RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-01-04_10:31 (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 11.3266 0.160909 2 to 25 15.72 10.9997 0.143423 3 to 26 15.48 22.8238 0.844926 4 to 27 15.91 15.8216 0.463481 5 to 28 15.68 23.0190 0.851367 6 to 29 15.73 17.1626 0.556597 7 to 30 15.52 24.9286 0.903680 8 to 31 15.74 11.3854 0.164157 9 to 32 16.08 12.3868 0.223829 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.725992 Tough bday spacings test for dh-ranFile-2016-01-04_10:31: 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 37 79 86 94 68 64 29 16 10 7 (O-E)^2/E 0.1 0.0 0.4 1.4 0.1 1.3 2.7 0.0 0.1 1.7 2.1 Birthday Spacings: Sum(O-E)^2/E= 10.055, p= 0.564 RESULTS OF GCD FOR dh-ranFile-2016-01-04_10:31 Euclid's algorithm: p-value, steps to gcd: 0.839646 p-value, dist. of gcd's: 0.496703 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-01-04_10:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.815 0.086 0.764 0.263 0.181 0.042 0.556 0.510 Bits 8 to 15---> 0.009 0.578 0.333 0.645 0.873 0.215 0.197 0.452 Bits 16 to 23---> 0.749 0.041 0.688 0.273 0.099 0.630 0.170 0.808 Bits 24 to 31---> 0.511 0.490 0.912 0.968 0.099 0.286 0.859 0.772 KS test for the above 32 p values: 0.224 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-01-04_10:31, p-values for 5 runs: 0.7129, 0.2026, 0.2100, 0.8965, 0.6040 Rank test for binary matrices (31x31) for dh-ranFile-2016-01-04_10:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 238 211.4 3.342 3.342 r= 29 5057 5134.0 1.155 4.497 r= 30 23276 23103.0 1.295 5.792 r= 31 11429 11551.5 1.300 7.092 chi-square = 7.092 with df = 3; p-value = 0.931 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-01-04_10:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 197 211.4 0.983 0.983 r= 30 5213 5134.0 1.215 2.199 r= 31 23060 23103.0 0.080 2.279 r= 32 11530 11551.5 0.040 2.319 chi-square = 2.319 with df = 3; p-value = 0.491 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-01-04_10:31 b-rank test for bits 1 to 8, p=0.23950 b-rank test for bits 2 to 9, p=0.63549 b-rank test for bits 3 to 10, p=0.01579 b-rank test for bits 4 to 11, p=0.80882 b-rank test for bits 5 to 12, p=0.46608 b-rank test for bits 6 to 13, p=0.42100 b-rank test for bits 7 to 14, p=0.77677 b-rank test for bits 8 to 15, p=0.22978 b-rank test for bits 9 to 16, p=0.42396 b-rank test for bits 10 to 17, p=0.17906 b-rank test for bits 11 to 18, p=0.25008 b-rank test for bits 12 to 19, p=0.68024 b-rank test for bits 13 to 20, p=0.55350 b-rank test for bits 14 to 21, p=0.84636 b-rank test for bits 15 to 22, p=0.76189 b-rank test for bits 16 to 23, p=0.74246 b-rank test for bits 17 to 24, p=0.81473 b-rank test for bits 18 to 25, p=0.79258 b-rank test for bits 19 to 26, p=0.11014 b-rank test for bits 20 to 27, p=0.01903 b-rank test for bits 21 to 28, p=0.12422 b-rank test for bits 22 to 29, p=0.91806 b-rank test for bits 23 to 30, p=0.83381 b-rank test for bits 24 to 31, p=0.95716 b-rank test for bits 25 to 32, p=0.38353 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 = 0.794118 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-01-04_10:31 (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 142124 0.50 0.692013 2 141885 -0.06 0.477334 3 140979 -2.17 0.014865 4 141747 -0.38 0.352242 5 142315 0.95 0.828391 6 141569 -0.80 0.213259 7 142930 2.38 0.991454 8 141546 -0.85 0.197968 9 141809 -0.23 0.407331 10 141437 -1.10 0.134889 11 142084 0.41 0.658403 12 142134 0.52 0.700184 13 141097 -1.90 0.028850 14 141759 -0.35 0.362705 15 142014 0.24 0.596600 16 141986 0.18 0.571084 17 141277 -1.48 0.069783 18 140957 -2.23 0.013038 19 142291 0.89 0.813737 20 141956 0.11 0.543415 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-01-04_10:31 Bits used No. missing words z-score p-value 23 to 32 141410 -1.7218 0.042550 22 to 31 141838 -0.2460 0.402855 21 to 30 141729 -0.6218 0.267028 20 to 29 141351 -1.9253 0.027097 19 to 28 141363 -1.8839 0.029789 18 to 27 142084 0.6023 0.726516 17 to 26 142268 1.2368 0.891918 16 to 25 142085 0.6058 0.727663 15 to 24 142469 1.9299 0.973190 14 to 23 141685 -0.7736 0.219598 13 to 22 142045 0.4678 0.680046 12 to 21 141497 -1.4218 0.077538 11 to 20 141744 -0.5701 0.284304 10 to 19 141898 -0.0391 0.484418 9 to 18 141421 -1.6839 0.046101 8 to 17 142283 1.2885 0.901217 7 to 16 141707 -0.6977 0.242686 6 to 15 141643 -0.9184 0.179210 5 to 14 141749 -0.5529 0.290179 4 to 13 141598 -1.0736 0.141512 3 to 12 141912 0.0092 0.503673 2 to 11 142112 0.6989 0.757681 1 to 10 141865 -0.1529 0.439254 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-01-04_10:31 Bits used No. missing words z-score p-value 28 to 32 141414 -1.6791 0.046568 27 to 31 142085 0.5955 0.724243 26 to 30 141340 -1.9299 0.026808 25 to 29 141377 -1.8045 0.035576 24 to 28 141641 -0.9096 0.181519 23 to 27 142079 0.5752 0.717406 22 to 26 141899 -0.0350 0.486033 21 to 25 142113 0.6904 0.755031 20 to 24 141582 -1.1096 0.133587 19 to 23 142057 0.5006 0.691665 18 to 22 141692 -0.7367 0.230649 17 to 21 142045 0.4599 0.677205 16 to 20 141711 -0.6723 0.250695 15 to 19 142119 0.7107 0.761379 14 to 18 142232 1.0938 0.862978 13 to 17 142369 1.5582 0.940407 12 to 16 142078 0.5718 0.716259 11 to 15 141808 -0.3435 0.365614 10 to 14 141900 -0.0316 0.487385 9 to 13 141553 -1.2079 0.113543 8 to 12 142320 1.3921 0.918054 7 to 11 141726 -0.6215 0.267149 6 to 10 141889 -0.0689 0.472529 5 to 9 142172 0.8904 0.813376 4 to 8 141836 -0.2486 0.401844 3 to 7 142178 0.9107 0.818785 2 to 6 142055 0.4938 0.689275 1 to 5 142578 2.2667 0.988295 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-01-04_10:31 Bits used No. missing words z-score p-value 31 to 32 141990 0.2380 0.594046 30 to 31 142112 0.5978 0.725029 29 to 30 141890 -0.0570 0.477264 28 to 29 141779 -0.3845 0.350321 27 to 28 141896 -0.0393 0.484317 26 to 27 141362 -1.6145 0.053205 25 to 26 141898 -0.0334 0.486669 24 to 25 141848 -0.1809 0.428217 23 to 24 142445 1.5801 0.942963 22 to 23 141296 -1.8092 0.035207 21 to 22 141209 -2.0659 0.019420 20 to 21 142694 2.3147 0.989684 19 to 20 141820 -0.2635 0.396079 18 to 19 142010 0.2970 0.616752 17 to 18 141921 0.0344 0.513731 16 to 17 141537 -1.0983 0.136033 15 to 16 142026 0.3442 0.634637 14 to 15 141911 0.0049 0.501965 13 to 14 141500 -1.2075 0.113627 12 to 13 142086 0.5212 0.698869 11 to 12 141315 -1.7532 0.039785 10 to 11 142126 0.6391 0.738636 9 to 10 142085 0.5182 0.697841 8 to 9 142319 1.2085 0.886566 7 to 8 141852 -0.1691 0.432853 6 to 7 141883 -0.0777 0.469045 5 to 6 141628 -0.8299 0.203303 4 to 5 141598 -0.9184 0.179211 3 to 4 141480 -1.2665 0.102674 2 to 3 141981 0.2114 0.583719 1 to 2 142455 1.6096 0.946262 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-01-04_10:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2593.47 1.322 0.906902 Test results for specific bytes for dh-ranFile-2016-01-04_10:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2477.58 -0.317 0.375571 2 to 9 2486.14 -0.196 0.422289 3 to 10 2521.16 0.299 0.617612 4 to 11 2526.29 0.372 0.644963 5 to 12 2540.24 0.569 0.715370 6 to 13 2508.54 0.121 0.548061 7 to 14 2436.02 -0.905 0.182790 8 to 15 2614.10 1.614 0.946700 9 to 16 2454.22 -0.647 0.258671 10 to 17 2397.42 -1.451 0.073441 11 to 18 2494.92 -0.072 0.471359 12 to 19 2518.89 0.267 0.605315 13 to 20 2496.92 -0.044 0.482615 14 to 21 2600.23 1.417 0.921831 15 to 22 2528.27 0.400 0.655324 16 to 23 2440.16 -0.846 0.198689 17 to 24 2647.08 2.080 0.981236 18 to 25 2549.93 0.706 0.759944 19 to 26 2399.00 -1.428 0.076598 20 to 27 2512.28 0.174 0.568958 21 to 28 2516.96 0.240 0.594797 22 to 29 2582.99 1.174 0.879746 23 to 30 2534.99 0.495 0.689656 24 to 31 2534.41 0.487 0.686726 25 to 32 2471.55 -0.402 0.343740 CDPARK for dh-ranFile-2016-01-04_10:31: 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 3492 -1.4155 0.078457 3535 0.5479 0.708135 3493 -1.3699 0.085365 3487 -1.6438 0.050105 3526 0.1370 0.554479 3502 -0.9589 0.168804 3535 0.5479 0.708135 3513 -0.4566 0.323972 3499 -1.0959 0.136563 3517 -0.2740 0.392053 Square side=100, avg. no. parked=3509.90 sample std.=17.00 p-value of the KSTEST for those 10 p-values: 0.068529 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-01-04_10:31 0.4494,0.3989,0.3872,0.8978,0.6978,0.2558,0.3732,0.7469,0.7437,0.5167, The KS test for those 10 p-values: 0.459826 The 3DSPHERES test for dh-ranFile-2016-01-04_10:31 sample no r^3 equiv. uni. 1 4.033 0.125776 2 71.418 0.907506 3 22.101 0.521304 4 84.291 0.939777 5 35.040 0.689014 6 36.953 0.708227 7 49.538 0.808191 8 27.920 0.605713 9 30.938 0.643439 10 5.438 0.165783 11 17.943 0.450140 12 34.082 0.678920 13 5.679 0.172469 14 6.673 0.199426 15 111.807 0.975932 16 100.775 0.965236 17 12.468 0.340048 18 14.595 0.385220 19 30.538 0.638658 20 72.009 0.909308 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.241956 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-01-04_10:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 -0.3 1.3 -1.3 -0.2 0.3 0.7 1.0 -0.9 -0.1 -0.9 -1.6 -0.3 1.0 0.9 -0.0 -0.3 -1.6 0.5 0.1 1.8 0.7 0.4 -0.0 -0.8 1.3 -1.9 -0.2 0.8 -1.8 -1.2 0.6 -1.2 1.0 0.2 0.6 -0.2 0.5 0.9 -0.1 -0.6 1.0 0.8 Chi-square with 42 degrees of freedom:38.382534 z-score=-0.394698, p-value=0.369461 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-01-04_10:31 Test no p-value 1 0.740428 2 0.003051 3 0.189884 4 0.003973 5 0.513754 6 0.070012 7 0.723926 8 0.010222 9 0.093680 10 0.343878 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.001752 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-01-04_10:31: (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 66433 0.82 66633 0.02 3 25000.00 25191 1.46 24978 0.02 4 6666.67 6735 0.70 6684 0.05 5 1388.89 1369 0.28 1420 0.70 6 238.10 222 1.09 240 0.02 7 34.72 44 2.48 43 1.97 8 4.96 5 0.00 1 3.16 p=0.66335 p=0.56889 Number of rngs required: 688792, p-value: 0.673 RESULTS OF CRAPS TEST for dh-ranFile-2016-01-04_10:31 No. of wins: Observed Expected 98848 98585.9 z-score= 1.172, pvalue=0.87949 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66798 66666.7 0.259 0.259 2 37677 37654.3 0.014 0.272 3 26810 26954.7 0.777 1.050 4 19474 19313.5 1.334 2.384 5 13650 13851.4 2.929 5.313 6 9928 9943.5 0.024 5.337 7 7204 7145.0 0.487 5.824 8 5088 5139.1 0.508 6.332 9 3805 3699.9 2.988 9.319 10 2646 2666.3 0.155 9.474 11 1977 1923.3 1.498 10.971 12 1367 1388.7 0.340 11.312 13 1013 1003.7 0.086 11.397 14 714 726.1 0.203 11.600 15 494 525.8 1.927 13.528 16 352 381.2 2.229 15.757 17 285 276.5 0.259 16.016 18 198 200.8 0.040 16.056 19 144 146.0 0.027 16.083 20 102 106.2 0.167 16.250 21 274 287.1 0.599 16.849 Chisq= 16.85 for 20 degrees of freedom, p= 0.33726 SUMMARY of craptest p-value for no. of wins: 0.879492 p-value for throws/game: 0.337265 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-01-04_10:31 No. of wins: Observed Expected 98808 98585.9 z-score= 0.994, pvalue=0.83978 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66514 66666.7 0.350 0.350 2 37583 37654.3 0.135 0.485 3 27161 26954.7 1.578 2.063 4 19268 19313.5 0.107 2.170 5 13927 13851.4 0.412 2.583 6 9994 9943.5 0.256 2.839 7 7113 7145.0 0.144 2.982 8 5007 5139.1 3.394 6.376 9 3697 3699.9 0.002 6.379 10 2658 2666.3 0.026 6.404 11 1967 1923.3 0.992 7.396 12 1488 1388.7 7.095 14.491 13 1013 1003.7 0.086 14.576 14 709 726.1 0.405 14.981 15 520 525.8 0.065 15.046 16 352 381.2 2.229 17.275 17 290 276.5 0.655 17.930 18 205 200.8 0.087 18.017 19 139 146.0 0.334 18.351 20 96 106.2 0.982 19.334 21 299 287.1 0.492 19.826 Chisq= 19.83 for 20 degrees of freedom, p= 0.53112 SUMMARY of craptest p-value for no. of wins: 0.839778 p-value for throws/game: 0.531118 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0018,0.0031,0.0040,0.0093,0.0102,0.0130,0.0149,0.0158,0.0190,0.0194, 0.0268,0.0271,0.0289,0.0298,0.0352,0.0356,0.0398,0.0406,0.0424,0.0426, 0.0461,0.0466,0.0501,0.0532,0.0685,0.0698,0.0700,0.0734,0.0766,0.0775, 0.0785,0.0854,0.0859,0.0937,0.0987,0.0994,0.1027,0.1101,0.1135,0.1136, 0.1242,0.1258,0.1336,0.1349,0.1360,0.1366,0.1415,0.1434,0.1609,0.1642, 0.1658,0.1688,0.1699,0.1725,0.1791,0.1792,0.1792,0.1809,0.1815,0.1828, 0.1899,0.1975,0.1980,0.1987,0.1994,0.2026,0.2033,0.2100,0.2133,0.2146, 0.2196,0.2238,0.2239,0.2298,0.2306,0.2395,0.2420,0.2427,0.2501,0.2507, 0.2558,0.2587,0.2626,0.2670,0.2671,0.2726,0.2843,0.2863,0.2902,0.3240, 0.3333,0.3373,0.3400,0.3437,0.3439,0.3503,0.3522,0.3627,0.3656,0.3695, 0.3732,0.3756,0.3835,0.3852,0.3872,0.3921,0.3961,0.3989,0.4018,0.4029, 0.4073,0.4210,0.4223,0.4240,0.4282,0.4329,0.4393,0.4494,0.4501,0.4524, 0.4598,0.4635,0.4661,0.4690,0.4714,0.4725,0.4773,0.4773,0.4826,0.4843, 0.4844,0.4860,0.4867,0.4874,0.4904,0.4911,0.4967,0.5020,0.5037,0.5100, 0.5115,0.5137,0.5138,0.5167,0.5213,0.5311,0.5434,0.5481,0.5535,0.5545, 0.5558,0.5566,0.5643,0.5689,0.5690,0.5711,0.5780,0.5837,0.5940,0.5948, 0.5966,0.6040,0.6053,0.6057,0.6168,0.6176,0.6303,0.6346,0.6355,0.6387, 0.6434,0.6450,0.6453,0.6553,0.6584,0.6634,0.6730,0.6772,0.6789,0.6800, 0.6802,0.6867,0.6876,0.6890,0.6893,0.6897,0.6917,0.6920,0.6978,0.6978, 0.6989,0.7002,0.7081,0.7081,0.7082,0.7129,0.7154,0.7163,0.7174,0.7239, 0.7242,0.7250,0.7260,0.7265,0.7277,0.7386,0.7404,0.7425,0.7437,0.7469, 0.7494,0.7550,0.7577,0.7599,0.7614,0.7619,0.7637,0.7720,0.7768,0.7926, 0.7941,0.8077,0.8082,0.8088,0.8134,0.8137,0.8147,0.8149,0.8188,0.8284, 0.8338,0.8396,0.8398,0.8449,0.8464,0.8514,0.8593,0.8630,0.8732,0.8795, 0.8797,0.8866,0.8919,0.8965,0.8978,0.9012,0.9037,0.9069,0.9075,0.9093, 0.9121,0.9181,0.9181,0.9218,0.9310,0.9398,0.9404,0.9430,0.9463,0.9467, 0.9572,0.9652,0.9684,0.9732,0.9759,0.9812,0.9883,0.9897,0.9915, Overall p-value after applying KStest on 269 p-values = 0.303406 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.