RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-08-07_14:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.81 18.5142 0.642884 2 to 25 15.79 14.5745 0.373900 3 to 26 15.60 32.4824 0.986901 4 to 27 15.75 12.0233 0.201273 5 to 28 16.00 19.2223 0.684079 6 to 29 15.88 10.6269 0.124711 7 to 30 15.87 13.1577 0.274433 8 to 31 15.69 21.4860 0.794696 9 to 32 16.07 24.7015 0.898407 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.847024 Tough bday spacings test for dh-ranFile-2015-08-07_14:31: 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 8 30 84 107 91 79 45 33 14 8 1 (O-E)^2/E 0.1 1.2 1.6 0.9 0.5 0.0 1.0 0.4 0.1 0.3 2.3 Birthday Spacings: Sum(O-E)^2/E= 8.247, p= 0.395 RESULTS OF GCD FOR dh-ranFile-2015-08-07_14:31 Euclid's algorithm: p-value, steps to gcd: 0.755027 p-value, dist. of gcd's: 0.844511 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-08-07_14:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.572 0.668 0.391 0.594 0.333 0.633 0.429 0.626 Bits 8 to 15---> 0.880 0.884 0.642 0.677 0.507 0.179 0.036 0.332 Bits 16 to 23---> 0.214 0.640 0.594 0.305 0.392 0.150 0.785 0.518 Bits 24 to 31---> 0.340 0.546 0.657 0.591 0.891 0.879 0.764 0.412 KS test for the above 32 p values: 0.828 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-08-07_14:31, p-values for 5 runs: 0.7633, 0.2642, 0.2895, 0.1149, 0.8702 Rank test for binary matrices (31x31) for dh-ranFile-2015-08-07_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 209 211.4 0.028 0.028 r= 29 5171 5134.0 0.267 0.294 r= 30 23277 23103.0 1.310 1.604 r= 31 11343 11551.5 3.764 5.368 chi-square = 5.368 with df = 3; p-value = 0.853 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-08-07_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 216 211.4 0.099 0.099 r= 30 5195 5134.0 0.725 0.824 r= 31 23037 23103.0 0.189 1.013 r= 32 11552 11551.5 0.000 1.013 chi-square = 1.013 with df = 3; p-value = 0.202 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-08-07_14:31 b-rank test for bits 1 to 8, p=0.40737 b-rank test for bits 2 to 9, p=0.29556 b-rank test for bits 3 to 10, p=0.09572 b-rank test for bits 4 to 11, p=0.68436 b-rank test for bits 5 to 12, p=0.87054 b-rank test for bits 6 to 13, p=0.11429 b-rank test for bits 7 to 14, p=0.93844 b-rank test for bits 8 to 15, p=0.50333 b-rank test for bits 9 to 16, p=0.49188 b-rank test for bits 10 to 17, p=0.96544 b-rank test for bits 11 to 18, p=0.54348 b-rank test for bits 12 to 19, p=0.96559 b-rank test for bits 13 to 20, p=0.56175 b-rank test for bits 14 to 21, p=0.48594 b-rank test for bits 15 to 22, p=0.38142 b-rank test for bits 16 to 23, p=0.79791 b-rank test for bits 17 to 24, p=0.51290 b-rank test for bits 18 to 25, p=0.88292 b-rank test for bits 19 to 26, p=0.26979 b-rank test for bits 20 to 27, p=0.44217 b-rank test for bits 21 to 28, p=0.59387 b-rank test for bits 22 to 29, p=0.65243 b-rank test for bits 23 to 30, p=0.52807 b-rank test for bits 24 to 31, p=0.21043 b-rank test for bits 25 to 32, p=0.31886 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 = 0.453862 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-08-07_14:31 (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 141926 0.04 0.515534 2 141968 0.14 0.554516 3 141862 -0.11 0.455973 4 141857 -0.12 0.451344 5 141773 -0.32 0.375042 6 141539 -0.87 0.193449 7 141411 -1.16 0.122147 8 143209 3.04 0.998804 9 142354 1.04 0.850586 10 142478 1.33 0.908021 11 141916 0.02 0.506217 12 142046 0.32 0.625259 13 143623 4.00 0.999969 14 141655 -0.59 0.276180 15 141917 0.02 0.507149 16 141912 0.01 0.502489 17 142452 1.27 0.897587 18 141156 -1.76 0.039194 19 141730 -0.42 0.337610 20 141966 0.13 0.552669 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-08-07_14:31 Bits used No. missing words z-score p-value 23 to 32 141927 0.0609 0.524293 22 to 31 142053 0.4954 0.689846 21 to 30 141728 -0.6253 0.265895 20 to 29 141547 -1.2494 0.105757 19 to 28 142488 1.9954 0.977001 18 to 27 141953 0.1506 0.559849 17 to 26 142356 1.5402 0.938249 16 to 25 141958 0.1678 0.566641 15 to 24 142183 0.9437 0.827336 14 to 23 141902 -0.0253 0.489918 13 to 22 141934 0.0851 0.533897 12 to 21 141790 -0.4115 0.340359 11 to 20 141387 -1.8011 0.035841 10 to 19 142005 0.3299 0.629261 9 to 18 141619 -1.0011 0.158380 8 to 17 141832 -0.2667 0.394867 7 to 16 141893 -0.0563 0.477547 6 to 15 142352 1.5264 0.936551 5 to 14 142012 0.3540 0.638344 4 to 13 141662 -0.8529 0.196868 3 to 12 142185 0.9506 0.829093 2 to 11 141716 -0.6667 0.252496 1 to 10 141473 -1.5046 0.066215 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-08-07_14:31 Bits used No. missing words z-score p-value 28 to 32 141704 -0.6960 0.243204 27 to 31 141581 -1.1130 0.132858 26 to 30 142064 0.5243 0.699967 25 to 29 141877 -0.1096 0.456366 24 to 28 141901 -0.0282 0.488737 23 to 27 142019 0.3718 0.644965 22 to 26 142081 0.5819 0.719694 21 to 25 142081 0.5819 0.719694 20 to 24 141140 -2.6079 0.004555 19 to 23 141624 -0.9672 0.166717 18 to 22 141806 -0.3503 0.363068 17 to 21 141750 -0.5401 0.294564 16 to 20 142055 0.4938 0.689275 15 to 19 141464 -1.5096 0.065574 14 to 18 141600 -1.0486 0.147187 13 to 17 142099 0.6429 0.739872 12 to 16 141863 -0.1571 0.437602 11 to 15 141837 -0.2452 0.403156 10 to 14 141914 0.0158 0.506315 9 to 13 141929 0.0667 0.526581 8 to 12 141912 0.0091 0.503611 7 to 11 141349 -1.8994 0.028754 6 to 10 141361 -1.8587 0.031532 5 to 9 142683 2.6226 0.995637 4 to 8 141709 -0.6791 0.248542 3 to 7 142028 0.4023 0.656258 2 to 6 141668 -0.8181 0.206659 1 to 5 141656 -0.8587 0.195240 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-08-07_14:31 Bits used No. missing words z-score p-value 31 to 32 142058 0.4386 0.669508 30 to 31 141714 -0.5762 0.282242 29 to 30 142361 1.3324 0.908629 28 to 29 141962 0.1554 0.561735 27 to 28 141810 -0.2930 0.384758 26 to 27 141971 0.1819 0.572176 25 to 26 142322 1.2173 0.888258 24 to 25 142113 0.6008 0.726012 23 to 24 142238 0.9695 0.833859 22 to 23 141816 -0.2753 0.391539 21 to 22 142401 1.4504 0.926520 20 to 21 141982 0.2144 0.584869 19 to 20 141946 0.1082 0.543070 18 to 19 141237 -1.9833 0.023668 17 to 18 141799 -0.3255 0.372418 16 to 17 142100 0.5624 0.713095 15 to 16 141834 -0.2222 0.412074 14 to 15 141770 -0.4110 0.340535 13 to 14 142949 3.0669 0.998918 12 to 13 141707 -0.5968 0.275306 11 to 12 141825 -0.2488 0.401773 10 to 11 141391 -1.5290 0.063133 9 to 10 142260 1.0344 0.849531 8 to 9 141767 -0.4199 0.337297 7 to 8 141807 -0.3019 0.381380 6 to 7 141862 -0.1396 0.444482 5 to 6 142282 1.0993 0.864186 4 to 5 142061 0.4474 0.672708 3 to 4 142278 1.0875 0.861597 2 to 3 141567 -1.0098 0.156290 1 to 2 141682 -0.6706 0.251241 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-08-07_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2643.34 2.027 0.978677 Test results for specific bytes for dh-ranFile-2015-08-07_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2506.21 0.088 0.535013 2 to 9 2531.44 0.445 0.671702 3 to 10 2508.51 0.120 0.547876 4 to 11 2470.07 -0.423 0.336067 5 to 12 2524.14 0.341 0.633607 6 to 13 2506.02 0.085 0.533905 7 to 14 2469.52 -0.431 0.333233 8 to 15 2405.54 -1.336 0.090798 9 to 16 2443.82 -0.795 0.213438 10 to 17 2608.94 1.541 0.938305 11 to 18 2472.68 -0.386 0.349612 12 to 19 2525.38 0.359 0.640198 13 to 20 2598.01 1.386 0.917130 14 to 21 2522.91 0.324 0.627024 15 to 22 2492.69 -0.103 0.458806 16 to 23 2462.52 -0.530 0.298022 17 to 24 2685.44 2.622 0.995635 18 to 25 2527.10 0.383 0.649227 19 to 26 2390.74 -1.545 0.061150 20 to 27 2525.77 0.364 0.642230 21 to 28 2577.44 1.095 0.863280 22 to 29 2643.75 2.033 0.978973 23 to 30 2400.16 -1.412 0.078987 24 to 31 2469.50 -0.431 0.333109 25 to 32 2404.94 -1.344 0.089409 CDPARK for dh-ranFile-2015-08-07_14:31: 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 3580 2.6027 0.995376 3538 0.6849 0.753306 3500 -1.0502 0.146807 3543 0.9132 0.819442 3495 -1.2785 0.100530 3555 1.4612 0.928018 3516 -0.3196 0.374623 3508 -0.6849 0.246694 3515 -0.3653 0.357445 3512 -0.5023 0.307734 Square side=100, avg. no. parked=3526.20 sample std.=25.63 p-value of the KSTEST for those 10 p-values: 0.662571 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-08-07_14:31 0.4329,0.5022,0.6218,0.1917,0.1915,0.3380,0.7876,0.7742,0.7432,0.9659, The KS test for those 10 p-values: 0.812534 The 3DSPHERES test for dh-ranFile-2015-08-07_14:31 sample no r^3 equiv. uni. 1 19.369 0.475662 2 5.706 0.173217 3 68.156 0.896881 4 9.295 0.266431 5 80.171 0.930912 6 0.863 0.028364 7 20.688 0.498227 8 28.128 0.608438 9 9.321 0.267074 10 49.608 0.808639 11 16.200 0.417261 12 5.570 0.169455 13 52.563 0.826591 14 36.706 0.705813 15 16.844 0.429628 16 12.142 0.332847 17 53.954 0.834449 18 19.551 0.478843 19 3.845 0.120303 20 31.942 0.655177 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.989158 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-08-07_14:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 0.1 -0.4 -1.6 -0.6 1.3 -2.7 1.6 0.1 1.2 -1.2 -0.4 0.4 0.7 0.5 0.7 -1.5 -0.6 1.4 -0.8 -0.2 -1.0 0.2 -0.3 0.9 -0.6 1.4 -0.6 -0.4 -0.7 2.0 0.6 -0.3 -0.9 1.6 0.4 1.2 1.8 0.1 -0.1 0.9 -1.0 -1.1 Chi-square with 42 degrees of freedom:45.227908 z-score=0.352194, p-value=0.661267 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-08-07_14:31 Test no p-value 1 0.387925 2 0.891538 3 0.017643 4 0.819205 5 0.725981 6 0.172173 7 0.314578 8 0.278348 9 0.587190 10 0.507040 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.982671 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-08-07_14:31: (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 66613 0.04 66849 0.50 3 25000.00 25095 0.36 24838 1.05 4 6666.67 6690 0.08 6673 0.01 5 1388.89 1343 1.52 1362 0.52 6 238.10 218 1.70 238 0.00 7 34.72 33 0.09 36 0.05 8 4.96 7 0.84 3 0.77 p=0.40692 p=0.17831 Number of rngs required: 688247, p-value: 0.429 RESULTS OF CRAPS TEST for dh-ranFile-2015-08-07_14:31 No. of wins: Observed Expected 98297 98585.9 z-score=-1.292, pvalue=0.09819 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66456 66666.7 0.666 0.666 2 37673 37654.3 0.009 0.675 3 27235 26954.7 2.914 3.589 4 19212 19313.5 0.533 4.122 5 13710 13851.4 1.444 5.566 6 10019 9943.5 0.573 6.139 7 7158 7145.0 0.024 6.162 8 5143 5139.1 0.003 6.165 9 3665 3699.9 0.329 6.494 10 2662 2666.3 0.007 6.501 11 1978 1923.3 1.554 8.055 12 1418 1388.7 0.616 8.671 13 993 1003.7 0.114 8.786 14 756 726.1 1.228 10.013 15 542 525.8 0.497 10.510 16 350 381.2 2.546 13.056 17 311 276.5 4.294 17.350 18 195 200.8 0.169 17.520 19 147 146.0 0.007 17.527 20 109 106.2 0.073 17.600 21 268 287.1 1.272 18.872 Chisq= 18.87 for 20 degrees of freedom, p= 0.46985 SUMMARY of craptest p-value for no. of wins: 0.098188 p-value for throws/game: 0.469851 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-08-07_14:31 No. of wins: Observed Expected 98514 98585.9 z-score=-0.321, pvalue=0.37396 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66805 66666.7 0.287 0.287 2 37628 37654.3 0.018 0.305 3 27019 26954.7 0.153 0.459 4 19203 19313.5 0.632 1.090 5 14089 13851.4 4.075 5.165 6 9975 9943.5 0.100 5.265 7 7005 7145.0 2.744 8.009 8 5046 5139.1 1.686 9.695 9 3665 3699.9 0.329 10.023 10 2666 2666.3 0.000 10.023 11 1860 1923.3 2.085 12.109 12 1430 1388.7 1.226 13.334 13 1012 1003.7 0.068 13.403 14 729 726.1 0.011 13.414 15 541 525.8 0.437 13.851 16 343 381.2 3.819 17.670 17 244 276.5 3.829 21.499 18 199 200.8 0.017 21.515 19 128 146.0 2.216 23.731 20 110 106.2 0.135 23.866 21 303 287.1 0.879 24.745 Chisq= 24.74 for 20 degrees of freedom, p= 0.78863 SUMMARY of craptest p-value for no. of wins: 0.373956 p-value for throws/game: 0.788631 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0046,0.0176,0.0237,0.0284,0.0288,0.0315,0.0358,0.0359,0.0392,0.0611, 0.0631,0.0656,0.0662,0.0790,0.0894,0.0908,0.0957,0.0982,0.1005,0.1058, 0.1143,0.1149,0.1203,0.1221,0.1247,0.1329,0.1468,0.1472,0.1496,0.1563, 0.1584,0.1667,0.1695,0.1722,0.1732,0.1783,0.1786,0.1915,0.1917,0.1934, 0.1952,0.1969,0.2013,0.2018,0.2067,0.2104,0.2134,0.2137,0.2432,0.2467, 0.2485,0.2512,0.2525,0.2642,0.2659,0.2664,0.2671,0.2698,0.2744,0.2753, 0.2762,0.2783,0.2822,0.2895,0.2946,0.2956,0.2980,0.3045,0.3077,0.3146, 0.3189,0.3318,0.3328,0.3329,0.3331,0.3332,0.3361,0.3373,0.3376,0.3380, 0.3398,0.3404,0.3405,0.3496,0.3574,0.3631,0.3724,0.3739,0.3740,0.3746, 0.3750,0.3814,0.3814,0.3848,0.3879,0.3914,0.3915,0.3918,0.3949,0.3953, 0.4018,0.4032,0.4069,0.4074,0.4121,0.4122,0.4173,0.4288,0.4294,0.4296, 0.4329,0.4376,0.4422,0.4445,0.4513,0.4539,0.4560,0.4564,0.4588,0.4699, 0.4757,0.4775,0.4788,0.4859,0.4887,0.4899,0.4919,0.4982,0.5022,0.5025, 0.5033,0.5036,0.5062,0.5063,0.5070,0.5071,0.5075,0.5129,0.5155,0.5183, 0.5243,0.5266,0.5281,0.5339,0.5339,0.5350,0.5431,0.5435,0.5461,0.5479, 0.5527,0.5545,0.5598,0.5617,0.5617,0.5666,0.5721,0.5722,0.5849,0.5872, 0.5912,0.5936,0.5939,0.5940,0.6084,0.6218,0.6253,0.6260,0.6270,0.6293, 0.6325,0.6336,0.6383,0.6402,0.6405,0.6416,0.6422,0.6429,0.6450,0.6492, 0.6524,0.6552,0.6563,0.6573,0.6613,0.6626,0.6681,0.6695,0.6717,0.6727, 0.6770,0.6841,0.6844,0.6893,0.6898,0.7000,0.7058,0.7131,0.7197,0.7197, 0.7260,0.7260,0.7399,0.7432,0.7533,0.7550,0.7633,0.7636,0.7742,0.7854, 0.7876,0.7886,0.7947,0.7979,0.8086,0.8125,0.8192,0.8194,0.8266,0.8273, 0.8276,0.8291,0.8339,0.8344,0.8445,0.8470,0.8495,0.8506,0.8533,0.8616, 0.8633,0.8642,0.8702,0.8705,0.8794,0.8798,0.8829,0.8838,0.8883,0.8910, 0.8915,0.8969,0.8976,0.8984,0.9080,0.9086,0.9171,0.9265,0.9280,0.9309, 0.9366,0.9382,0.9383,0.9384,0.9654,0.9656,0.9659,0.9770,0.9787,0.9790, 0.9827,0.9869,0.9892,0.9954,0.9956,0.9956,0.9988,0.9989,1.0000, Overall p-value after applying KStest on 269 p-values = 0.149140 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.