RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-06-20_05:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.38 25.7445 0.920757 2 to 25 15.86 8.3591 0.041747 3 to 26 15.60 28.7885 0.963473 4 to 27 15.79 20.5472 0.752798 5 to 28 15.71 12.1134 0.206777 6 to 29 15.68 21.2552 0.784919 7 to 30 15.64 11.9163 0.194820 8 to 31 15.82 14.7376 0.385625 9 to 32 15.74 21.6191 0.800187 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.561538 Tough bday spacings test for dh-ranFile-2015-06-20_05:31: 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 7 46 86 81 100 81 43 30 16 9 1 (O-E)^2/E 0.5 2.4 2.2 2.8 0.1 0.1 1.6 0.0 0.1 0.9 2.3 Birthday Spacings: Sum(O-E)^2/E= 12.973, p= 0.775 RESULTS OF GCD FOR dh-ranFile-2015-06-20_05:31 Euclid's algorithm: p-value, steps to gcd: 0.286218 p-value, dist. of gcd's: 0.801977 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-06-20_05:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.308 0.357 0.127 0.051 0.972 0.566 0.741 0.679 Bits 8 to 15---> 0.696 0.741 0.029 0.313 0.586 0.532 0.655 0.498 Bits 16 to 23---> 0.321 0.187 0.557 0.081 0.723 0.266 0.653 0.598 Bits 24 to 31---> 0.848 0.612 0.639 0.924 0.285 0.551 0.956 0.020 KS test for the above 32 p values: 0.266 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-06-20_05:31, p-values for 5 runs: 0.6357, 0.4455, 0.1702, 0.5127, 0.6007 Rank test for binary matrices (31x31) for dh-ranFile-2015-06-20_05:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 210 211.4 0.010 0.010 r= 29 5064 5134.0 0.955 0.964 r= 30 23073 23103.0 0.039 1.003 r= 31 11653 11551.5 0.891 1.895 chi-square = 1.895 with df = 3; p-value = 0.405 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-06-20_05:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 208 211.4 0.055 0.055 r= 30 5201 5134.0 0.874 0.929 r= 31 22899 23103.0 1.802 2.732 r= 32 11692 11551.5 1.708 4.440 chi-square = 4.440 with df = 3; p-value = 0.782 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-06-20_05:31 b-rank test for bits 1 to 8, p=0.32934 b-rank test for bits 2 to 9, p=0.03360 b-rank test for bits 3 to 10, p=0.54637 b-rank test for bits 4 to 11, p=0.41834 b-rank test for bits 5 to 12, p=0.49662 b-rank test for bits 6 to 13, p=0.48449 b-rank test for bits 7 to 14, p=0.37128 b-rank test for bits 8 to 15, p=0.23176 b-rank test for bits 9 to 16, p=0.30193 b-rank test for bits 10 to 17, p=0.74464 b-rank test for bits 11 to 18, p=0.20987 b-rank test for bits 12 to 19, p=0.76409 b-rank test for bits 13 to 20, p=0.86869 b-rank test for bits 14 to 21, p=0.80675 b-rank test for bits 15 to 22, p=0.00504 b-rank test for bits 16 to 23, p=0.36673 b-rank test for bits 17 to 24, p=0.43282 b-rank test for bits 18 to 25, p=0.06040 b-rank test for bits 19 to 26, p=0.28256 b-rank test for bits 20 to 27, p=0.89136 b-rank test for bits 21 to 28, p=0.67717 b-rank test for bits 22 to 29, p=0.47455 b-rank test for bits 23 to 30, p=0.80390 b-rank test for bits 24 to 31, p=0.69147 b-rank test for bits 25 to 32, p=0.30073 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 = 0.572935 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-06-20_05:31 (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 142633 1.69 0.954564 2 141790 -0.28 0.390196 3 141848 -0.14 0.443029 4 143186 2.98 0.998572 5 142118 0.49 0.687065 6 141801 -0.25 0.400093 7 141785 -0.29 0.385720 8 142449 1.26 0.896330 9 142171 0.61 0.729526 10 142334 0.99 0.839455 11 142128 0.51 0.695293 12 142200 0.68 0.751474 13 141803 -0.25 0.401899 14 141838 -0.17 0.433819 15 142103 0.45 0.674546 16 142007 0.23 0.590255 17 141608 -0.70 0.240703 18 142745 1.95 0.974561 19 142286 0.88 0.810589 20 141900 -0.02 0.491304 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-06-20_05:31 Bits used No. missing words z-score p-value 23 to 32 141425 -1.6701 0.047449 22 to 31 141706 -0.7011 0.241609 21 to 30 142052 0.4920 0.688628 20 to 29 142358 1.5471 0.939085 19 to 28 141572 -1.1632 0.122373 18 to 27 142051 0.4885 0.687408 17 to 26 141862 -0.1632 0.435178 16 to 25 141959 0.1713 0.567997 15 to 24 141434 -1.6391 0.050599 14 to 23 141863 -0.1598 0.436536 13 to 22 142215 1.0540 0.854066 12 to 21 141908 -0.0046 0.498170 11 to 20 141871 -0.1322 0.447424 10 to 19 141831 -0.2701 0.393540 9 to 18 141990 0.2782 0.609560 8 to 17 142041 0.4540 0.675098 7 to 16 142059 0.5161 0.697109 6 to 15 142156 0.8506 0.802500 5 to 14 142390 1.6575 0.951289 4 to 13 141604 -1.0529 0.146202 3 to 12 141704 -0.7080 0.239462 2 to 11 141553 -1.2287 0.109588 1 to 10 142106 0.6782 0.751169 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-06-20_05:31 Bits used No. missing words z-score p-value 28 to 32 141688 -0.7503 0.226546 27 to 31 141937 0.0938 0.537365 26 to 30 142155 0.8328 0.797516 25 to 29 141712 -0.6689 0.251775 24 to 28 142230 1.0870 0.861485 23 to 27 141681 -0.7740 0.219465 22 to 26 141910 0.0023 0.500906 21 to 25 141489 -1.4248 0.077101 20 to 24 141540 -1.2520 0.105291 19 to 23 141764 -0.4926 0.311132 18 to 22 141805 -0.3537 0.361797 17 to 21 141869 -0.1367 0.445629 16 to 20 141729 -0.6113 0.270504 15 to 19 141423 -1.6486 0.049617 14 to 18 141912 0.0091 0.503611 13 to 17 142115 0.6972 0.757157 12 to 16 141788 -0.4113 0.340431 11 to 15 141968 0.1989 0.578822 10 to 14 142250 1.1548 0.875917 9 to 13 141870 -0.1333 0.446969 8 to 12 142012 0.3480 0.636093 7 to 11 141414 -1.6791 0.046568 6 to 10 141482 -1.4486 0.073728 5 to 9 142092 0.6192 0.732114 4 to 8 141888 -0.0723 0.471180 3 to 7 142028 0.4023 0.656258 2 to 6 141801 -0.3672 0.356727 1 to 5 142075 0.5616 0.712803 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-06-20_05:31 Bits used No. missing words z-score p-value 31 to 32 142439 1.5624 0.940909 30 to 31 141850 -0.1750 0.430534 29 to 30 142093 0.5418 0.706022 28 to 29 142556 1.9076 0.971777 27 to 28 141817 -0.2724 0.392673 26 to 27 142172 0.7748 0.780782 25 to 26 141897 -0.0364 0.485493 24 to 25 141651 -0.7620 0.223019 23 to 24 141812 -0.2871 0.387014 22 to 23 142232 0.9518 0.829408 21 to 22 142102 0.5683 0.715101 20 to 21 141760 -0.4405 0.329787 19 to 20 141332 -1.7030 0.044280 18 to 19 142162 0.7453 0.771967 17 to 18 142119 0.6185 0.731876 16 to 17 142080 0.5035 0.692677 15 to 16 141750 -0.4700 0.319178 14 to 15 141473 -1.2871 0.099028 13 to 14 141378 -1.5673 0.058517 12 to 13 141821 -0.2606 0.397216 11 to 12 141914 0.0138 0.505496 10 to 11 142357 1.3206 0.906676 9 to 10 142318 1.2055 0.885998 8 to 9 141738 -0.5054 0.306640 7 to 8 141884 -0.0747 0.470219 6 to 7 142013 0.3058 0.620126 5 to 6 141895 -0.0423 0.483141 4 to 5 141458 -1.3314 0.091536 3 to 4 142289 1.1200 0.868637 2 to 3 141715 -0.5732 0.283240 1 to 2 142053 0.4238 0.664146 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-06-20_05:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2454.48 -0.644 0.259866 Test results for specific bytes for dh-ranFile-2015-06-20_05:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2533.13 0.469 0.680298 2 to 9 2530.10 0.426 0.664809 3 to 10 2469.72 -0.428 0.334244 4 to 11 2380.00 -1.697 0.044849 5 to 12 2401.27 -1.396 0.081313 6 to 13 2411.20 -1.256 0.104594 7 to 14 2598.34 1.391 0.917857 8 to 15 2576.92 1.088 0.861659 9 to 16 2423.11 -1.087 0.138430 10 to 17 2505.39 0.076 0.530383 11 to 18 2619.64 1.692 0.954667 12 to 19 2413.58 -1.222 0.110812 13 to 20 2540.34 0.570 0.715818 14 to 21 2536.86 0.521 0.698922 15 to 22 2501.17 0.017 0.506612 16 to 23 2522.15 0.313 0.622978 17 to 24 2621.47 1.718 0.957092 18 to 25 2589.48 1.265 0.897132 19 to 26 2498.69 -0.019 0.492584 20 to 27 2449.77 -0.710 0.238746 21 to 28 2483.74 -0.230 0.409062 22 to 29 2527.44 0.388 0.651017 23 to 30 2464.02 -0.509 0.305448 24 to 31 2551.06 0.722 0.764868 25 to 32 2507.75 0.110 0.543648 CDPARK for dh-ranFile-2015-06-20_05:31: 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 3541 0.8219 0.794438 3535 0.5479 0.708135 3515 -0.3653 0.357445 3477 -2.1005 0.017844 3506 -0.7763 0.218799 3513 -0.4566 0.323972 3538 0.6849 0.753306 3502 -0.9589 0.168804 3505 -0.8219 0.205562 3499 -1.0959 0.136563 Square side=100, avg. no. parked=3513.10 sample std.=19.03 p-value of the KSTEST for those 10 p-values: 0.211912 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-06-20_05:31 0.6484,0.2508,0.0847,0.4426,0.1942,0.6961,0.6549,0.6831,0.7574,0.7300, The KS test for those 10 p-values: 0.535798 The 3DSPHERES test for dh-ranFile-2015-06-20_05:31 sample no r^3 equiv. uni. 1 87.262 0.945455 2 29.065 0.620479 3 93.653 0.955920 4 19.494 0.477849 5 25.925 0.578600 6 7.377 0.217998 7 6.009 0.181526 8 8.619 0.249723 9 18.850 0.466516 10 20.995 0.503336 11 28.778 0.616824 12 97.482 0.961203 13 3.398 0.107083 14 48.940 0.804334 15 0.889 0.029186 16 7.857 0.230420 17 47.753 0.796432 18 7.675 0.225734 19 10.030 0.284185 20 34.350 0.681777 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.936421 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-06-20_05:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.1 -1.1 -1.6 -0.2 0.2 0.3 1.5 -0.3 -0.4 -1.6 0.2 -0.4 0.1 0.2 -0.2 -1.4 -0.9 -0.8 -0.5 0.2 0.7 1.6 0.1 0.8 0.6 1.2 1.9 0.1 0.1 1.3 0.4 -0.2 -0.1 2.0 1.9 0.3 -0.4 -0.8 -0.7 0.1 -1.0 -1.1 Chi-square with 42 degrees of freedom:34.746299 z-score=-0.791444, p-value=0.221152 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-06-20_05:31 Test no p-value 1 0.837343 2 0.034276 3 0.885936 4 0.647924 5 0.210233 6 0.147647 7 0.977897 8 0.022984 9 0.260952 10 0.714610 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.469756 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-06-20_05:31: (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 66681 0.00 66813 0.32 3 25000.00 24948 0.11 24887 0.51 4 6666.67 6744 0.90 6666 0.00 5 1388.89 1361 0.56 1357 0.73 6 238.10 222 1.09 242 0.06 7 34.72 39 0.53 31 0.40 8 4.96 4 0.19 3 0.77 p=0.23879 p=0.16667 Number of rngs required: 688342, p-value: 0.472 RESULTS OF CRAPS TEST for dh-ranFile-2015-06-20_05:31 No. of wins: Observed Expected 98641 98585.9 z-score= 0.247, pvalue=0.59740 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66685 66666.7 0.005 0.005 2 37923 37654.3 1.917 1.922 3 26977 26954.7 0.018 1.941 4 19004 19313.5 4.959 6.899 5 13685 13851.4 1.999 8.899 6 10140 9943.5 3.881 12.780 7 7001 7145.0 2.903 15.683 8 5197 5139.1 0.653 16.336 9 3698 3699.9 0.001 16.337 10 2627 2666.3 0.579 16.916 11 1929 1923.3 0.017 16.933 12 1407 1388.7 0.240 17.173 13 981 1003.7 0.514 17.687 14 738 726.1 0.194 17.881 15 534 525.8 0.127 18.008 16 390 381.2 0.205 18.213 17 299 276.5 1.824 20.037 18 226 200.8 3.155 23.192 19 126 146.0 2.736 25.928 20 127 106.2 4.067 29.995 21 306 287.1 1.242 31.237 Chisq= 31.24 for 20 degrees of freedom, p= 0.94786 SUMMARY of craptest p-value for no. of wins: 0.597401 p-value for throws/game: 0.947865 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-06-20_05:31 No. of wins: Observed Expected 98838 98585.9 z-score= 1.128, pvalue=0.87028 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66651 66666.7 0.004 0.004 2 37891 37654.3 1.488 1.491 3 26889 26954.7 0.160 1.652 4 19161 19313.5 1.204 2.855 5 13882 13851.4 0.068 2.923 6 9975 9943.5 0.100 3.022 7 7167 7145.0 0.068 3.090 8 5109 5139.1 0.176 3.266 9 3687 3699.9 0.045 3.311 10 2645 2666.3 0.170 3.481 11 1837 1923.3 3.875 7.356 12 1370 1388.7 0.253 7.608 13 1029 1003.7 0.637 8.245 14 743 726.1 0.391 8.637 15 519 525.8 0.089 8.726 16 379 381.2 0.012 8.738 17 293 276.5 0.980 9.718 18 232 200.8 4.838 14.555 19 148 146.0 0.028 14.583 20 112 106.2 0.315 14.898 21 281 287.1 0.130 15.028 Chisq= 15.03 for 20 degrees of freedom, p= 0.22522 SUMMARY of craptest p-value for no. of wins: 0.870282 p-value for throws/game: 0.225224 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0050,0.0178,0.0204,0.0230,0.0291,0.0292,0.0336,0.0343,0.0417,0.0443, 0.0448,0.0466,0.0474,0.0496,0.0506,0.0513,0.0585,0.0604,0.0737,0.0771, 0.0813,0.0813,0.0847,0.0915,0.0990,0.1046,0.1053,0.1071,0.1096,0.1108, 0.1224,0.1273,0.1366,0.1384,0.1462,0.1476,0.1667,0.1688,0.1702,0.1815, 0.1873,0.1942,0.1948,0.2056,0.2068,0.2099,0.2102,0.2119,0.2180,0.2188, 0.2195,0.2212,0.2230,0.2252,0.2257,0.2265,0.2304,0.2318,0.2387,0.2388, 0.2395,0.2407,0.2416,0.2497,0.2508,0.2518,0.2599,0.2610,0.2657,0.2659, 0.2705,0.2826,0.2832,0.2842,0.2848,0.2862,0.3007,0.3019,0.3054,0.3066, 0.3080,0.3111,0.3128,0.3192,0.3214,0.3240,0.3293,0.3298,0.3342,0.3404, 0.3567,0.3574,0.3575,0.3618,0.3667,0.3713,0.3856,0.3857,0.3870,0.3902, 0.3927,0.3935,0.3972,0.4001,0.4019,0.4055,0.4091,0.4183,0.4305,0.4328, 0.4338,0.4352,0.4365,0.4426,0.4430,0.4455,0.4456,0.4470,0.4474,0.4665, 0.4698,0.4702,0.4712,0.4720,0.4745,0.4778,0.4831,0.4845,0.4855,0.4913, 0.4926,0.4966,0.4976,0.4982,0.5009,0.5033,0.5036,0.5055,0.5066,0.5127, 0.5304,0.5320,0.5358,0.5374,0.5436,0.5464,0.5507,0.5566,0.5615,0.5662, 0.5680,0.5729,0.5786,0.5788,0.5860,0.5903,0.5974,0.5979,0.6007,0.6096, 0.6122,0.6168,0.6201,0.6205,0.6230,0.6357,0.6361,0.6391,0.6479,0.6484, 0.6510,0.6529,0.6549,0.6554,0.6563,0.6641,0.6648,0.6745,0.6751,0.6772, 0.6788,0.6803,0.6818,0.6831,0.6871,0.6874,0.6886,0.6915,0.6927,0.6953, 0.6961,0.6962,0.6971,0.6989,0.7060,0.7081,0.7128,0.7146,0.7151,0.7158, 0.7225,0.7295,0.7300,0.7319,0.7321,0.7406,0.7413,0.7446,0.7512,0.7515, 0.7528,0.7533,0.7572,0.7574,0.7641,0.7649,0.7720,0.7748,0.7808,0.7823, 0.7849,0.7944,0.7964,0.7975,0.8002,0.8020,0.8025,0.8039,0.8043,0.8068, 0.8106,0.8294,0.8373,0.8395,0.8484,0.8541,0.8615,0.8617,0.8686,0.8687, 0.8703,0.8759,0.8859,0.8860,0.8914,0.8963,0.8971,0.9067,0.9179,0.9208, 0.9238,0.9364,0.9391,0.9409,0.9455,0.9479,0.9513,0.9546,0.9547,0.9557, 0.9559,0.9571,0.9612,0.9635,0.9718,0.9718,0.9746,0.9779,0.9986, Overall p-value after applying KStest on 269 p-values = 0.562815 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.