RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-01-06_14:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.99 14.8771 0.395668 2 to 25 16.00 14.9265 0.399222 3 to 26 15.84 25.4442 0.914801 4 to 27 15.55 30.9089 0.979512 5 to 28 15.73 19.1352 0.679171 6 to 29 15.75 33.8563 0.991238 7 to 30 15.71 11.2359 0.155961 8 to 31 15.75 12.1709 0.210322 9 to 32 16.06 15.6524 0.451404 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.290305 Tough bday spacings test for dh-ranFile-2016-01-06_14:31: 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 9 34 76 112 85 80 58 28 10 4 4 (O-E)^2/E 0.0 0.2 0.1 2.1 1.6 0.0 0.7 0.1 1.6 1.0 0.0 Birthday Spacings: Sum(O-E)^2/E= 7.495, p= 0.322 RESULTS OF GCD FOR dh-ranFile-2016-01-06_14:31 Euclid's algorithm: p-value, steps to gcd: 0.137285 p-value, dist. of gcd's: 0.874550 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-01-06_14:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.774 0.246 0.755 0.245 0.135 0.634 0.409 0.343 Bits 8 to 15---> 0.559 0.969 0.925 0.141 0.732 0.788 0.884 0.758 Bits 16 to 23---> 0.681 0.749 0.423 0.004 0.195 0.628 0.262 0.782 Bits 24 to 31---> 0.013 0.649 0.582 0.431 0.557 0.033 0.207 0.244 KS test for the above 32 p values: 0.182 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-01-06_14:31, p-values for 5 runs: 0.6850, 0.2124, 0.1576, 0.5445, 0.7053 Rank test for binary matrices (31x31) for dh-ranFile-2016-01-06_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 206 211.4 0.139 0.139 r= 29 5081 5134.0 0.547 0.686 r= 30 23033 23103.0 0.212 0.899 r= 31 11680 11551.5 1.429 2.327 chi-square = 2.327 with df = 3; p-value = 0.493 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-01-06_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 211 211.4 0.001 0.001 r= 30 5122 5134.0 0.028 0.029 r= 31 23084 23103.0 0.016 0.045 r= 32 11583 11551.5 0.086 0.130 chi-square = 0.130 with df = 3; p-value = 0.012 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-01-06_14:31 b-rank test for bits 1 to 8, p=0.02833 b-rank test for bits 2 to 9, p=0.47296 b-rank test for bits 3 to 10, p=0.58534 b-rank test for bits 4 to 11, p=0.93445 b-rank test for bits 5 to 12, p=0.03601 b-rank test for bits 6 to 13, p=0.75317 b-rank test for bits 7 to 14, p=0.50582 b-rank test for bits 8 to 15, p=0.15147 b-rank test for bits 9 to 16, p=0.36215 b-rank test for bits 10 to 17, p=0.35728 b-rank test for bits 11 to 18, p=0.41527 b-rank test for bits 12 to 19, p=0.44087 b-rank test for bits 13 to 20, p=0.93600 b-rank test for bits 14 to 21, p=0.05994 b-rank test for bits 15 to 22, p=0.29532 b-rank test for bits 16 to 23, p=0.27007 b-rank test for bits 17 to 24, p=0.22902 b-rank test for bits 18 to 25, p=0.98241 b-rank test for bits 19 to 26, p=0.87919 b-rank test for bits 20 to 27, p=0.94212 b-rank test for bits 21 to 28, p=0.93255 b-rank test for bits 22 to 29, p=0.08825 b-rank test for bits 23 to 30, p=0.34858 b-rank test for bits 24 to 31, p=0.49563 b-rank test for bits 25 to 32, p=0.94079 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 = 0.400292 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-01-06_14:31 (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 142335 0.99 0.840024 2 142637 1.70 0.955450 3 141787 -0.29 0.387509 4 142044 0.31 0.623486 5 142089 0.42 0.662681 6 142417 1.19 0.882217 7 140890 -2.38 0.008619 8 141982 0.17 0.567412 9 141979 0.16 0.564654 10 142189 0.65 0.743262 11 141816 -0.22 0.413691 12 142668 1.77 0.961852 13 142032 0.29 0.612795 14 142054 0.34 0.632324 15 142847 2.19 0.985768 16 141535 -0.87 0.190895 17 141399 -1.19 0.116560 18 141957 0.11 0.544342 19 142260 0.82 0.793699 20 142495 1.37 0.914405 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-01-06_14:31 Bits used No. missing words z-score p-value 23 to 32 142049 0.4816 0.684962 22 to 31 141878 -0.1080 0.456984 21 to 30 141988 0.2713 0.606911 20 to 29 142076 0.5747 0.717261 19 to 28 142048 0.4782 0.683736 18 to 27 141494 -1.4322 0.076047 17 to 26 142083 0.5989 0.725368 16 to 25 141546 -1.2529 0.105128 15 to 24 142137 0.7851 0.783793 14 to 23 141771 -0.4770 0.316681 13 to 22 141825 -0.2908 0.385605 12 to 21 141587 -1.1115 0.133180 11 to 20 142251 1.1782 0.880636 10 to 19 142340 1.4851 0.931237 9 to 18 141866 -0.1494 0.440614 8 to 17 142295 1.3299 0.908224 7 to 16 142057 0.5092 0.694696 6 to 15 141892 -0.0598 0.476174 5 to 14 141866 -0.1494 0.440614 4 to 13 142203 1.0127 0.844388 3 to 12 141936 0.0920 0.536637 2 to 11 142050 0.4851 0.686186 1 to 10 141780 -0.4460 0.327811 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-01-06_14:31 Bits used No. missing words z-score p-value 28 to 32 141874 -0.1198 0.452336 27 to 31 142111 0.6836 0.752895 26 to 30 141796 -0.3842 0.350426 25 to 29 141705 -0.6926 0.244267 24 to 28 142099 0.6429 0.739872 23 to 27 141561 -1.1808 0.118845 22 to 26 142070 0.5446 0.707001 21 to 25 142183 0.9277 0.823217 20 to 24 142079 0.5752 0.717406 19 to 23 142004 0.3209 0.625863 18 to 22 141396 -1.7401 0.040921 17 to 21 141348 -1.9028 0.028532 16 to 20 141647 -0.8893 0.186933 15 to 19 141563 -1.1740 0.120198 14 to 18 142113 0.6904 0.755031 13 to 17 141839 -0.2384 0.405783 12 to 16 141991 0.2768 0.609051 11 to 15 141437 -1.6011 0.054675 10 to 14 141856 -0.1808 0.428270 9 to 13 141844 -0.2215 0.412368 8 to 12 142517 2.0599 0.980296 7 to 11 142262 1.1955 0.884053 6 to 10 141665 -0.8282 0.203768 5 to 9 141761 -0.5028 0.307548 4 to 8 142056 0.4972 0.690471 3 to 7 142313 1.3684 0.914402 2 to 6 141730 -0.6079 0.271628 1 to 5 141995 0.2904 0.614248 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-01-06_14:31 Bits used No. missing words z-score p-value 31 to 32 141707 -0.5968 0.275306 30 to 31 141729 -0.5319 0.297381 29 to 30 142253 1.0138 0.844655 28 to 29 141888 -0.0629 0.474915 27 to 28 142196 0.8456 0.801122 26 to 27 141896 -0.0393 0.484317 25 to 26 141574 -0.9892 0.161289 24 to 25 141952 0.1259 0.550083 23 to 24 141951 0.1229 0.548915 22 to 23 142267 1.0551 0.854304 21 to 22 142211 0.8899 0.813235 20 to 21 142106 0.5801 0.719092 19 to 20 141631 -0.8210 0.205814 18 to 19 141923 0.0403 0.516083 17 to 18 141951 0.1229 0.548915 16 to 17 141923 0.0403 0.516083 15 to 16 141905 -0.0128 0.494905 14 to 15 141623 -0.8446 0.199158 13 to 14 141851 -0.1721 0.431693 12 to 13 141845 -0.1898 0.424747 11 to 12 142372 1.3648 0.913843 10 to 11 141713 -0.5791 0.281246 9 to 10 141688 -0.6529 0.256913 8 to 9 141814 -0.2812 0.389275 7 to 8 141438 -1.3904 0.082211 6 to 7 141901 -0.0246 0.490198 5 to 6 141965 0.1642 0.565220 4 to 5 141450 -1.3550 0.087716 3 to 4 141923 0.0403 0.516083 2 to 3 142254 1.0167 0.845358 1 to 2 141880 -0.0865 0.465527 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-01-06_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2429.89 -0.991 0.160721 Test results for specific bytes for dh-ranFile-2016-01-06_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2590.76 1.284 0.900345 2 to 9 2424.56 -1.067 0.143016 3 to 10 2494.85 -0.073 0.470958 4 to 11 2603.34 1.461 0.928060 5 to 12 2571.79 1.015 0.844998 6 to 13 2497.73 -0.032 0.487191 7 to 14 2448.54 -0.728 0.233379 8 to 15 2612.10 1.585 0.943554 9 to 16 2541.58 0.588 0.721758 10 to 17 2521.82 0.309 0.621172 11 to 18 2473.42 -0.376 0.353519 12 to 19 2641.97 2.008 0.977666 13 to 20 2539.59 0.560 0.712211 14 to 21 2466.76 -0.470 0.319170 15 to 22 2497.08 -0.041 0.483524 16 to 23 2397.78 -1.446 0.074138 17 to 24 2388.29 -1.580 0.057074 18 to 25 2614.55 1.620 0.947383 19 to 26 2528.90 0.409 0.658644 20 to 27 2527.76 0.393 0.652685 21 to 28 2368.79 -1.856 0.031761 22 to 29 2619.35 1.688 0.954279 23 to 30 2397.16 -1.454 0.072913 24 to 31 2561.96 0.876 0.809551 25 to 32 2373.37 -1.791 0.036656 CDPARK for dh-ranFile-2016-01-06_14:31: 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 3547 1.0959 0.863437 3517 -0.2740 0.392053 3534 0.5023 0.692266 3499 -1.0959 0.136563 3544 0.9589 0.831196 3507 -0.7306 0.232514 3521 -0.0913 0.463617 3473 -2.2831 0.011212 3515 -0.3653 0.357445 3534 0.5023 0.692266 Square side=100, avg. no. parked=3519.10 sample std.=21.31 p-value of the KSTEST for those 10 p-values: 0.934069 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-01-06_14:31 0.1137,0.0050,0.1932,0.7697,0.8094,0.8789,0.7829,0.7021,0.9299,0.6815, The KS test for those 10 p-values: 0.217942 The 3DSPHERES test for dh-ranFile-2016-01-06_14:31 sample no r^3 equiv. uni. 1 3.731 0.116950 2 15.026 0.394000 3 98.078 0.961966 4 34.210 0.680292 5 109.383 0.973907 6 18.938 0.468086 7 14.757 0.388530 8 17.108 0.434626 9 22.770 0.531870 10 31.417 0.649090 11 39.429 0.731340 12 6.645 0.198684 13 1.655 0.053663 14 32.430 0.660744 15 132.070 0.987751 16 13.291 0.357911 17 9.347 0.267692 18 5.752 0.174486 19 4.677 0.144369 20 13.135 0.354573 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.684123 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-01-06_14:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.1 0.8 1.8 -0.6 0.3 0.0 -0.1 -0.5 -1.9 0.3 -0.6 1.0 -0.4 -0.7 -0.4 0.0 0.4 0.5 0.2 0.9 -0.6 1.1 -1.2 -0.3 -0.3 0.7 0.2 -0.2 1.1 -0.3 0.9 0.2 -0.4 -0.2 1.1 -0.5 -0.4 0.5 1.0 2.4 0.0 -0.1 Chi-square with 42 degrees of freedom:26.510977 z-score=-1.689991, p-value=0.029842 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-01-06_14:31 Test no p-value 1 0.666290 2 0.137005 3 0.676078 4 0.047801 5 0.031947 6 0.134884 7 0.446668 8 0.069820 9 0.596715 10 0.272451 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.040602 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-01-06_14:31: (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 66666 0.00 66594 0.08 3 25000.00 24921 0.25 25146 0.85 4 6666.67 6659 0.01 6609 0.50 5 1388.89 1468 4.51 1374 0.16 6 238.10 245 0.20 235 0.04 7 34.72 33 0.09 39 0.53 8 4.96 7 0.84 2 1.77 p=0.56426 p=0.31313 Number of rngs required: 688615, p-value: 0.596 RESULTS OF CRAPS TEST for dh-ranFile-2016-01-06_14:31 No. of wins: Observed Expected 98472 98585.9 z-score=-0.509, pvalue=0.30529 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66970 66666.7 1.380 1.380 2 37256 37654.3 4.214 5.594 3 26954 26954.7 0.000 5.594 4 19355 19313.5 0.089 5.683 5 13816 13851.4 0.091 5.774 6 9927 9943.5 0.028 5.801 7 7108 7145.0 0.192 5.993 8 5364 5139.1 9.845 15.838 9 3693 3699.9 0.013 15.850 10 2685 2666.3 0.131 15.982 11 1872 1923.3 1.370 17.352 12 1385 1388.7 0.010 17.362 13 990 1003.7 0.187 17.549 14 726 726.1 0.000 17.549 15 493 525.8 2.050 19.599 16 393 381.2 0.368 19.968 17 288 276.5 0.475 20.443 18 212 200.8 0.621 21.064 19 149 146.0 0.062 21.126 20 93 106.2 1.644 22.771 21 271 287.1 0.904 23.675 Chisq= 23.67 for 20 degrees of freedom, p= 0.74312 SUMMARY of craptest p-value for no. of wins: 0.305291 p-value for throws/game: 0.743123 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-01-06_14:31 No. of wins: Observed Expected 98544 98585.9 z-score=-0.187, pvalue=0.42575 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66878 66666.7 0.670 0.670 2 37960 37654.3 2.482 3.151 3 26775 26954.7 1.198 4.350 4 19153 19313.5 1.333 5.683 5 13893 13851.4 0.125 5.808 6 9889 9943.5 0.299 6.107 7 7110 7145.0 0.172 6.279 8 5105 5139.1 0.226 6.505 9 3697 3699.9 0.002 6.507 10 2645 2666.3 0.170 6.677 11 1945 1923.3 0.244 6.921 12 1336 1388.7 2.003 8.924 13 976 1003.7 0.765 9.689 14 727 726.1 0.001 9.690 15 501 525.8 1.173 10.863 16 382 381.2 0.002 10.865 17 265 276.5 0.482 11.347 18 216 200.8 1.146 12.493 19 142 146.0 0.109 12.601 20 107 106.2 0.006 12.607 21 298 287.1 0.413 13.020 Chisq= 13.02 for 20 degrees of freedom, p= 0.12348 SUMMARY of craptest p-value for no. of wins: 0.425746 p-value for throws/game: 0.123477 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0042,0.0050,0.0086,0.0112,0.0120,0.0134,0.0283,0.0285,0.0298,0.0318, 0.0319,0.0328,0.0360,0.0367,0.0406,0.0409,0.0478,0.0537,0.0547,0.0571, 0.0599,0.0698,0.0729,0.0741,0.0760,0.0822,0.0877,0.0882,0.1051,0.1137, 0.1166,0.1169,0.1188,0.1202,0.1235,0.1332,0.1348,0.1349,0.1366,0.1370, 0.1373,0.1409,0.1430,0.1444,0.1515,0.1560,0.1576,0.1607,0.1613,0.1745, 0.1820,0.1869,0.1909,0.1932,0.1950,0.1987,0.1992,0.2038,0.2058,0.2070, 0.2103,0.2124,0.2179,0.2290,0.2325,0.2334,0.2438,0.2443,0.2450,0.2456, 0.2569,0.2625,0.2677,0.2701,0.2716,0.2725,0.2753,0.2812,0.2903,0.2953, 0.2974,0.3053,0.3075,0.3131,0.3167,0.3192,0.3220,0.3278,0.3434,0.3486, 0.3504,0.3535,0.3546,0.3573,0.3574,0.3579,0.3621,0.3856,0.3875,0.3885, 0.3893,0.3921,0.3940,0.3957,0.3992,0.4003,0.4058,0.4086,0.4124,0.4137, 0.4153,0.4226,0.4247,0.4257,0.4283,0.4313,0.4317,0.4346,0.4406,0.4406, 0.4409,0.4467,0.4514,0.4523,0.4570,0.4636,0.4655,0.4681,0.4710,0.4730, 0.4749,0.4762,0.4835,0.4843,0.4872,0.4902,0.4927,0.4949,0.4956,0.5058, 0.5161,0.5161,0.5161,0.5319,0.5366,0.5443,0.5445,0.5489,0.5489,0.5501, 0.5574,0.5590,0.5643,0.5647,0.5652,0.5674,0.5821,0.5853,0.5964,0.5967, 0.6069,0.6091,0.6128,0.6142,0.6212,0.6235,0.6259,0.6277,0.6323,0.6344, 0.6491,0.6491,0.6527,0.6586,0.6607,0.6627,0.6663,0.6761,0.6792,0.6803, 0.6806,0.6815,0.6837,0.6841,0.6850,0.6850,0.6862,0.6905,0.6923,0.6923, 0.6947,0.7021,0.7053,0.7070,0.7122,0.7173,0.7174,0.7191,0.7218,0.7254, 0.7313,0.7319,0.7399,0.7431,0.7433,0.7491,0.7529,0.7532,0.7550,0.7552, 0.7579,0.7697,0.7739,0.7818,0.7829,0.7838,0.7879,0.7937,0.8011,0.8094, 0.8096,0.8132,0.8232,0.8312,0.8400,0.8444,0.8447,0.8450,0.8454,0.8543, 0.8634,0.8746,0.8789,0.8792,0.8806,0.8822,0.8840,0.8841,0.9003,0.9082, 0.9138,0.9144,0.9144,0.9148,0.9247,0.9281,0.9299,0.9312,0.9326,0.9341, 0.9345,0.9360,0.9408,0.9421,0.9436,0.9474,0.9543,0.9554,0.9619,0.9620, 0.9691,0.9739,0.9777,0.9795,0.9803,0.9824,0.9858,0.9878,0.9912, Overall p-value after applying KStest on 269 p-values = 0.977920 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.