to 6 141804 -0.3107 0.378011 4 to 5 141824 -0.2517 0.400632 3 to 4 141715 -0.5732 0.283240 2 to 3 142274 1.0757 0.858974 1 to 2 141914 0.0138 0.505496 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-01-13_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2476.10 -0.338 0.367675 Test results for specific bytes for dh-ranFile-2016-01-13_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2425.98 -1.047 0.147611 2 to 9 2433.41 -0.942 0.173184 3 to 10 2552.08 0.736 0.769281 4 to 11 2432.77 -0.951 0.170850 5 to 12 2570.49 0.997 0.840578 6 to 13 2610.73 1.566 0.941315 7 to 14 2450.49 -0.700 0.241897 8 to 15 2534.06 0.482 0.684966 9 to 16 2518.15 0.257 0.601296 10 to 17 2574.06 1.047 0.852530 11 to 18 2479.71 -0.287 0.387083 12 to 19 2505.88 0.083 0.533152 13 to 20 2638.58 1.960 0.974994 14 to 21 2543.97 0.622 0.732969 15 to 22 2720.22 3.114 0.999078 16 to 23 2440.88 -0.836 0.201558 17 to 24 2548.70 0.689 0.754502 18 to 25 2421.07 -1.116 0.132148 19 to 26 2511.04 0.156 0.562026 20 to 27 2438.84 -0.865 0.193557 21 to 28 2523.13 0.327 0.628208 22 to 29 2616.50 1.648 0.950281 23 to 30 2461.58 -0.543 0.293429 24 to 31 2482.10 -0.253 0.400062 25 to 32 2428.63 -1.009 0.156421 CDPARK for dh-ranFile-2016-01-13_14:31: 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 3511 -0.5479 0.291865 3523 0.0000 0.500000 3559 1.6438 0.949895 3527 0.1826 0.572463 3548 1.1416 0.873180 3521 -0.0913 0.463617 3510 -0.5936 0.276387 3563 1.8265 0.966111 3503 -0.9132 0.180558 3507 -0.7306 0.232514 Square side=100, avg. no. parked=3527.20 sample std.=20.82 p-value of the KSTEST for those 10 p-values: 0.662642 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-01-13_14:31 0.7666,0.7011,0.0347,0.5677,0.3133,0.0032,0.6750,0.7852,0.9628,0.6857, The KS test for those 10 p-values: 0.340156 The 3DSPHERES test for dh-ranFile-2016-01-13_14:31 sample no r^3 equiv. uni. 1 59.628 0.862974 2 4.942 0.151893 3 64.164 0.882205 4 15.484 0.403177 5 8.246 0.240336 6 21.119 0.505377 7 98.938 0.963040 8 20.422 0.493761 9 44.491 0.773055 10 43.923 0.768711 11 45.757 0.782429 12 75.329 0.918810 13 34.745 0.685935 14 28.782 0.616878 15 36.489 0.703675 16 77.412 0.924257 17 7.551 0.222514 18 15.401 0.401526 19 5.914 0.178911 20 0.820 0.026953 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.434754 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-01-13_14:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -0.7 2.0 0.3 -0.3 -0.9 0.7 -0.1 -1.2 -0.7 -0.8 0.7 -0.5 -0.3 -0.2 0.5 -0.4 0.1 0.4 0.0 0.4 -1.4 0.3 0.4 0.9 0.7 0.1 -0.7 1.1 0.8 -1.1 -0.1 0.6 1.5 0.1 1.1 0.7 -1.7 -1.6 1.0 -1.3 2.0 -1.1 Chi-square with 42 degrees of freedom:35.406018 z-score=-0.719462, p-value=0.245987 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-01-13_14:31 Test no p-value 1 0.375683 2 0.159082 3 0.726413 4 0.043808 5 0.173845 6 0.812776 7 0.859941 8 0.671697 9 0.658912 10 0.497528 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.953678 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-01-13_14:31: (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 66707 0.02 66795 0.25 3 25000.00 24992 0.00 24828 1.18 4 6666.67 6606 0.55 6656 0.02 5 1388.89 1406 0.21 1434 1.47 6 238.10 242 0.06 238 0.00 7 34.72 40 0.80 39 0.53 8 4.96 6 0.22 9 3.29 p=0.06916 p=0.65355 Number of rngs required: 687477, p-value: 0.141 RESULTS OF CRAPS TEST for dh-ranFile-2016-01-13_14:31 No. of wins: Observed Expected 98447 98585.9 z-score=-0.621, pvalue=0.26728 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66354 66666.7 1.466 1.466 2 37766 37654.3 0.331 1.798 3 27003 26954.7 0.086 1.884 4 19417 19313.5 0.555 2.439 5 13606 13851.4 4.348 6.787 6 9948 9943.5 0.002 6.789 7 7331 7145.0 4.841 11.630 8 5184 5139.1 0.393 12.023 9 3531 3699.9 7.707 19.730 10 2721 2666.3 1.122 20.852 11 1936 1923.3 0.083 20.936 12 1496 1388.7 8.284 29.220 13 990 1003.7 0.187 29.407 14 724 726.1 0.006 29.414 15 518 525.8 0.117 29.531 16 401 381.2 1.034 30.564 17 299 276.5 1.824 32.388 18 205 200.8 0.087 32.475 19 164 146.0 2.223 34.698 20 101 106.2 0.256 34.954 21 305 287.1 1.114 36.069 Chisq= 36.07 for 20 degrees of freedom, p= 0.98490 SUMMARY of craptest p-value for no. of wins: 0.267281 p-value for throws/game: 0.984902 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-01-13_14:31 No. of wins: Observed Expected 98760 98585.9 z-score= 0.779, pvalue=0.78197 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66618 66666.7 0.036 0.036 2 37764 37654.3 0.319 0.355 3 26747 26954.7 1.601 1.956 4 19193 19313.5 0.751 2.707 5 13888 13851.4 0.097 2.804 6 10042 9943.5 0.975 3.779 7 7265 7145.0 2.015 5.793 8 5140 5139.1 0.000 5.793 9 3693 3699.9 0.013 5.806 10 2718 2666.3 1.003 6.809 11 1879 1923.3 1.022 7.830 12 1390 1388.7 0.001 7.832 13 968 1003.7 1.271 9.102 14 718 726.1 0.091 9.194 15 567 525.8 3.222 12.416 16 395 381.2 0.503 12.919 17 235 276.5 6.240 19.159 18 206 200.8 0.133 19.292 19 166 146.0 2.744 22.037 20 109 106.2 0.073 22.110 21 299 287.1 0.492 22.602 Chisq= 22.60 for 20 degrees of freedom, p= 0.69122 SUMMARY of craptest p-value for no. of wins: 0.781969 p-value for throws/game: 0.691223 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0027,0.0032,0.0045,0.0099,0.0233,0.0270,0.0283,0.0311,0.0342,0.0347, 0.0438,0.0470,0.0656,0.0663,0.0692,0.0694,0.0714,0.0874,0.0937,0.0981, 0.1122,0.1248,0.1284,0.1303,0.1321,0.1346,0.1402,0.1406,0.1414,0.1476, 0.1510,0.1511,0.1519,0.1558,0.1564,0.1591,0.1653,0.1669,0.1693,0.1708, 0.1721,0.1732,0.1738,0.1774,0.1786,0.1789,0.1806,0.1936,0.1969,0.1996, 0.2008,0.2016,0.2076,0.2076,0.2078,0.2138,0.2140,0.2225,0.2225,0.2226, 0.2299,0.2303,0.2325,0.2346,0.2356,0.2403,0.2419,0.2460,0.2475,0.2510, 0.2605,0.2643,0.2659,0.2673,0.2723,0.2727,0.2728,0.2764,0.2813,0.2832, 0.2889,0.2919,0.2934,0.2970,0.2985,0.3091,0.3133,0.3142,0.3155,0.3226, 0.3288,0.3319,0.3342,0.3402,0.3430,0.3438,0.3512,0.3558,0.3647,0.3677, 0.3680,0.3724,0.3757,0.3780,0.3823,0.3825,0.3871,0.3989,0.4001,0.4001, 0.4006,0.4015,0.4021,0.4032,0.4047,0.4084,0.4146,0.4270,0.4340,0.4348, 0.4468,0.4503,0.4523,0.4560,0.4625,0.4636,0.4690,0.4716,0.4726,0.4758, 0.4938,0.4949,0.4954,0.4975,0.5000,0.5054,0.5055,0.5079,0.5091,0.5134, 0.5144,0.5243,0.5293,0.5306,0.5332,0.5379,0.5384,0.5620,0.5665,0.5677, 0.5709,0.5713,0.5725,0.5736,0.5745,0.5775,0.5829,0.5903,0.5923,0.5974, 0.6013,0.6075,0.6169,0.6208,0.6282,0.6323,0.6334,0.6367,0.6511,0.6525, 0.6525,0.6535,0.6575,0.6589,0.6626,0.6699,0.6711,0.6717,0.6750,0.6803, 0.6821,0.6850,0.6857,0.6859,0.6912,0.6947,0.7011,0.7037,0.7040,0.7070, 0.7140,0.7201,0.7264,0.7299,0.7300,0.7323,0.7330,0.7357,0.7443,0.7545, 0.7566,0.7567,0.7577,0.7583,0.7625,0.7666,0.7672,0.7684,0.7687,0.7693, 0.7731,0.7765,0.7820,0.7824,0.7852,0.7868,0.7883,0.7888,0.7914,0.7983, 0.8041,0.8050,0.8097,0.8128,0.8156,0.8172,0.8187,0.8226,0.8246,0.8354, 0.8406,0.8411,0.8509,0.8525,0.8549,0.8577,0.8578,0.8590,0.8599,0.8630, 0.8634,0.8732,0.8806,0.8822,0.8831,0.8860,0.8916,0.8986,0.9030,0.9030, 0.9092,0.9123,0.9188,0.9243,0.9413,0.9417,0.9469,0.9499,0.9503,0.9537, 0.9554,0.9571,0.9623,0.9628,0.9630,0.9661,0.9750,0.9849,0.9991, Overall p-value after applying KStest on 269 p-values = 0.629215 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.