RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-02-21_15:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.61 28.1272 0.956526 2 to 25 15.83 16.8290 0.533993 3 to 26 15.64 13.5599 0.302025 4 to 27 15.75 17.2465 0.562208 5 to 28 15.76 25.0948 0.907392 6 to 29 15.39 24.9126 0.903317 7 to 30 15.88 18.8155 0.660773 8 to 31 15.78 19.6998 0.710128 9 to 32 15.90 16.9000 0.538840 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.101140 Tough bday spacings test for dh-ranFile-2016-02-21_15:31: 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 43 55 93 101 84 58 32 20 3 3 (O-E)^2/E 0.1 1.1 4.6 0.2 0.1 0.4 0.7 0.2 1.8 2.0 0.3 Birthday Spacings: Sum(O-E)^2/E= 11.430, p= 0.675 RESULTS OF GCD FOR dh-ranFile-2016-02-21_15:31 Euclid's algorithm: p-value, steps to gcd: 0.847894 p-value, dist. of gcd's: 0.584877 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-02-21_15:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.303 0.055 0.404 0.471 0.236 0.744 0.483 0.509 Bits 8 to 15---> 0.740 0.633 0.454 0.902 0.581 0.278 0.873 0.742 Bits 16 to 23---> 0.917 0.520 0.906 0.603 0.787 0.070 0.471 0.166 Bits 24 to 31---> 0.403 0.526 0.840 0.305 0.818 0.118 0.985 0.270 KS test for the above 32 p values: 0.266 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-02-21_15:31, p-values for 5 runs: 0.5773, 0.6002, 0.8247, 0.6330, 0.5988 Rank test for binary matrices (31x31) for dh-ranFile-2016-02-21_15:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 220 211.4 0.348 0.348 r= 29 5108 5134.0 0.132 0.480 r= 30 23064 23103.0 0.066 0.546 r= 31 11608 11551.5 0.276 0.822 chi-square = 0.822 with df = 3; p-value = 0.156 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-02-21_15:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 224 211.4 0.749 0.749 r= 30 5148 5134.0 0.038 0.787 r= 31 23008 23103.0 0.391 1.178 r= 32 11620 11551.5 0.406 1.584 chi-square = 1.584 with df = 3; p-value = 0.337 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-02-21_15:31 b-rank test for bits 1 to 8, p=0.52199 b-rank test for bits 2 to 9, p=0.36729 b-rank test for bits 3 to 10, p=0.70523 b-rank test for bits 4 to 11, p=0.50139 b-rank test for bits 5 to 12, p=0.11245 b-rank test for bits 6 to 13, p=0.93840 b-rank test for bits 7 to 14, p=0.90549 b-rank test for bits 8 to 15, p=0.11919 b-rank test for bits 9 to 16, p=0.52370 b-rank test for bits 10 to 17, p=0.37494 b-rank test for bits 11 to 18, p=0.03700 b-rank test for bits 12 to 19, p=0.74713 b-rank test for bits 13 to 20, p=0.97783 b-rank test for bits 14 to 21, p=0.86361 b-rank test for bits 15 to 22, p=0.54723 b-rank test for bits 16 to 23, p=0.18208 b-rank test for bits 17 to 24, p=0.40138 b-rank test for bits 18 to 25, p=0.24136 b-rank test for bits 19 to 26, p=0.06990 b-rank test for bits 20 to 27, p=0.80089 b-rank test for bits 21 to 28, p=0.98982 b-rank test for bits 22 to 29, p=0.33932 b-rank test for bits 23 to 30, p=0.50111 b-rank test for bits 24 to 31, p=0.58270 b-rank test for bits 25 to 32, p=0.50260 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 = 0.921815 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-02-21_15:31 (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 141664 -0.57 0.283254 2 141699 -0.49 0.311563 3 141849 -0.14 0.443952 4 141592 -0.74 0.229218 5 141843 -0.15 0.438420 6 141900 -0.02 0.491304 7 141279 -1.47 0.070411 8 142009 0.23 0.592070 9 141999 0.21 0.582975 10 141902 -0.02 0.493168 11 141377 -1.24 0.106794 12 142650 1.73 0.958233 13 141689 -0.51 0.303350 14 141945 0.08 0.533210 15 142398 1.14 0.873222 16 142601 1.62 0.946958 17 141737 -0.40 0.343607 18 140903 -2.35 0.009356 19 142294 0.90 0.815610 20 142134 0.52 0.700184 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-02-21_15:31 Bits used No. missing words z-score p-value 23 to 32 141444 -1.6046 0.054292 22 to 31 141942 0.1127 0.544848 21 to 30 142269 1.2402 0.892557 20 to 29 141377 -1.8356 0.033207 19 to 28 142221 1.0747 0.858751 18 to 27 141944 0.1196 0.547581 17 to 26 142138 0.7885 0.784803 16 to 25 141881 -0.0977 0.461089 15 to 24 141852 -0.1977 0.421644 14 to 23 141747 -0.5598 0.287822 13 to 22 141709 -0.6908 0.244848 12 to 21 141970 0.2092 0.582857 11 to 20 141650 -0.8942 0.185596 10 to 19 141380 -1.8253 0.033980 9 to 18 141462 -1.5425 0.061474 8 to 17 141910 0.0023 0.500922 7 to 16 141702 -0.7149 0.237326 6 to 15 142283 1.2885 0.901217 5 to 14 141982 0.2506 0.598933 4 to 13 141960 0.1747 0.569352 3 to 12 141873 -0.1253 0.450153 2 to 11 141722 -0.6460 0.259151 1 to 10 142230 1.1058 0.865585 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-02-21_15:31 Bits used No. missing words z-score p-value 28 to 32 142229 1.0836 0.860735 27 to 31 141466 -1.5028 0.066444 26 to 30 142185 0.9345 0.824970 25 to 29 142196 0.9718 0.834416 24 to 28 141571 -1.1469 0.125715 23 to 27 142016 0.3616 0.641172 22 to 26 142244 1.1345 0.871702 21 to 25 141562 -1.1774 0.119520 20 to 24 141487 -1.4316 0.076125 19 to 23 141862 -0.1604 0.436267 18 to 22 141944 0.1175 0.546778 17 to 21 142254 1.1684 0.878672 16 to 20 141333 -1.9537 0.025371 15 to 19 141627 -0.9571 0.169271 14 to 18 141756 -0.5198 0.301615 13 to 17 141457 -1.5333 0.062598 12 to 16 141828 -0.2757 0.391391 11 to 15 141799 -0.3740 0.354202 10 to 14 142011 0.3446 0.634819 9 to 13 141640 -0.9130 0.180626 8 to 12 141680 -0.7774 0.218464 7 to 11 142235 1.1040 0.865196 6 to 10 141795 -0.3876 0.349171 5 to 9 141925 0.0531 0.521181 4 to 8 141601 -1.0452 0.147968 3 to 7 141552 -1.2113 0.112893 2 to 6 142641 2.4802 0.993435 1 to 5 142241 1.1243 0.869558 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-02-21_15:31 Bits used No. missing words z-score p-value 31 to 32 141918 0.0256 0.510202 30 to 31 141529 -1.1219 0.130949 29 to 30 141657 -0.7443 0.228337 28 to 29 141933 0.0698 0.527833 27 to 28 141851 -0.1721 0.431693 26 to 27 142253 1.0138 0.844655 25 to 26 141837 -0.2134 0.415522 24 to 25 141886 -0.0688 0.472566 23 to 24 141929 0.0580 0.523135 22 to 23 141135 -2.2842 0.011181 21 to 22 141752 -0.4641 0.321288 20 to 21 142104 0.5742 0.717100 19 to 20 142253 1.0138 0.844655 18 to 19 142661 2.2173 0.986699 17 to 18 142177 0.7896 0.785116 16 to 17 141730 -0.5290 0.298404 15 to 16 141630 -0.8240 0.204975 14 to 15 141588 -0.9479 0.171596 13 to 14 142200 0.8574 0.804397 12 to 13 142081 0.5064 0.693713 11 to 12 141374 -1.5791 0.057151 10 to 11 142323 1.2203 0.888818 9 to 10 142289 1.1200 0.868637 8 to 9 141552 -1.0541 0.145925 7 to 8 142766 2.5271 0.994249 6 to 7 141945 0.1052 0.541900 5 to 6 141720 -0.5585 0.288253 4 to 5 141641 -0.7915 0.214316 3 to 4 141955 0.1347 0.553583 2 to 3 142804 2.6391 0.995844 1 to 2 141922 0.0374 0.514907 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-02-21_15:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2336.25 -2.316 0.010286 Test results for specific bytes for dh-ranFile-2016-02-21_15:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2491.67 -0.118 0.453116 2 to 9 2543.14 0.610 0.729085 3 to 10 2465.76 -0.484 0.314090 4 to 11 2551.70 0.731 0.767656 5 to 12 2607.63 1.522 0.936003 6 to 13 2557.63 0.815 0.792481 7 to 14 2510.24 0.145 0.557599 8 to 15 2378.41 -1.720 0.042761 9 to 16 2580.70 1.141 0.873112 10 to 17 2457.84 -0.596 0.275510 11 to 18 2572.48 1.025 0.847316 12 to 19 2580.86 1.143 0.873584 13 to 20 2457.18 -0.606 0.272392 14 to 21 2540.37 0.571 0.715984 15 to 22 2502.98 0.042 0.516786 16 to 23 2574.09 1.048 0.852638 17 to 24 2515.33 0.217 0.585795 18 to 25 2481.49 -0.262 0.396763 19 to 26 2547.59 0.673 0.749526 20 to 27 2562.43 0.883 0.811345 21 to 28 2521.96 0.311 0.621945 22 to 29 2494.22 -0.082 0.467433 23 to 30 2453.68 -0.655 0.256226 24 to 31 2586.19 1.219 0.888561 25 to 32 2539.23 0.555 0.710506 CDPARK for dh-ranFile-2016-02-21_15:31: 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 3543 0.9132 0.819442 3495 -1.2785 0.100530 3509 -0.6393 0.261324 3523 0.0000 0.500000 3520 -0.1370 0.445521 3559 1.6438 0.949895 3514 -0.4110 0.340551 3526 0.1370 0.554479 3492 -1.4155 0.078457 3527 0.1826 0.572463 Square side=100, avg. no. parked=3520.80 sample std.=19.24 p-value of the KSTEST for those 10 p-values: 0.933896 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-02-21_15:31 0.8546,0.8215,0.2872,0.0011,0.4572,0.3198,0.5259,0.4438,0.1130,0.4226, The KS test for those 10 p-values: 0.413533 The 3DSPHERES test for dh-ranFile-2016-02-21_15:31 sample no r^3 equiv. uni. 1 33.463 0.672229 2 4.641 0.143336 3 64.416 0.883188 4 15.506 0.403604 5 35.922 0.698021 6 46.875 0.790386 7 30.564 0.638970 8 1.044 0.034216 9 41.391 0.748343 10 6.565 0.196540 11 21.703 0.514918 12 43.894 0.768493 13 40.442 0.740259 14 71.711 0.908405 15 8.719 0.252206 16 21.128 0.505525 17 1.428 0.046473 18 31.465 0.649649 19 6.442 0.193244 20 24.354 0.555937 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.762403 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-02-21_15:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -0.3 0.1 -0.7 -0.1 -0.1 -0.7 0.8 -0.1 -0.2 -0.5 2.8 0.6 0.1 2.2 -2.3 0.4 -1.1 0.3 -1.4 0.1 -0.6 0.5 0.7 -0.6 0.5 -1.7 -0.7 -1.6 0.7 1.6 1.4 1.6 1.8 -1.6 0.1 -1.9 0.2 -1.2 3.2 0.1 -1.0 0.8 Chi-square with 42 degrees of freedom:61.573925 z-score=2.135690, p-value=0.973979 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-02-21_15:31 Test no p-value 1 0.055718 2 0.790206 3 0.012851 4 0.777631 5 0.111914 6 0.664464 7 0.538000 8 0.109198 9 0.553219 10 0.882126 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.401377 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-02-21_15:31: (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 66515 0.35 66450 0.70 3 25000.00 25093 0.35 25173 1.20 4 6666.67 6723 0.48 6728 0.56 5 1388.89 1391 0.00 1350 1.09 6 238.10 233 0.11 256 1.35 7 34.72 40 0.80 37 0.15 8 4.96 4 0.19 5 0.00 p=0.10652 p=0.46271 Number of rngs required: 687842, p-value: 0.259 RESULTS OF CRAPS TEST for dh-ranFile-2016-02-21_15:31 No. of wins: Observed Expected 98432 98585.9 z-score=-0.688, pvalue=0.24568 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66463 66666.7 0.622 0.622 2 37553 37654.3 0.273 0.895 3 27082 26954.7 0.601 1.496 4 19229 19313.5 0.369 1.865 5 13854 13851.4 0.000 1.866 6 9923 9943.5 0.042 1.908 7 7195 7145.0 0.350 2.258 8 5175 5139.1 0.251 2.509 9 3623 3699.9 1.597 4.106 10 2699 2666.3 0.401 4.507 11 1983 1923.3 1.851 6.358 12 1429 1388.7 1.167 7.525 13 1002 1003.7 0.003 7.528 14 737 726.1 0.162 7.690 15 588 525.8 7.349 15.039 16 389 381.2 0.162 15.201 17 315 276.5 5.349 20.550 18 216 200.8 1.146 21.696 19 145 146.0 0.007 21.703 20 106 106.2 0.000 21.703 21 294 287.1 0.165 21.868 Chisq= 21.87 for 20 degrees of freedom, p= 0.65230 SUMMARY of craptest p-value for no. of wins: 0.245681 p-value for throws/game: 0.652299 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-02-21_15:31 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 66532 66666.7 0.272 0.272 2 37559 37654.3 0.241 0.513 3 27048 26954.7 0.323 0.836 4 19485 19313.5 1.524 2.360 5 13762 13851.4 0.577 2.937 6 9908 9943.5 0.127 3.064 7 7130 7145.0 0.032 3.096 8 5252 5139.1 2.482 5.577 9 3697 3699.9 0.002 5.579 10 2605 2666.3 1.409 6.988 11 1918 1923.3 0.015 7.003 12 1445 1388.7 2.279 9.282 13 989 1003.7 0.216 9.498 14 758 726.1 1.398 10.896 15 512 525.8 0.364 11.260 16 399 381.2 0.836 12.096 17 284 276.5 0.201 12.297 18 196 200.8 0.116 12.413 19 131 146.0 1.538 13.951 20 100 106.2 0.364 14.315 21 290 287.1 0.029 14.344 Chisq= 14.34 for 20 degrees of freedom, p= 0.18737 SUMMARY of craptest p-value for no. of wins: 0.098188 p-value for throws/game: 0.187369 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0011,0.0094,0.0103,0.0112,0.0129,0.0254,0.0332,0.0340,0.0342,0.0370, 0.0428,0.0465,0.0543,0.0551,0.0557,0.0572,0.0615,0.0626,0.0664,0.0699, 0.0699,0.0704,0.0761,0.0785,0.0982,0.1005,0.1011,0.1065,0.1068,0.1092, 0.1119,0.1124,0.1129,0.1130,0.1175,0.1192,0.1195,0.1257,0.1309,0.1433, 0.1459,0.1480,0.1559,0.1658,0.1693,0.1716,0.1806,0.1821,0.1856,0.1874, 0.1932,0.1965,0.2050,0.2143,0.2185,0.2283,0.2292,0.2357,0.2373,0.2414, 0.2448,0.2457,0.2522,0.2562,0.2587,0.2592,0.2613,0.2663,0.2701,0.2724, 0.2755,0.2778,0.2833,0.2872,0.2878,0.2883,0.2984,0.3016,0.3020,0.3033, 0.3034,0.3050,0.3116,0.3141,0.3198,0.3213,0.3369,0.3393,0.3406,0.3436, 0.3492,0.3542,0.3673,0.3749,0.3914,0.3968,0.4014,0.4014,0.4029,0.4036, 0.4043,0.4135,0.4155,0.4216,0.4226,0.4317,0.4363,0.4384,0.4438,0.4440, 0.4455,0.4502,0.4531,0.4540,0.4572,0.4611,0.4627,0.4674,0.4706,0.4709, 0.4726,0.4828,0.4913,0.4932,0.5000,0.5009,0.5011,0.5014,0.5026,0.5055, 0.5091,0.5102,0.5149,0.5149,0.5168,0.5202,0.5212,0.5220,0.5231,0.5237, 0.5258,0.5259,0.5278,0.5332,0.5340,0.5380,0.5388,0.5419,0.5448,0.5468, 0.5472,0.5476,0.5532,0.5536,0.5545,0.5559,0.5576,0.5622,0.5694,0.5725, 0.5773,0.5810,0.5827,0.5829,0.5830,0.5849,0.5858,0.5921,0.5988,0.5989, 0.6002,0.6027,0.6219,0.6330,0.6332,0.6348,0.6390,0.6412,0.6496,0.6523, 0.6608,0.6645,0.6722,0.6750,0.6937,0.6980,0.7002,0.7052,0.7101,0.7105, 0.7160,0.7171,0.7291,0.7399,0.7403,0.7420,0.7438,0.7471,0.7483,0.7495, 0.7624,0.7677,0.7685,0.7776,0.7848,0.7851,0.7869,0.7902,0.7904,0.7925, 0.8009,0.8044,0.8113,0.8156,0.8184,0.8194,0.8215,0.8247,0.8250,0.8344, 0.8402,0.8447,0.8447,0.8473,0.8479,0.8526,0.8546,0.8588,0.8607,0.8636, 0.8652,0.8656,0.8686,0.8696,0.8717,0.8731,0.8732,0.8735,0.8736,0.8787, 0.8821,0.8832,0.8886,0.8888,0.8926,0.9012,0.9020,0.9033,0.9055,0.9057, 0.9074,0.9084,0.9171,0.9218,0.9339,0.9360,0.9384,0.9470,0.9499,0.9565, 0.9582,0.9740,0.9778,0.9852,0.9867,0.9898,0.9934,0.9942,0.9958, Overall p-value after applying KStest on 269 p-values = 0.750031 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.