RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-11-15_00:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.45 24.9800 0.904843 2 to 25 15.82 25.4119 0.914138 3 to 26 15.56 20.2137 0.736555 4 to 27 15.84 18.2109 0.624345 5 to 28 15.71 14.9151 0.398405 6 to 29 15.74 14.8037 0.390379 7 to 30 15.66 17.3953 0.572091 8 to 31 15.59 20.3871 0.745089 9 to 32 15.96 14.9385 0.400089 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.216414 Tough bday spacings test for dh-ranFile-2016-11-15_00:31: 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 13 42 88 87 93 65 56 34 15 5 2 (O-E)^2/E 1.6 0.8 3.0 1.2 0.2 2.2 0.3 0.6 0.0 0.4 1.0 Birthday Spacings: Sum(O-E)^2/E= 11.307, p= 0.666 RESULTS OF GCD FOR dh-ranFile-2016-11-15_00:31 Euclid's algorithm: p-value, steps to gcd: 0.938687 p-value, dist. of gcd's: 0.226272 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-11-15_00:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.670 0.044 0.560 0.732 0.340 0.869 0.247 0.485 Bits 8 to 15---> 0.059 0.848 0.067 0.598 0.798 0.184 0.381 0.289 Bits 16 to 23---> 0.907 0.276 0.300 0.998 0.430 0.792 0.370 0.412 Bits 24 to 31---> 0.113 0.186 0.978 0.224 0.251 0.922 0.410 0.756 KS test for the above 32 p values: 0.149 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-11-15_00:31, p-values for 5 runs: 0.9215, 0.9072, 0.5960, 0.2328, 0.6993 Rank test for binary matrices (31x31) for dh-ranFile-2016-11-15_00:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 227 211.4 1.148 1.148 r= 29 5028 5134.0 2.189 3.337 r= 30 23067 23103.0 0.056 3.394 r= 31 11678 11551.5 1.385 4.778 chi-square = 4.778 with df = 3; p-value = 0.811 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-11-15_00:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 205 211.4 0.195 0.195 r= 30 5140 5134.0 0.007 0.202 r= 31 23037 23103.0 0.189 0.391 r= 32 11618 11551.5 0.383 0.773 chi-square = 0.773 with df = 3; p-value = 0.144 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-11-15_00:31 b-rank test for bits 1 to 8, p=0.23666 b-rank test for bits 2 to 9, p=0.11731 b-rank test for bits 3 to 10, p=0.58367 b-rank test for bits 4 to 11, p=0.25289 b-rank test for bits 5 to 12, p=0.64164 b-rank test for bits 6 to 13, p=0.00452 b-rank test for bits 7 to 14, p=0.61736 b-rank test for bits 8 to 15, p=0.48140 b-rank test for bits 9 to 16, p=0.78370 b-rank test for bits 10 to 17, p=0.93145 b-rank test for bits 11 to 18, p=0.69206 b-rank test for bits 12 to 19, p=0.55891 b-rank test for bits 13 to 20, p=0.67824 b-rank test for bits 14 to 21, p=0.69102 b-rank test for bits 15 to 22, p=0.99085 b-rank test for bits 16 to 23, p=0.86581 b-rank test for bits 17 to 24, p=0.98984 b-rank test for bits 18 to 25, p=0.45381 b-rank test for bits 19 to 26, p=0.30324 b-rank test for bits 20 to 27, p=0.49636 b-rank test for bits 21 to 28, p=0.77168 b-rank test for bits 22 to 29, p=0.07532 b-rank test for bits 23 to 30, p=0.79269 b-rank test for bits 24 to 31, p=0.38601 b-rank test for bits 25 to 32, p=0.15994 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 = 0.707759 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-11-15_00:31 (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 141760 -0.35 0.363582 2 141870 -0.09 0.463392 3 141471 -1.02 0.152886 4 141702 -0.48 0.314045 5 142458 1.28 0.900068 6 143289 3.22 0.999367 7 142127 0.51 0.694475 8 141979 0.16 0.564654 9 140711 -2.80 0.002556 10 141141 -1.80 0.036314 11 142617 1.65 0.950879 12 141275 -1.48 0.069160 13 141417 -1.15 0.125009 14 140846 -2.48 0.006488 15 141297 -1.43 0.076261 16 141172 -1.72 0.042468 17 141171 -1.73 0.042257 18 142403 1.15 0.875634 19 142345 1.02 0.845642 20 141971 0.14 0.557285 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-11-15_00:31 Bits used No. missing words z-score p-value 23 to 32 141856 -0.1839 0.427047 22 to 31 142218 1.0644 0.856422 21 to 30 141696 -0.7356 0.230981 20 to 29 141587 -1.1115 0.133180 19 to 28 142083 0.5989 0.725368 18 to 27 141935 0.0885 0.535267 17 to 26 141345 -1.9460 0.025829 16 to 25 142228 1.0989 0.864086 15 to 24 141695 -0.7391 0.229933 14 to 23 141973 0.2196 0.586890 13 to 22 142278 1.2713 0.898185 12 to 21 141929 0.0678 0.527039 11 to 20 142130 0.7609 0.776651 10 to 19 141786 -0.4253 0.335318 9 to 18 142194 0.9816 0.836857 8 to 17 141864 -0.1563 0.437894 7 to 16 141852 -0.1977 0.421644 6 to 15 141641 -0.9253 0.177411 5 to 14 142035 0.4333 0.667618 4 to 13 141878 -0.1080 0.456984 3 to 12 141756 -0.5287 0.298498 2 to 11 141969 0.2058 0.581510 1 to 10 141861 -0.1667 0.433821 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-11-15_00:31 Bits used No. missing words z-score p-value 28 to 32 141808 -0.3435 0.365614 27 to 31 142225 1.0701 0.857706 26 to 30 141746 -0.5537 0.289905 25 to 29 141472 -1.4825 0.069107 24 to 28 141218 -2.3435 0.009552 23 to 27 141172 -2.4994 0.006220 22 to 26 141934 0.0836 0.533324 21 to 25 142022 0.3819 0.648744 20 to 24 141887 -0.0757 0.469831 19 to 23 141549 -1.2215 0.110956 18 to 22 141925 0.0531 0.521181 17 to 21 141983 0.2497 0.598602 16 to 20 141984 0.2531 0.599912 15 to 19 142238 1.1141 0.867390 14 to 18 141924 0.0497 0.519831 13 to 17 141930 0.0701 0.527930 12 to 16 142029 0.4057 0.657504 11 to 15 142107 0.6701 0.748593 10 to 14 142033 0.4192 0.662473 9 to 13 142552 2.1785 0.985317 8 to 12 142215 1.0362 0.849938 7 to 11 141934 0.0836 0.533324 6 to 10 142089 0.6091 0.728755 5 to 9 142021 0.3785 0.647486 4 to 8 141338 -1.9367 0.026390 3 to 7 141851 -0.1977 0.421629 2 to 6 142682 2.6192 0.995593 1 to 5 141654 -0.8655 0.193375 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-11-15_00:31 Bits used No. missing words z-score p-value 31 to 32 142169 0.7660 0.778158 30 to 31 141940 0.0905 0.536044 29 to 30 142025 0.3412 0.633527 28 to 29 141750 -0.4700 0.319178 27 to 28 142336 1.2586 0.895915 26 to 27 141749 -0.4729 0.318125 25 to 26 141428 -1.4199 0.077825 24 to 25 142100 0.5624 0.713095 23 to 24 142063 0.4533 0.674835 22 to 23 142071 0.4769 0.683284 21 to 22 142430 1.5359 0.937719 20 to 21 142319 1.2085 0.886566 19 to 20 140971 -2.7679 0.002821 18 to 19 141802 -0.3166 0.375771 17 to 18 142163 0.7483 0.772857 16 to 17 142480 1.6834 0.953850 15 to 16 142085 0.5182 0.697841 14 to 15 141325 -1.7237 0.042382 13 to 14 141955 0.1347 0.553583 12 to 13 141497 -1.2163 0.111933 11 to 12 141928 0.0551 0.521960 10 to 11 141745 -0.4847 0.313927 9 to 10 141584 -0.9597 0.168609 8 to 9 142467 1.6450 0.950020 7 to 8 141625 -0.8387 0.200810 6 to 7 141477 -1.2753 0.101100 5 to 6 142394 1.4297 0.923599 4 to 5 141626 -0.8358 0.201639 3 to 4 142218 0.9105 0.818729 2 to 3 141602 -0.9066 0.182315 1 to 2 141776 -0.3933 0.347048 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-11-15_00:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2508.89 0.126 0.550044 Test results for specific bytes for dh-ranFile-2016-11-15_00:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2518.20 0.257 0.601538 2 to 9 2456.72 -0.612 0.270241 3 to 10 2460.95 -0.552 0.290371 4 to 11 2575.63 1.070 0.857587 5 to 12 2469.60 -0.430 0.333643 6 to 13 2391.49 -1.535 0.062453 7 to 14 2540.97 0.579 0.718853 8 to 15 2523.19 0.328 0.628549 9 to 16 2524.97 0.353 0.638019 10 to 17 2592.65 1.310 0.904939 11 to 18 2540.42 0.572 0.716192 12 to 19 2479.79 -0.286 0.387511 13 to 20 2476.66 -0.330 0.370694 14 to 21 2603.54 1.464 0.928442 15 to 22 2522.36 0.316 0.624062 16 to 23 2528.57 0.404 0.656903 17 to 24 2493.68 -0.089 0.464363 18 to 25 2615.67 1.636 0.949065 19 to 26 2403.48 -1.365 0.086124 20 to 27 2510.00 0.141 0.556220 21 to 28 2505.03 0.071 0.528355 22 to 29 2456.97 -0.609 0.271409 23 to 30 2440.66 -0.839 0.200696 24 to 31 2474.55 -0.360 0.359457 25 to 32 2595.23 1.347 0.910972 CDPARK for dh-ranFile-2016-11-15_00:31: 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 3549 1.1872 0.882429 3512 -0.5023 0.307734 3572 2.2374 0.987371 3536 0.5936 0.723613 3568 2.0548 0.980051 3486 -1.6895 0.045562 3521 -0.0913 0.463617 3508 -0.6849 0.246694 3514 -0.4110 0.340551 3474 -2.2374 0.012629 Square side=100, avg. no. parked=3524.00 sample std.=30.76 p-value of the KSTEST for those 10 p-values: 0.369332 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-11-15_00:31 0.2067,0.0039,0.2493,0.1114,0.9278,0.1082,0.8623,0.3236,0.1204,0.2812, The KS test for those 10 p-values: 0.033519 The 3DSPHERES test for dh-ranFile-2016-11-15_00:31 sample no r^3 equiv. uni. 1 51.279 0.819005 2 40.419 0.740056 3 30.995 0.644125 4 93.014 0.954971 5 33.782 0.675698 6 4.357 0.135187 7 63.328 0.878877 8 60.980 0.869016 9 11.743 0.323922 10 38.831 0.725927 11 8.392 0.244020 12 31.596 0.651177 13 40.762 0.743010 14 9.137 0.262547 15 37.278 0.711365 16 6.802 0.202866 17 18.147 0.453875 18 2.937 0.093274 19 3.553 0.111687 20 21.162 0.506090 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.732584 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-11-15_00:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -2.4 -0.4 -1.3 -0.8 -1.5 0.7 0.3 -1.4 -0.1 -0.0 -0.3 -0.4 1.3 -0.4 0.1 -0.6 0.5 1.8 0.4 -1.9 0.9 0.2 -0.8 0.3 -0.5 0.2 -1.3 -0.9 0.3 1.6 -0.1 -0.3 0.1 1.7 0.6 2.1 0.5 -0.8 1.0 0.1 0.0 0.8 Chi-square with 42 degrees of freedom:41.036974 z-score=-0.105075, p-value=0.486866 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-11-15_00:31 Test no p-value 1 0.062202 2 0.422211 3 0.678155 4 0.091694 5 0.328306 6 0.072198 7 0.140803 8 0.054314 9 0.959296 10 0.052886 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.008419 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-11-15_00:31: (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 66704 0.02 66507 0.38 3 25000.00 25187 1.40 25240 2.30 4 6666.67 6496 4.37 6563 1.61 5 1388.89 1333 2.25 1406 0.21 6 238.10 240 0.02 250 0.60 7 34.72 34 0.01 30 0.64 8 4.96 5 0.00 3 0.77 p=0.76687 p=0.63255 Number of rngs required: 689968, p-value: 0.967 RESULTS OF CRAPS TEST for dh-ranFile-2016-11-15_00:31 No. of wins: Observed Expected 98564 98585.9 z-score=-0.098, pvalue=0.46106 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66926 66666.7 1.009 1.009 2 37476 37654.3 0.844 1.853 3 27093 26954.7 0.709 2.563 4 19355 19313.5 0.089 2.652 5 13734 13851.4 0.995 3.647 6 9925 9943.5 0.035 3.682 7 7016 7145.0 2.330 6.012 8 5126 5139.1 0.033 6.045 9 3710 3699.9 0.028 6.073 10 2636 2666.3 0.344 6.417 11 1904 1923.3 0.194 6.611 12 1401 1388.7 0.108 6.720 13 1047 1003.7 1.867 8.586 14 716 726.1 0.142 8.728 15 529 525.8 0.019 8.747 16 377 381.2 0.045 8.792 17 272 276.5 0.075 8.867 18 214 200.8 0.864 9.730 19 140 146.0 0.245 9.976 20 101 106.2 0.256 10.232 21 302 287.1 0.772 11.003 Chisq= 11.00 for 20 degrees of freedom, p= 0.05387 SUMMARY of craptest p-value for no. of wins: 0.461060 p-value for throws/game: 0.053867 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-11-15_00:31 No. of wins: Observed Expected 98841 98585.9 z-score= 1.141, pvalue=0.87309 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67120 66666.7 3.083 3.083 2 37366 37654.3 2.208 5.290 3 26796 26954.7 0.935 6.225 4 19348 19313.5 0.062 6.287 5 13675 13851.4 2.247 8.534 6 10066 9943.5 1.508 10.042 7 7072 7145.0 0.746 10.788 8 5150 5139.1 0.023 10.812 9 3744 3699.9 0.526 11.338 10 2653 2666.3 0.066 11.404 11 1928 1923.3 0.011 11.416 12 1425 1388.7 0.947 12.362 13 1045 1003.7 1.698 14.061 14 676 726.1 3.462 17.523 15 563 525.8 2.627 20.149 16 408 381.2 1.891 22.041 17 273 276.5 0.045 22.086 18 193 200.8 0.305 22.391 19 129 146.0 1.976 24.367 20 104 106.2 0.046 24.414 21 266 287.1 1.553 25.966 Chisq= 25.97 for 20 degrees of freedom, p= 0.83307 SUMMARY of craptest p-value for no. of wins: 0.873094 p-value for throws/game: 0.833071 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0026,0.0028,0.0039,0.0045,0.0062,0.0065,0.0084,0.0096,0.0126,0.0258, 0.0264,0.0335,0.0363,0.0423,0.0424,0.0425,0.0437,0.0456,0.0529,0.0539, 0.0543,0.0594,0.0622,0.0625,0.0669,0.0691,0.0692,0.0722,0.0753,0.0763, 0.0778,0.0861,0.0917,0.0933,0.1011,0.1082,0.1110,0.1114,0.1117,0.1119, 0.1129,0.1173,0.1204,0.1250,0.1332,0.1352,0.1408,0.1441,0.1494,0.1529, 0.1599,0.1686,0.1774,0.1823,0.1841,0.1859,0.1934,0.2007,0.2008,0.2016, 0.2029,0.2067,0.2164,0.2243,0.2263,0.2299,0.2310,0.2328,0.2367,0.2440, 0.2467,0.2469,0.2493,0.2505,0.2529,0.2625,0.2702,0.2714,0.2757,0.2812, 0.2895,0.2899,0.2904,0.2985,0.3004,0.3032,0.3077,0.3139,0.3140,0.3181, 0.3192,0.3236,0.3239,0.3283,0.3336,0.3353,0.3403,0.3406,0.3470,0.3595, 0.3636,0.3656,0.3693,0.3704,0.3707,0.3758,0.3813,0.3860,0.3875,0.3904, 0.3984,0.4001,0.4101,0.4118,0.4216,0.4216,0.4222,0.4270,0.4298,0.4338, 0.4379,0.4538,0.4539,0.4570,0.4611,0.4634,0.4636,0.4644,0.4698,0.4814, 0.4849,0.4869,0.4964,0.5061,0.5198,0.5212,0.5220,0.5270,0.5279,0.5284, 0.5333,0.5333,0.5353,0.5360,0.5500,0.5536,0.5562,0.5573,0.5589,0.5598, 0.5647,0.5721,0.5815,0.5837,0.5869,0.5960,0.5979,0.5986,0.5999,0.6015, 0.6174,0.6241,0.6243,0.6285,0.6326,0.6335,0.6380,0.6416,0.6441,0.6475, 0.6487,0.6512,0.6569,0.6575,0.6625,0.6659,0.6676,0.6702,0.6748,0.6757, 0.6782,0.6782,0.6833,0.6910,0.6921,0.6945,0.6978,0.6993,0.7078,0.7114, 0.7131,0.7162,0.7189,0.7236,0.7254,0.7259,0.7288,0.7320,0.7326,0.7366, 0.7401,0.7430,0.7451,0.7486,0.7565,0.7669,0.7717,0.7729,0.7767,0.7782, 0.7837,0.7920,0.7927,0.7981,0.8112,0.8187,0.8190,0.8331,0.8369,0.8456, 0.8483,0.8499,0.8564,0.8576,0.8577,0.8623,0.8641,0.8658,0.8674,0.8690, 0.8691,0.8731,0.8756,0.8789,0.8824,0.8866,0.8959,0.8982,0.9001,0.9048, 0.9049,0.9072,0.9073,0.9110,0.9141,0.9215,0.9224,0.9236,0.9278,0.9284, 0.9315,0.9377,0.9387,0.9491,0.9500,0.9509,0.9539,0.9550,0.9593,0.9672, 0.9783,0.9801,0.9853,0.9874,0.9898,0.9909,0.9956,0.9978,0.9994, Overall p-value after applying KStest on 269 p-values = 0.545954 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.