RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-08-15_13:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.75 17.5469 0.582050 2 to 25 15.48 26.1359 0.927980 3 to 26 15.66 19.1766 0.681509 4 to 27 15.77 24.2757 0.887864 5 to 28 15.60 15.9381 0.471769 6 to 29 15.61 23.0693 0.852992 7 to 30 16.00 11.0803 0.147643 8 to 31 15.81 13.1861 0.276359 9 to 32 15.93 28.2676 0.958093 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.218469 Tough bday spacings test for dh-ranFile-2016-08-15_13:31: 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 11 28 85 109 95 77 32 34 21 4 4 (O-E)^2/E 0.4 2.0 1.9 1.3 0.1 0.0 7.8 0.6 2.5 1.0 0.0 Birthday Spacings: Sum(O-E)^2/E= 17.588, p= 0.938 RESULTS OF GCD FOR dh-ranFile-2016-08-15_13:31 Euclid's algorithm: p-value, steps to gcd: 0.995318 p-value, dist. of gcd's: 0.266145 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-08-15_13:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.772 0.668 0.621 0.804 0.775 0.653 0.509 0.063 Bits 8 to 15---> 0.605 0.884 0.557 0.141 0.324 0.315 0.516 0.959 Bits 16 to 23---> 0.435 0.917 0.592 0.360 0.325 0.582 0.466 0.920 Bits 24 to 31---> 0.837 0.159 0.468 0.028 0.048 0.269 0.174 0.318 KS test for the above 32 p values: 0.026 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-08-15_13:31, p-values for 5 runs: 0.9299, 0.8443, 0.7543, 0.2488, 0.2630 Rank test for binary matrices (31x31) for dh-ranFile-2016-08-15_13:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 216 211.4 0.099 0.099 r= 29 5189 5134.0 0.589 0.688 r= 30 22853 23103.0 2.706 3.395 r= 31 11742 11551.5 3.141 6.535 chi-square = 6.535 with df = 3; p-value = 0.912 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-08-15_13:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 201 211.4 0.513 0.513 r= 30 5120 5134.0 0.038 0.552 r= 31 23036 23103.0 0.195 0.746 r= 32 11643 11551.5 0.724 1.471 chi-square = 1.471 with df = 3; p-value = 0.311 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-08-15_13:31 b-rank test for bits 1 to 8, p=0.84527 b-rank test for bits 2 to 9, p=0.96709 b-rank test for bits 3 to 10, p=0.96346 b-rank test for bits 4 to 11, p=0.20739 b-rank test for bits 5 to 12, p=0.41355 b-rank test for bits 6 to 13, p=0.25981 b-rank test for bits 7 to 14, p=0.37807 b-rank test for bits 8 to 15, p=0.01679 b-rank test for bits 9 to 16, p=0.95342 b-rank test for bits 10 to 17, p=0.31695 b-rank test for bits 11 to 18, p=0.26344 b-rank test for bits 12 to 19, p=0.46880 b-rank test for bits 13 to 20, p=0.46107 b-rank test for bits 14 to 21, p=0.74687 b-rank test for bits 15 to 22, p=0.06244 b-rank test for bits 16 to 23, p=0.72732 b-rank test for bits 17 to 24, p=0.41326 b-rank test for bits 18 to 25, p=0.45961 b-rank test for bits 19 to 26, p=0.61893 b-rank test for bits 20 to 27, p=0.77638 b-rank test for bits 21 to 28, p=0.34485 b-rank test for bits 22 to 29, p=0.76032 b-rank test for bits 23 to 30, p=0.12533 b-rank test for bits 24 to 31, p=0.20651 b-rank test for bits 25 to 32, p=0.45617 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 = 0.873747 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-08-15_13:31 (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 142269 0.84 0.799644 2 142509 1.40 0.919408 3 141814 -0.22 0.411871 4 141768 -0.33 0.370621 5 142421 1.20 0.884052 6 142113 0.48 0.682915 7 141998 0.21 0.582063 8 142285 0.88 0.809956 9 141578 -0.77 0.219425 10 142594 1.60 0.945167 11 142575 1.56 0.940063 12 142188 0.65 0.742508 13 141724 -0.43 0.332502 14 141632 -0.65 0.258503 15 141291 -1.44 0.074272 16 141535 -0.87 0.190895 17 142022 0.26 0.603820 18 141977 0.16 0.562814 19 142529 1.45 0.926167 20 141549 -0.84 0.199924 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-08-15_13:31 Bits used No. missing words z-score p-value 23 to 32 141882 -0.0942 0.462459 22 to 31 141855 -0.1873 0.425695 21 to 30 141711 -0.6839 0.247020 20 to 29 141883 -0.0908 0.463829 19 to 28 141843 -0.2287 0.409542 18 to 27 141957 0.1644 0.565284 17 to 26 142301 1.3506 0.911586 16 to 25 142017 0.3713 0.644784 15 to 24 141674 -0.8115 0.208544 14 to 23 142006 0.3333 0.630563 13 to 22 141644 -0.9149 0.180114 12 to 21 141709 -0.6908 0.244848 11 to 20 141694 -0.7425 0.228887 10 to 19 141544 -1.2598 0.103878 9 to 18 141829 -0.2770 0.390890 8 to 17 141840 -0.2391 0.405526 7 to 16 141656 -0.8736 0.191181 6 to 15 141672 -0.8184 0.206570 5 to 14 141872 -0.1287 0.448788 4 to 13 141882 -0.0942 0.462459 3 to 12 141900 -0.0322 0.487167 2 to 11 141750 -0.5494 0.291361 1 to 10 142131 0.7644 0.777679 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-08-15_13:31 Bits used No. missing words z-score p-value 28 to 32 141954 0.1514 0.560179 27 to 31 141640 -0.9130 0.180626 26 to 30 141797 -0.3808 0.351683 25 to 29 141832 -0.2621 0.396609 24 to 28 141579 -1.1198 0.131407 23 to 27 141470 -1.4893 0.068210 22 to 26 142034 0.4226 0.663710 21 to 25 141970 0.2057 0.581472 20 to 24 141732 -0.6011 0.273881 19 to 23 142242 1.1277 0.870276 18 to 22 141735 -0.5909 0.277277 17 to 21 141970 0.2057 0.581472 16 to 20 142101 0.6497 0.742066 15 to 19 142370 1.5616 0.940808 14 to 18 141431 -1.6215 0.052460 13 to 17 142102 0.6531 0.743160 12 to 16 141661 -0.8418 0.199951 11 to 15 142313 1.3684 0.914402 10 to 14 142090 0.6124 0.729877 9 to 13 141813 -0.3265 0.372007 8 to 12 142003 0.3175 0.624578 7 to 11 141975 0.2226 0.588081 6 to 10 141729 -0.6113 0.270504 5 to 9 142054 0.4904 0.688077 4 to 8 142456 1.8531 0.968067 3 to 7 141576 -1.1299 0.129252 2 to 6 142155 0.8328 0.797516 1 to 5 142153 0.8260 0.795598 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-08-15_13:31 Bits used No. missing words z-score p-value 31 to 32 142173 0.7778 0.781653 30 to 31 141929 0.0580 0.523135 29 to 30 141933 0.0698 0.527833 28 to 29 142189 0.8250 0.795310 27 to 28 141882 -0.0806 0.467872 26 to 27 141995 0.2527 0.599755 25 to 26 141426 -1.4258 0.076970 24 to 25 141942 0.0964 0.538387 23 to 24 141452 -1.3491 0.088660 22 to 23 142111 0.5949 0.724044 21 to 22 141775 -0.3963 0.345959 20 to 21 142156 0.7276 0.766583 19 to 20 141849 -0.1780 0.429375 18 to 19 141641 -0.7915 0.214316 17 to 18 141647 -0.7738 0.219514 16 to 17 141841 -0.2016 0.420129 15 to 16 141508 -1.1839 0.118233 14 to 15 141960 0.1495 0.559408 13 to 14 142279 1.0905 0.862247 12 to 13 141924 0.0433 0.517259 11 to 12 141797 -0.3314 0.370187 10 to 11 141137 -2.2783 0.011356 9 to 10 141981 0.2114 0.583719 8 to 9 141757 -0.4494 0.326589 7 to 8 142819 2.6834 0.996356 6 to 7 142498 1.7365 0.958761 5 to 6 141251 -1.9420 0.026070 4 to 5 141752 -0.4641 0.321288 3 to 4 141958 0.1436 0.557080 2 to 3 141870 -0.1160 0.453819 1 to 2 142301 1.1554 0.876030 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-08-15_13:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2656.69 2.216 0.986650 Test results for specific bytes for dh-ranFile-2016-08-15_13:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2500.99 0.014 0.505600 2 to 9 2484.73 -0.216 0.414498 3 to 10 2493.92 -0.086 0.465753 4 to 11 2501.44 0.020 0.508110 5 to 12 2417.39 -1.168 0.121342 6 to 13 2399.08 -1.427 0.076755 7 to 14 2367.43 -1.875 0.030405 8 to 15 2517.05 0.241 0.595272 9 to 16 2487.62 -0.175 0.430502 10 to 17 2523.82 0.337 0.631868 11 to 18 2458.68 -0.584 0.279494 12 to 19 2533.88 0.479 0.684080 13 to 20 2448.80 -0.724 0.234508 14 to 21 2497.96 -0.029 0.488478 15 to 22 2559.67 0.844 0.800609 16 to 23 2588.63 1.253 0.894978 17 to 24 2466.34 -0.476 0.317019 18 to 25 2440.20 -0.846 0.198853 19 to 26 2479.97 -0.283 0.388470 20 to 27 2544.91 0.635 0.737331 21 to 28 2313.57 -2.636 0.004189 22 to 29 2530.04 0.425 0.664528 23 to 30 2468.88 -0.440 0.329953 24 to 31 2490.99 -0.127 0.449304 25 to 32 2615.46 1.633 0.948745 CDPARK for dh-ranFile-2016-08-15_13:31: 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 3557 1.5525 0.939730 3542 0.8676 0.807188 3535 0.5479 0.708135 3530 0.3196 0.625377 3554 1.4155 0.921543 3531 0.3653 0.642555 3513 -0.4566 0.323972 3518 -0.2283 0.409702 3564 1.8721 0.969407 3526 0.1370 0.554479 Square side=100, avg. no. parked=3537.00 sample std.=16.09 p-value of the KSTEST for those 10 p-values: 0.060737 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-08-15_13:31 0.9033,0.8834,0.7671,0.8023,0.7188,0.2444,0.0730,0.5569,0.5886,0.6483, The KS test for those 10 p-values: 0.276527 The 3DSPHERES test for dh-ranFile-2016-08-15_13:31 sample no r^3 equiv. uni. 1 14.320 0.379561 2 8.833 0.255037 3 12.785 0.346982 4 13.563 0.363718 5 12.702 0.345190 6 5.797 0.175719 7 1.463 0.047586 8 24.099 0.552156 9 3.387 0.106747 10 8.330 0.242439 11 54.389 0.836829 12 46.356 0.786728 13 0.756 0.024873 14 0.644 0.021230 15 31.912 0.654840 16 17.339 0.438955 17 6.845 0.204017 18 11.113 0.309572 19 11.688 0.322668 20 26.785 0.590503 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.029045 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-08-15_13:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 -1.2 1.8 -0.8 0.1 -0.2 0.7 1.0 0.1 0.4 -0.6 -0.4 -0.9 -1.5 -0.0 0.1 -0.5 -1.6 2.3 1.8 -1.6 0.3 1.3 0.5 -0.8 1.2 1.7 -1.3 -1.1 -0.5 -0.3 0.7 0.6 0.3 0.2 -0.3 -0.5 0.8 0.9 -1.3 -0.6 -1.0 -0.1 Chi-square with 42 degrees of freedom:43.099439 z-score=0.119959, p-value=0.575969 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-08-15_13:31 Test no p-value 1 0.810481 2 0.524774 3 0.120727 4 0.257862 5 0.773938 6 0.283659 7 0.507053 8 0.043033 9 0.097641 10 0.008897 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.108054 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-08-15_13:31: (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 66640 0.01 66874 0.64 3 25000.00 25124 0.62 24867 0.71 4 6666.67 6618 0.36 6604 0.59 5 1388.89 1355 0.83 1372 0.21 6 238.10 222 1.09 247 0.33 7 34.72 31 0.40 31 0.40 8 4.96 9 3.29 4 0.19 p=0.63909 p=0.19926 Number of rngs required: 690788, p-value: 0.998 RESULTS OF CRAPS TEST for dh-ranFile-2016-08-15_13:31 No. of wins: Observed Expected 98376 98585.9 z-score=-0.939, pvalue=0.17397 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66677 66666.7 0.002 0.002 2 37639 37654.3 0.006 0.008 3 26905 26954.7 0.092 0.100 4 19241 19313.5 0.272 0.371 5 13867 13851.4 0.018 0.389 6 9806 9943.5 1.903 2.292 7 7210 7145.0 0.591 2.882 8 5181 5139.1 0.342 3.224 9 3751 3699.9 0.707 3.931 10 2550 2666.3 5.073 9.004 11 1968 1923.3 1.038 10.041 12 1440 1388.7 1.892 11.933 13 1021 1003.7 0.298 12.231 14 732 726.1 0.047 12.278 15 548 525.8 0.934 13.213 16 385 381.2 0.039 13.251 17 282 276.5 0.108 13.359 18 206 200.8 0.133 13.492 19 183 146.0 9.386 22.878 20 93 106.2 1.644 24.522 21 315 287.1 2.708 27.231 Chisq= 27.23 for 20 degrees of freedom, p= 0.87110 SUMMARY of craptest p-value for no. of wins: 0.173966 p-value for throws/game: 0.871101 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-08-15_13:31 No. of wins: Observed Expected 98913 98585.9 z-score= 1.463, pvalue=0.92829 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66429 66666.7 0.847 0.847 2 37645 37654.3 0.002 0.850 3 27277 26954.7 3.853 4.703 4 19081 19313.5 2.798 7.501 5 13929 13851.4 0.435 7.935 6 10108 9943.5 2.720 10.655 7 7243 7145.0 1.343 11.998 8 5106 5139.1 0.213 12.211 9 3634 3699.9 1.173 13.384 10 2546 2666.3 5.428 18.811 11 1879 1923.3 1.022 19.833 12 1402 1388.7 0.127 19.960 13 1027 1003.7 0.540 20.500 14 750 726.1 0.784 21.284 15 527 525.8 0.003 21.286 16 402 381.2 1.140 22.427 17 275 276.5 0.009 22.435 18 197 200.8 0.073 22.509 19 137 146.0 0.553 23.061 20 104 106.2 0.046 23.108 21 302 287.1 0.772 23.879 Chisq= 23.88 for 20 degrees of freedom, p= 0.75230 SUMMARY of craptest p-value for no. of wins: 0.928289 p-value for throws/game: 0.752302 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0042,0.0089,0.0114,0.0168,0.0212,0.0249,0.0261,0.0262,0.0284,0.0290, 0.0304,0.0430,0.0476,0.0478,0.0525,0.0607,0.0624,0.0627,0.0682,0.0730, 0.0743,0.0768,0.0770,0.0887,0.0976,0.1039,0.1067,0.1081,0.1182,0.1207, 0.1213,0.1253,0.1293,0.1314,0.1413,0.1476,0.1585,0.1740,0.1744,0.1757, 0.1801,0.1806,0.1909,0.1912,0.1989,0.1993,0.1999,0.2000,0.2040,0.2065, 0.2066,0.2074,0.2085,0.2143,0.2185,0.2194,0.2195,0.2289,0.2345,0.2424, 0.2444,0.2448,0.2470,0.2488,0.2550,0.2579,0.2585,0.2598,0.2630,0.2634, 0.2661,0.2689,0.2705,0.2739,0.2764,0.2765,0.2773,0.2795,0.2837,0.2914, 0.3096,0.3109,0.3148,0.3170,0.3170,0.3181,0.3213,0.3227,0.3240,0.3243, 0.3246,0.3266,0.3300,0.3325,0.3448,0.3452,0.3460,0.3470,0.3517,0.3603, 0.3637,0.3702,0.3706,0.3720,0.3781,0.3796,0.3885,0.3909,0.3966,0.4055, 0.4095,0.4097,0.4119,0.4133,0.4135,0.4145,0.4201,0.4257,0.4294,0.4305, 0.4347,0.4390,0.4488,0.4493,0.4538,0.4562,0.4596,0.4611,0.4625,0.4625, 0.4638,0.4656,0.4658,0.4679,0.4679,0.4688,0.4718,0.4872,0.4885,0.5056, 0.5071,0.5081,0.5093,0.5159,0.5173,0.5231,0.5248,0.5278,0.5384,0.5522, 0.5545,0.5568,0.5569,0.5571,0.5594,0.5602,0.5628,0.5653,0.5760,0.5815, 0.5815,0.5820,0.5820,0.5821,0.5837,0.5881,0.5886,0.5905,0.5920,0.5953, 0.5998,0.6038,0.6048,0.6189,0.6207,0.6246,0.6254,0.6306,0.6319,0.6391, 0.6426,0.6448,0.6483,0.6530,0.6548,0.6637,0.6645,0.6680,0.6815,0.6829, 0.6841,0.6881,0.7081,0.7188,0.7240,0.7273,0.7299,0.7373,0.7421,0.7425, 0.7432,0.7469,0.7523,0.7543,0.7603,0.7666,0.7671,0.7722,0.7739,0.7753, 0.7764,0.7777,0.7817,0.7867,0.7953,0.7956,0.7975,0.7996,0.8006,0.8023, 0.8040,0.8072,0.8100,0.8105,0.8368,0.8373,0.8443,0.8453,0.8530,0.8622, 0.8703,0.8711,0.8737,0.8760,0.8834,0.8835,0.8841,0.8879,0.8950,0.9033, 0.9116,0.9117,0.9144,0.9167,0.9194,0.9197,0.9215,0.9262,0.9280,0.9283, 0.9299,0.9377,0.9397,0.9401,0.9408,0.9452,0.9487,0.9534,0.9581,0.9588, 0.9594,0.9635,0.9671,0.9681,0.9694,0.9866,0.9953,0.9964,0.9979, Overall p-value after applying KStest on 269 p-values = 0.867980 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.