RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-08-11_15:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.48 19.6176 0.705747 2 to 25 15.93 10.4254 0.115170 3 to 26 15.89 26.5590 0.935140 4 to 27 15.81 12.6543 0.240994 5 to 28 15.80 23.3833 0.862817 6 to 29 16.16 19.6444 0.707178 7 to 30 15.86 14.7979 0.389966 8 to 31 15.83 15.8270 0.463871 9 to 32 15.83 23.2779 0.859580 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.647932 Tough bday spacings test for dh-ranFile-2015-08-11_15:31: 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 34 55 95 111 86 47 29 16 11 4 (O-E)^2/E 0.9 0.2 4.6 0.1 1.8 0.8 0.5 0.0 0.1 2.9 0.0 Birthday Spacings: Sum(O-E)^2/E= 11.811, p= 0.702 RESULTS OF GCD FOR dh-ranFile-2015-08-11_15:31 Euclid's algorithm: p-value, steps to gcd: 0.129054 p-value, dist. of gcd's: 0.504044 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-08-11_15:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.882 0.067 0.951 0.045 0.224 0.222 0.597 0.279 Bits 8 to 15---> 0.838 0.265 0.224 0.098 0.543 0.560 0.584 0.467 Bits 16 to 23---> 0.255 0.704 0.865 0.436 0.187 0.374 0.623 0.750 Bits 24 to 31---> 0.569 0.995 0.470 0.510 0.819 0.462 0.650 0.647 KS test for the above 32 p values: 0.142 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-08-11_15:31, p-values for 5 runs: 0.4432, 0.6536, 0.8236, 0.8479, 0.1492 Rank test for binary matrices (31x31) for dh-ranFile-2015-08-11_15:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 206 211.4 0.139 0.139 r= 29 5172 5134.0 0.281 0.420 r= 30 23113 23103.0 0.004 0.424 r= 31 11509 11551.5 0.157 0.581 chi-square = 0.581 with df = 3; p-value = 0.099 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-08-11_15:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 223 211.4 0.634 0.634 r= 30 4999 5134.0 3.550 4.185 r= 31 23117 23103.0 0.008 4.193 r= 32 11661 11551.5 1.038 5.231 chi-square = 5.231 with df = 3; p-value = 0.844 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-08-11_15:31 b-rank test for bits 1 to 8, p=0.10088 b-rank test for bits 2 to 9, p=0.85907 b-rank test for bits 3 to 10, p=0.14891 b-rank test for bits 4 to 11, p=0.76336 b-rank test for bits 5 to 12, p=0.08981 b-rank test for bits 6 to 13, p=0.30420 b-rank test for bits 7 to 14, p=0.36074 b-rank test for bits 8 to 15, p=0.77203 b-rank test for bits 9 to 16, p=0.31730 b-rank test for bits 10 to 17, p=0.19671 b-rank test for bits 11 to 18, p=0.27105 b-rank test for bits 12 to 19, p=0.32525 b-rank test for bits 13 to 20, p=0.71343 b-rank test for bits 14 to 21, p=0.11386 b-rank test for bits 15 to 22, p=0.00155 b-rank test for bits 16 to 23, p=0.01713 b-rank test for bits 17 to 24, p=0.31364 b-rank test for bits 18 to 25, p=0.97684 b-rank test for bits 19 to 26, p=0.32785 b-rank test for bits 20 to 27, p=0.64072 b-rank test for bits 21 to 28, p=0.05194 b-rank test for bits 22 to 29, p=0.90813 b-rank test for bits 23 to 30, p=0.83286 b-rank test for bits 24 to 31, p=0.56407 b-rank test for bits 25 to 32, p=0.14332 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 = 0.099862 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-08-11_15:31 (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 141337 -1.34 0.090575 2 142898 2.31 0.989555 3 142565 1.53 0.937231 4 142130 0.52 0.696928 5 141898 -0.03 0.489440 6 141788 -0.28 0.388404 7 141682 -0.53 0.297659 8 141674 -0.55 0.291216 9 141293 -1.44 0.074930 10 141597 -0.73 0.232774 11 141865 -0.10 0.458753 12 141857 -0.12 0.451344 13 142069 0.37 0.645448 14 142065 0.36 0.641965 15 141569 -0.80 0.213259 16 141784 -0.29 0.384827 17 141874 -0.08 0.467106 18 141939 0.07 0.527634 19 142638 1.70 0.955669 20 141322 -1.37 0.084990 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-08-11_15:31 Bits used No. missing words z-score p-value 23 to 32 141931 0.0747 0.529783 22 to 31 141594 -1.0873 0.138442 21 to 30 141407 -1.7322 0.041621 20 to 29 141731 -0.6149 0.269300 19 to 28 141644 -0.9149 0.180114 18 to 27 142012 0.3540 0.638344 17 to 26 141703 -0.7115 0.238393 16 to 25 141450 -1.5839 0.056609 15 to 24 141992 0.2851 0.612204 14 to 23 142254 1.1885 0.882685 13 to 22 141783 -0.4356 0.331556 12 to 21 142054 0.4989 0.691062 11 to 20 141383 -1.8149 0.034767 10 to 19 141749 -0.5529 0.290179 9 to 18 141699 -0.7253 0.234141 8 to 17 141791 -0.4080 0.341624 7 to 16 141592 -1.0942 0.136925 6 to 15 142262 1.2161 0.888027 5 to 14 142089 0.6196 0.732224 4 to 13 142159 0.8609 0.805362 3 to 12 141655 -0.8770 0.190243 2 to 11 142256 1.1954 0.884037 1 to 10 141963 0.1851 0.573413 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-08-11_15:31 Bits used No. missing words z-score p-value 28 to 32 141759 -0.5096 0.305168 27 to 31 141692 -0.7367 0.230649 26 to 30 141932 0.0768 0.530628 25 to 29 141906 -0.0113 0.495497 24 to 28 141986 0.2599 0.602529 23 to 27 142446 1.8192 0.965561 22 to 26 141752 -0.5333 0.296905 21 to 25 141458 -1.5299 0.063017 20 to 24 141907 -0.0079 0.496849 19 to 23 141847 -0.2113 0.416331 18 to 22 141939 0.1006 0.540057 17 to 21 141913 0.0124 0.504963 16 to 20 142007 0.3311 0.629710 15 to 19 141891 -0.0621 0.475227 14 to 18 141782 -0.4316 0.333006 13 to 17 141720 -0.6418 0.260503 12 to 16 142221 1.0565 0.854632 11 to 15 141684 -0.7638 0.222484 10 to 14 142095 0.6294 0.735453 9 to 13 141645 -0.8960 0.185117 8 to 12 141501 -1.3842 0.083153 7 to 11 141863 -0.1571 0.437602 6 to 10 141773 -0.4621 0.321992 5 to 9 142337 1.4497 0.926433 4 to 8 141502 -1.3808 0.083673 3 to 7 142235 1.1040 0.865196 2 to 6 142222 1.0599 0.855405 1 to 5 141823 -0.2926 0.384897 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-08-11_15:31 Bits used No. missing words z-score p-value 31 to 32 141423 -1.4346 0.075700 30 to 31 142107 0.5831 0.720086 29 to 30 142143 0.6893 0.754680 28 to 29 141533 -1.1101 0.133474 27 to 28 141660 -0.7355 0.231022 26 to 27 141978 0.2026 0.580263 25 to 26 142246 0.9931 0.839676 24 to 25 141574 -0.9892 0.161289 23 to 24 142505 1.7571 0.960553 22 to 23 142623 2.1052 0.982364 21 to 22 142152 0.7158 0.762955 20 to 21 142165 0.7542 0.774632 19 to 20 141769 -0.4140 0.339454 18 to 19 141843 -0.1957 0.422437 17 to 18 141638 -0.8004 0.211744 16 to 17 141600 -0.9125 0.180759 15 to 16 141790 -0.3520 0.362417 14 to 15 141778 -0.3874 0.349229 13 to 14 142670 2.2439 0.987579 12 to 13 142453 1.6037 0.945615 11 to 12 142381 1.3914 0.917941 10 to 11 141907 -0.0069 0.497258 9 to 10 141804 -0.3107 0.378011 8 to 9 141824 -0.2517 0.400632 7 to 8 141483 -1.2576 0.104266 6 to 7 141599 -0.9154 0.179984 5 to 6 141975 0.1937 0.576801 4 to 5 141094 -2.4051 0.008084 3 to 4 141621 -0.8505 0.197515 2 to 3 141957 0.1406 0.555915 1 to 2 141816 -0.2753 0.391539 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-08-11_15:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2478.39 -0.306 0.379929 Test results for specific bytes for dh-ranFile-2015-08-11_15:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2667.75 2.372 0.991162 2 to 9 2464.86 -0.497 0.309619 3 to 10 2499.25 -0.011 0.495784 4 to 11 2468.00 -0.453 0.325432 5 to 12 2489.50 -0.148 0.440985 6 to 13 2423.26 -1.085 0.138904 7 to 14 2539.51 0.559 0.711830 8 to 15 2523.57 0.333 0.630574 9 to 16 2387.81 -1.587 0.056294 10 to 17 2508.64 0.122 0.548638 11 to 18 2547.75 0.675 0.750275 12 to 19 2536.97 0.523 0.699462 13 to 20 2556.06 0.793 0.786051 14 to 21 2383.17 -1.652 0.049241 15 to 22 2501.88 0.027 0.510628 16 to 23 2488.48 -0.163 0.435319 17 to 24 2433.24 -0.944 0.172548 18 to 25 2434.27 -0.930 0.176309 19 to 26 2562.26 0.880 0.810704 20 to 27 2543.85 0.620 0.732413 21 to 28 2434.94 -0.920 0.178750 22 to 29 2677.58 2.511 0.993986 23 to 30 2642.62 2.017 0.978146 24 to 31 2516.90 0.239 0.594451 25 to 32 2454.08 -0.649 0.258021 CDPARK for dh-ranFile-2015-08-11_15:31: 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 3517 -0.2740 0.392053 3521 -0.0913 0.463617 3509 -0.6393 0.261324 3504 -0.8676 0.192812 3514 -0.4110 0.340551 3524 0.0457 0.518210 3558 1.5982 0.944998 3540 0.7763 0.781201 3501 -1.0046 0.157553 3518 -0.2283 0.409702 Square side=100, avg. no. parked=3520.60 sample std.=16.26 p-value of the KSTEST for those 10 p-values: 0.562986 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-08-11_15:31 0.6145,0.0072,0.2681,0.5921,0.0373,0.1854,0.7472,0.6026,0.0485,0.2281, The KS test for those 10 p-values: 0.065510 The 3DSPHERES test for dh-ranFile-2015-08-11_15:31 sample no r^3 equiv. uni. 1 27.632 0.601901 2 2.738 0.087216 3 7.696 0.226270 4 66.365 0.890537 5 19.141 0.471670 6 12.316 0.336696 7 27.838 0.604629 8 12.795 0.347206 9 0.758 0.024949 10 24.694 0.560948 11 1.891 0.061081 12 53.433 0.831546 13 11.972 0.329046 14 25.176 0.567943 15 5.810 0.176059 16 55.052 0.840398 17 163.902 0.995761 18 21.499 0.511600 19 7.560 0.222760 20 26.291 0.583709 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.821181 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-08-11_15:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -0.7 -0.4 -0.3 0.7 0.3 0.4 0.9 1.5 1.9 -1.0 -0.6 -0.3 2.1 -1.7 -1.7 1.1 1.8 0.2 -0.2 -0.9 -0.5 1.8 -0.7 -1.2 0.5 -1.6 -2.1 -0.1 0.2 0.4 -0.9 0.6 1.4 -1.7 -0.1 -0.9 0.5 0.5 -0.1 0.9 -1.0 -0.1 Chi-square with 42 degrees of freedom:47.829103 z-score=0.636007, p-value=0.751993 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-08-11_15:31 Test no p-value 1 0.099985 2 0.014585 3 0.115078 4 0.511539 5 0.051454 6 0.347817 7 0.550758 8 0.472931 9 0.155903 10 0.371532 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.016424 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-08-11_15:31: (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 66698 0.01 66662 0.00 3 25000.00 24977 0.02 25125 0.62 4 6666.67 6712 0.31 6580 1.13 5 1388.89 1335 2.09 1332 2.33 6 238.10 242 0.06 258 1.66 7 34.72 33 0.09 38 0.31 8 4.96 2 1.77 4 0.19 p=0.37068 p=0.60337 Number of rngs required: 688532, p-value: 0.559 RESULTS OF CRAPS TEST for dh-ranFile-2015-08-11_15:31 No. of wins: Observed Expected 98625 98585.9 z-score= 0.175, pvalue=0.56949 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66789 66666.7 0.224 0.224 2 37597 37654.3 0.087 0.312 3 26975 26954.7 0.015 0.327 4 19286 19313.5 0.039 0.366 5 13777 13851.4 0.400 0.766 6 9923 9943.5 0.042 0.808 7 7152 7145.0 0.007 0.815 8 5166 5139.1 0.141 0.956 9 3639 3699.9 1.001 1.957 10 2688 2666.3 0.177 2.134 11 1971 1923.3 1.182 3.316 12 1382 1388.7 0.033 3.348 13 1001 1003.7 0.007 3.356 14 727 726.1 0.001 3.357 15 539 525.8 0.330 3.686 16 372 381.2 0.220 3.906 17 268 276.5 0.264 4.170 18 201 200.8 0.000 4.170 19 143 146.0 0.061 4.231 20 121 106.2 2.058 6.289 21 283 287.1 0.059 6.348 Chisq= 6.35 for 20 degrees of freedom, p= 0.00166 SUMMARY of craptest p-value for no. of wins: 0.569485 p-value for throws/game: 0.001661 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-08-11_15:31 No. of wins: Observed Expected 98678 98585.9 z-score= 0.412, pvalue=0.65987 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66960 66666.7 1.291 1.291 2 37836 37654.3 0.877 2.167 3 26863 26954.7 0.312 2.479 4 19090 19313.5 2.586 5.065 5 13971 13851.4 1.032 6.097 6 9928 9943.5 0.024 6.122 7 7105 7145.0 0.224 6.346 8 5085 5139.1 0.569 6.915 9 3549 3699.9 6.152 13.066 10 2659 2666.3 0.020 13.086 11 1941 1923.3 0.162 13.249 12 1424 1388.7 0.895 14.144 13 982 1003.7 0.470 14.614 14 695 726.1 1.335 15.949 15 524 525.8 0.006 15.956 16 407 381.2 1.753 17.709 17 255 276.5 1.678 19.386 18 190 200.8 0.584 19.970 19 136 146.0 0.683 20.653 20 120 106.2 1.789 22.442 21 280 287.1 0.176 22.619 Chisq= 22.62 for 20 degrees of freedom, p= 0.69209 SUMMARY of craptest p-value for no. of wins: 0.659871 p-value for throws/game: 0.692090 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0016,0.0017,0.0072,0.0081,0.0146,0.0164,0.0171,0.0249,0.0348,0.0373, 0.0416,0.0451,0.0485,0.0492,0.0515,0.0519,0.0563,0.0566,0.0611,0.0630, 0.0655,0.0669,0.0749,0.0757,0.0832,0.0837,0.0850,0.0872,0.0898,0.0906, 0.0980,0.0992,0.0999,0.1000,0.1009,0.1043,0.1139,0.1151,0.1152,0.1291, 0.1335,0.1369,0.1384,0.1389,0.1418,0.1433,0.1489,0.1492,0.1559,0.1576, 0.1613,0.1725,0.1761,0.1763,0.1788,0.1800,0.1801,0.1808,0.1851,0.1854, 0.1871,0.1902,0.1928,0.1967,0.1975,0.2117,0.2133,0.2218,0.2225,0.2228, 0.2238,0.2242,0.2263,0.2281,0.2306,0.2310,0.2328,0.2341,0.2384,0.2410, 0.2548,0.2580,0.2605,0.2613,0.2653,0.2681,0.2693,0.2710,0.2788,0.2902, 0.2912,0.2969,0.2977,0.3042,0.3052,0.3096,0.3136,0.3173,0.3220,0.3253, 0.3254,0.3278,0.3290,0.3316,0.3330,0.3367,0.3395,0.3406,0.3416,0.3472, 0.3478,0.3492,0.3607,0.3624,0.3707,0.3715,0.3738,0.3780,0.3799,0.3848, 0.3849,0.3884,0.3900,0.3915,0.3921,0.4006,0.4097,0.4163,0.4224,0.4353, 0.4361,0.4376,0.4410,0.4432,0.4513,0.4588,0.4621,0.4636,0.4639,0.4669, 0.4671,0.4699,0.4717,0.4729,0.4752,0.4894,0.4955,0.4958,0.4968,0.4973, 0.5040,0.5050,0.5103,0.5106,0.5115,0.5116,0.5182,0.5276,0.5298,0.5306, 0.5401,0.5432,0.5486,0.5508,0.5559,0.5590,0.5602,0.5609,0.5630,0.5641, 0.5679,0.5690,0.5695,0.5734,0.5768,0.5803,0.5837,0.5837,0.5921,0.5945, 0.5967,0.6019,0.6025,0.6026,0.6034,0.6046,0.6122,0.6145,0.6228,0.6297, 0.6306,0.6383,0.6407,0.6420,0.6454,0.6470,0.6479,0.6502,0.6536,0.6599, 0.6911,0.6921,0.6969,0.6995,0.7021,0.7038,0.7057,0.7072,0.7118,0.7134, 0.7201,0.7322,0.7324,0.7355,0.7472,0.7499,0.7503,0.7520,0.7547,0.7630, 0.7634,0.7720,0.7746,0.7812,0.7861,0.8054,0.8107,0.8194,0.8212,0.8236, 0.8315,0.8329,0.8377,0.8397,0.8404,0.8443,0.8479,0.8546,0.8554,0.8591, 0.8596,0.8628,0.8652,0.8654,0.8820,0.8827,0.8840,0.8880,0.8905,0.9081, 0.9179,0.9264,0.9351,0.9372,0.9450,0.9456,0.9512,0.9557,0.9606,0.9656, 0.9768,0.9781,0.9824,0.9876,0.9896,0.9912,0.9940,0.9947,0.9958, Overall p-value after applying KStest on 269 p-values = 0.027883 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.