RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-07-27_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 15.99 13.2558 0.281097 2 to 25 15.85 19.2680 0.686630 3 to 26 15.59 17.5085 0.579538 4 to 27 15.53 19.6136 0.705532 5 to 28 15.66 26.0995 0.927333 6 to 29 15.87 10.0229 0.097353 7 to 30 15.86 8.9463 0.058070 8 to 31 15.64 19.9744 0.724457 9 to 32 15.50 36.5650 0.996147 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.509720 Tough bday spacings test for dh-ranFile-2015-07-27_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 14 42 69 111 93 60 56 25 17 8 5 (O-E)^2/E 2.6 0.8 0.2 1.8 0.2 4.2 0.3 0.8 0.3 0.3 0.2 Birthday Spacings: Sum(O-E)^2/E= 11.710, p= 0.695 RESULTS OF GCD FOR dh-ranFile-2015-07-27_04:31 Euclid's algorithm: p-value, steps to gcd: 0.969384 p-value, dist. of gcd's: 0.262837 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-07-27_04:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.025 0.092 0.639 0.397 0.355 0.213 0.476 0.003 Bits 8 to 15---> 0.054 0.555 0.155 0.799 0.821 0.686 0.666 0.272 Bits 16 to 23---> 0.468 0.705 0.632 0.957 0.282 0.824 0.860 0.647 Bits 24 to 31---> 0.378 0.190 0.952 0.508 0.160 0.207 0.515 0.210 KS test for the above 32 p values: 0.241 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-07-27_04:31, p-values for 5 runs: 0.8189, 0.1496, 0.7434, 0.8230, 0.8504 Rank test for binary matrices (31x31) for dh-ranFile-2015-07-27_04:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 221 211.4 0.434 0.434 r= 29 5104 5134.0 0.175 0.610 r= 30 23061 23103.0 0.077 0.686 r= 31 11614 11551.5 0.338 1.024 chi-square = 1.024 with df = 3; p-value = 0.205 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-07-27_04:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 208 211.4 0.055 0.055 r= 30 4972 5134.0 5.112 5.168 r= 31 23079 23103.0 0.025 5.193 r= 32 11741 11551.5 3.108 8.301 chi-square = 8.301 with df = 3; p-value = 0.960 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-07-27_04:31 b-rank test for bits 1 to 8, p=0.47617 b-rank test for bits 2 to 9, p=0.31386 b-rank test for bits 3 to 10, p=0.93288 b-rank test for bits 4 to 11, p=0.07394 b-rank test for bits 5 to 12, p=0.72765 b-rank test for bits 6 to 13, p=0.08040 b-rank test for bits 7 to 14, p=0.27117 b-rank test for bits 8 to 15, p=0.43950 b-rank test for bits 9 to 16, p=0.30280 b-rank test for bits 10 to 17, p=0.62892 b-rank test for bits 11 to 18, p=0.11619 b-rank test for bits 12 to 19, p=0.01066 b-rank test for bits 13 to 20, p=0.40032 b-rank test for bits 14 to 21, p=0.38507 b-rank test for bits 15 to 22, p=0.22643 b-rank test for bits 16 to 23, p=0.42836 b-rank test for bits 17 to 24, p=0.64944 b-rank test for bits 18 to 25, p=0.38404 b-rank test for bits 19 to 26, p=0.37833 b-rank test for bits 20 to 27, p=0.91074 b-rank test for bits 21 to 28, p=0.21635 b-rank test for bits 22 to 29, p=0.61330 b-rank test for bits 23 to 30, p=0.93200 b-rank test for bits 24 to 31, p=0.84125 b-rank test for bits 25 to 32, p=0.63608 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 = 0.636243 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-07-27_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 142076 0.39 0.651516 2 141472 -1.02 0.153438 3 142039 0.30 0.619043 4 141010 -2.10 0.017810 5 141825 -0.20 0.421901 6 141906 -0.01 0.496896 7 141566 -0.80 0.211227 8 142354 1.04 0.850586 9 142108 0.46 0.678741 10 141723 -0.44 0.331654 11 140812 -2.56 0.005176 12 142144 0.55 0.708255 13 142706 1.86 0.968655 14 141297 -1.43 0.076261 15 141828 -0.19 0.424645 16 141932 0.05 0.521121 17 142045 0.32 0.624373 18 142273 0.85 0.802253 19 141501 -0.95 0.170031 20 141349 -1.31 0.095236 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-07-27_04:31 Bits used No. missing words z-score p-value 23 to 32 141843 -0.2287 0.409542 22 to 31 141747 -0.5598 0.287822 21 to 30 141729 -0.6218 0.267028 20 to 29 141851 -0.2011 0.420295 19 to 28 141897 -0.0425 0.483043 18 to 27 141698 -0.7287 0.233085 17 to 26 141597 -1.0770 0.140740 16 to 25 142072 0.5609 0.712578 15 to 24 142197 0.9920 0.839393 14 to 23 141881 -0.0977 0.461089 13 to 22 141941 0.1092 0.543481 12 to 21 141667 -0.8356 0.201684 11 to 20 141577 -1.1460 0.125905 10 to 19 141771 -0.4770 0.316681 9 to 18 141326 -2.0115 0.022137 8 to 17 141753 -0.5391 0.294920 7 to 16 142039 0.4471 0.672612 6 to 15 141685 -0.7736 0.219598 5 to 14 142000 0.3127 0.622729 4 to 13 141696 -0.7356 0.230981 3 to 12 142025 0.3989 0.655003 2 to 11 142110 0.6920 0.755521 1 to 10 141236 -2.3218 0.010121 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-07-27_04:31 Bits used No. missing words z-score p-value 28 to 32 142016 0.3616 0.641172 27 to 31 141591 -1.0791 0.140275 26 to 30 141487 -1.4316 0.076125 25 to 29 141862 -0.1604 0.436267 24 to 28 141733 -0.5977 0.275010 23 to 27 141927 0.0599 0.523882 22 to 26 141892 -0.0587 0.476577 21 to 25 141793 -0.3943 0.346665 20 to 24 142322 1.3989 0.919076 19 to 23 142151 0.8192 0.793670 18 to 22 141279 -2.1367 0.016311 17 to 21 141871 -0.1299 0.448310 16 to 20 141892 -0.0587 0.476577 15 to 19 142315 1.3752 0.915458 14 to 18 142530 2.1040 0.982309 13 to 17 141395 -1.7435 0.040624 12 to 16 142328 1.4192 0.922083 11 to 15 141652 -0.8723 0.191521 10 to 14 141899 -0.0350 0.486033 9 to 13 141939 0.1006 0.540057 8 to 12 141524 -1.3062 0.095742 7 to 11 141817 -0.3130 0.377147 6 to 10 142139 0.7785 0.781875 5 to 9 142276 1.2429 0.893057 4 to 8 142319 1.3887 0.917540 3 to 7 141773 -0.4621 0.321992 2 to 6 142511 2.0396 0.979303 1 to 5 141490 -1.4215 0.077592 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-07-27_04:31 Bits used No. missing words z-score p-value 31 to 32 141417 -1.4523 0.073209 30 to 31 141954 0.1318 0.552417 29 to 30 141147 -2.2488 0.012264 28 to 29 141539 -1.0924 0.137325 27 to 28 141969 0.1760 0.569860 26 to 27 141998 0.2616 0.603171 25 to 26 141360 -1.6204 0.052569 24 to 25 142140 0.6804 0.751888 23 to 24 141684 -0.6647 0.253124 22 to 23 142029 0.3530 0.637959 21 to 22 141544 -1.0777 0.140591 20 to 21 141640 -0.7945 0.213457 19 to 20 141221 -2.0305 0.021154 18 to 19 141867 -0.1249 0.450314 17 to 18 142020 0.3265 0.627962 16 to 17 141733 -0.5201 0.301480 15 to 16 141294 -1.8151 0.034752 14 to 15 141873 -0.1072 0.457328 13 to 14 142223 0.9253 0.822590 12 to 13 141676 -0.6883 0.245635 11 to 12 141728 -0.5349 0.296361 10 to 11 142496 1.7306 0.958238 9 to 10 142251 1.0079 0.843243 8 to 9 141808 -0.2989 0.382505 7 to 8 142284 1.1052 0.865468 6 to 7 142305 1.1672 0.878429 5 to 6 142326 1.2291 0.890486 4 to 5 141642 -0.7886 0.215178 3 to 4 141907 -0.0069 0.497258 2 to 3 142140 0.6804 0.751888 1 to 2 142328 1.2350 0.891588 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-07-27_04:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2410.47 -1.266 0.102737 Test results for specific bytes for dh-ranFile-2015-07-27_04:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2426.26 -1.043 0.148502 2 to 9 2680.15 2.548 0.994579 3 to 10 2500.21 0.003 0.501197 4 to 11 2504.16 0.059 0.523457 5 to 12 2609.16 1.544 0.938682 6 to 13 2548.27 0.683 0.752579 7 to 14 2494.93 -0.072 0.471409 8 to 15 2468.03 -0.452 0.325589 9 to 16 2349.02 -2.135 0.016371 10 to 17 2492.17 -0.111 0.455929 11 to 18 2508.70 0.123 0.548957 12 to 19 2444.97 -0.778 0.218196 13 to 20 2596.81 1.369 0.914519 14 to 21 2498.69 -0.019 0.492604 15 to 22 2504.21 0.060 0.523723 16 to 23 2536.45 0.516 0.696901 17 to 24 2458.15 -0.592 0.276965 18 to 25 2374.14 -1.780 0.037549 19 to 26 2475.19 -0.351 0.362827 20 to 27 2589.85 1.271 0.898074 21 to 28 2512.00 0.170 0.567378 22 to 29 2492.24 -0.110 0.456302 23 to 30 2620.14 1.699 0.955350 24 to 31 2539.45 0.558 0.711540 25 to 32 2395.67 -1.475 0.070047 CDPARK for dh-ranFile-2015-07-27_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 3539 0.7306 0.767486 3493 -1.3699 0.085365 3544 0.9589 0.831196 3535 0.5479 0.708135 3528 0.2283 0.590298 3529 0.2740 0.607947 3519 -0.1826 0.427537 3500 -1.0502 0.146807 3521 -0.0913 0.463617 3551 1.2785 0.899470 Square side=100, avg. no. parked=3525.90 sample std.=17.47 p-value of the KSTEST for those 10 p-values: 0.815688 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-07-27_04:31 0.2419,0.0386,0.2539,0.1835,0.4719,0.0408,0.5404,0.0145,0.1300,0.6672, The KS test for those 10 p-values: 0.009577 The 3DSPHERES test for dh-ranFile-2015-07-27_04:31 sample no r^3 equiv. uni. 1 2.288 0.073435 2 31.889 0.654569 3 5.755 0.174549 4 1.246 0.040678 5 17.336 0.438915 6 10.721 0.300473 7 13.322 0.358573 8 6.184 0.186278 9 55.583 0.843196 10 25.078 0.566534 11 53.338 0.831012 12 46.729 0.789368 13 66.127 0.889667 14 12.463 0.339954 15 9.418 0.269441 16 21.279 0.508004 17 29.757 0.629131 18 16.560 0.424205 19 9.206 0.264241 20 101.095 0.965604 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.976772 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-07-27_04:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.1 0.6 0.0 -0.2 -0.5 -1.3 -0.7 -0.5 0.4 -0.2 1.2 1.9 -0.3 -0.2 0.1 -0.3 -0.7 -0.7 -1.2 0.5 1.4 -0.5 0.4 1.1 -0.7 1.1 0.3 -0.9 -2.8 0.1 0.4 0.6 -1.8 0.8 -1.2 0.5 1.8 1.7 -1.3 1.6 0.0 1.8 Chi-square with 42 degrees of freedom:44.831188 z-score=0.308908, p-value=0.646040 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-07-27_04:31 Test no p-value 1 0.212772 2 0.107185 3 0.121119 4 0.089728 5 0.063434 6 0.127118 7 0.004829 8 0.772970 9 0.014650 10 0.242831 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000109 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-07-27_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 66619 0.03 66736 0.07 3 25000.00 25027 0.03 25058 0.13 4 6666.67 6684 0.05 6518 3.32 5 1388.89 1383 0.02 1403 0.14 6 238.10 246 0.26 242 0.06 7 34.72 34 0.01 38 0.31 8 4.96 6 0.22 4 0.19 p=0.00410 p=0.35376 Number of rngs required: 689247, p-value: 0.836 RESULTS OF CRAPS TEST for dh-ranFile-2015-07-27_04:31 No. of wins: Observed Expected 98443 98585.9 z-score=-0.639, pvalue=0.26143 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66158 66666.7 3.881 3.881 2 37737 37654.3 0.182 4.063 3 27289 26954.7 4.145 8.208 4 19466 19313.5 1.205 9.413 5 13928 13851.4 0.423 9.836 6 9873 9943.5 0.500 10.337 7 7009 7145.0 2.590 12.926 8 5202 5139.1 0.771 13.697 9 3714 3699.9 0.054 13.751 10 2639 2666.3 0.279 14.030 11 1945 1923.3 0.244 14.274 12 1387 1388.7 0.002 14.277 13 1044 1003.7 1.617 15.893 14 744 726.1 0.439 16.333 15 490 525.8 2.442 18.775 16 396 381.2 0.579 19.353 17 287 276.5 0.396 19.749 18 198 200.8 0.040 19.789 19 145 146.0 0.007 19.796 20 84 106.2 4.646 24.442 21 265 287.1 1.703 26.145 Chisq= 26.15 for 20 degrees of freedom, p= 0.83893 SUMMARY of craptest p-value for no. of wins: 0.261429 p-value for throws/game: 0.838932 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-07-27_04:31 No. of wins: Observed Expected 98292 98585.9 z-score=-1.314, pvalue=0.09437 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66635 66666.7 0.015 0.015 2 37596 37654.3 0.090 0.105 3 26910 26954.7 0.074 0.180 4 19340 19313.5 0.036 0.216 5 13801 13851.4 0.184 0.400 6 9936 9943.5 0.006 0.405 7 7236 7145.0 1.158 1.564 8 5187 5139.1 0.447 2.011 9 3619 3699.9 1.767 3.778 10 2778 2666.3 4.680 8.458 11 1989 1923.3 2.242 10.700 12 1355 1388.7 0.820 11.520 13 1033 1003.7 0.854 12.374 14 710 726.1 0.359 12.733 15 510 525.8 0.477 13.210 16 371 381.2 0.270 13.480 17 276 276.5 0.001 13.481 18 199 200.8 0.017 13.498 19 131 146.0 1.538 15.036 20 103 106.2 0.097 15.133 21 285 287.1 0.016 15.149 Chisq= 15.15 for 20 degrees of freedom, p= 0.23217 SUMMARY of craptest p-value for no. of wins: 0.094371 p-value for throws/game: 0.232174 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0001,0.0032,0.0041,0.0048,0.0052,0.0096,0.0101,0.0107,0.0123,0.0145, 0.0147,0.0163,0.0164,0.0178,0.0212,0.0221,0.0250,0.0348,0.0375,0.0386, 0.0406,0.0407,0.0408,0.0526,0.0539,0.0581,0.0634,0.0700,0.0732,0.0734, 0.0739,0.0761,0.0763,0.0776,0.0804,0.0854,0.0897,0.0923,0.0944,0.0952, 0.0957,0.0974,0.1027,0.1072,0.1162,0.1211,0.1259,0.1271,0.1300,0.1373, 0.1403,0.1406,0.1407,0.1468,0.1485,0.1496,0.1534,0.1548,0.1597,0.1700, 0.1745,0.1835,0.1863,0.1896,0.1915,0.2017,0.2046,0.2071,0.2095,0.2112, 0.2128,0.2130,0.2135,0.2152,0.2163,0.2182,0.2196,0.2264,0.2310,0.2322, 0.2331,0.2408,0.2419,0.2428,0.2456,0.2531,0.2539,0.2614,0.2628,0.2642, 0.2670,0.2694,0.2712,0.2717,0.2750,0.2770,0.2811,0.2822,0.2878,0.2949, 0.2964,0.3005,0.3015,0.3028,0.3139,0.3167,0.3220,0.3256,0.3317,0.3400, 0.3467,0.3538,0.3549,0.3586,0.3628,0.3771,0.3783,0.3783,0.3825,0.3840, 0.3851,0.3974,0.4003,0.4095,0.4203,0.4219,0.4242,0.4246,0.4275,0.4284, 0.4363,0.4389,0.4395,0.4483,0.4503,0.4559,0.4563,0.4573,0.4611,0.4636, 0.4681,0.4714,0.4719,0.4757,0.4762,0.4766,0.4766,0.4830,0.4860,0.4926, 0.4969,0.4973,0.5012,0.5076,0.5080,0.5097,0.5154,0.5211,0.5235,0.5237, 0.5239,0.5401,0.5404,0.5435,0.5490,0.5524,0.5552,0.5665,0.5674,0.5699, 0.5795,0.5903,0.6032,0.6079,0.6133,0.6190,0.6227,0.6244,0.6280,0.6289, 0.6291,0.6317,0.6361,0.6362,0.6380,0.6386,0.6412,0.6460,0.6466,0.6494, 0.6515,0.6546,0.6550,0.6663,0.6672,0.6726,0.6787,0.6865,0.6866,0.6951, 0.6969,0.7047,0.7055,0.7081,0.7083,0.7115,0.7126,0.7245,0.7276,0.7434, 0.7519,0.7519,0.7526,0.7555,0.7675,0.7730,0.7819,0.7894,0.7937,0.7991, 0.8023,0.8157,0.8189,0.8210,0.8226,0.8230,0.8241,0.8310,0.8312,0.8359, 0.8389,0.8394,0.8413,0.8432,0.8432,0.8504,0.8506,0.8603,0.8655,0.8784, 0.8897,0.8905,0.8916,0.8931,0.8981,0.8995,0.9107,0.9145,0.9155,0.9175, 0.9191,0.9221,0.9273,0.9320,0.9329,0.9387,0.9524,0.9553,0.9571,0.9582, 0.9598,0.9656,0.9687,0.9694,0.9768,0.9793,0.9823,0.9946,0.9961, Overall p-value after applying KStest on 269 p-values = 0.010407 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.