RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-01-25_09:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.86 21.0460 0.775762 2 to 25 15.66 31.1761 0.980991 3 to 26 15.60 22.2654 0.825272 4 to 27 15.69 15.3307 0.428323 5 to 28 15.92 27.0427 0.942555 6 to 29 15.66 26.7130 0.937587 7 to 30 15.60 22.3576 0.828647 8 to 31 15.99 26.4258 0.932956 9 to 32 16.02 14.5291 0.370643 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.002627 Tough bday spacings test for dh-ranFile-2016-01-25_09:31: 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 10 34 71 103 87 74 58 32 14 9 8 (O-E)^2/E 0.1 0.2 0.1 0.3 1.2 0.2 0.7 0.2 0.1 0.9 3.8 Birthday Spacings: Sum(O-E)^2/E= 7.568, p= 0.329 RESULTS OF GCD FOR dh-ranFile-2016-01-25_09:31 Euclid's algorithm: p-value, steps to gcd: 0.340056 p-value, dist. of gcd's: 0.906801 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-01-25_09:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.511 0.471 0.988 0.334 0.353 0.815 0.835 0.108 Bits 8 to 15---> 0.998 0.097 0.534 0.933 0.903 0.188 0.976 0.020 Bits 16 to 23---> 0.945 0.767 0.360 0.946 0.752 0.509 0.901 0.668 Bits 24 to 31---> 0.892 0.723 0.241 0.830 0.509 0.701 0.117 0.498 KS test for the above 32 p values: 0.964 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-01-25_09:31, p-values for 5 runs: 0.8910, 0.7366, 0.1862, 0.5012, 0.9336 Rank test for binary matrices (31x31) for dh-ranFile-2016-01-25_09:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 193 211.4 1.605 1.605 r= 29 5123 5134.0 0.024 1.628 r= 30 23061 23103.0 0.077 1.705 r= 31 11623 11551.5 0.442 2.147 chi-square = 2.147 with df = 3; p-value = 0.458 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-01-25_09:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 201 211.4 0.513 0.513 r= 30 5213 5134.0 1.215 1.729 r= 31 23208 23103.0 0.477 2.205 r= 32 11378 11551.5 2.607 4.812 chi-square = 4.812 with df = 3; p-value = 0.814 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-01-25_09:31 b-rank test for bits 1 to 8, p=0.92193 b-rank test for bits 2 to 9, p=0.32696 b-rank test for bits 3 to 10, p=0.92560 b-rank test for bits 4 to 11, p=0.53036 b-rank test for bits 5 to 12, p=0.06445 b-rank test for bits 6 to 13, p=0.66358 b-rank test for bits 7 to 14, p=0.05061 b-rank test for bits 8 to 15, p=0.33738 b-rank test for bits 9 to 16, p=0.56768 b-rank test for bits 10 to 17, p=0.82414 b-rank test for bits 11 to 18, p=0.81737 b-rank test for bits 12 to 19, p=0.91926 b-rank test for bits 13 to 20, p=0.98865 b-rank test for bits 14 to 21, p=0.64606 b-rank test for bits 15 to 22, p=0.70144 b-rank test for bits 16 to 23, p=0.13898 b-rank test for bits 17 to 24, p=0.86594 b-rank test for bits 18 to 25, p=0.47864 b-rank test for bits 19 to 26, p=0.22034 b-rank test for bits 20 to 27, p=0.06057 b-rank test for bits 21 to 28, p=0.72071 b-rank test for bits 22 to 29, p=0.24941 b-rank test for bits 23 to 30, p=0.59820 b-rank test for bits 24 to 31, p=0.01673 b-rank test for bits 25 to 32, p=0.20202 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 = 0.845178 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-01-25_09:31 (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 141865 -0.10 0.458753 2 142336 1.00 0.840592 3 142196 0.67 0.748504 4 141873 -0.08 0.466177 5 141723 -0.44 0.331654 6 141892 -0.04 0.483851 7 141712 -0.46 0.322381 8 141722 -0.44 0.330807 9 141488 -0.98 0.162456 10 141475 -1.01 0.155103 11 141438 -1.10 0.135396 12 141542 -0.86 0.195378 13 141730 -0.42 0.337610 14 141710 -0.47 0.320706 15 141541 -0.86 0.194734 16 142009 0.23 0.592070 17 142025 0.27 0.606519 18 141810 -0.23 0.408238 19 142438 1.24 0.891624 20 142052 0.33 0.630562 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-01-25_09:31 Bits used No. missing words z-score p-value 23 to 32 142138 0.7885 0.784803 22 to 31 142021 0.3851 0.649907 21 to 30 141884 -0.0873 0.465199 20 to 29 141952 0.1471 0.558488 19 to 28 142151 0.8333 0.797675 18 to 27 141930 0.0713 0.528411 17 to 26 142233 1.1161 0.867811 16 to 25 142127 0.7506 0.773549 15 to 24 141681 -0.7873 0.215540 14 to 23 142257 1.1989 0.884709 13 to 22 142123 0.7368 0.769376 12 to 21 141872 -0.1287 0.448788 11 to 20 142214 1.0506 0.853276 10 to 19 142093 0.6333 0.736746 9 to 18 141642 -0.9218 0.178309 8 to 17 142724 2.8092 0.997517 7 to 16 141498 -1.4184 0.078040 6 to 15 141748 -0.5563 0.288999 5 to 14 141250 -2.2736 0.011496 4 to 13 142083 0.5989 0.725368 3 to 12 141724 -0.6391 0.261389 2 to 11 141832 -0.2667 0.394867 1 to 10 141730 -0.6184 0.268163 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-01-25_09:31 Bits used No. missing words z-score p-value 28 to 32 141756 -0.5198 0.301615 27 to 31 142160 0.8497 0.802262 26 to 30 142068 0.5379 0.704665 25 to 29 142059 0.5074 0.694048 24 to 28 141885 -0.0825 0.467135 23 to 27 142209 1.0158 0.845145 22 to 26 142157 0.8396 0.799422 21 to 25 141819 -0.3062 0.379725 20 to 24 141467 -1.4994 0.066882 19 to 23 142469 1.8972 0.971098 18 to 22 141505 -1.3706 0.085248 17 to 21 141574 -1.1367 0.127829 16 to 20 141968 0.1989 0.578822 15 to 19 142157 0.8396 0.799422 14 to 18 141919 0.0328 0.513075 13 to 17 142470 1.9006 0.971321 12 to 16 141166 -2.5198 0.005872 11 to 15 141774 -0.4587 0.323208 10 to 14 141398 -1.7333 0.041519 9 to 13 141268 -2.1740 0.014853 8 to 12 142484 1.9480 0.974295 7 to 11 141934 0.0836 0.533324 6 to 10 142325 1.4091 0.920590 5 to 9 142153 0.8260 0.795598 4 to 8 141815 -0.3198 0.374574 3 to 7 142347 1.4836 0.931046 2 to 6 142280 1.2565 0.895534 1 to 5 142140 0.7819 0.782873 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-01-25_09:31 Bits used No. missing words z-score p-value 31 to 32 141768 -0.4169 0.338375 30 to 31 142029 0.3530 0.637959 29 to 30 141837 -0.2134 0.415522 28 to 29 141842 -0.1986 0.421283 27 to 28 141997 0.2586 0.602033 26 to 27 141882 -0.0806 0.467872 25 to 26 141773 -0.4022 0.343786 24 to 25 142483 1.6922 0.954700 23 to 24 141972 0.1849 0.573333 22 to 23 141488 -1.2429 0.106959 21 to 22 142468 1.6480 0.950323 20 to 21 141619 -0.8564 0.195880 19 to 20 142288 1.1170 0.868007 18 to 19 142505 1.7571 0.960553 17 to 18 142012 0.3029 0.619002 16 to 17 142106 0.5801 0.719092 15 to 16 141932 0.0669 0.526659 14 to 15 141317 -1.7473 0.040294 13 to 14 141735 -0.5142 0.303539 12 to 13 141916 0.0197 0.507849 11 to 12 141750 -0.4700 0.319178 10 to 11 142328 1.2350 0.891588 9 to 10 141718 -0.5644 0.286243 8 to 9 142454 1.6067 0.945939 7 to 8 141715 -0.5732 0.283240 6 to 7 141724 -0.5467 0.292294 5 to 6 142147 0.7011 0.758377 4 to 5 141640 -0.7945 0.213457 3 to 4 141602 -0.9066 0.182315 2 to 3 141951 0.1229 0.548915 1 to 2 141362 -1.6145 0.053205 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-01-25_09:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2391.79 -1.530 0.062961 Test results for specific bytes for dh-ranFile-2016-01-25_09:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2582.81 1.171 0.879221 2 to 9 2565.13 0.921 0.821493 3 to 10 2565.42 0.925 0.822566 4 to 11 2443.97 -0.792 0.214065 5 to 12 2466.39 -0.475 0.317272 6 to 13 2480.33 -0.278 0.390422 7 to 14 2504.19 0.059 0.523620 8 to 15 2585.03 1.203 0.885426 9 to 16 2430.09 -0.989 0.161425 10 to 17 2481.64 -0.260 0.397575 11 to 18 2492.64 -0.104 0.458542 12 to 19 2539.22 0.555 0.710414 13 to 20 2520.69 0.293 0.615063 14 to 21 2495.56 -0.063 0.474981 15 to 22 2494.44 -0.079 0.468649 16 to 23 2508.66 0.123 0.548754 17 to 24 2461.27 -0.548 0.291953 18 to 25 2390.61 -1.547 0.060924 19 to 26 2474.40 -0.362 0.358686 20 to 27 2469.66 -0.429 0.333946 21 to 28 2551.02 0.722 0.764714 22 to 29 2487.05 -0.183 0.427350 23 to 30 2482.10 -0.253 0.400064 24 to 31 2511.25 0.159 0.563186 25 to 32 2541.01 0.580 0.719009 CDPARK for dh-ranFile-2016-01-25_09:31: 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 3532 0.4110 0.659449 3542 0.8676 0.807188 3545 1.0046 0.842447 3544 0.9589 0.831196 3475 -2.1918 0.014198 3534 0.5023 0.692266 3505 -0.8219 0.205562 3523 0.0000 0.500000 3533 0.4566 0.676028 3483 -1.8265 0.033889 Square side=100, avg. no. parked=3521.60 sample std.=24.08 p-value of the KSTEST for those 10 p-values: 0.439767 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-01-25_09:31 0.3126,0.6839,0.3935,0.5984,0.6618,0.4572,0.4155,0.1783,0.6653,0.2818, The KS test for those 10 p-values: 0.330748 The 3DSPHERES test for dh-ranFile-2016-01-25_09:31 sample no r^3 equiv. uni. 1 69.905 0.902721 2 31.369 0.648532 3 49.273 0.806494 4 15.063 0.394739 5 63.590 0.879930 6 27.980 0.606497 7 17.816 0.447817 8 23.769 0.547192 9 9.059 0.260629 10 19.276 0.474039 11 4.118 0.128266 12 9.002 0.259227 13 89.694 0.949702 14 117.969 0.980402 15 126.087 0.985048 16 18.367 0.457860 17 23.653 0.545438 18 40.571 0.741371 19 58.713 0.858732 20 3.708 0.116278 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.189492 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-01-25_09:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 0.1 1.8 0.6 -1.1 -1.7 0.3 -0.6 0.2 0.3 -0.8 0.2 -0.5 -0.7 0.2 -1.3 1.3 0.7 1.1 0.4 -0.2 -0.6 -0.3 -0.9 0.4 0.8 0.9 -1.6 -1.3 1.7 1.3 1.5 -1.1 -0.4 -1.6 0.1 0.5 -0.1 0.1 0.4 -0.6 2.0 -0.1 Chi-square with 42 degrees of freedom:38.372335 z-score=-0.395811, p-value=0.369016 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-01-25_09:31 Test no p-value 1 0.212313 2 0.661858 3 0.994761 4 0.012655 5 0.146698 6 0.076728 7 0.037649 8 0.073922 9 0.534412 10 0.547508 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.032174 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-01-25_09:31: (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 66777 0.18 66702 0.02 3 25000.00 25023 0.02 24905 0.36 4 6666.67 6563 1.61 6646 0.06 5 1388.89 1380 0.06 1457 3.34 6 238.10 211 3.08 254 1.06 7 34.72 39 0.53 31 0.40 8 4.96 6 0.22 4 0.19 p=0.54260 p=0.51013 Number of rngs required: 691736, p-value: 1.000 RESULTS OF CRAPS TEST for dh-ranFile-2016-01-25_09:31 No. of wins: Observed Expected 98491 98585.9 z-score=-0.424, pvalue=0.33569 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66399 66666.7 1.075 1.075 2 37863 37654.3 1.156 2.231 3 26713 26954.7 2.168 4.399 4 19308 19313.5 0.002 4.401 5 14046 13851.4 2.733 7.134 6 10047 9943.5 1.076 8.210 7 7210 7145.0 0.591 8.801 8 5107 5139.1 0.200 9.001 9 3698 3699.9 0.001 9.002 10 2628 2666.3 0.550 9.552 11 1935 1923.3 0.071 9.623 12 1399 1388.7 0.076 9.699 13 988 1003.7 0.246 9.945 14 710 726.1 0.359 10.304 15 520 525.8 0.065 10.369 16 404 381.2 1.370 11.738 17 289 276.5 0.561 12.300 18 215 200.8 1.000 13.300 19 137 146.0 0.553 13.853 20 100 106.2 0.364 14.216 21 284 287.1 0.034 14.250 Chisq= 14.25 for 20 degrees of freedom, p= 0.18241 SUMMARY of craptest p-value for no. of wins: 0.335687 p-value for throws/game: 0.182407 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-01-25_09:31 No. of wins: Observed Expected 98759 98585.9 z-score= 0.774, pvalue=0.78065 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66757 66666.7 0.122 0.122 2 37575 37654.3 0.167 0.289 3 26705 26954.7 2.314 2.603 4 19547 19313.5 2.824 5.427 5 13998 13851.4 1.551 6.978 6 9897 9943.5 0.218 7.196 7 7122 7145.0 0.074 7.270 8 5210 5139.1 0.979 8.249 9 3675 3699.9 0.167 8.416 10 2662 2666.3 0.007 8.423 11 1944 1923.3 0.222 8.645 12 1307 1388.7 4.811 13.457 13 993 1003.7 0.114 13.571 14 681 726.1 2.806 16.377 15 519 525.8 0.089 16.466 16 390 381.2 0.205 16.672 17 294 276.5 1.102 17.774 18 201 200.8 0.000 17.774 19 136 146.0 0.683 18.457 20 95 106.2 1.184 19.641 21 292 287.1 0.083 19.724 Chisq= 19.72 for 20 degrees of freedom, p= 0.52471 SUMMARY of craptest p-value for no. of wins: 0.780650 p-value for throws/game: 0.524715 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0026,0.0059,0.0115,0.0127,0.0142,0.0149,0.0167,0.0204,0.0322,0.0339, 0.0376,0.0403,0.0415,0.0506,0.0532,0.0606,0.0609,0.0630,0.0644,0.0669, 0.0739,0.0767,0.0780,0.0852,0.0966,0.1070,0.1078,0.1163,0.1171,0.1278, 0.1283,0.1354,0.1390,0.1467,0.1551,0.1614,0.1625,0.1783,0.1783,0.1823, 0.1824,0.1862,0.1875,0.1895,0.1947,0.1954,0.1959,0.2020,0.2056,0.2123, 0.2135,0.2141,0.2155,0.2203,0.2414,0.2494,0.2592,0.2606,0.2614,0.2682, 0.2818,0.2832,0.2862,0.2890,0.2920,0.2923,0.3016,0.3035,0.3126,0.3173, 0.3192,0.3207,0.3224,0.3232,0.3270,0.3290,0.3307,0.3308,0.3317,0.3339, 0.3341,0.3357,0.3374,0.3376,0.3384,0.3401,0.3438,0.3533,0.3587,0.3603, 0.3690,0.3706,0.3746,0.3797,0.3904,0.3935,0.3947,0.3949,0.3976,0.4001, 0.4082,0.4155,0.4155,0.4213,0.4274,0.4283,0.4398,0.4478,0.4488,0.4572, 0.4575,0.4579,0.4585,0.4588,0.4652,0.4662,0.4671,0.4679,0.4686,0.4707, 0.4740,0.4750,0.4786,0.4839,0.4977,0.5000,0.5012,0.5078,0.5087,0.5088, 0.5101,0.5115,0.5131,0.5236,0.5247,0.5267,0.5284,0.5304,0.5333,0.5336, 0.5344,0.5426,0.5454,0.5472,0.5475,0.5488,0.5489,0.5585,0.5632,0.5677, 0.5733,0.5788,0.5921,0.5982,0.5984,0.6020,0.6065,0.6065,0.6151,0.6190, 0.6306,0.6380,0.6461,0.6485,0.6499,0.6594,0.6618,0.6619,0.6636,0.6653, 0.6679,0.6760,0.6839,0.6923,0.6940,0.7012,0.7014,0.7047,0.7104,0.7190, 0.7191,0.7207,0.7228,0.7254,0.7366,0.7367,0.7414,0.7485,0.7515,0.7584, 0.7647,0.7671,0.7694,0.7735,0.7758,0.7806,0.7829,0.7848,0.7956,0.7977, 0.7994,0.7994,0.8023,0.8065,0.8072,0.8139,0.8155,0.8174,0.8215,0.8226, 0.8241,0.8253,0.8286,0.8296,0.8312,0.8346,0.8406,0.8424,0.8451,0.8452, 0.8533,0.8587,0.8659,0.8678,0.8680,0.8792,0.8799,0.8847,0.8854,0.8910, 0.8916,0.8916,0.8916,0.8955,0.9010,0.9027,0.9029,0.9068,0.9193,0.9206, 0.9219,0.9256,0.9310,0.9326,0.9330,0.9336,0.9376,0.9426,0.9451,0.9459, 0.9461,0.9497,0.9503,0.9547,0.9606,0.9643,0.9711,0.9713,0.9743,0.9761, 0.9804,0.9810,0.9850,0.9879,0.9886,0.9948,0.9975,0.9983,1.0000, Overall p-value after applying KStest on 269 p-values = 0.113132 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.