RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-02-03_08:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.46 19.6890 0.709556 2 to 25 15.65 19.7494 0.712751 3 to 26 16.02 15.8651 0.466584 4 to 27 15.89 20.1979 0.735769 5 to 28 15.97 14.6639 0.380326 6 to 29 15.75 30.5051 0.977076 7 to 30 15.64 16.1663 0.487920 8 to 31 15.49 24.8450 0.901768 9 to 32 15.57 18.1341 0.619572 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.120442 Tough bday spacings test for dh-ranFile-2016-02-03_08:31: 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 6 54 79 116 80 77 50 26 7 2 3 (O-E)^2/E 1.1 8.2 0.4 3.4 3.2 0.0 0.1 0.5 4.2 3.2 0.3 Birthday Spacings: Sum(O-E)^2/E= 24.665, p= 0.994 RESULTS OF GCD FOR dh-ranFile-2016-02-03_08:31 Euclid's algorithm: p-value, steps to gcd: 0.616562 p-value, dist. of gcd's: 0.996456 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-02-03_08:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.093 0.177 0.832 0.132 0.271 0.029 0.808 0.018 Bits 8 to 15---> 0.736 0.696 0.195 0.748 0.705 0.085 0.397 0.369 Bits 16 to 23---> 0.597 0.847 0.351 0.869 0.657 0.268 0.051 0.485 Bits 24 to 31---> 0.621 0.331 0.132 0.513 0.759 0.645 0.627 0.643 KS test for the above 32 p values: 0.541 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-02-03_08:31, p-values for 5 runs: 0.5033, 0.4000, 0.6725, 0.6019, 0.6937 Rank test for binary matrices (31x31) for dh-ranFile-2016-02-03_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 206 211.4 0.139 0.139 r= 29 5218 5134.0 1.374 1.513 r= 30 23024 23103.0 0.270 1.783 r= 31 11552 11551.5 0.000 1.783 chi-square = 1.783 with df = 3; p-value = 0.381 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-02-03_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 216 211.4 0.099 0.099 r= 30 5116 5134.0 0.063 0.162 r= 31 23170 23103.0 0.194 0.357 r= 32 11498 11551.5 0.248 0.605 chi-square = 0.605 with df = 3; p-value = 0.105 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-02-03_08:31 b-rank test for bits 1 to 8, p=0.36855 b-rank test for bits 2 to 9, p=0.77842 b-rank test for bits 3 to 10, p=0.56245 b-rank test for bits 4 to 11, p=0.17939 b-rank test for bits 5 to 12, p=0.29030 b-rank test for bits 6 to 13, p=0.51779 b-rank test for bits 7 to 14, p=0.62459 b-rank test for bits 8 to 15, p=0.05607 b-rank test for bits 9 to 16, p=0.06845 b-rank test for bits 10 to 17, p=0.22642 b-rank test for bits 11 to 18, p=0.37625 b-rank test for bits 12 to 19, p=0.98140 b-rank test for bits 13 to 20, p=0.59424 b-rank test for bits 14 to 21, p=0.82158 b-rank test for bits 15 to 22, p=0.96123 b-rank test for bits 16 to 23, p=0.97485 b-rank test for bits 17 to 24, p=0.05777 b-rank test for bits 18 to 25, p=0.84352 b-rank test for bits 19 to 26, p=0.69740 b-rank test for bits 20 to 27, p=0.27007 b-rank test for bits 21 to 28, p=0.18587 b-rank test for bits 22 to 29, p=0.91726 b-rank test for bits 23 to 30, p=0.48594 b-rank test for bits 24 to 31, p=0.29268 b-rank test for bits 25 to 32, p=0.30553 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 = 0.895855 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-02-03_08:31 (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 142082 0.40 0.656686 2 141840 -0.16 0.435658 3 142269 0.84 0.799644 4 141697 -0.50 0.309913 5 141353 -1.30 0.096829 6 141641 -0.63 0.265350 7 142092 0.43 0.665237 8 141245 -1.55 0.060310 9 141719 -0.44 0.328270 10 141883 -0.06 0.475473 11 141956 0.11 0.543415 12 142232 0.75 0.774546 13 141539 -0.87 0.193449 14 142562 1.52 0.936362 15 141473 -1.02 0.153992 16 141832 -0.18 0.428310 17 142654 1.74 0.959060 18 141975 0.15 0.560972 19 142634 1.69 0.954787 20 141855 -0.13 0.449494 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-02-03_08:31 Bits used No. missing words z-score p-value 23 to 32 141884 -0.0873 0.465199 22 to 31 141718 -0.6598 0.254704 21 to 30 141785 -0.4287 0.334062 20 to 29 141881 -0.0977 0.461089 19 to 28 141796 -0.3908 0.347975 18 to 27 142068 0.5471 0.707858 17 to 26 141982 0.2506 0.598933 16 to 25 142155 0.8471 0.801541 15 to 24 141876 -0.1149 0.454250 14 to 23 141907 -0.0080 0.496795 13 to 22 141593 -1.0908 0.137682 12 to 21 142000 0.3127 0.622729 11 to 20 141769 -0.4839 0.314230 10 to 19 141788 -0.4184 0.337835 9 to 18 141803 -0.3667 0.356938 8 to 17 142042 0.4575 0.676338 7 to 16 142431 1.7989 0.963980 6 to 15 141895 -0.0494 0.480295 5 to 14 141541 -1.2701 0.102024 4 to 13 141965 0.1920 0.576115 3 to 12 142120 0.7264 0.766218 2 to 11 142119 0.7230 0.765160 1 to 10 142071 0.5575 0.711401 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-02-03_08:31 Bits used No. missing words z-score p-value 28 to 32 142122 0.7209 0.764519 27 to 31 142419 1.7277 0.957979 26 to 30 142392 1.6362 0.949098 25 to 29 142182 0.9243 0.822336 24 to 28 141977 0.2294 0.590717 23 to 27 141866 -0.1469 0.441613 22 to 26 142084 0.5921 0.723109 21 to 25 142267 1.2124 0.887328 20 to 24 141657 -0.8554 0.196177 19 to 23 141630 -0.9469 0.171850 18 to 22 141522 -1.3130 0.094594 17 to 21 142153 0.8260 0.795598 16 to 20 142322 1.3989 0.919076 15 to 19 142323 1.4023 0.919583 14 to 18 142029 0.4057 0.657504 13 to 17 141992 0.2802 0.610352 12 to 16 141900 -0.0316 0.487385 11 to 15 141621 -0.9774 0.164188 10 to 14 141912 0.0091 0.503611 9 to 13 141826 -0.2825 0.388790 8 to 12 142526 2.0904 0.981709 7 to 11 141776 -0.4520 0.325647 6 to 10 141492 -1.4147 0.078581 5 to 9 141952 0.1446 0.557504 4 to 8 141593 -1.0723 0.141792 3 to 7 141398 -1.7333 0.041519 2 to 6 141709 -0.6791 0.248542 1 to 5 141821 -0.2994 0.382308 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-02-03_08:31 Bits used No. missing words z-score p-value 31 to 32 142808 2.6509 0.995987 30 to 31 141747 -0.4788 0.316023 29 to 30 142154 0.7217 0.764773 28 to 29 142563 1.9282 0.973087 27 to 28 142155 0.7247 0.765679 26 to 27 141027 -2.6027 0.004624 25 to 26 141154 -2.2281 0.012937 24 to 25 142003 0.2763 0.608846 23 to 24 141905 -0.0128 0.494905 22 to 23 141512 -1.1721 0.120586 21 to 22 141925 0.0462 0.518434 20 to 21 141584 -0.9597 0.168609 19 to 20 141123 -2.3196 0.010182 18 to 19 142300 1.1524 0.875426 17 to 18 141945 0.1052 0.541900 16 to 17 141709 -0.5909 0.277279 15 to 16 141623 -0.8446 0.199158 14 to 15 142519 1.7984 0.963946 13 to 14 141278 -1.8623 0.031278 12 to 13 141915 0.0167 0.506672 11 to 12 142188 0.8220 0.794472 10 to 11 141423 -1.4346 0.075700 9 to 10 141549 -1.0629 0.143909 8 to 9 142032 0.3619 0.641271 7 to 8 141576 -0.9833 0.162736 6 to 7 141753 -0.4612 0.322345 5 to 6 142003 0.2763 0.608846 4 to 5 141205 -2.0777 0.018870 3 to 4 141648 -0.7709 0.220388 2 to 3 141573 -0.9921 0.160569 1 to 2 141904 -0.0157 0.493728 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-02-03_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2413.12 -1.229 0.109588 Test results for specific bytes for dh-ranFile-2016-02-03_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2498.18 -0.026 0.489753 2 to 9 2490.02 -0.141 0.443878 3 to 10 2551.46 0.728 0.766634 4 to 11 2572.00 1.018 0.845730 5 to 12 2623.73 1.750 0.959920 6 to 13 2384.79 -1.629 0.051628 7 to 14 2421.67 -1.108 0.133988 8 to 15 2410.91 -1.260 0.103846 9 to 16 2486.58 -0.190 0.424711 10 to 17 2497.22 -0.039 0.484347 11 to 18 2494.62 -0.076 0.469695 12 to 19 2610.23 1.559 0.940494 13 to 20 2496.64 -0.047 0.481066 14 to 21 2564.45 0.911 0.818963 15 to 22 2547.75 0.675 0.750266 16 to 23 2527.18 0.384 0.649671 17 to 24 2479.40 -0.291 0.385393 18 to 25 2389.83 -1.558 0.059608 19 to 26 2631.81 1.864 0.968845 20 to 27 2573.04 1.033 0.849186 21 to 28 2532.26 0.456 0.675901 22 to 29 2606.11 1.501 0.933277 23 to 30 2529.51 0.417 0.661802 24 to 31 2527.48 0.389 0.651211 25 to 32 2469.57 -0.430 0.333452 CDPARK for dh-ranFile-2016-02-03_08:31: 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 3558 1.5982 0.944998 3526 0.1370 0.554479 3524 0.0457 0.518210 3490 -1.5068 0.065925 3561 1.7352 0.958644 3517 -0.2740 0.392053 3519 -0.1826 0.427537 3543 0.9132 0.819442 3532 0.4110 0.659449 3489 -1.5525 0.060270 Square side=100, avg. no. parked=3525.90 sample std.=23.18 p-value of the KSTEST for those 10 p-values: 0.796487 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-02-03_08:31 0.8556,0.8926,0.8118,0.4073,0.8027,0.6946,0.4469,0.7479,0.2338,0.5074, The KS test for those 10 p-values: 0.166349 The 3DSPHERES test for dh-ranFile-2016-02-03_08:31 sample no r^3 equiv. uni. 1 91.414 0.952506 2 16.264 0.418495 3 15.946 0.412292 4 10.518 0.295733 5 27.435 0.599281 6 36.845 0.707174 7 31.515 0.650239 8 37.446 0.712983 9 12.145 0.332914 10 25.643 0.574614 11 31.071 0.645022 12 69.007 0.899764 13 56.620 0.848524 14 80.584 0.931856 15 4.186 0.130248 16 27.142 0.595344 17 27.907 0.605537 18 43.527 0.765639 19 17.311 0.438443 20 4.455 0.138001 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.254657 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-02-03_08:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -1.2 0.8 2.1 -0.7 0.0 -0.6 0.3 0.5 0.1 0.4 0.7 -2.3 -0.6 1.0 -0.6 0.3 -1.0 0.1 -0.4 -0.2 0.3 1.0 -0.2 -0.8 -0.1 1.8 1.3 0.4 1.4 -0.4 0.2 0.7 0.7 -1.5 2.4 1.0 -1.3 1.3 -0.1 -1.3 -1.0 -1.1 Chi-square with 42 degrees of freedom:43.127020 z-score=0.122968, p-value=0.577126 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-02-03_08:31 Test no p-value 1 0.969959 2 0.204011 3 0.091908 4 0.492683 5 0.006458 6 0.029219 7 0.037277 8 0.250698 9 0.056439 10 0.438009 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.002981 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-02-03_08:31: (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 66432 0.83 66734 0.07 3 25000.00 25104 0.43 24837 1.06 4 6666.67 6778 1.86 6685 0.05 5 1388.89 1424 0.89 1468 4.51 6 238.10 216 2.05 233 0.11 7 34.72 39 0.53 37 0.15 8 4.96 6 0.22 5 0.00 p=0.66040 p=0.57077 Number of rngs required: 687992, p-value: 0.318 RESULTS OF CRAPS TEST for dh-ranFile-2016-02-03_08:31 No. of wins: Observed Expected 98831 98585.9 z-score= 1.096, pvalue=0.86355 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66646 66666.7 0.006 0.006 2 37678 37654.3 0.015 0.021 3 26965 26954.7 0.004 0.025 4 19327 19313.5 0.009 0.035 5 13782 13851.4 0.348 0.383 6 9970 9943.5 0.070 0.453 7 7056 7145.0 1.109 1.562 8 5167 5139.1 0.152 1.714 9 3778 3699.9 1.650 3.364 10 2642 2666.3 0.221 3.586 11 1960 1923.3 0.699 4.285 12 1394 1388.7 0.020 4.305 13 985 1003.7 0.349 4.654 14 691 726.1 1.701 6.354 15 569 525.8 3.543 9.897 16 377 381.2 0.045 9.943 17 290 276.5 0.655 10.598 18 195 200.8 0.169 10.767 19 132 146.0 1.340 12.107 20 110 106.2 0.135 12.241 21 286 287.1 0.004 12.246 Chisq= 12.25 for 20 degrees of freedom, p= 0.09264 SUMMARY of craptest p-value for no. of wins: 0.863551 p-value for throws/game: 0.092644 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-02-03_08:31 No. of wins: Observed Expected 98198 98585.9 z-score=-1.735, pvalue=0.04139 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66358 66666.7 1.429 1.429 2 37601 37654.3 0.076 1.505 3 27102 26954.7 0.805 2.309 4 19310 19313.5 0.001 2.310 5 13781 13851.4 0.358 2.668 6 10000 9943.5 0.321 2.988 7 7258 7145.0 1.786 4.775 8 5189 5139.1 0.485 5.260 9 3768 3699.9 1.255 6.515 10 2707 2666.3 0.621 7.136 11 1907 1923.3 0.139 7.275 12 1434 1388.7 1.475 8.750 13 1003 1003.7 0.001 8.750 14 700 726.1 0.941 9.691 15 539 525.8 0.330 10.021 16 364 381.2 0.772 10.792 17 273 276.5 0.045 10.838 18 190 200.8 0.584 11.422 19 124 146.0 3.311 14.732 20 101 106.2 0.256 14.988 21 291 287.1 0.053 15.041 Chisq= 15.04 for 20 degrees of freedom, p= 0.22595 SUMMARY of craptest p-value for no. of wins: 0.041394 p-value for throws/game: 0.225948 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0030,0.0046,0.0065,0.0102,0.0129,0.0179,0.0189,0.0289,0.0292,0.0313, 0.0373,0.0414,0.0415,0.0514,0.0516,0.0561,0.0564,0.0578,0.0596,0.0603, 0.0603,0.0659,0.0685,0.0757,0.0786,0.0853,0.0919,0.0925,0.0926,0.0946, 0.0968,0.1020,0.1038,0.1046,0.1096,0.1204,0.1206,0.1302,0.1319,0.1323, 0.1340,0.1377,0.1380,0.1418,0.1439,0.1540,0.1606,0.1627,0.1642,0.1663, 0.1686,0.1718,0.1767,0.1794,0.1859,0.1934,0.1954,0.1962,0.1992,0.2040, 0.2204,0.2259,0.2264,0.2338,0.2485,0.2507,0.2547,0.2547,0.2653,0.2683, 0.2701,0.2706,0.2773,0.2903,0.2927,0.2957,0.3055,0.3099,0.3142,0.3160, 0.3179,0.3223,0.3256,0.3283,0.3313,0.3329,0.3335,0.3341,0.3378,0.3480, 0.3509,0.3569,0.3686,0.3686,0.3762,0.3803,0.3814,0.3823,0.3854,0.3888, 0.3921,0.3969,0.4000,0.4073,0.4123,0.4185,0.4247,0.4275,0.4283,0.4357, 0.4380,0.4384,0.4416,0.4439,0.4469,0.4495,0.4542,0.4611,0.4652,0.4666, 0.4697,0.4755,0.4803,0.4811,0.4843,0.4846,0.4859,0.4874,0.4879,0.4898, 0.4927,0.4937,0.4949,0.4968,0.5033,0.5036,0.5067,0.5074,0.5132,0.5178, 0.5182,0.5184,0.5409,0.5419,0.5434,0.5545,0.5575,0.5610,0.5624,0.5708, 0.5746,0.5761,0.5771,0.5907,0.5942,0.5953,0.5971,0.5989,0.5993,0.6019, 0.6055,0.6088,0.6088,0.6104,0.6166,0.6196,0.6211,0.6227,0.6246,0.6275, 0.6413,0.6431,0.6447,0.6450,0.6497,0.6502,0.6512,0.6567,0.6567,0.6575, 0.6594,0.6604,0.6618,0.6652,0.6725,0.6759,0.6763,0.6937,0.6946,0.6957, 0.6974,0.7052,0.7072,0.7079,0.7096,0.7114,0.7128,0.7130,0.7231,0.7358, 0.7365,0.7477,0.7479,0.7503,0.7594,0.7645,0.7648,0.7652,0.7656,0.7657, 0.7662,0.7666,0.7745,0.7784,0.7945,0.7956,0.7965,0.7996,0.8015,0.8027, 0.8081,0.8118,0.8190,0.8194,0.8216,0.8223,0.8323,0.8435,0.8457,0.8469, 0.8485,0.8492,0.8556,0.8636,0.8693,0.8754,0.8873,0.8926,0.8959,0.8998, 0.9018,0.9173,0.9191,0.9196,0.9319,0.9333,0.9364,0.9405,0.9450,0.9491, 0.9525,0.9548,0.9580,0.9586,0.9591,0.9599,0.9612,0.9639,0.9640,0.9688, 0.9700,0.9731,0.9749,0.9771,0.9814,0.9817,0.9940,0.9960,0.9965, Overall p-value after applying KStest on 269 p-values = 0.878016 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.