RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-02-02_11:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.97 11.4200 0.166085 2 to 25 15.68 17.8315 0.600458 3 to 26 15.52 22.8870 0.847033 4 to 27 15.82 13.9703 0.330796 5 to 28 15.80 12.0036 0.200083 6 to 29 15.58 22.5391 0.835135 7 to 30 15.76 11.2820 0.158463 8 to 31 15.86 13.2419 0.280151 9 to 32 15.96 16.9867 0.544735 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.675127 Tough bday spacings test for dh-ranFile-2017-02-02_11:31: 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 10 29 86 92 83 76 62 36 16 4 6 (O-E)^2/E 0.1 1.6 2.2 0.3 2.2 0.1 1.9 1.3 0.1 1.0 0.9 Birthday Spacings: Sum(O-E)^2/E= 11.702, p= 0.694 RESULTS OF GCD FOR dh-ranFile-2017-02-02_11:31 Euclid's algorithm: p-value, steps to gcd: 0.872077 p-value, dist. of gcd's: 0.186432 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-02-02_11:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.301 0.201 0.806 0.273 0.882 0.678 0.309 0.699 Bits 8 to 15---> 0.426 0.340 0.810 0.856 0.041 0.670 0.187 0.544 Bits 16 to 23---> 0.058 0.002 0.677 0.904 0.581 0.289 0.797 0.244 Bits 24 to 31---> 0.194 0.821 0.662 0.193 0.510 0.625 0.907 0.502 KS test for the above 32 p values: 0.160 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-02-02_11:31, p-values for 5 runs: 0.7946, 0.5383, 0.1242, 0.4157, 0.5317 Rank test for binary matrices (31x31) for dh-ranFile-2017-02-02_11:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 187 211.4 2.820 2.820 r= 29 5182 5134.0 0.449 3.269 r= 30 23027 23103.0 0.250 3.519 r= 31 11604 11551.5 0.238 3.757 chi-square = 3.757 with df = 3; p-value = 0.711 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2017-02-02_11:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 199 211.4 0.729 0.729 r= 30 5159 5134.0 0.122 0.851 r= 31 23074 23103.0 0.037 0.888 r= 32 11568 11551.5 0.024 0.911 chi-square = 0.911 with df = 3; p-value = 0.177 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2017-02-02_11:31 b-rank test for bits 1 to 8, p=0.66769 b-rank test for bits 2 to 9, p=0.66235 b-rank test for bits 3 to 10, p=0.70637 b-rank test for bits 4 to 11, p=0.64847 b-rank test for bits 5 to 12, p=0.43901 b-rank test for bits 6 to 13, p=0.12254 b-rank test for bits 7 to 14, p=0.55744 b-rank test for bits 8 to 15, p=0.04854 b-rank test for bits 9 to 16, p=0.61967 b-rank test for bits 10 to 17, p=0.79421 b-rank test for bits 11 to 18, p=0.18378 b-rank test for bits 12 to 19, p=0.12496 b-rank test for bits 13 to 20, p=0.32281 b-rank test for bits 14 to 21, p=0.17271 b-rank test for bits 15 to 22, p=0.19032 b-rank test for bits 16 to 23, p=0.64133 b-rank test for bits 17 to 24, p=0.80888 b-rank test for bits 18 to 25, p=0.43056 b-rank test for bits 19 to 26, p=0.49640 b-rank test for bits 20 to 27, p=0.21491 b-rank test for bits 21 to 28, p=0.29469 b-rank test for bits 22 to 29, p=0.65969 b-rank test for bits 23 to 30, p=0.62831 b-rank test for bits 24 to 31, p=0.98717 b-rank test for bits 25 to 32, p=0.79493 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 = 0.624034 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-02-02_11:31 (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 142125 0.50 0.692835 2 142319 0.96 0.830760 3 142344 1.02 0.845086 4 142463 1.29 0.902102 5 141473 -1.02 0.153992 6 142538 1.47 0.929064 7 140784 -2.63 0.004278 8 141960 0.12 0.547120 9 142009 0.23 0.592070 10 141415 -1.15 0.124050 11 141554 -0.83 0.203210 12 142235 0.76 0.776645 13 141898 -0.03 0.489440 14 142154 0.57 0.716223 15 142077 0.39 0.652379 16 141292 -1.44 0.074600 17 142481 1.34 0.909173 18 142218 0.72 0.764604 19 141750 -0.37 0.354847 20 141782 -0.30 0.383042 ---------------------------------------------------------------- OPSO test for dh-ranFile-2017-02-02_11:31 Bits used No. missing words z-score p-value 23 to 32 142018 0.3747 0.646067 22 to 31 142007 0.3368 0.631864 21 to 30 141735 -0.6011 0.273874 20 to 29 141954 0.1540 0.561209 19 to 28 142120 0.7264 0.766218 18 to 27 142321 1.4196 0.922131 17 to 26 142065 0.5368 0.704295 16 to 25 141810 -0.3425 0.365981 15 to 24 141976 0.2299 0.590914 14 to 23 141527 -1.3184 0.093688 13 to 22 141957 0.1644 0.565284 12 to 21 142237 1.1299 0.870740 11 to 20 142416 1.7471 0.959693 10 to 19 141689 -0.7598 0.223699 9 to 18 142085 0.6058 0.727663 8 to 17 141610 -1.0322 0.150996 7 to 16 141895 -0.0494 0.480295 6 to 15 142204 1.0161 0.845210 5 to 14 142678 2.6506 0.995982 4 to 13 142334 1.4644 0.928455 3 to 12 141370 -1.8598 0.031460 2 to 11 141841 -0.2356 0.406864 1 to 10 141920 0.0368 0.514675 ----------------------------------------------------------------- OQSO test for dh-ranFile-2017-02-02_11:31 Bits used No. missing words z-score p-value 28 to 32 142622 2.4158 0.992150 27 to 31 142412 1.7040 0.955806 26 to 30 141854 -0.1876 0.425611 25 to 29 141734 -0.5943 0.276143 24 to 28 141770 -0.4723 0.318355 23 to 27 141807 -0.3469 0.364340 22 to 26 141781 -0.4350 0.331775 21 to 25 142125 0.7311 0.767636 20 to 24 141612 -1.0079 0.156752 19 to 23 141965 0.1887 0.574841 18 to 22 141385 -1.7774 0.037752 17 to 21 141693 -0.7333 0.231681 16 to 20 142069 0.5413 0.705834 15 to 19 141789 -0.4079 0.341674 14 to 18 142257 1.1785 0.880710 13 to 17 142133 0.7582 0.775835 12 to 16 141979 0.2362 0.593349 11 to 15 141897 -0.0418 0.483330 10 to 14 142130 0.7480 0.772780 9 to 13 141447 -1.5672 0.058532 8 to 12 141895 -0.0486 0.480629 7 to 11 142302 1.3311 0.908419 6 to 10 142047 0.4667 0.679635 5 to 9 141777 -0.4486 0.326869 4 to 8 141324 -1.9842 0.023618 3 to 7 141704 -0.6960 0.243204 2 to 6 142001 0.3107 0.622003 1 to 5 141672 -0.8045 0.210552 ----------------------------------------------------------------- DNA test for dh-ranFile-2017-02-02_11:31 Bits used No. missing words z-score p-value 31 to 32 141551 -1.0570 0.145251 30 to 31 142101 0.5654 0.714099 29 to 30 141758 -0.4464 0.327654 28 to 29 141877 -0.0954 0.462011 27 to 28 141767 -0.4199 0.337297 26 to 27 141118 -2.3343 0.009790 25 to 26 142253 1.0138 0.844655 24 to 25 141605 -0.8977 0.184665 23 to 24 142221 0.9194 0.821052 22 to 23 141780 -0.3815 0.351415 21 to 22 141908 -0.0039 0.498435 20 to 21 141138 -2.2753 0.011444 19 to 20 141389 -1.5349 0.062405 18 to 19 141743 -0.4906 0.311837 17 to 18 142371 1.3619 0.913379 16 to 17 141690 -0.6470 0.258819 15 to 16 141671 -0.7030 0.241016 14 to 15 141971 0.1819 0.572176 13 to 14 142399 1.4445 0.925694 12 to 13 141581 -0.9685 0.166391 11 to 12 141760 -0.4405 0.329787 10 to 11 141723 -0.5496 0.291281 9 to 10 141515 -1.1632 0.122371 8 to 9 141963 0.1583 0.562897 7 to 8 141763 -0.4317 0.332997 6 to 7 142162 0.7453 0.771967 5 to 6 141745 -0.4847 0.313927 4 to 5 142099 0.5595 0.712089 3 to 4 141386 -1.5437 0.061325 2 to 3 141921 0.0344 0.513731 1 to 2 141786 -0.3638 0.358002 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2017-02-02_11:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2531.89 0.451 0.674025 Test results for specific bytes for dh-ranFile-2017-02-02_11:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2572.14 1.020 0.846183 2 to 9 2542.12 0.596 0.724278 3 to 10 2442.34 -0.816 0.207393 4 to 11 2491.85 -0.115 0.454133 5 to 12 2472.52 -0.389 0.348776 6 to 13 2612.21 1.587 0.943727 7 to 14 2465.17 -0.493 0.311163 8 to 15 2567.43 0.954 0.829858 9 to 16 2562.02 0.877 0.809787 10 to 17 2499.73 -0.004 0.498484 11 to 18 2566.72 0.944 0.827315 12 to 19 2587.38 1.236 0.891713 13 to 20 2387.00 -1.598 0.055011 14 to 21 2497.46 -0.036 0.485663 15 to 22 2471.04 -0.410 0.341076 16 to 23 2457.72 -0.598 0.274924 17 to 24 2539.71 0.562 0.712823 18 to 25 2510.92 0.154 0.561352 19 to 26 2480.78 -0.272 0.392857 20 to 27 2435.69 -0.910 0.181537 21 to 28 2611.25 1.573 0.942174 22 to 29 2566.32 0.938 0.825858 23 to 30 2505.85 0.083 0.532961 24 to 31 2432.32 -0.957 0.169243 25 to 32 2393.27 -1.509 0.065603 CDPARK for dh-ranFile-2017-02-02_11:31: 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 3488 -1.5982 0.055002 3508 -0.6849 0.246694 3523 0.0000 0.500000 3505 -0.8219 0.205562 3538 0.6849 0.753306 3503 -0.9132 0.180558 3505 -0.8219 0.205562 3542 0.8676 0.807188 3527 0.1826 0.572463 Square side=100, avg. no. parked=3517.30 sample std.=17.02 p-value of the KSTEST for those 10 p-values: 0.572446 Results for the MINIMUM DISTANCE test for dh-ranFile-2017-02-02_11:31 0.2218,0.9256,0.0289,0.7537,0.8533,0.7910,0.0564,0.7835,0.8396,0.2087, The KS test for those 10 p-values: 0.284312 The 3DSPHERES test for dh-ranFile-2017-02-02_11:31 sample no r^3 equiv. uni. 1 86.778 0.944568 2 15.482 0.403130 3 6.156 0.185511 4 17.524 0.442403 5 40.868 0.743918 6 0.418 0.013846 7 1.647 0.053413 8 81.832 0.934632 9 2.203 0.070791 10 36.641 0.705171 11 7.603 0.223877 12 6.303 0.189484 13 7.600 0.223783 14 31.972 0.655523 15 9.852 0.279914 16 8.947 0.257873 17 8.792 0.254037 18 62.708 0.876346 19 7.504 0.221314 20 13.134 0.354549 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.146364 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-02-02_11:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 1.3 0.6 1.4 0.7 0.1 -0.1 -1.5 0.3 0.4 -0.8 2.3 1.2 1.3 -1.5 0.8 -0.2 -0.8 -0.4 0.5 -1.2 0.3 -1.0 -0.5 0.3 0.3 -1.0 -0.3 -0.2 0.6 1.3 -0.3 -0.0 1.1 -1.0 -1.9 1.7 0.8 -1.2 2.1 -1.3 0.0 -1.1 Chi-square with 42 degrees of freedom:45.089750 z-score=0.337119, p-value=0.656002 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2017-02-02_11:31 Test no p-value 1 0.046558 2 0.062313 3 0.088809 4 0.011183 5 0.016346 6 0.007731 7 0.287134 8 0.046464 9 0.175273 10 0.909068 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000007 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-02-02_11:31: (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 66782 0.20 66796 0.25 3 25000.00 24784 1.87 24913 0.30 4 6666.67 6752 1.09 6634 0.16 5 1388.89 1371 0.23 1381 0.04 6 238.10 266 3.27 227 0.52 7 34.72 39 0.53 38 0.31 8 4.96 5 0.00 10 5.12 p=0.69608 p=0.65118 Number of rngs required: 688343, p-value: 0.472 RESULTS OF CRAPS TEST for dh-ranFile-2017-02-02_11:31 No. of wins: Observed Expected 98679 98585.9 z-score= 0.417, pvalue=0.66151 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66693 66666.7 0.010 0.010 2 37359 37654.3 2.316 2.327 3 27028 26954.7 0.199 2.526 4 19569 19313.5 3.381 5.907 5 13730 13851.4 1.064 6.971 6 9962 9943.5 0.034 7.005 7 7056 7145.0 1.109 8.115 8 5185 5139.1 0.410 8.525 9 3639 3699.9 1.001 9.526 10 2685 2666.3 0.131 9.658 11 1963 1923.3 0.818 10.476 12 1449 1388.7 2.615 13.091 13 1040 1003.7 1.312 14.402 14 716 726.1 0.142 14.544 15 503 525.8 0.992 15.536 16 378 381.2 0.026 15.562 17 310 276.5 4.049 19.610 18 191 200.8 0.481 20.091 19 129 146.0 1.976 22.067 20 109 106.2 0.073 22.140 21 306 287.1 1.242 23.383 Chisq= 23.38 for 20 degrees of freedom, p= 0.72961 SUMMARY of craptest p-value for no. of wins: 0.661508 p-value for throws/game: 0.729607 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2017-02-02_11:31 No. of wins: Observed Expected 98796 98585.9 z-score= 0.940, pvalue=0.82636 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66851 66666.7 0.510 0.510 2 37328 37654.3 2.828 3.338 3 27050 26954.7 0.337 3.674 4 19436 19313.5 0.777 4.452 5 13681 13851.4 2.097 6.549 6 9892 9943.5 0.267 6.816 7 7230 7145.0 1.011 7.826 8 5199 5139.1 0.699 8.525 9 3700 3699.9 0.000 8.525 10 2685 2666.3 0.131 8.656 11 1916 1923.3 0.028 8.684 12 1418 1388.7 0.616 9.301 13 996 1003.7 0.059 9.360 14 643 726.1 9.519 18.879 15 523 525.8 0.015 18.895 16 388 381.2 0.123 19.018 17 295 276.5 1.232 20.250 18 210 200.8 0.419 20.669 19 155 146.0 0.557 21.226 20 98 106.2 0.635 21.861 21 306 287.1 1.242 23.103 Chisq= 23.10 for 20 degrees of freedom, p= 0.71625 SUMMARY of craptest p-value for no. of wins: 0.826359 p-value for throws/game: 0.716250 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0000,0.0022,0.0043,0.0077,0.0098,0.0112,0.0114,0.0138,0.0163,0.0236, 0.0289,0.0315,0.0378,0.0413,0.0465,0.0466,0.0485,0.0534,0.0550,0.0550, 0.0564,0.0579,0.0585,0.0613,0.0623,0.0624,0.0656,0.0708,0.0746,0.0888, 0.0937,0.1224,0.1225,0.1241,0.1242,0.1250,0.1453,0.1464,0.1510,0.1540, 0.1568,0.1585,0.1602,0.1661,0.1664,0.1692,0.1727,0.1753,0.1772,0.1806, 0.1815,0.1838,0.1847,0.1855,0.1864,0.1869,0.1895,0.1903,0.1933,0.1943, 0.2001,0.2012,0.2032,0.2056,0.2056,0.2074,0.2087,0.2106,0.2149,0.2213, 0.2218,0.2237,0.2238,0.2239,0.2317,0.2410,0.2432,0.2438,0.2467,0.2540, 0.2579,0.2588,0.2730,0.2739,0.2749,0.2761,0.2799,0.2802,0.2843,0.2871, 0.2890,0.2913,0.2947,0.3007,0.3094,0.3112,0.3118,0.3139,0.3184,0.3228, 0.3269,0.3277,0.3298,0.3308,0.3318,0.3330,0.3373,0.3403,0.3411,0.3417, 0.3488,0.3514,0.3545,0.3548,0.3580,0.3643,0.3660,0.3830,0.3929,0.4031, 0.4069,0.4157,0.4256,0.4256,0.4306,0.4390,0.4424,0.4541,0.4620,0.4725, 0.4803,0.4806,0.4833,0.4857,0.4894,0.4964,0.4984,0.4985,0.5000,0.5021, 0.5100,0.5137,0.5147,0.5317,0.5330,0.5383,0.5440,0.5447,0.5471,0.5574, 0.5612,0.5614,0.5629,0.5653,0.5722,0.5724,0.5725,0.5748,0.5807,0.5909, 0.5921,0.5933,0.6005,0.6197,0.6220,0.6240,0.6247,0.6283,0.6319,0.6413, 0.6461,0.6485,0.6512,0.6524,0.6555,0.6560,0.6597,0.6615,0.6623,0.6624, 0.6677,0.6702,0.6740,0.6751,0.6770,0.6782,0.6796,0.6923,0.6928,0.6945, 0.6961,0.6992,0.7043,0.7052,0.7058,0.7064,0.7111,0.7121,0.7128,0.7141, 0.7162,0.7162,0.7243,0.7277,0.7296,0.7439,0.7533,0.7537,0.7646,0.7662, 0.7676,0.7720,0.7728,0.7758,0.7766,0.7835,0.7910,0.7942,0.7946,0.7949, 0.7975,0.8061,0.8072,0.8089,0.8098,0.8098,0.8211,0.8212,0.8259,0.8264, 0.8273,0.8299,0.8308,0.8351,0.8396,0.8447,0.8451,0.8452,0.8462,0.8470, 0.8533,0.8564,0.8707,0.8721,0.8763,0.8807,0.8815,0.8917,0.9021,0.9040, 0.9069,0.9084,0.9091,0.9092,0.9134,0.9221,0.9256,0.9257,0.9285,0.9291, 0.9346,0.9422,0.9437,0.9446,0.9558,0.9597,0.9872,0.9922,0.9960, Overall p-value after applying KStest on 269 p-values = 0.165325 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.