RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-11-10_17:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.81 16.8439 0.535014 2 to 25 15.48 21.1619 0.780869 3 to 26 15.78 15.4234 0.434986 4 to 27 15.78 10.6414 0.125413 5 to 28 15.76 30.0026 0.973674 6 to 29 15.70 26.4705 0.933696 7 to 30 15.97 18.9742 0.669983 8 to 31 15.70 17.1058 0.552779 9 to 32 15.88 11.2802 0.158368 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.728258 Tough bday spacings test for dh-ranFile-2016-11-10_17:31: 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 34 70 94 101 90 40 34 13 8 3 (O-E)^2/E 1.6 0.2 0.1 0.1 0.1 1.8 2.8 0.6 0.2 0.3 0.3 Birthday Spacings: Sum(O-E)^2/E= 8.214, p= 0.392 RESULTS OF GCD FOR dh-ranFile-2016-11-10_17:31 Euclid's algorithm: p-value, steps to gcd: 0.574330 p-value, dist. of gcd's: 0.939533 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-11-10_17:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.059 0.458 0.518 0.295 0.720 0.265 0.637 0.236 Bits 8 to 15---> 0.104 0.653 0.469 0.229 0.323 0.919 0.888 0.559 Bits 16 to 23---> 0.973 0.154 0.165 0.144 0.152 0.108 0.438 0.003 Bits 24 to 31---> 0.261 0.596 0.854 0.455 0.838 0.488 0.184 0.259 KS test for the above 32 p values: 0.833 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-11-10_17:31, p-values for 5 runs: 0.0091, 0.6718, 0.9473, 0.0605, 0.7484 Rank test for binary matrices (31x31) for dh-ranFile-2016-11-10_17:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 219 211.4 0.272 0.272 r= 29 5126 5134.0 0.012 0.284 r= 30 23130 23103.0 0.031 0.316 r= 31 11525 11551.5 0.061 0.377 chi-square = 0.377 with df = 3; p-value = 0.055 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-11-10_17:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 227 211.4 1.148 1.148 r= 30 5137 5134.0 0.002 1.150 r= 31 23208 23103.0 0.477 1.627 r= 32 11428 11551.5 1.321 2.948 chi-square = 2.948 with df = 3; p-value = 0.600 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-11-10_17:31 b-rank test for bits 1 to 8, p=0.88877 b-rank test for bits 2 to 9, p=0.82361 b-rank test for bits 3 to 10, p=0.42787 b-rank test for bits 4 to 11, p=0.26937 b-rank test for bits 5 to 12, p=0.02044 b-rank test for bits 6 to 13, p=0.63294 b-rank test for bits 7 to 14, p=0.20563 b-rank test for bits 8 to 15, p=0.73396 b-rank test for bits 9 to 16, p=0.00751 b-rank test for bits 10 to 17, p=0.55554 b-rank test for bits 11 to 18, p=0.90608 b-rank test for bits 12 to 19, p=0.32474 b-rank test for bits 13 to 20, p=0.59417 b-rank test for bits 14 to 21, p=0.30084 b-rank test for bits 15 to 22, p=0.84752 b-rank test for bits 16 to 23, p=0.93500 b-rank test for bits 17 to 24, p=0.44757 b-rank test for bits 18 to 25, p=0.28213 b-rank test for bits 19 to 26, p=0.35148 b-rank test for bits 20 to 27, p=0.25437 b-rank test for bits 21 to 28, p=0.78141 b-rank test for bits 22 to 29, p=0.34174 b-rank test for bits 23 to 30, p=0.18214 b-rank test for bits 24 to 31, p=0.53627 b-rank test for bits 25 to 32, p=0.81967 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 = 0.877339 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-11-10_17:31 (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 142279 0.86 0.806128 2 142177 0.63 0.734145 3 141260 -1.52 0.064617 4 141936 0.06 0.524843 5 141774 -0.32 0.375929 6 141903 -0.01 0.494100 7 141668 -0.56 0.286426 8 142396 1.14 0.872247 9 141531 -0.88 0.188362 10 141342 -1.33 0.092497 11 142083 0.41 0.657545 12 142483 1.34 0.909934 13 141949 0.09 0.536924 14 142069 0.37 0.645448 15 141870 -0.09 0.463392 16 141939 0.07 0.527634 17 141677 -0.54 0.293624 18 141652 -0.60 0.273841 19 141539 -0.87 0.193449 20 141765 -0.34 0.367976 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-11-10_17:31 Bits used No. missing words z-score p-value 23 to 32 142207 1.0264 0.847660 22 to 31 141988 0.2713 0.606911 21 to 30 141836 -0.2529 0.400187 20 to 29 141994 0.2920 0.614844 19 to 28 141569 -1.1736 0.120287 18 to 27 141681 -0.7873 0.215540 17 to 26 142436 1.8161 0.965323 16 to 25 141948 0.1333 0.553040 15 to 24 142003 0.3230 0.626652 14 to 23 142041 0.4540 0.675098 13 to 22 142018 0.3747 0.646067 12 to 21 142069 0.5506 0.709041 11 to 20 141941 0.1092 0.543481 10 to 19 141817 -0.3184 0.375099 9 to 18 141549 -1.2425 0.107023 8 to 17 141857 -0.1804 0.428400 7 to 16 142023 0.3920 0.652458 6 to 15 141691 -0.7529 0.225766 5 to 14 141858 -0.1770 0.429754 4 to 13 142407 1.7161 0.956928 3 to 12 142404 1.7058 0.955973 2 to 11 142214 1.0506 0.853276 1 to 10 142453 1.8747 0.969585 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-11-10_17:31 Bits used No. missing words z-score p-value 28 to 32 141805 -0.3537 0.361797 27 to 31 141742 -0.5672 0.285282 26 to 30 141247 -2.2452 0.012378 25 to 29 141384 -1.7808 0.037474 24 to 28 141649 -0.8825 0.188760 23 to 27 141317 -2.0079 0.022327 22 to 26 141640 -0.9130 0.180626 21 to 25 141838 -0.2418 0.404469 20 to 24 141736 -0.5876 0.278414 19 to 23 142071 0.5480 0.708166 18 to 22 141831 -0.2655 0.395302 17 to 21 142070 0.5446 0.707001 16 to 20 141815 -0.3198 0.374574 15 to 19 141927 0.0599 0.523882 14 to 18 141653 -0.8689 0.192447 13 to 17 142285 1.2735 0.898572 12 to 16 141861 -0.1638 0.434932 11 to 15 141930 0.0701 0.527930 10 to 14 142192 0.9582 0.831020 9 to 13 141778 -0.4452 0.328093 8 to 12 141800 -0.3706 0.355464 7 to 11 141633 -0.9367 0.174453 6 to 10 142038 0.4362 0.668643 5 to 9 142224 1.0667 0.856941 4 to 8 141356 -1.8757 0.030349 3 to 7 141650 -0.8791 0.189678 2 to 6 141571 -1.1469 0.125715 1 to 5 142077 0.5684 0.715109 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-11-10_17:31 Bits used No. missing words z-score p-value 31 to 32 142028 0.3501 0.636853 30 to 31 141668 -0.7119 0.238267 29 to 30 141674 -0.6942 0.243782 28 to 29 142682 2.2793 0.988674 27 to 28 142210 0.8869 0.812442 26 to 27 141840 -0.2045 0.418976 25 to 26 141293 -1.8181 0.034526 24 to 25 142236 0.9636 0.832384 23 to 24 142917 2.9725 0.998523 22 to 23 142243 0.9843 0.837510 21 to 22 141482 -1.2606 0.103734 20 to 21 142491 1.7158 0.956904 19 to 20 142199 0.8545 0.803582 18 to 19 141965 0.1642 0.565220 17 to 18 142068 0.4681 0.680127 16 to 17 141818 -0.2694 0.393807 15 to 16 141920 0.0315 0.512555 14 to 15 141892 -0.0511 0.479615 13 to 14 141439 -1.3874 0.082659 12 to 13 141572 -0.9951 0.159850 11 to 12 142066 0.4622 0.678014 10 to 11 141872 -0.1101 0.456158 9 to 10 141755 -0.4553 0.324464 8 to 9 141828 -0.2399 0.405199 7 to 8 142006 0.2852 0.612240 6 to 7 142582 1.9843 0.976388 5 to 6 142220 0.9164 0.820280 4 to 5 141688 -0.6529 0.256913 3 to 4 142043 0.3943 0.653323 2 to 3 141524 -1.1367 0.127839 1 to 2 142243 0.9843 0.837510 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-11-10_17:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2455.30 -0.632 0.263640 Test results for specific bytes for dh-ranFile-2016-11-10_17:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2478.58 -0.303 0.380953 2 to 9 2422.41 -1.097 0.136258 3 to 10 2491.66 -0.118 0.453070 4 to 11 2615.59 1.635 0.948947 5 to 12 2540.25 0.569 0.715374 6 to 13 2471.24 -0.407 0.342087 7 to 14 2471.58 -0.402 0.343873 8 to 15 2533.41 0.472 0.681703 9 to 16 2539.24 0.555 0.710525 10 to 17 2584.95 1.201 0.885190 11 to 18 2463.82 -0.512 0.304426 12 to 19 2557.73 0.816 0.792860 13 to 20 2475.16 -0.351 0.362693 14 to 21 2352.94 -2.080 0.018773 15 to 22 2512.32 0.174 0.569169 16 to 23 2559.32 0.839 0.799247 17 to 24 2433.10 -0.946 0.172045 18 to 25 2426.62 -1.038 0.149687 19 to 26 2570.92 1.003 0.842069 20 to 27 2534.70 0.491 0.688194 21 to 28 2503.29 0.047 0.518561 22 to 29 2583.52 1.181 0.881228 23 to 30 2467.35 -0.462 0.322157 24 to 31 2423.59 -1.081 0.139952 25 to 32 2499.32 -0.010 0.496185 CDPARK for dh-ranFile-2016-11-10_17:31: 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 3493 -1.3699 0.085365 3503 -0.9132 0.180558 3504 -0.8676 0.192812 3490 -1.5068 0.065925 3558 1.5982 0.944998 3523 0.0000 0.500000 3520 -0.1370 0.445521 3523 0.0000 0.500000 3511 -0.5479 0.291865 3528 0.2283 0.590298 Square side=100, avg. no. parked=3515.30 sample std.=18.87 p-value of the KSTEST for those 10 p-values: 0.300504 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-11-10_17:31 0.0281,0.4684,0.0976,0.0731,0.5835,0.0607,0.2248,0.4957,0.3208,0.2813, The KS test for those 10 p-values: 0.014177 The 3DSPHERES test for dh-ranFile-2016-11-10_17:31 sample no r^3 equiv. uni. 1 53.223 0.830366 2 17.448 0.441004 3 32.390 0.660289 4 18.333 0.457253 5 22.795 0.532254 6 19.702 0.481451 7 65.098 0.885815 8 27.216 0.596347 9 12.957 0.350722 10 21.926 0.518505 11 12.985 0.351334 12 12.772 0.346712 13 52.891 0.828477 14 52.169 0.824301 15 13.892 0.370658 16 12.398 0.338518 17 16.432 0.421747 18 6.790 0.202537 19 15.911 0.411607 20 19.507 0.478073 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.117321 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-11-10_17:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -0.3 -1.1 -0.3 0.5 0.5 -0.8 -0.3 -0.2 -0.4 0.4 0.0 0.1 -0.2 -0.2 0.4 -2.3 0.6 1.8 0.6 0.6 -1.2 -0.4 0.6 -0.2 0.1 0.8 -1.0 -1.3 0.8 -0.1 -0.6 1.0 0.1 0.8 1.3 1.2 -0.4 0.9 -0.7 -0.6 1.0 -0.1 Chi-square with 42 degrees of freedom:26.725366 z-score=-1.666599, p-value=0.032065 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-11-10_17:31 Test no p-value 1 0.510898 2 0.004054 3 0.026523 4 0.317045 5 0.805246 6 0.179328 7 0.911655 8 0.405517 9 0.091746 10 0.625914 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.248625 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-11-10_17:31: (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 66505 0.39 66777 0.18 3 25000.00 25140 0.78 24829 1.17 4 6666.67 6641 0.10 6707 0.24 5 1388.89 1430 1.22 1387 0.00 6 238.10 237 0.01 259 1.84 7 34.72 42 1.53 34 0.01 8 4.96 4 0.19 6 0.22 p=0.35159 p=0.27839 Number of rngs required: 688538, p-value: 0.562 RESULTS OF CRAPS TEST for dh-ranFile-2016-11-10_17:31 No. of wins: Observed Expected 98387 98585.9 z-score=-0.889, pvalue=0.18689 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66994 66666.7 1.607 1.607 2 37675 37654.3 0.011 1.619 3 26913 26954.7 0.065 1.683 4 19312 19313.5 0.000 1.683 5 13957 13851.4 0.805 2.488 6 9651 9943.5 8.607 11.095 7 7023 7145.0 2.084 13.179 8 5172 5139.1 0.211 13.390 9 3654 3699.9 0.569 13.958 10 2694 2666.3 0.288 14.246 11 1910 1923.3 0.092 14.339 12 1382 1388.7 0.033 14.371 13 988 1003.7 0.246 14.617 14 685 726.1 2.331 16.948 15 576 525.8 4.786 21.734 16 383 381.2 0.009 21.743 17 269 276.5 0.206 21.948 18 178 200.8 2.595 24.544 19 142 146.0 0.109 24.652 20 129 106.2 4.888 29.540 21 313 287.1 2.334 31.874 Chisq= 31.87 for 20 degrees of freedom, p= 0.95534 SUMMARY of craptest p-value for no. of wins: 0.186891 p-value for throws/game: 0.955339 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-11-10_17:31 No. of wins: Observed Expected 98378 98585.9 z-score=-0.930, pvalue=0.17627 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66226 66666.7 2.913 2.913 2 37949 37654.3 2.306 5.219 3 27046 26954.7 0.309 5.528 4 19289 19313.5 0.031 5.559 5 13937 13851.4 0.529 6.088 6 9842 9943.5 1.037 7.125 7 7279 7145.0 2.512 9.637 8 5236 5139.1 1.828 11.465 9 3720 3699.9 0.110 11.574 10 2634 2666.3 0.391 11.966 11 1881 1923.3 0.932 12.897 12 1381 1388.7 0.043 12.940 13 1040 1003.7 1.312 14.252 14 734 726.1 0.085 14.337 15 470 525.8 5.929 20.266 16 339 381.2 4.661 24.928 17 264 276.5 0.569 25.496 18 208 200.8 0.256 25.752 19 166 146.0 2.744 28.496 20 108 106.2 0.030 28.526 21 251 287.1 4.543 33.069 Chisq= 33.07 for 20 degrees of freedom, p= 0.96684 SUMMARY of craptest p-value for no. of wins: 0.176272 p-value for throws/game: 0.966842 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0034,0.0041,0.0075,0.0091,0.0124,0.0142,0.0188,0.0204,0.0223,0.0265, 0.0281,0.0303,0.0321,0.0345,0.0375,0.0550,0.0588,0.0605,0.0607,0.0646, 0.0659,0.0731,0.0827,0.0854,0.0917,0.0925,0.0976,0.1037,0.1041,0.1070, 0.1084,0.1173,0.1203,0.1254,0.1257,0.1278,0.1363,0.1400,0.1441,0.1497, 0.1517,0.1541,0.1584,0.1599,0.1652,0.1720,0.1745,0.1763,0.1793,0.1806, 0.1806,0.1821,0.1839,0.1869,0.1884,0.1888,0.1897,0.1924,0.1928,0.1934, 0.2025,0.2056,0.2155,0.2248,0.2258,0.2292,0.2356,0.2383,0.2438,0.2486, 0.2544,0.2569,0.2594,0.2605,0.2636,0.2648,0.2694,0.2738,0.2784,0.2784, 0.2813,0.2821,0.2853,0.2864,0.2919,0.2936,0.2952,0.3005,0.3008,0.3044, 0.3170,0.3208,0.3222,0.3230,0.3245,0.3247,0.3281,0.3385,0.3417,0.3421, 0.3439,0.3467,0.3507,0.3513,0.3515,0.3516,0.3555,0.3618,0.3627,0.3680, 0.3707,0.3746,0.3751,0.3759,0.3810,0.3921,0.3938,0.3953,0.4002,0.4045, 0.4052,0.4055,0.4116,0.4190,0.4217,0.4279,0.4284,0.4298,0.4349,0.4350, 0.4382,0.4410,0.4455,0.4476,0.4531,0.4547,0.4562,0.4573,0.4584,0.4634, 0.4684,0.4689,0.4781,0.4796,0.4815,0.4879,0.4941,0.4957,0.4962,0.5000, 0.5000,0.5109,0.5126,0.5178,0.5185,0.5186,0.5239,0.5248,0.5276,0.5279, 0.5323,0.5350,0.5363,0.5369,0.5435,0.5528,0.5530,0.5555,0.5591,0.5617, 0.5652,0.5692,0.5743,0.5835,0.5903,0.5942,0.5955,0.5963,0.6003,0.6069, 0.6122,0.6148,0.6259,0.6267,0.6329,0.6369,0.6373,0.6454,0.6461,0.6525, 0.6527,0.6533,0.6575,0.6603,0.6686,0.6700,0.6718,0.6751,0.6780,0.6801, 0.6817,0.6882,0.7070,0.7082,0.7090,0.7105,0.7151,0.7154,0.7197,0.7283, 0.7340,0.7341,0.7484,0.7809,0.7814,0.7929,0.7992,0.8036,0.8052,0.8061, 0.8124,0.8197,0.8203,0.8236,0.8243,0.8285,0.8304,0.8310,0.8324,0.8335, 0.8375,0.8375,0.8377,0.8421,0.8475,0.8477,0.8533,0.8544,0.8569,0.8722, 0.8773,0.8812,0.8852,0.8858,0.8883,0.8888,0.8986,0.9061,0.9099,0.9117, 0.9186,0.9337,0.9350,0.9395,0.9450,0.9473,0.9489,0.9553,0.9560,0.9569, 0.9569,0.9653,0.9668,0.9696,0.9729,0.9737,0.9764,0.9887,0.9985, Overall p-value after applying KStest on 269 p-values = 0.138554 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.