RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-16_04:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.73 22.3765 0.829332 2 to 25 15.63 19.5278 0.700908 3 to 26 15.65 13.9328 0.328149 4 to 27 15.79 12.9775 0.262310 5 to 28 15.65 22.2111 0.823263 6 to 29 15.42 22.8160 0.844662 7 to 30 16.01 14.4442 0.364553 8 to 31 15.90 25.0902 0.907292 9 to 32 15.70 22.0810 0.818376 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.115492 Tough bday spacings test for dh-ranFile-2018-06-16_04:31: 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 33 60 89 105 88 61 30 9 7 5 (O-E)^2/E 1.6 0.4 2.4 0.8 0.5 1.2 1.5 0.0 2.3 0.0 0.2 Birthday Spacings: Sum(O-E)^2/E= 11.022, p= 0.644 RESULTS OF GCD FOR dh-ranFile-2018-06-16_04:31 Euclid's algorithm: p-value, steps to gcd: 0.688182 p-value, dist. of gcd's: 0.415890 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-16_04:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.160 0.605 0.564 0.142 0.577 0.042 0.414 0.841 Bits 8 to 15---> 0.518 0.303 0.994 0.145 0.979 0.456 0.248 0.257 Bits 16 to 23---> 0.506 0.959 0.751 0.237 0.628 0.126 0.918 0.769 Bits 24 to 31---> 0.526 0.817 0.635 0.033 0.234 0.577 0.345 0.108 KS test for the above 32 p values: 0.089 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-16_04:31, p-values for 5 runs: 0.1437, 0.3652, 0.6405, 0.1954, 0.3643 Rank test for binary matrices (31x31) for dh-ranFile-2018-06-16_04:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 162 211.4 11.551 11.551 r= 29 5198 5134.0 0.798 12.349 r= 30 23074 23103.0 0.037 12.385 r= 31 11566 11551.5 0.018 12.403 chi-square = 12.403 with df = 3; p-value = 0.994 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-06-16_04:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 198 211.4 0.852 0.852 r= 30 5136 5134.0 0.001 0.852 r= 31 23251 23103.0 0.947 1.800 r= 32 11415 11551.5 1.614 3.413 chi-square = 3.413 with df = 3; p-value = 0.668 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-06-16_04:31 b-rank test for bits 1 to 8, p=0.23002 b-rank test for bits 2 to 9, p=0.38389 b-rank test for bits 3 to 10, p=0.71161 b-rank test for bits 4 to 11, p=0.70911 b-rank test for bits 5 to 12, p=0.98656 b-rank test for bits 6 to 13, p=0.80963 b-rank test for bits 7 to 14, p=0.81944 b-rank test for bits 8 to 15, p=0.31758 b-rank test for bits 9 to 16, p=0.77098 b-rank test for bits 10 to 17, p=0.19689 b-rank test for bits 11 to 18, p=0.34346 b-rank test for bits 12 to 19, p=0.72754 b-rank test for bits 13 to 20, p=0.63971 b-rank test for bits 14 to 21, p=0.53054 b-rank test for bits 15 to 22, p=0.84105 b-rank test for bits 16 to 23, p=0.73401 b-rank test for bits 17 to 24, p=0.82104 b-rank test for bits 18 to 25, p=0.29200 b-rank test for bits 19 to 26, p=0.22655 b-rank test for bits 20 to 27, p=0.30436 b-rank test for bits 21 to 28, p=0.30063 b-rank test for bits 22 to 29, p=0.24831 b-rank test for bits 23 to 30, p=0.11551 b-rank test for bits 24 to 31, p=0.59774 b-rank test for bits 25 to 32, p=0.52224 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 = 0.470686 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-16_04:31 (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 141639 -0.63 0.263820 2 142407 1.16 0.877541 3 142017 0.25 0.599312 4 142735 1.93 0.973143 5 141888 -0.05 0.480126 6 141765 -0.34 0.367976 7 141309 -1.40 0.080362 8 141593 -0.74 0.229927 9 140579 -3.11 0.000941 10 142409 1.17 0.878486 11 141358 -1.29 0.098846 12 141219 -1.61 0.053381 13 141768 -0.33 0.370621 14 142143 0.55 0.707453 15 141981 0.17 0.566493 16 141501 -0.95 0.170031 17 142092 0.43 0.665237 18 141812 -0.23 0.410054 19 142570 1.54 0.938660 20 142186 0.65 0.740998 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-06-16_04:31 Bits used No. missing words z-score p-value 23 to 32 142041 0.4540 0.675098 22 to 31 142318 1.4092 0.920613 21 to 30 141620 -0.9977 0.159215 20 to 29 142271 1.2471 0.893827 19 to 28 142042 0.4575 0.676338 18 to 27 141369 -1.8632 0.031217 17 to 26 141714 -0.6736 0.250298 16 to 25 142007 0.3368 0.631864 15 to 24 141416 -1.7011 0.044459 14 to 23 142114 0.7058 0.759831 13 to 22 141987 0.2678 0.605584 12 to 21 142059 0.5161 0.697109 11 to 20 141439 -1.6218 0.052420 10 to 19 141927 0.0609 0.524293 9 to 18 141958 0.1678 0.566641 8 to 17 141510 -1.3770 0.084256 7 to 16 141858 -0.1770 0.429754 6 to 15 142034 0.4299 0.666365 5 to 14 142043 0.4609 0.677576 4 to 13 141917 0.0264 0.510550 3 to 12 142075 0.5713 0.716094 2 to 11 141790 -0.4115 0.340359 1 to 10 141788 -0.4184 0.337835 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-06-16_04:31 Bits used No. missing words z-score p-value 28 to 32 142251 1.1582 0.876610 27 to 31 142261 1.1921 0.883389 26 to 30 142208 1.0124 0.844336 25 to 29 141922 0.0429 0.517129 24 to 28 141700 -0.7096 0.238978 23 to 27 141977 0.2294 0.590717 22 to 26 142190 0.9514 0.829305 21 to 25 141930 0.0701 0.527930 20 to 24 141874 -0.1198 0.452336 19 to 23 142051 0.4802 0.684471 18 to 22 141347 -1.9062 0.028312 17 to 21 141982 0.2463 0.597290 16 to 20 142014 0.3548 0.638635 15 to 19 141894 -0.0520 0.479278 14 to 18 141749 -0.5435 0.293396 13 to 17 142092 0.6192 0.732114 12 to 16 142137 0.7718 0.779873 11 to 15 142384 1.6091 0.946197 10 to 14 142107 0.6701 0.748593 9 to 13 142387 1.6192 0.947300 8 to 12 142067 0.5345 0.703493 7 to 11 141558 -1.1909 0.116837 6 to 10 141978 0.2328 0.592034 5 to 9 141634 -0.9333 0.175327 4 to 8 141899 -0.0350 0.486033 3 to 7 142240 1.1209 0.868838 2 to 6 141786 -0.4181 0.337949 1 to 5 142150 0.8158 0.792702 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-06-16_04:31 Bits used No. missing words z-score p-value 31 to 32 141737 -0.5083 0.305605 30 to 31 142046 0.4032 0.656583 29 to 30 141661 -0.7325 0.231921 28 to 29 141917 0.0226 0.509025 27 to 28 142105 0.5772 0.718097 26 to 27 142129 0.6480 0.741506 25 to 26 141646 -0.7768 0.218643 24 to 25 141607 -0.8918 0.186242 23 to 24 142454 1.6067 0.945939 22 to 23 141738 -0.5054 0.306640 21 to 22 141248 -1.9508 0.025539 20 to 21 141289 -1.8299 0.033634 19 to 20 142038 0.3796 0.647863 18 to 19 141374 -1.5791 0.057151 17 to 18 142276 1.0816 0.860290 16 to 17 141190 -2.1219 0.016922 15 to 16 142101 0.5654 0.714099 14 to 15 142145 0.6952 0.756532 13 to 14 142509 1.7689 0.961548 12 to 13 142061 0.4474 0.672708 11 to 12 141983 0.2173 0.586019 10 to 11 142080 0.5035 0.692677 9 to 10 142671 2.2468 0.987674 8 to 9 142175 0.7837 0.783388 7 to 8 141696 -0.6293 0.264579 6 to 7 142029 0.3530 0.637959 5 to 6 141782 -0.3756 0.353605 4 to 5 141588 -0.9479 0.171596 3 to 4 142167 0.7601 0.776399 2 to 3 141510 -1.1780 0.119405 1 to 2 141719 -0.5614 0.287247 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-16_04:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2389.43 -1.564 0.058949 Test results for specific bytes for dh-ranFile-2018-06-16_04:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2501.04 0.015 0.505875 2 to 9 2479.13 -0.295 0.383934 3 to 10 2486.88 -0.186 0.426374 4 to 11 2546.81 0.662 0.746010 5 to 12 2436.41 -0.899 0.184233 6 to 13 2336.70 -2.309 0.010460 7 to 14 2393.05 -1.512 0.065206 8 to 15 2506.93 0.098 0.539031 9 to 16 2376.10 -1.752 0.039870 10 to 17 2339.04 -2.276 0.011413 11 to 18 2428.50 -1.011 0.155980 12 to 19 2497.78 -0.031 0.487452 13 to 20 2584.91 1.201 0.885097 14 to 21 2517.86 0.253 0.599702 15 to 22 2502.19 0.031 0.512333 16 to 23 2362.92 -1.939 0.026278 17 to 24 2539.28 0.556 0.710748 18 to 25 2323.49 -2.496 0.006277 19 to 26 2506.19 0.088 0.534877 20 to 27 2565.30 0.924 0.822129 21 to 28 2487.49 -0.177 0.429784 22 to 29 2531.56 0.446 0.672324 23 to 30 2534.72 0.491 0.688273 24 to 31 2500.02 0.000 0.500104 25 to 32 2506.55 0.093 0.536901 CDPARK for dh-ranFile-2018-06-16_04:31: 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 3534 0.5023 0.692266 3532 0.4110 0.659449 3531 0.3653 0.642555 3508 -0.6849 0.246694 3511 -0.5479 0.291865 3546 1.0502 0.853193 3504 -0.8676 0.192812 3496 -1.2329 0.108811 3512 -0.5023 0.307734 3527 0.1826 0.572463 Square side=100, avg. no. parked=3520.10 sample std.=15.19 p-value of the KSTEST for those 10 p-values: 0.738430 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-16_04:31 0.5584,0.4927,0.1014,0.9900,0.6289,0.9316,0.1873,0.4863,0.7565,0.2752, The KS test for those 10 p-values: 0.875749 The 3DSPHERES test for dh-ranFile-2018-06-16_04:31 sample no r^3 equiv. uni. 1 0.077 0.002559 2 15.534 0.404178 3 3.760 0.117799 4 20.652 0.497628 5 38.058 0.718778 6 61.722 0.872212 7 6.104 0.184090 8 51.836 0.822339 9 26.035 0.580137 10 100.479 0.964891 11 8.025 0.234717 12 1.529 0.049690 13 49.567 0.808379 14 41.796 0.751721 15 12.271 0.335705 16 27.111 0.594927 17 77.489 0.924451 18 20.800 0.500085 19 65.924 0.888917 20 60.417 0.866532 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.530315 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-16_04:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -0.7 -0.8 0.6 0.2 0.9 -1.6 0.4 0.1 -0.1 -1.0 -0.2 -0.4 -0.0 1.1 1.2 -0.3 -0.6 -0.8 0.8 -0.3 0.9 0.5 -1.0 0.5 -1.5 0.6 -0.4 -1.9 2.1 -0.6 0.3 1.5 1.4 -0.5 -0.5 0.0 1.8 -0.4 -1.3 -0.6 0.0 -0.1 Chi-square with 42 degrees of freedom:34.966557 z-score=-0.767412, p-value=0.229315 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-06-16_04:31 Test no p-value 1 0.623303 2 0.090845 3 0.053487 4 0.213412 5 0.420954 6 0.005426 7 0.000691 8 0.157684 9 0.324609 10 0.032356 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000232 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-16_04:31: (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 66565 0.16 66583 0.11 3 25000.00 25196 1.54 25082 0.27 4 6666.67 6559 1.74 6628 0.22 5 1388.89 1417 0.57 1407 0.24 6 238.10 230 0.28 250 0.60 7 34.72 22 4.66 46 3.66 8 4.96 10 5.12 3 0.77 p=0.97098 p=0.56196 Number of rngs required: 687880, p-value: 0.273 RESULTS OF CRAPS TEST for dh-ranFile-2018-06-16_04:31 No. of wins: Observed Expected 98465 98585.9 z-score=-0.541, pvalue=0.29441 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66649 66666.7 0.005 0.005 2 37599 37654.3 0.081 0.086 3 26935 26954.7 0.014 0.100 4 19257 19313.5 0.165 0.265 5 14078 13851.4 3.706 3.972 6 10034 9943.5 0.823 4.795 7 7112 7145.0 0.153 4.947 8 5035 5139.1 2.108 7.055 9 3707 3699.9 0.014 7.069 10 2607 2666.3 1.319 8.387 11 2004 1923.3 3.384 11.771 12 1341 1388.7 1.641 13.412 13 970 1003.7 1.132 14.545 14 736 726.1 0.134 14.679 15 539 525.8 0.330 15.008 16 385 381.2 0.039 15.047 17 270 276.5 0.155 15.202 18 208 200.8 0.256 15.458 19 144 146.0 0.027 15.485 20 101 106.2 0.256 15.741 21 289 287.1 0.012 15.753 Chisq= 15.75 for 20 degrees of freedom, p= 0.26818 SUMMARY of craptest p-value for no. of wins: 0.294409 p-value for throws/game: 0.268182 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-16_04:31 No. of wins: Observed Expected 98652 98585.9 z-score= 0.296, pvalue=0.61632 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66453 66666.7 0.685 0.685 2 37644 37654.3 0.003 0.688 3 27014 26954.7 0.130 0.818 4 19218 19313.5 0.472 1.290 5 13991 13851.4 1.407 2.696 6 10086 9943.5 2.041 4.737 7 7174 7145.0 0.117 4.855 8 5155 5139.1 0.049 4.904 9 3664 3699.9 0.348 5.252 10 2694 2666.3 0.288 5.540 11 1886 1923.3 0.725 6.264 12 1405 1388.7 0.190 6.454 13 1032 1003.7 0.797 7.252 14 740 726.1 0.265 7.516 15 513 525.8 0.313 7.829 16 375 381.2 0.099 7.929 17 276 276.5 0.001 7.930 18 199 200.8 0.017 7.946 19 137 146.0 0.553 8.499 20 118 106.2 1.308 9.807 21 226 287.1 13.008 22.815 Chisq= 22.82 for 20 degrees of freedom, p= 0.70205 SUMMARY of craptest p-value for no. of wins: 0.616317 p-value for throws/game: 0.702048 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0002,0.0007,0.0009,0.0026,0.0054,0.0063,0.0105,0.0114,0.0169,0.0255, 0.0263,0.0283,0.0312,0.0324,0.0334,0.0336,0.0399,0.0421,0.0445,0.0497, 0.0524,0.0534,0.0535,0.0572,0.0589,0.0652,0.0804,0.0843,0.0892,0.0908, 0.0988,0.1014,0.1082,0.1088,0.1155,0.1155,0.1168,0.1178,0.1194,0.1262, 0.1422,0.1437,0.1451,0.1560,0.1577,0.1592,0.1597,0.1700,0.1716,0.1753, 0.1841,0.1842,0.1862,0.1873,0.1928,0.1954,0.1969,0.2134,0.2186,0.2265, 0.2293,0.2299,0.2300,0.2319,0.2340,0.2347,0.2371,0.2390,0.2467,0.2483, 0.2484,0.2503,0.2567,0.2623,0.2638,0.2646,0.2682,0.2732,0.2752,0.2872, 0.2919,0.2920,0.2934,0.2944,0.3006,0.3033,0.3044,0.3056,0.3066,0.3077, 0.3176,0.3246,0.3281,0.3357,0.3378,0.3379,0.3404,0.3435,0.3451,0.3536, 0.3643,0.3646,0.3652,0.3680,0.3706,0.3839,0.3839,0.4042,0.4101,0.4140, 0.4159,0.4210,0.4264,0.4298,0.4298,0.4523,0.4556,0.4707,0.4793,0.4801, 0.4860,0.4863,0.4875,0.4927,0.4976,0.5001,0.5001,0.5059,0.5060,0.5090, 0.5106,0.5123,0.5171,0.5185,0.5222,0.5243,0.5256,0.5279,0.5303,0.5305, 0.5349,0.5369,0.5390,0.5584,0.5620,0.5640,0.5665,0.5666,0.5725,0.5768, 0.5775,0.5801,0.5860,0.5907,0.5920,0.5949,0.5973,0.5977,0.5993,0.5997, 0.6054,0.6056,0.6163,0.6233,0.6283,0.6289,0.6319,0.6354,0.6380,0.6386, 0.6397,0.6405,0.6426,0.6442,0.6479,0.6566,0.6594,0.6652,0.6664,0.6678, 0.6723,0.6727,0.6751,0.6763,0.6776,0.6845,0.6882,0.6883,0.6923,0.6927, 0.6971,0.7009,0.7020,0.7035,0.7075,0.7091,0.7107,0.7116,0.7141,0.7161, 0.7181,0.7188,0.7275,0.7321,0.7340,0.7384,0.7410,0.7415,0.7460,0.7486, 0.7511,0.7517,0.7565,0.7565,0.7598,0.7694,0.7710,0.7764,0.7799,0.7834, 0.7927,0.8084,0.8096,0.8170,0.8184,0.8194,0.8210,0.8221,0.8223,0.8233, 0.8293,0.8293,0.8410,0.8415,0.8443,0.8447,0.8532,0.8603,0.8665,0.8688, 0.8722,0.8757,0.8766,0.8775,0.8785,0.8834,0.8851,0.8889,0.8938,0.9073, 0.9181,0.9206,0.9245,0.9316,0.9387,0.9459,0.9462,0.9473,0.9590,0.9615, 0.9649,0.9710,0.9731,0.9791,0.9866,0.9877,0.9900,0.9936,0.9939, Overall p-value after applying KStest on 269 p-values = 0.444707 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.