RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-01-17_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 15.84 13.4988 0.297796 2 to 25 15.71 17.0899 0.551709 3 to 26 15.72 23.3432 0.861593 4 to 27 15.71 10.6250 0.124618 5 to 28 15.64 13.8928 0.325322 6 to 29 15.90 39.4818 0.998469 7 to 30 15.77 18.3370 0.632116 8 to 31 15.91 33.1830 0.989315 9 to 32 15.83 10.9220 0.139412 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.255923 Tough bday spacings test for dh-ranFile-2017-01-17_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 12 30 84 106 105 71 43 25 14 7 3 (O-E)^2/E 0.9 1.2 1.6 0.7 0.5 0.7 1.6 0.8 0.1 0.0 0.3 Birthday Spacings: Sum(O-E)^2/E= 8.273, p= 0.398 RESULTS OF GCD FOR dh-ranFile-2017-01-17_09:31 Euclid's algorithm: p-value, steps to gcd: 0.376168 p-value, dist. of gcd's: 0.355412 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-01-17_09:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.171 0.052 0.533 0.455 0.010 0.342 0.222 0.627 Bits 8 to 15---> 0.618 0.677 0.845 0.507 0.598 0.186 0.080 0.049 Bits 16 to 23---> 0.966 0.982 0.143 0.936 0.545 0.899 0.454 0.027 Bits 24 to 31---> 0.951 0.516 0.036 0.061 0.354 0.504 0.784 0.224 KS test for the above 32 p values: 0.744 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-01-17_09:31, p-values for 5 runs: 0.8014, 0.4841, 0.8309, 0.8323, 0.9471 Rank test for binary matrices (31x31) for dh-ranFile-2017-01-17_09:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 197 211.4 0.983 0.983 r= 29 5095 5134.0 0.296 1.280 r= 30 23146 23103.0 0.080 1.360 r= 31 11562 11551.5 0.010 1.369 chi-square = 1.369 with df = 3; p-value = 0.287 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2017-01-17_09:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 175 211.4 6.273 6.273 r= 30 5142 5134.0 0.012 6.286 r= 31 23090 23103.0 0.007 6.293 r= 32 11593 11551.5 0.149 6.442 chi-square = 6.442 with df = 3; p-value = 0.908 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2017-01-17_09:31 b-rank test for bits 1 to 8, p=0.08114 b-rank test for bits 2 to 9, p=0.15419 b-rank test for bits 3 to 10, p=0.57807 b-rank test for bits 4 to 11, p=0.60960 b-rank test for bits 5 to 12, p=0.88130 b-rank test for bits 6 to 13, p=0.55902 b-rank test for bits 7 to 14, p=0.82355 b-rank test for bits 8 to 15, p=0.25766 b-rank test for bits 9 to 16, p=0.84507 b-rank test for bits 10 to 17, p=0.09031 b-rank test for bits 11 to 18, p=0.73148 b-rank test for bits 12 to 19, p=0.08178 b-rank test for bits 13 to 20, p=0.55813 b-rank test for bits 14 to 21, p=0.40953 b-rank test for bits 15 to 22, p=0.91411 b-rank test for bits 16 to 23, p=0.67373 b-rank test for bits 17 to 24, p=0.19155 b-rank test for bits 18 to 25, p=0.87944 b-rank test for bits 19 to 26, p=0.72177 b-rank test for bits 20 to 27, p=0.44129 b-rank test for bits 21 to 28, p=0.46247 b-rank test for bits 22 to 29, p=0.34655 b-rank test for bits 23 to 30, p=0.29635 b-rank test for bits 24 to 31, p=0.82326 b-rank test for bits 25 to 32, p=0.43830 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 = 0.911938 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-01-17_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 141471 -1.02 0.152886 2 142058 0.35 0.635840 3 142461 1.29 0.901292 4 141690 -0.51 0.304167 5 141788 -0.28 0.388404 6 141833 -0.18 0.429228 7 141386 -1.22 0.110715 8 141995 0.20 0.579324 9 141965 0.13 0.551745 10 141601 -0.72 0.235640 11 141408 -1.17 0.120733 12 141367 -1.27 0.102555 13 141946 0.09 0.534139 14 140780 -2.64 0.004162 15 142072 0.38 0.648053 16 141629 -0.65 0.256241 17 142296 0.90 0.816852 18 141760 -0.35 0.363582 19 141822 -0.20 0.419160 20 141962 0.12 0.548971 ---------------------------------------------------------------- OPSO test for dh-ranFile-2017-01-17_09:31 Bits used No. missing words z-score p-value 23 to 32 141544 -1.2598 0.103878 22 to 31 142230 1.1058 0.865585 21 to 30 141972 0.2161 0.585547 20 to 29 141851 -0.2011 0.420295 19 to 28 142236 1.1264 0.870012 18 to 27 142187 0.9575 0.830838 17 to 26 142516 2.0920 0.981779 16 to 25 142103 0.6678 0.747878 15 to 24 141514 -1.3632 0.086409 14 to 23 141658 -0.8667 0.193066 13 to 22 141995 0.2954 0.616161 12 to 21 142341 1.4885 0.931693 11 to 20 141896 -0.0460 0.481669 10 to 19 141956 0.1609 0.563926 9 to 18 141433 -1.6425 0.050241 8 to 17 142413 1.7368 0.958788 7 to 16 141633 -0.9529 0.170330 6 to 15 142017 0.3713 0.644784 5 to 14 142283 1.2885 0.901217 4 to 13 141928 0.0644 0.525666 3 to 12 142248 1.1678 0.878562 2 to 11 142202 1.0092 0.843562 1 to 10 141710 -0.6873 0.245933 ----------------------------------------------------------------- OQSO test for dh-ranFile-2017-01-17_09:31 Bits used No. missing words z-score p-value 28 to 32 142025 0.3921 0.652509 27 to 31 141832 -0.2621 0.396609 26 to 30 142043 0.4531 0.674768 25 to 29 142084 0.5921 0.723109 24 to 28 142279 1.2531 0.894919 23 to 27 141733 -0.5977 0.275010 22 to 26 141768 -0.4791 0.315939 21 to 25 141874 -0.1198 0.452336 20 to 24 141815 -0.3198 0.374574 19 to 23 141751 -0.5367 0.295733 18 to 22 142523 2.0802 0.981248 17 to 21 141634 -0.9333 0.175327 16 to 20 141597 -1.0587 0.144858 15 to 19 142069 0.5413 0.705834 14 to 18 141935 0.0870 0.534671 13 to 17 141753 -0.5299 0.298080 12 to 16 141914 0.0158 0.506315 11 to 15 141923 0.0463 0.518480 10 to 14 141543 -1.2418 0.107156 9 to 13 142045 0.4599 0.677205 8 to 12 142184 0.9311 0.824095 7 to 11 142154 0.8294 0.796558 6 to 10 141947 0.1277 0.550805 5 to 9 141762 -0.4994 0.308741 4 to 8 141837 -0.2452 0.403156 3 to 7 142008 0.3345 0.630989 2 to 6 142093 0.6226 0.733230 1 to 5 142213 1.0294 0.848352 ----------------------------------------------------------------- DNA test for dh-ranFile-2017-01-17_09:31 Bits used No. missing words z-score p-value 31 to 32 141737 -0.5083 0.305605 30 to 31 141396 -1.5142 0.064982 29 to 30 141738 -0.5054 0.306640 28 to 29 141358 -1.6263 0.051938 27 to 28 141512 -1.1721 0.120586 26 to 27 141978 0.2026 0.580263 25 to 26 141722 -0.5526 0.290270 24 to 25 141924 0.0433 0.517259 23 to 24 141810 -0.2930 0.384758 22 to 23 141754 -0.4582 0.323404 21 to 22 141855 -0.1603 0.436336 20 to 21 141805 -0.3078 0.379133 19 to 20 142727 2.4120 0.992067 18 to 19 141811 -0.2901 0.385886 17 to 18 142150 0.7099 0.761130 16 to 17 142251 1.0079 0.843243 15 to 16 141990 0.2380 0.594046 14 to 15 141697 -0.6263 0.265545 13 to 14 141861 -0.1426 0.443316 12 to 13 141345 -1.6647 0.047987 11 to 12 142063 0.4533 0.674835 10 to 11 141609 -0.8859 0.187828 9 to 10 141833 -0.2252 0.410927 8 to 9 141663 -0.7266 0.233724 7 to 8 141959 0.1465 0.558244 6 to 7 142059 0.4415 0.670576 5 to 6 142096 0.5506 0.709063 4 to 5 141513 -1.1691 0.121179 3 to 4 142147 0.7011 0.758377 2 to 3 141967 0.1701 0.567541 1 to 2 142358 1.3235 0.907167 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2017-01-17_09:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2564.83 0.917 0.820393 Test results for specific bytes for dh-ranFile-2017-01-17_09:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2447.38 -0.744 0.228407 2 to 9 2511.14 0.158 0.562593 3 to 10 2680.81 2.557 0.994722 4 to 11 2589.71 1.269 0.897734 5 to 12 2557.25 0.810 0.790918 6 to 13 2454.71 -0.641 0.260907 7 to 14 2601.45 1.435 0.924315 8 to 15 2484.12 -0.225 0.411174 9 to 16 2483.34 -0.236 0.406887 10 to 17 2360.34 -1.975 0.024127 11 to 18 2509.96 0.141 0.556007 12 to 19 2522.34 0.316 0.623984 13 to 20 2476.62 -0.331 0.370466 14 to 21 2358.87 -1.996 0.022977 15 to 22 2494.66 -0.076 0.469903 16 to 23 2523.80 0.337 0.631766 17 to 24 2501.27 0.018 0.507170 18 to 25 2496.87 -0.044 0.482354 19 to 26 2407.08 -1.314 0.094404 20 to 27 2512.04 0.170 0.567624 21 to 28 2599.46 1.407 0.920232 22 to 29 2518.46 0.261 0.602999 23 to 30 2479.21 -0.294 0.384360 24 to 31 2360.50 -1.973 0.024254 25 to 32 2566.08 0.935 0.824996 CDPARK for dh-ranFile-2017-01-17_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 3537 0.6393 0.738676 3521 -0.0913 0.463617 3502 -0.9589 0.168804 3525 0.0913 0.536383 3512 -0.5023 0.307734 3540 0.7763 0.781201 3519 -0.1826 0.427537 3532 0.4110 0.659449 3548 1.1416 0.873180 3551 1.2785 0.899470 Square side=100, avg. no. parked=3528.70 sample std.=14.95 p-value of the KSTEST for those 10 p-values: 0.562548 Results for the MINIMUM DISTANCE test for dh-ranFile-2017-01-17_09:31 0.5733,0.1167,0.3650,0.7244,0.5897,0.4824,0.2896,0.3979,0.7986,0.1359, The KS test for those 10 p-values: 0.659704 The 3DSPHERES test for dh-ranFile-2017-01-17_09:31 sample no r^3 equiv. uni. 1 32.366 0.660021 2 253.060 0.999783 3 30.754 0.641248 4 10.570 0.296965 5 51.492 0.820286 6 25.169 0.567843 7 64.226 0.882448 8 8.586 0.248881 9 47.472 0.794520 10 38.908 0.726632 11 37.587 0.714325 12 30.493 0.638115 13 11.241 0.312506 14 0.995 0.032625 15 22.295 0.524396 16 75.013 0.917949 17 0.476 0.015755 18 15.172 0.396932 19 4.848 0.149230 20 10.970 0.306276 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.734510 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-01-17_09:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 4.1 0.1 0.1 -0.7 0.4 1.2 -0.3 -2.0 1.2 0.2 1.1 -2.6 0.1 0.5 -1.1 -0.4 0.4 -0.6 -1.1 0.0 1.2 -0.5 0.1 1.0 0.1 2.6 -0.8 0.3 0.9 0.2 1.8 0.2 -0.0 -0.8 0.3 -1.6 -1.2 -1.0 0.5 -0.7 0.9 -1.0 -1.1 Chi-square with 42 degrees of freedom:59.436323 z-score=1.902459, p-value=0.960754 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2017-01-17_09:31 Test no p-value 1 0.384278 2 0.388080 3 0.146590 4 0.015570 5 0.277757 6 0.132266 7 0.927136 8 0.024310 9 0.315037 10 0.423095 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.035428 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-01-17_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 66453 0.68 66495 0.44 3 25000.00 25208 1.73 25128 0.66 4 6666.67 6732 0.64 6665 0.00 5 1388.89 1346 1.32 1436 1.60 6 238.10 214 2.44 239 0.00 7 34.72 39 0.53 32 0.21 8 4.96 7 0.84 4 0.19 p=0.77515 p=0.20356 Number of rngs required: 688153, p-value: 0.387 RESULTS OF CRAPS TEST for dh-ranFile-2017-01-17_09:31 No. of wins: Observed Expected 98397 98585.9 z-score=-0.845, pvalue=0.19914 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66365 66666.7 1.365 1.365 2 37585 37654.3 0.128 1.493 3 27102 26954.7 0.805 2.297 4 19325 19313.5 0.007 2.304 5 13801 13851.4 0.184 2.488 6 10110 9943.5 2.787 5.274 7 7083 7145.0 0.538 5.813 8 5193 5139.1 0.566 6.379 9 3682 3699.9 0.086 6.465 10 2675 2666.3 0.028 6.493 11 1933 1923.3 0.049 6.542 12 1418 1388.7 0.616 7.158 13 1004 1003.7 0.000 7.158 14 718 726.1 0.091 7.250 15 546 525.8 0.773 8.023 16 404 381.2 1.370 9.393 17 282 276.5 0.108 9.501 18 201 200.8 0.000 9.501 19 173 146.0 4.999 14.500 20 116 106.2 0.901 15.402 21 284 287.1 0.034 15.435 Chisq= 15.44 for 20 degrees of freedom, p= 0.24902 SUMMARY of craptest p-value for no. of wins: 0.199143 p-value for throws/game: 0.249017 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2017-01-17_09:31 No. of wins: Observed Expected 98719 98585.9 z-score= 0.595, pvalue=0.72424 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66886 66666.7 0.722 0.722 2 37629 37654.3 0.017 0.739 3 27118 26954.7 0.989 1.728 4 19177 19313.5 0.964 2.692 5 14052 13851.4 2.905 5.596 6 9760 9943.5 3.388 8.984 7 6945 7145.0 5.600 14.584 8 5168 5139.1 0.163 14.747 9 3669 3699.9 0.257 15.004 10 2593 2666.3 2.015 17.019 11 1919 1923.3 0.010 17.029 12 1424 1388.7 0.895 17.924 13 1008 1003.7 0.018 17.943 14 705 726.1 0.615 18.558 15 557 525.8 1.847 20.405 16 369 381.2 0.387 20.792 17 298 276.5 1.665 22.458 18 186 200.8 1.095 23.553 19 138 146.0 0.437 23.990 20 109 106.2 0.073 24.063 21 290 287.1 0.029 24.092 Chisq= 24.09 for 20 degrees of freedom, p= 0.76158 SUMMARY of craptest p-value for no. of wins: 0.724241 p-value for throws/game: 0.761584 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0042,0.0100,0.0156,0.0158,0.0230,0.0241,0.0243,0.0243,0.0270,0.0326, 0.0354,0.0355,0.0480,0.0495,0.0502,0.0519,0.0522,0.0606,0.0650,0.0803, 0.0811,0.0818,0.0864,0.0903,0.0944,0.1026,0.1039,0.1072,0.1107,0.1167, 0.1206,0.1207,0.1212,0.1246,0.1323,0.1359,0.1394,0.1428,0.1449,0.1466, 0.1492,0.1529,0.1542,0.1688,0.1703,0.1709,0.1753,0.1857,0.1878,0.1915, 0.1931,0.1991,0.2036,0.2223,0.2235,0.2284,0.2337,0.2356,0.2459,0.2489, 0.2490,0.2559,0.2562,0.2577,0.2609,0.2655,0.2750,0.2778,0.2872,0.2896, 0.2903,0.2957,0.2964,0.2970,0.2978,0.2981,0.3042,0.3056,0.3063,0.3066, 0.3077,0.3087,0.3125,0.3150,0.3159,0.3234,0.3253,0.3419,0.3466,0.3536, 0.3554,0.3636,0.3650,0.3705,0.3746,0.3762,0.3791,0.3843,0.3844,0.3848, 0.3859,0.3868,0.3881,0.3884,0.3966,0.3969,0.3979,0.3979,0.4032,0.4069, 0.4095,0.4109,0.4112,0.4192,0.4203,0.4231,0.4275,0.4292,0.4363,0.4383, 0.4413,0.4433,0.4523,0.4535,0.4545,0.4625,0.4636,0.4699,0.4817,0.4824, 0.4824,0.4841,0.5039,0.5063,0.5071,0.5072,0.5158,0.5173,0.5185,0.5244, 0.5257,0.5328,0.5341,0.5347,0.5364,0.5454,0.5490,0.5508,0.5517,0.5517, 0.5560,0.5581,0.5582,0.5590,0.5625,0.5626,0.5639,0.5675,0.5676,0.5678, 0.5733,0.5781,0.5793,0.5803,0.5855,0.5897,0.5940,0.5980,0.6030,0.6096, 0.6162,0.6176,0.6240,0.6266,0.6310,0.6318,0.6321,0.6358,0.6381,0.6412, 0.6448,0.6481,0.6525,0.6594,0.6597,0.6600,0.6706,0.6737,0.6748,0.6748, 0.6767,0.6772,0.7058,0.7091,0.7143,0.7218,0.7231,0.7242,0.7244,0.7266, 0.7315,0.7332,0.7345,0.7387,0.7437,0.7479,0.7584,0.7611,0.7616,0.7751, 0.7812,0.7843,0.7909,0.7945,0.7966,0.7986,0.8014,0.8169,0.8203,0.8204, 0.8233,0.8236,0.8241,0.8250,0.8308,0.8309,0.8323,0.8432,0.8436,0.8451, 0.8452,0.8484,0.8616,0.8656,0.8700,0.8732,0.8786,0.8794,0.8813,0.8824, 0.8949,0.8977,0.8993,0.8995,0.9012,0.9013,0.9072,0.9080,0.9119,0.9141, 0.9179,0.9202,0.9243,0.9271,0.9317,0.9364,0.9471,0.9512,0.9588,0.9608, 0.9655,0.9812,0.9818,0.9819,0.9893,0.9921,0.9947,0.9985,0.9998, Overall p-value after applying KStest on 269 p-values = 0.926345 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.