RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-04-01_21:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.39 23.2446 0.858545 2 to 25 15.73 23.2865 0.859846 3 to 26 15.89 20.4399 0.747650 4 to 27 15.82 11.6520 0.179263 5 to 28 15.76 21.5988 0.799354 6 to 29 15.69 14.0607 0.337202 7 to 30 15.97 21.9877 0.814809 8 to 31 15.69 11.9982 0.199752 9 to 32 15.82 14.3282 0.356249 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.449833 Tough bday spacings test for dh-ranFile-2016-04-01_21:31: 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 35 56 93 110 75 53 35 18 9 5 (O-E)^2/E 0.4 0.1 4.1 0.2 1.6 0.1 0.0 0.9 0.7 0.9 0.2 Birthday Spacings: Sum(O-E)^2/E= 9.075, p= 0.475 RESULTS OF GCD FOR dh-ranFile-2016-04-01_21:31 Euclid's algorithm: p-value, steps to gcd: 0.405743 p-value, dist. of gcd's: 0.695407 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-04-01_21:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.676 0.115 0.318 0.031 0.906 0.459 0.248 0.252 Bits 8 to 15---> 0.015 0.634 0.540 0.088 0.021 0.935 0.843 0.198 Bits 16 to 23---> 0.482 0.759 0.976 0.711 0.707 0.760 0.498 0.378 Bits 24 to 31---> 0.387 0.140 0.325 0.960 0.513 0.765 0.568 0.025 KS test for the above 32 p values: 0.196 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-04-01_21:31, p-values for 5 runs: 0.6331, 0.3792, 0.0753, 0.9315, 0.9419 Rank test for binary matrices (31x31) for dh-ranFile-2016-04-01_21:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 181 211.4 4.376 4.376 r= 29 5077 5134.0 0.633 5.009 r= 30 22955 23103.0 0.949 5.958 r= 31 11787 11551.5 4.800 10.758 chi-square = 10.758 with df = 3; p-value = 0.987 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-04-01_21:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 227 211.4 1.148 1.148 r= 30 5275 5134.0 3.872 5.020 r= 31 23059 23103.0 0.084 5.104 r= 32 11439 11551.5 1.096 6.200 chi-square = 6.200 with df = 3; p-value = 0.898 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-04-01_21:31 b-rank test for bits 1 to 8, p=0.54941 b-rank test for bits 2 to 9, p=0.86825 b-rank test for bits 3 to 10, p=0.03838 b-rank test for bits 4 to 11, p=0.01028 b-rank test for bits 5 to 12, p=0.04784 b-rank test for bits 6 to 13, p=0.24369 b-rank test for bits 7 to 14, p=0.21213 b-rank test for bits 8 to 15, p=0.58420 b-rank test for bits 9 to 16, p=0.27545 b-rank test for bits 10 to 17, p=0.65856 b-rank test for bits 11 to 18, p=0.02958 b-rank test for bits 12 to 19, p=0.20944 b-rank test for bits 13 to 20, p=0.39608 b-rank test for bits 14 to 21, p=0.81205 b-rank test for bits 15 to 22, p=0.29557 b-rank test for bits 16 to 23, p=0.05241 b-rank test for bits 17 to 24, p=0.21381 b-rank test for bits 18 to 25, p=0.84626 b-rank test for bits 19 to 26, p=0.36565 b-rank test for bits 20 to 27, p=0.76433 b-rank test for bits 21 to 28, p=0.49763 b-rank test for bits 22 to 29, p=0.89921 b-rank test for bits 23 to 30, p=0.36518 b-rank test for bits 24 to 31, p=0.89731 b-rank test for bits 25 to 32, p=0.41175 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 = 0.217780 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-04-01_21:31 (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 142676 1.79 0.963376 2 141549 -0.84 0.199924 3 141940 0.07 0.528563 4 140994 -2.14 0.016233 5 141672 -0.55 0.289615 6 142054 0.34 0.632324 7 141855 -0.13 0.449494 8 142241 0.77 0.780809 9 142051 0.33 0.629680 10 141456 -1.06 0.144758 11 141858 -0.12 0.452269 12 142299 0.91 0.818706 13 142027 0.27 0.608315 14 141248 -1.55 0.061153 15 141893 -0.04 0.484782 16 141769 -0.33 0.371504 17 141520 -0.91 0.181504 18 142355 1.04 0.851128 19 141381 -1.23 0.108524 20 142055 0.34 0.633204 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-04-01_21:31 Bits used No. missing words z-score p-value 23 to 32 141786 -0.4253 0.335318 22 to 31 142260 1.2092 0.886708 21 to 30 142148 0.8230 0.794746 20 to 29 142285 1.2954 0.902411 19 to 28 141347 -1.9391 0.026246 18 to 27 142458 1.8920 0.970752 17 to 26 141776 -0.4598 0.322845 16 to 25 141773 -0.4701 0.319141 15 to 24 141824 -0.2942 0.384287 14 to 23 141509 -1.3804 0.083724 13 to 22 141690 -0.7563 0.224732 12 to 21 142141 0.7989 0.787815 11 to 20 141721 -0.6494 0.258036 10 to 19 141883 -0.0908 0.463829 9 to 18 142332 1.4575 0.927508 8 to 17 141981 0.2471 0.597599 7 to 16 142139 0.7920 0.785810 6 to 15 141789 -0.4149 0.339096 5 to 14 141957 0.1644 0.565284 4 to 13 142143 0.8058 0.789809 3 to 12 141800 -0.3770 0.353087 2 to 11 141864 -0.1563 0.437894 1 to 10 141614 -1.0184 0.154249 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-04-01_21:31 Bits used No. missing words z-score p-value 28 to 32 141508 -1.3604 0.086845 27 to 31 142669 2.5752 0.994990 26 to 30 142214 1.0328 0.849147 25 to 29 142525 2.0870 0.981557 24 to 28 142124 0.7277 0.766600 23 to 27 141659 -0.8486 0.198059 22 to 26 141631 -0.9435 0.172715 21 to 25 141666 -0.8248 0.204729 20 to 24 142238 1.1141 0.867390 19 to 23 141719 -0.6452 0.259403 18 to 22 141825 -0.2859 0.387491 17 to 21 141840 -0.2350 0.407098 16 to 20 142360 1.5277 0.936706 15 to 19 142252 1.1616 0.877300 14 to 18 141728 -0.6147 0.269384 13 to 17 142298 1.3175 0.906169 12 to 16 142071 0.5480 0.708166 11 to 15 141984 0.2531 0.599912 10 to 14 141892 -0.0587 0.476577 9 to 13 142548 2.1650 0.984806 8 to 12 142078 0.5718 0.716259 7 to 11 142172 0.8904 0.813376 6 to 10 141433 -1.6147 0.053190 5 to 9 141908 -0.0045 0.498201 4 to 8 142262 1.1955 0.884053 3 to 7 142044 0.4565 0.675988 2 to 6 142216 1.0396 0.850728 1 to 5 142061 0.5141 0.696421 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-04-01_21:31 Bits used No. missing words z-score p-value 31 to 32 142104 0.5742 0.717100 30 to 31 142447 1.5860 0.943636 29 to 30 141434 -1.4022 0.080435 28 to 29 141621 -0.8505 0.197515 27 to 28 142197 0.8486 0.801944 26 to 27 141710 -0.5880 0.278268 25 to 26 141733 -0.5201 0.301480 24 to 25 141698 -0.6234 0.266513 23 to 24 142028 0.3501 0.636853 22 to 23 141824 -0.2517 0.400632 21 to 22 141132 -2.2930 0.010924 20 to 21 141804 -0.3107 0.378011 19 to 20 141259 -1.9184 0.027532 18 to 19 141766 -0.4228 0.336220 17 to 18 141910 0.0020 0.500789 16 to 17 141893 -0.0482 0.480790 15 to 16 141893 -0.0482 0.480790 14 to 15 141501 -1.2045 0.114196 13 to 14 141841 -0.2016 0.420129 12 to 13 142058 0.4386 0.669508 11 to 12 141365 -1.6057 0.054171 10 to 11 141956 0.1377 0.554749 9 to 10 142155 0.7247 0.765679 8 to 9 142389 1.4150 0.921459 7 to 8 141488 -1.2429 0.106959 6 to 7 142263 1.0433 0.851589 5 to 6 141542 -1.0836 0.139278 4 to 5 141727 -0.5378 0.295342 3 to 4 141624 -0.8417 0.199983 2 to 3 141183 -2.1426 0.016074 1 to 2 141685 -0.6617 0.254069 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-04-01_21:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2475.96 -0.340 0.366956 Test results for specific bytes for dh-ranFile-2016-04-01_21:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2464.86 -0.497 0.309615 2 to 9 2446.79 -0.753 0.225853 3 to 10 2535.96 0.508 0.694443 4 to 11 2400.55 -1.406 0.079791 5 to 12 2378.97 -1.712 0.043481 6 to 13 2640.22 1.983 0.976316 7 to 14 2597.14 1.374 0.915240 8 to 15 2583.67 1.183 0.881648 9 to 16 2625.18 1.770 0.961660 10 to 17 2618.34 1.674 0.952888 11 to 18 2636.29 1.927 0.973038 12 to 19 2627.62 1.805 0.964447 13 to 20 2564.61 0.914 0.819567 14 to 21 2498.05 -0.028 0.488981 15 to 22 2464.93 -0.496 0.309972 16 to 23 2454.88 -0.638 0.261691 17 to 24 2455.72 -0.626 0.265593 18 to 25 2518.77 0.265 0.604677 19 to 26 2580.19 1.134 0.871616 20 to 27 2476.58 -0.331 0.370227 21 to 28 2539.24 0.555 0.710516 22 to 29 2532.31 0.457 0.676157 23 to 30 2689.44 2.679 0.996308 24 to 31 2529.01 0.410 0.659177 25 to 32 2491.78 -0.116 0.453728 CDPARK for dh-ranFile-2016-04-01_21:31: 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 3540 0.7763 0.781201 3556 1.5068 0.934075 3483 -1.8265 0.033889 3480 -1.9635 0.024796 3533 0.4566 0.676028 3534 0.5023 0.692266 3503 -0.9132 0.180558 3555 1.4612 0.928018 3522 -0.0457 0.481790 3536 0.5936 0.723613 Square side=100, avg. no. parked=3524.20 sample std.=25.74 p-value of the KSTEST for those 10 p-values: 0.454368 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-04-01_21:31 0.8423,0.2838,0.5006,0.6386,0.3801,0.7821,0.0567,0.6800,0.8513,0.9049, The KS test for those 10 p-values: 0.524753 The 3DSPHERES test for dh-ranFile-2016-04-01_21:31 sample no r^3 equiv. uni. 1 9.299 0.266521 2 53.361 0.831141 3 69.792 0.902354 4 1.322 0.043117 5 16.697 0.426832 6 37.764 0.716004 7 25.105 0.566927 8 98.359 0.962321 9 81.417 0.933722 10 46.764 0.789612 11 73.865 0.914751 12 47.659 0.795798 13 36.781 0.706548 14 2.453 0.078508 15 40.098 0.737260 16 49.516 0.808050 17 46.437 0.787304 18 1.588 0.051566 19 6.085 0.183576 20 41.045 0.745427 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.056193 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-04-01_21:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -0.3 0.1 -0.8 -0.3 -0.6 1.4 0.1 1.3 -0.3 -0.4 1.8 1.0 -0.4 -0.5 -0.3 -0.7 -0.7 -0.2 1.1 -0.6 -0.3 0.1 0.2 -0.2 0.5 -0.5 -0.5 0.8 0.0 0.3 -1.3 0.8 -0.8 -0.1 1.7 -0.9 -1.3 0.5 -1.8 0.1 -1.0 -0.1 Chi-square with 42 degrees of freedom:27.745312 z-score=-1.555314, p-value=0.044365 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-04-01_21:31 Test no p-value 1 0.158060 2 0.627892 3 0.320797 4 0.430385 5 0.048860 6 0.619442 7 0.113281 8 0.980337 9 0.001529 10 0.124611 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.071494 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-04-01_21:31: (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 66543 0.23 66910 0.89 3 25000.00 25069 0.19 24831 1.14 4 6666.67 6758 1.25 6555 1.87 5 1388.89 1366 0.38 1396 0.04 6 238.10 224 0.83 279 7.03 7 34.72 35 0.00 27 1.72 8 4.96 4 0.19 1 3.16 p=0.20009 p=0.98538 Number of rngs required: 687501, p-value: 0.148 RESULTS OF CRAPS TEST for dh-ranFile-2016-04-01_21:31 No. of wins: Observed Expected 98255 98585.9 z-score=-1.480, pvalue=0.06946 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66933 66666.7 1.064 1.064 2 37577 37654.3 0.159 1.223 3 26993 26954.7 0.054 1.277 4 19227 19313.5 0.387 1.664 5 13772 13851.4 0.455 2.120 6 9960 9943.5 0.027 2.147 7 7067 7145.0 0.852 2.999 8 5200 5139.1 0.722 3.721 9 3704 3699.9 0.005 3.726 10 2701 2666.3 0.452 4.177 11 1886 1923.3 0.725 4.902 12 1324 1388.7 3.018 7.920 13 1018 1003.7 0.203 8.123 14 722 726.1 0.024 8.147 15 513 525.8 0.313 8.460 16 361 381.2 1.065 9.526 17 313 276.5 4.807 14.333 18 207 200.8 0.190 14.522 19 143 146.0 0.061 14.583 20 96 106.2 0.982 15.566 21 283 287.1 0.059 15.625 Chisq= 15.62 for 20 degrees of freedom, p= 0.26039 SUMMARY of craptest p-value for no. of wins: 0.069464 p-value for throws/game: 0.260385 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-04-01_21:31 No. of wins: Observed Expected 98635 98585.9 z-score= 0.220, pvalue=0.58698 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66892 66666.7 0.762 0.762 2 37574 37654.3 0.171 0.933 3 26762 26954.7 1.378 2.311 4 19161 19313.5 1.204 3.515 5 13821 13851.4 0.067 3.581 6 9974 9943.5 0.093 3.675 7 7216 7145.0 0.705 4.380 8 5081 5139.1 0.656 5.036 9 3728 3699.9 0.214 5.250 10 2749 2666.3 2.565 7.815 11 1926 1923.3 0.004 7.819 12 1411 1388.7 0.357 8.176 13 1076 1003.7 5.206 13.381 14 716 726.1 0.142 13.523 15 511 525.8 0.419 13.942 16 410 381.2 2.184 16.125 17 246 276.5 3.373 19.498 18 200 200.8 0.003 19.501 19 149 146.0 0.062 19.564 20 89 106.2 2.790 22.354 21 308 287.1 1.519 23.873 Chisq= 23.87 for 20 degrees of freedom, p= 0.75202 SUMMARY of craptest p-value for no. of wins: 0.586982 p-value for throws/game: 0.752021 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0015,0.0103,0.0109,0.0152,0.0161,0.0162,0.0207,0.0246,0.0248,0.0262, 0.0275,0.0296,0.0310,0.0339,0.0384,0.0431,0.0435,0.0444,0.0478,0.0489, 0.0516,0.0524,0.0532,0.0542,0.0562,0.0567,0.0612,0.0695,0.0715,0.0753, 0.0785,0.0798,0.0804,0.0837,0.0868,0.0876,0.1070,0.1085,0.1133,0.1142, 0.1149,0.1246,0.1393,0.1397,0.1448,0.1478,0.1542,0.1581,0.1727,0.1793, 0.1806,0.1815,0.1836,0.1955,0.1975,0.1981,0.1984,0.1998,0.1999,0.2000, 0.2001,0.2047,0.2094,0.2121,0.2138,0.2178,0.2247,0.2259,0.2437,0.2483, 0.2517,0.2541,0.2580,0.2594,0.2604,0.2617,0.2656,0.2665,0.2665,0.2694, 0.2755,0.2783,0.2838,0.2896,0.2953,0.2956,0.3015,0.3096,0.3100,0.3176, 0.3191,0.3208,0.3228,0.3254,0.3353,0.3362,0.3372,0.3391,0.3531,0.3562, 0.3652,0.3656,0.3670,0.3702,0.3715,0.3779,0.3780,0.3792,0.3801,0.3843, 0.3866,0.3875,0.3961,0.4006,0.4057,0.4071,0.4117,0.4201,0.4268,0.4304, 0.4379,0.4495,0.4498,0.4523,0.4537,0.4544,0.4592,0.4638,0.4750,0.4766, 0.4808,0.4808,0.4818,0.4820,0.4848,0.4890,0.4976,0.4981,0.4982,0.5006, 0.5008,0.5132,0.5248,0.5286,0.5399,0.5494,0.5547,0.5653,0.5669,0.5677, 0.5842,0.5870,0.5976,0.5999,0.6047,0.6083,0.6194,0.6279,0.6297,0.6323, 0.6331,0.6332,0.6342,0.6369,0.6386,0.6586,0.6592,0.6695,0.6759,0.6760, 0.6760,0.6762,0.6800,0.6923,0.6944,0.6954,0.6964,0.7065,0.7069,0.7082, 0.7105,0.7109,0.7160,0.7163,0.7171,0.7236,0.7373,0.7454,0.7476,0.7520, 0.7586,0.7598,0.7643,0.7647,0.7657,0.7666,0.7808,0.7812,0.7821,0.7858, 0.7873,0.7878,0.7896,0.7898,0.7947,0.7958,0.7994,0.8019,0.8081,0.8120, 0.8134,0.8148,0.8187,0.8196,0.8311,0.8423,0.8425,0.8463,0.8491,0.8507, 0.8511,0.8513,0.8516,0.8585,0.8598,0.8674,0.8682,0.8716,0.8773,0.8816, 0.8841,0.8867,0.8973,0.8977,0.8992,0.9024,0.9024,0.9049,0.9058,0.9062, 0.9148,0.9152,0.9215,0.9275,0.9280,0.9315,0.9337,0.9341,0.9348,0.9367, 0.9419,0.9436,0.9529,0.9597,0.9617,0.9623,0.9634,0.9644,0.9708,0.9730, 0.9763,0.9764,0.9803,0.9816,0.9848,0.9854,0.9869,0.9950,0.9963, Overall p-value after applying KStest on 269 p-values = 0.223836 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.