RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-07-11_07:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.79 19.2792 0.687259 2 to 25 15.63 9.0461 0.061195 3 to 26 16.07 16.0056 0.476561 4 to 27 15.99 21.9839 0.814661 5 to 28 15.78 14.4183 0.362694 6 to 29 15.53 19.9720 0.724338 7 to 30 15.74 17.9956 0.610883 8 to 31 15.52 25.5513 0.916968 9 to 32 15.71 17.9393 0.607318 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.541974 Tough bday spacings test for dh-ranFile-2015-07-11_07:31: 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 11 42 75 107 87 75 45 30 21 5 2 (O-E)^2/E 0.4 0.8 0.0 0.9 1.2 0.1 1.0 0.0 2.5 0.4 1.0 Birthday Spacings: Sum(O-E)^2/E= 8.308, p= 0.401 RESULTS OF GCD FOR dh-ranFile-2015-07-11_07:31 Euclid's algorithm: p-value, steps to gcd: 0.604415 p-value, dist. of gcd's: 0.745316 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-07-11_07:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.787 0.547 0.501 0.852 0.824 0.037 0.513 0.990 Bits 8 to 15---> 0.992 0.780 0.424 0.535 0.695 0.916 0.867 0.491 Bits 16 to 23---> 0.867 0.289 0.003 0.474 0.083 0.469 0.931 0.327 Bits 24 to 31---> 0.942 0.289 0.410 0.836 0.044 0.099 0.197 0.059 KS test for the above 32 p values: 0.599 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-07-11_07:31, p-values for 5 runs: 0.1815, 0.3306, 0.0032, 0.3961, 0.1142 Rank test for binary matrices (31x31) for dh-ranFile-2015-07-11_07:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 217 211.4 0.147 0.147 r= 29 5214 5134.0 1.246 1.394 r= 30 22955 23103.0 0.949 2.342 r= 31 11614 11551.5 0.338 2.680 chi-square = 2.680 with df = 3; p-value = 0.556 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-07-11_07:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 214 211.4 0.032 0.032 r= 30 5121 5134.0 0.033 0.065 r= 31 23161 23103.0 0.145 0.210 r= 32 11504 11551.5 0.196 0.405 chi-square = 0.405 with df = 3; p-value = 0.061 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-07-11_07:31 b-rank test for bits 1 to 8, p=0.32856 b-rank test for bits 2 to 9, p=0.27016 b-rank test for bits 3 to 10, p=0.38659 b-rank test for bits 4 to 11, p=0.87868 b-rank test for bits 5 to 12, p=0.55366 b-rank test for bits 6 to 13, p=0.02833 b-rank test for bits 7 to 14, p=0.35148 b-rank test for bits 8 to 15, p=0.58694 b-rank test for bits 9 to 16, p=0.97762 b-rank test for bits 10 to 17, p=0.51677 b-rank test for bits 11 to 18, p=0.54476 b-rank test for bits 12 to 19, p=0.76932 b-rank test for bits 13 to 20, p=0.69143 b-rank test for bits 14 to 21, p=0.75038 b-rank test for bits 15 to 22, p=0.78686 b-rank test for bits 16 to 23, p=0.24663 b-rank test for bits 17 to 24, p=0.92035 b-rank test for bits 18 to 25, p=0.88647 b-rank test for bits 19 to 26, p=0.35927 b-rank test for bits 20 to 27, p=0.85354 b-rank test for bits 21 to 28, p=0.36331 b-rank test for bits 22 to 29, p=0.58025 b-rank test for bits 23 to 30, p=0.36853 b-rank test for bits 24 to 31, p=0.03565 b-rank test for bits 25 to 32, p=0.34573 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 = 0.640135 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-07-11_07:31 (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 142212 0.71 0.760271 2 142285 0.88 0.809956 3 141260 -1.52 0.064617 4 141584 -0.76 0.223592 5 142187 0.65 0.741754 6 141890 -0.05 0.481989 7 142489 1.35 0.912191 8 142137 0.53 0.702616 9 141939 0.07 0.527634 10 142154 0.57 0.716223 11 141932 0.05 0.521121 12 142218 0.72 0.764604 13 142016 0.25 0.598408 14 141354 -1.30 0.097230 15 141928 0.04 0.517397 16 142597 1.61 0.945941 17 141010 -2.10 0.017810 18 142319 0.96 0.830760 19 141621 -0.67 0.250261 20 142442 1.24 0.893353 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-07-11_07:31 Bits used No. missing words z-score p-value 23 to 32 141369 -1.8632 0.031217 22 to 31 141821 -0.3046 0.380341 21 to 30 141812 -0.3356 0.368579 20 to 29 141768 -0.4873 0.313007 19 to 28 141861 -0.1667 0.433821 18 to 27 141755 -0.5322 0.297303 17 to 26 142123 0.7368 0.769376 16 to 25 141607 -1.0425 0.148586 15 to 24 141621 -0.9942 0.160053 14 to 23 142408 1.7196 0.957243 13 to 22 141913 0.0127 0.505049 12 to 21 142400 1.6920 0.954674 11 to 20 141858 -0.1770 0.429754 10 to 19 142675 2.6402 0.995858 9 to 18 141859 -0.1736 0.431109 8 to 17 142304 1.3609 0.913232 7 to 16 141710 -0.6873 0.245933 6 to 15 142036 0.4368 0.668869 5 to 14 141972 0.2161 0.585547 4 to 13 141504 -1.3977 0.081103 3 to 12 141209 -2.4149 0.007869 2 to 11 142247 1.1644 0.877865 1 to 10 141982 0.2506 0.598933 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-07-11_07:31 Bits used No. missing words z-score p-value 28 to 32 141736 -0.5876 0.278414 27 to 31 142024 0.3887 0.651255 26 to 30 141845 -0.2181 0.413688 25 to 29 141865 -0.1503 0.440275 24 to 28 141732 -0.6011 0.273881 23 to 27 141857 -0.1774 0.429601 22 to 26 142061 0.5141 0.696421 21 to 25 142218 1.0463 0.852298 20 to 24 141811 -0.3333 0.369446 19 to 23 142047 0.4667 0.679635 18 to 22 141391 -1.7571 0.039455 17 to 21 141607 -1.0248 0.152718 16 to 20 142243 1.1311 0.870990 15 to 19 142026 0.3955 0.653760 14 to 18 141658 -0.8520 0.197116 13 to 17 141447 -1.5672 0.058532 12 to 16 141665 -0.8282 0.203768 11 to 15 141635 -0.9299 0.176203 10 to 14 141786 -0.4181 0.337949 9 to 13 142519 2.0667 0.980618 8 to 12 142520 2.0701 0.980777 7 to 11 141524 -1.3062 0.095742 6 to 10 141917 0.0260 0.510371 5 to 9 142021 0.3785 0.647486 4 to 8 141904 -0.0181 0.492792 3 to 7 141943 0.1141 0.545435 2 to 6 141610 -1.0147 0.155130 1 to 5 141575 -1.1333 0.128540 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-07-11_07:31 Bits used No. missing words z-score p-value 31 to 32 142202 0.8633 0.806023 30 to 31 142717 2.3825 0.991402 29 to 30 142132 0.6568 0.744359 28 to 29 141565 -1.0157 0.154881 27 to 28 141803 -0.3137 0.376891 26 to 27 141957 0.1406 0.555915 25 to 26 141668 -0.7119 0.238267 24 to 25 141909 -0.0010 0.499612 23 to 24 141845 -0.1898 0.424747 22 to 23 142427 1.5271 0.936626 21 to 22 142121 0.6244 0.733816 20 to 21 141890 -0.0570 0.477264 19 to 20 141735 -0.5142 0.303539 18 to 19 141619 -0.8564 0.195880 17 to 18 142246 0.9931 0.839676 16 to 17 141722 -0.5526 0.290270 15 to 16 141692 -0.6411 0.260732 14 to 15 142179 0.7955 0.786835 13 to 14 141459 -1.3284 0.092022 12 to 13 142117 0.6126 0.729928 11 to 12 142166 0.7571 0.775517 10 to 11 142291 1.1259 0.869890 9 to 10 142652 2.1908 0.985766 8 to 9 142237 0.9666 0.833123 7 to 8 141911 0.0049 0.501965 6 to 7 141556 -1.0423 0.148643 5 to 6 141760 -0.4405 0.329787 4 to 5 141735 -0.5142 0.303539 3 to 4 142569 1.9459 0.974168 2 to 3 142239 0.9725 0.834594 1 to 2 141715 -0.5732 0.283240 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-07-11_07:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2446.76 -0.753 0.225729 Test results for specific bytes for dh-ranFile-2015-07-11_07:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2550.26 0.711 0.761406 2 to 9 2409.37 -1.282 0.099977 3 to 10 2526.09 0.369 0.643914 4 to 11 2554.41 0.770 0.779211 5 to 12 2497.64 -0.033 0.486687 6 to 13 2470.61 -0.416 0.338837 7 to 14 2429.49 -0.997 0.159351 8 to 15 2515.94 0.225 0.589196 9 to 16 2434.64 -0.924 0.177642 10 to 17 2606.33 1.504 0.933668 11 to 18 2552.21 0.738 0.769835 12 to 19 2492.15 -0.111 0.455777 13 to 20 2545.97 0.650 0.742213 14 to 21 2423.06 -1.088 0.138287 15 to 22 2693.54 2.737 0.996900 16 to 23 2531.01 0.439 0.669527 17 to 24 2582.67 1.169 0.878823 18 to 25 2344.67 -2.197 0.014023 19 to 26 2493.24 -0.096 0.461905 20 to 27 2552.27 0.739 0.770122 21 to 28 2643.95 2.036 0.979112 22 to 29 2432.12 -0.960 0.168541 23 to 30 2444.80 -0.781 0.217518 24 to 31 2425.12 -1.059 0.144815 25 to 32 2552.67 0.745 0.771841 CDPARK for dh-ranFile-2015-07-11_07:31: 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 3511 -0.5479 0.291865 3534 0.5023 0.692266 3528 0.2283 0.590298 3534 0.5023 0.692266 3517 -0.2740 0.392053 3514 -0.4110 0.340551 3524 0.0457 0.518210 3553 1.3699 0.914635 3531 0.3653 0.642555 3521 -0.0913 0.463617 Square side=100, avg. no. parked=3526.70 sample std.=11.66 p-value of the KSTEST for those 10 p-values: 0.367481 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-07-11_07:31 0.7870,0.7231,0.9057,0.0973,0.0189,0.9348,0.0594,0.4555,0.5434,0.7501, The KS test for those 10 p-values: 0.540644 The 3DSPHERES test for dh-ranFile-2015-07-11_07:31 sample no r^3 equiv. uni. 1 12.268 0.335639 2 3.102 0.098220 3 2.026 0.065308 4 40.076 0.737071 5 68.447 0.897875 6 2.898 0.092093 7 50.395 0.813596 8 16.304 0.419272 9 27.979 0.606481 10 0.895 0.029385 11 27.467 0.599713 12 15.285 0.399206 13 0.563 0.018599 14 4.233 0.131593 15 56.664 0.848748 16 66.416 0.890723 17 144.554 0.991921 18 18.512 0.460481 19 2.794 0.088942 20 40.497 0.740736 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.366527 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-07-11_07:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 1.3 0.1 -1.9 -1.2 1.1 -0.4 0.6 0.0 1.2 -0.3 -0.7 0.1 -0.0 0.5 -0.6 0.6 -0.4 -0.8 1.3 -0.2 0.8 0.2 -0.6 -1.3 1.7 -0.9 -1.4 -0.2 -0.1 0.8 -1.1 2.4 0.9 -1.0 -1.2 -1.4 -1.0 0.9 0.4 0.1 -1.0 -1.1 Chi-square with 42 degrees of freedom:39.763996 z-score=-0.243968, p-value=0.430426 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-07-11_07:31 Test no p-value 1 0.188220 2 0.162591 3 0.855849 4 0.383644 5 0.497011 6 0.121037 7 0.191390 8 0.379483 9 0.407302 10 0.759175 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.316990 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-07-11_07:31: (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 66531 0.28 66944 1.15 3 25000.00 25133 0.71 24944 0.13 4 6666.67 6635 0.15 6494 4.47 5 1388.89 1425 0.94 1336 2.01 6 238.10 222 1.09 231 0.21 7 34.72 42 1.53 45 3.04 8 4.96 11 7.36 5 0.00 p=0.93897 p=0.91227 Number of rngs required: 687854, p-value: 0.263 RESULTS OF CRAPS TEST for dh-ranFile-2015-07-11_07:31 No. of wins: Observed Expected 98895 98585.9 z-score= 1.383, pvalue=0.91662 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66595 66666.7 0.077 0.077 2 37380 37654.3 1.998 2.076 3 26921 26954.7 0.042 2.118 4 19369 19313.5 0.160 2.277 5 13946 13851.4 0.646 2.923 6 9968 9943.5 0.060 2.983 7 7227 7145.0 0.940 3.924 8 5202 5139.1 0.771 4.694 9 3661 3699.9 0.408 5.103 10 2652 2666.3 0.077 5.179 11 1965 1923.3 0.903 6.082 12 1402 1388.7 0.127 6.209 13 1008 1003.7 0.018 6.227 14 788 726.1 5.270 11.497 15 468 525.8 6.361 17.858 16 397 381.2 0.659 18.517 17 266 276.5 0.402 18.919 18 208 200.8 0.256 19.175 19 176 146.0 6.171 25.346 20 114 106.2 0.571 25.917 21 287 287.1 0.000 25.917 Chisq= 25.92 for 20 degrees of freedom, p= 0.83143 SUMMARY of craptest p-value for no. of wins: 0.916616 p-value for throws/game: 0.831428 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-07-11_07:31 No. of wins: Observed Expected 98494 98585.9 z-score=-0.411, pvalue=0.34059 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66882 66666.7 0.696 0.696 2 37762 37654.3 0.308 1.003 3 27042 26954.7 0.283 1.286 4 19267 19313.5 0.112 1.398 5 13793 13851.4 0.246 1.644 6 9795 9943.5 2.219 3.863 7 7216 7145.0 0.705 4.568 8 5198 5139.1 0.676 5.244 9 3652 3699.9 0.619 5.863 10 2622 2666.3 0.736 6.599 11 1897 1923.3 0.360 6.960 12 1298 1388.7 5.929 12.888 13 996 1003.7 0.059 12.948 14 719 726.1 0.070 13.018 15 483 525.8 3.490 16.508 16 376 381.2 0.070 16.577 17 292 276.5 0.864 17.441 18 192 200.8 0.388 17.830 19 149 146.0 0.062 17.892 20 106 106.2 0.000 17.892 21 263 287.1 2.025 19.918 Chisq= 19.92 for 20 degrees of freedom, p= 0.53691 SUMMARY of craptest p-value for no. of wins: 0.340593 p-value for throws/game: 0.536912 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0032,0.0032,0.0079,0.0140,0.0178,0.0186,0.0189,0.0283,0.0294,0.0312, 0.0357,0.0367,0.0395,0.0436,0.0585,0.0585,0.0594,0.0609,0.0612,0.0646, 0.0653,0.0811,0.0831,0.0889,0.0920,0.0921,0.0957,0.0972,0.0973,0.0982, 0.0989,0.1000,0.1142,0.1210,0.1285,0.1316,0.1383,0.1448,0.1486,0.1486, 0.1527,0.1549,0.1551,0.1594,0.1601,0.1626,0.1685,0.1762,0.1776,0.1815, 0.1882,0.1914,0.1959,0.1967,0.1971,0.2038,0.2175,0.2236,0.2257,0.2383, 0.2459,0.2466,0.2503,0.2607,0.2632,0.2702,0.2739,0.2784,0.2832,0.2894, 0.2894,0.2903,0.2919,0.2973,0.3035,0.3035,0.3130,0.3170,0.3273,0.3286, 0.3298,0.3306,0.3356,0.3379,0.3388,0.3406,0.3406,0.3457,0.3515,0.3593, 0.3627,0.3633,0.3665,0.3675,0.3685,0.3686,0.3694,0.3769,0.3795,0.3803, 0.3836,0.3866,0.3921,0.3961,0.3992,0.4012,0.4073,0.4095,0.4137,0.4193, 0.4238,0.4247,0.4296,0.4298,0.4304,0.4311,0.4338,0.4403,0.4555,0.4558, 0.4605,0.4619,0.4636,0.4689,0.4736,0.4766,0.4773,0.4820,0.4867,0.4908, 0.4928,0.4970,0.4996,0.5009,0.5020,0.5050,0.5104,0.5130,0.5168,0.5174, 0.5182,0.5211,0.5276,0.5351,0.5369,0.5406,0.5420,0.5434,0.5448,0.5454, 0.5471,0.5537,0.5559,0.5564,0.5802,0.5855,0.5869,0.5892,0.5903,0.5984, 0.5989,0.5991,0.5997,0.6044,0.6065,0.6073,0.6109,0.6401,0.6426,0.6439, 0.6475,0.6513,0.6538,0.6689,0.6695,0.6796,0.6873,0.6914,0.6923,0.6923, 0.6949,0.6964,0.7026,0.7162,0.7231,0.7243,0.7299,0.7338,0.7371,0.7407, 0.7418,0.7422,0.7444,0.7453,0.7501,0.7504,0.7592,0.7603,0.7614,0.7646, 0.7693,0.7694,0.7698,0.7701,0.7718,0.7755,0.7792,0.7799,0.7868,0.7869, 0.7870,0.7870,0.8060,0.8100,0.8136,0.8147,0.8238,0.8308,0.8314,0.8331, 0.8346,0.8359,0.8397,0.8487,0.8517,0.8523,0.8535,0.8558,0.8670,0.8675, 0.8699,0.8710,0.8779,0.8787,0.8788,0.8865,0.8907,0.8934,0.8979,0.9057, 0.9122,0.9123,0.9132,0.9146,0.9164,0.9166,0.9170,0.9204,0.9313,0.9337, 0.9348,0.9366,0.9390,0.9415,0.9459,0.9547,0.9572,0.9742,0.9776,0.9791, 0.9806,0.9808,0.9858,0.9899,0.9914,0.9919,0.9921,0.9959,0.9969, Overall p-value after applying KStest on 269 p-values = 0.835114 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.