RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-10-31_11:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.46 25.1277 0.908112 2 to 25 15.81 12.3170 0.219428 3 to 26 15.84 15.6991 0.454746 4 to 27 15.88 13.4924 0.297352 5 to 28 16.07 10.5314 0.120140 6 to 29 16.04 30.0760 0.974198 7 to 30 16.21 17.7942 0.598065 8 to 31 15.83 14.4520 0.365115 9 to 32 15.96 15.3715 0.431257 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.829285 Tough bday spacings test for dh-ranFile-2015-10-31_11:31: 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 41 71 88 105 77 53 31 20 3 2 (O-E)^2/E 0.0 0.5 0.1 1.0 0.5 0.0 0.0 0.1 1.8 2.0 1.0 Birthday Spacings: Sum(O-E)^2/E= 6.968, p= 0.272 RESULTS OF GCD FOR dh-ranFile-2015-10-31_11:31 Euclid's algorithm: p-value, steps to gcd: 0.572091 p-value, dist. of gcd's: 0.031616 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-10-31_11:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.030 0.736 0.783 0.170 0.475 0.685 0.280 0.667 Bits 8 to 15---> 0.028 0.273 0.520 0.342 0.809 0.746 0.925 0.649 Bits 16 to 23---> 0.626 0.622 0.118 0.762 0.277 0.637 0.093 0.842 Bits 24 to 31---> 0.216 0.520 0.555 0.882 0.827 0.703 0.718 0.128 KS test for the above 32 p values: 0.474 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-10-31_11:31, p-values for 5 runs: 0.0566, 0.7814, 0.7641, 0.3845, 0.4218 Rank test for binary matrices (31x31) for dh-ranFile-2015-10-31_11:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 228 211.4 1.301 1.301 r= 29 5206 5134.0 1.009 2.310 r= 30 23106 23103.0 0.000 2.310 r= 31 11460 11551.5 0.725 3.036 chi-square = 3.036 with df = 3; p-value = 0.614 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-10-31_11:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 224 211.4 0.749 0.749 r= 30 5122 5134.0 0.028 0.777 r= 31 23008 23103.0 0.391 1.168 r= 32 11646 11551.5 0.773 1.941 chi-square = 1.941 with df = 3; p-value = 0.415 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-10-31_11:31 b-rank test for bits 1 to 8, p=0.02825 b-rank test for bits 2 to 9, p=0.29635 b-rank test for bits 3 to 10, p=0.07335 b-rank test for bits 4 to 11, p=0.08986 b-rank test for bits 5 to 12, p=0.48140 b-rank test for bits 6 to 13, p=0.70791 b-rank test for bits 7 to 14, p=0.01393 b-rank test for bits 8 to 15, p=0.66420 b-rank test for bits 9 to 16, p=0.96643 b-rank test for bits 10 to 17, p=0.79005 b-rank test for bits 11 to 18, p=0.61646 b-rank test for bits 12 to 19, p=0.19815 b-rank test for bits 13 to 20, p=0.27407 b-rank test for bits 14 to 21, p=0.02124 b-rank test for bits 15 to 22, p=0.34795 b-rank test for bits 16 to 23, p=0.12501 b-rank test for bits 17 to 24, p=0.06092 b-rank test for bits 18 to 25, p=0.86967 b-rank test for bits 19 to 26, p=0.45608 b-rank test for bits 20 to 27, p=0.36339 b-rank test for bits 21 to 28, p=0.47702 b-rank test for bits 22 to 29, p=0.63908 b-rank test for bits 23 to 30, p=0.31471 b-rank test for bits 24 to 31, p=0.70152 b-rank test for bits 25 to 32, p=0.31695 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 = 0.099899 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-10-31_11:31 (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 142135 0.53 0.700996 2 140998 -2.13 0.016616 3 141780 -0.30 0.381260 4 141458 -1.05 0.145825 5 141955 0.11 0.542489 6 142287 0.88 0.811222 7 142578 1.56 0.940893 8 141970 0.14 0.556362 9 142658 1.75 0.959874 10 141994 0.20 0.578410 11 142419 1.19 0.883137 12 142615 1.65 0.950402 13 141850 -0.14 0.444875 14 142137 0.53 0.702616 15 141866 -0.10 0.459681 16 141623 -0.67 0.251749 17 141684 -0.53 0.299280 18 142551 1.50 0.933093 19 141317 -1.38 0.083187 20 142000 0.21 0.583886 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-10-31_11:31 Bits used No. missing words z-score p-value 23 to 32 141981 0.2471 0.597599 22 to 31 142324 1.4299 0.923627 21 to 30 142237 1.1299 0.870740 20 to 29 141646 -0.9080 0.181930 19 to 28 141855 -0.1873 0.425695 18 to 27 142081 0.5920 0.723063 17 to 26 141520 -1.3425 0.089714 16 to 25 141495 -1.4287 0.076542 15 to 24 142170 0.8989 0.815637 14 to 23 141889 -0.0701 0.472056 13 to 22 142097 0.6471 0.741229 12 to 21 142009 0.3437 0.634460 11 to 20 141358 -1.9011 0.028642 10 to 19 142601 2.3851 0.991462 9 to 18 142357 1.5437 0.938668 8 to 17 141912 0.0092 0.503673 7 to 16 142076 0.5747 0.717261 6 to 15 141575 -1.1529 0.124484 5 to 14 141930 0.0713 0.528411 4 to 13 142099 0.6540 0.743455 3 to 12 142122 0.7333 0.768326 2 to 11 142192 0.9747 0.835151 1 to 10 142048 0.4782 0.683736 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-10-31_11:31 Bits used No. missing words z-score p-value 28 to 32 141202 -2.3977 0.008249 27 to 31 142193 0.9616 0.831873 26 to 30 142317 1.3819 0.916504 25 to 29 141785 -0.4215 0.336711 24 to 28 141980 0.2396 0.594664 23 to 27 141814 -0.3232 0.373290 22 to 26 142096 0.6328 0.736561 21 to 25 142137 0.7718 0.779873 20 to 24 141882 -0.0926 0.463093 19 to 23 141714 -0.6621 0.253942 18 to 22 141935 0.0870 0.534671 17 to 21 142158 0.8429 0.800372 16 to 20 141417 -1.6689 0.047567 15 to 19 141850 -0.2011 0.420303 14 to 18 142108 0.6735 0.749672 13 to 17 142015 0.3582 0.639905 12 to 16 142271 1.2260 0.889901 11 to 15 141956 0.1582 0.562852 10 to 14 142018 0.3684 0.643702 9 to 13 141851 -0.1977 0.421629 8 to 12 142198 0.9785 0.836097 7 to 11 142142 0.7887 0.784860 6 to 10 142040 0.4429 0.671099 5 to 9 141849 -0.2045 0.418978 4 to 8 141878 -0.1062 0.457711 3 to 7 142070 0.5446 0.707001 2 to 6 141646 -0.8926 0.186024 1 to 5 141916 0.0226 0.509019 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-10-31_11:31 Bits used No. missing words z-score p-value 31 to 32 142245 0.9902 0.838956 30 to 31 142254 1.0167 0.845358 29 to 30 141462 -1.3196 0.093491 28 to 29 142056 0.4327 0.667367 27 to 28 141831 -0.2311 0.408633 26 to 27 142124 0.6332 0.736713 25 to 26 142434 1.5477 0.939153 24 to 25 142081 0.5064 0.693713 23 to 24 141951 0.1229 0.548915 22 to 23 142216 0.9046 0.817170 21 to 22 141711 -0.5850 0.279259 20 to 21 142072 0.4799 0.684334 19 to 20 142302 1.1583 0.876633 18 to 19 141893 -0.0482 0.480790 17 to 18 141950 0.1200 0.547747 16 to 17 141751 -0.4671 0.320232 15 to 16 141999 0.2645 0.604308 14 to 15 141406 -1.4847 0.068805 13 to 14 142077 0.4946 0.689559 12 to 13 141729 -0.5319 0.297381 11 to 12 141574 -0.9892 0.161289 10 to 11 141992 0.2439 0.596332 9 to 10 141744 -0.4877 0.312882 8 to 9 141730 -0.5290 0.298404 7 to 8 141350 -1.6499 0.049478 6 to 7 141717 -0.5673 0.285240 5 to 6 142007 0.2881 0.613370 4 to 5 142021 0.3294 0.629077 3 to 4 141515 -1.1632 0.122371 2 to 3 142260 1.0344 0.849531 1 to 2 141504 -1.1957 0.115914 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-10-31_11:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2517.28 0.244 0.596518 Test results for specific bytes for dh-ranFile-2015-10-31_11:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2625.79 1.779 0.962379 2 to 9 2310.53 -2.680 0.003686 3 to 10 2356.48 -2.030 0.021196 4 to 11 2413.47 -1.224 0.110528 5 to 12 2474.30 -0.364 0.358115 6 to 13 2534.03 0.481 0.684832 7 to 14 2527.12 0.384 0.649350 8 to 15 2460.70 -0.556 0.289202 9 to 16 2454.55 -0.643 0.260176 10 to 17 2573.06 1.033 0.849242 11 to 18 2479.00 -0.297 0.383218 12 to 19 2398.58 -1.434 0.075750 13 to 20 2492.87 -0.101 0.459838 14 to 21 2381.49 -1.676 0.046875 15 to 22 2489.91 -0.143 0.443278 16 to 23 2572.27 1.022 0.846613 17 to 24 2385.68 -1.617 0.052964 18 to 25 2451.38 -0.688 0.245861 19 to 26 2598.41 1.392 0.918003 20 to 27 2498.13 -0.027 0.489428 21 to 28 2603.88 1.469 0.929096 22 to 29 2481.70 -0.259 0.397871 23 to 30 2451.70 -0.683 0.247285 24 to 31 2432.56 -0.954 0.170104 25 to 32 2434.58 -0.925 0.177453 CDPARK for dh-ranFile-2015-10-31_11:31: 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 3557 1.5525 0.939730 3540 0.7763 0.781201 3507 -0.7306 0.232514 3525 0.0913 0.536383 3512 -0.5023 0.307734 3550 1.2329 0.891189 3496 -1.2329 0.108811 3507 -0.7306 0.232514 3519 -0.1826 0.427537 3507 -0.7306 0.232514 Square side=100, avg. no. parked=3522.00 sample std.=19.50 p-value of the KSTEST for those 10 p-values: 0.787762 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-10-31_11:31 0.3994,0.5660,0.8949,0.0692,0.6968,0.7539,0.2821,0.0859,0.4148,0.9545, The KS test for those 10 p-values: 0.995260 The 3DSPHERES test for dh-ranFile-2015-10-31_11:31 sample no r^3 equiv. uni. 1 9.160 0.263132 2 14.305 0.379244 3 18.158 0.454067 4 6.132 0.184852 5 0.861 0.028303 6 1.197 0.039115 7 21.166 0.506157 8 3.299 0.104135 9 67.668 0.895190 10 14.188 0.376830 11 11.152 0.310452 12 30.148 0.633929 13 15.005 0.393575 14 22.809 0.532480 15 54.217 0.835895 16 18.024 0.451624 17 3.849 0.120408 18 9.890 0.280831 19 42.348 0.756250 20 10.639 0.298574 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.140913 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-10-31_11:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -1.2 -0.4 -0.8 -0.4 0.0 0.6 1.5 0.5 1.0 -0.4 -0.7 -0.2 0.9 -1.6 0.2 2.2 0.5 0.3 0.9 -0.5 -1.1 -0.7 -0.7 1.3 -0.9 -2.4 0.3 -1.0 -1.5 -0.8 1.5 -0.8 2.1 -0.8 -1.4 -1.2 -1.0 -0.4 1.0 -1.3 0.0 -0.1 Chi-square with 42 degrees of freedom:46.288020 z-score=0.467861, p-value=0.700225 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-10-31_11:31 Test no p-value 1 0.143634 2 0.005914 3 0.964004 4 0.329106 5 0.417845 6 0.375553 7 0.038531 8 0.208831 9 0.266941 10 0.000219 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.004906 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-10-31_11:31: (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 66721 0.04 66586 0.10 3 25000.00 24990 0.00 25158 1.00 4 6666.67 6666 0.00 6681 0.03 5 1388.89 1344 1.45 1310 4.48 6 238.10 236 0.02 237 0.01 7 34.72 38 0.31 23 3.96 8 4.96 4 0.19 4 0.19 p=0.08153 p=0.86464 Number of rngs required: 689316, p-value: 0.855 RESULTS OF CRAPS TEST for dh-ranFile-2015-10-31_11:31 No. of wins: Observed Expected 98528 98585.9 z-score=-0.259, pvalue=0.39790 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66742 66666.7 0.085 0.085 2 37712 37654.3 0.088 0.173 3 26926 26954.7 0.031 0.204 4 19322 19313.5 0.004 0.208 5 13675 13851.4 2.247 2.455 6 9987 9943.5 0.190 2.645 7 7207 7145.0 0.538 3.182 8 5226 5139.1 1.470 4.653 9 3700 3699.9 0.000 4.653 10 2649 2666.3 0.112 4.765 11 1813 1923.3 6.329 11.094 12 1406 1388.7 0.215 11.308 13 1035 1003.7 0.975 12.283 14 690 726.1 1.799 14.082 15 531 525.8 0.051 14.133 16 356 381.2 1.660 15.793 17 250 276.5 2.547 18.340 18 214 200.8 0.864 19.203 19 139 146.0 0.334 19.537 20 139 106.2 10.119 29.657 21 281 287.1 0.130 29.787 Chisq= 29.79 for 20 degrees of freedom, p= 0.92662 SUMMARY of craptest p-value for no. of wins: 0.397904 p-value for throws/game: 0.926621 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-10-31_11:31 No. of wins: Observed Expected 98606 98585.9 z-score= 0.090, pvalue=0.53589 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66658 66666.7 0.001 0.001 2 37754 37654.3 0.264 0.265 3 27070 26954.7 0.493 0.758 4 19146 19313.5 1.452 2.210 5 14153 13851.4 6.566 8.776 6 9986 9943.5 0.181 8.957 7 7081 7145.0 0.574 9.531 8 5123 5139.1 0.050 9.581 9 3618 3699.9 1.811 11.393 10 2644 2666.3 0.186 11.579 11 1826 1923.3 4.925 16.505 12 1407 1388.7 0.240 16.745 13 985 1003.7 0.349 17.094 14 679 726.1 3.060 20.154 15 495 525.8 1.808 21.962 16 386 381.2 0.062 22.024 17 294 276.5 1.102 23.126 18 177 200.8 2.828 25.954 19 128 146.0 2.216 28.169 20 110 106.2 0.135 28.304 21 280 287.1 0.176 28.481 Chisq= 28.48 for 20 degrees of freedom, p= 0.90150 SUMMARY of craptest p-value for no. of wins: 0.535890 p-value for throws/game: 0.901498 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0002,0.0037,0.0049,0.0059,0.0082,0.0139,0.0166,0.0212,0.0212,0.0282, 0.0283,0.0284,0.0286,0.0302,0.0316,0.0385,0.0391,0.0469,0.0476,0.0495, 0.0530,0.0566,0.0609,0.0688,0.0692,0.0734,0.0758,0.0765,0.0815,0.0832, 0.0859,0.0897,0.0899,0.0931,0.0935,0.0999,0.1041,0.1088,0.1105,0.1159, 0.1184,0.1201,0.1204,0.1224,0.1245,0.1250,0.1284,0.1409,0.1436,0.1458, 0.1613,0.1698,0.1701,0.1775,0.1819,0.1849,0.1860,0.1982,0.2088,0.2163, 0.2194,0.2325,0.2325,0.2325,0.2459,0.2473,0.2517,0.2539,0.2602,0.2631, 0.2669,0.2716,0.2731,0.2741,0.2774,0.2793,0.2804,0.2808,0.2821,0.2852, 0.2892,0.2964,0.2974,0.2974,0.2984,0.2986,0.2993,0.3077,0.3105,0.3129, 0.3147,0.3170,0.3202,0.3291,0.3367,0.3415,0.3479,0.3581,0.3634,0.3651, 0.3733,0.3756,0.3768,0.3792,0.3813,0.3832,0.3845,0.3936,0.3979,0.3979, 0.3994,0.4086,0.4148,0.4152,0.4178,0.4190,0.4203,0.4216,0.4218,0.4257, 0.4275,0.4313,0.4433,0.4449,0.4516,0.4541,0.4547,0.4561,0.4577,0.4597, 0.4598,0.4631,0.4721,0.4738,0.4751,0.4770,0.4808,0.4814,0.4894,0.5037, 0.5062,0.5090,0.5200,0.5201,0.5284,0.5325,0.5347,0.5359,0.5364,0.5425, 0.5477,0.5489,0.5547,0.5564,0.5629,0.5660,0.5721,0.5784,0.5839,0.5947, 0.5963,0.5965,0.5976,0.5981,0.6043,0.6134,0.6138,0.6165,0.6220,0.6258, 0.6291,0.6339,0.6345,0.6371,0.6391,0.6399,0.6437,0.6485,0.6493,0.6642, 0.6666,0.6674,0.6711,0.6837,0.6843,0.6848,0.6854,0.6896,0.6937,0.6968, 0.7002,0.7010,0.7015,0.7026,0.7028,0.7070,0.7079,0.7173,0.7183,0.7231, 0.7359,0.7366,0.7367,0.7412,0.7435,0.7463,0.7497,0.7539,0.7562,0.7620, 0.7641,0.7683,0.7799,0.7812,0.7814,0.7833,0.7849,0.7878,0.7901,0.8004, 0.8090,0.8112,0.8156,0.8172,0.8274,0.8293,0.8319,0.8352,0.8359,0.8361, 0.8390,0.8421,0.8454,0.8466,0.8492,0.8495,0.8551,0.8646,0.8697,0.8707, 0.8766,0.8823,0.8831,0.8899,0.8912,0.8949,0.8952,0.9015,0.9081,0.9165, 0.9180,0.9236,0.9250,0.9266,0.9291,0.9331,0.9387,0.9392,0.9397,0.9409, 0.9504,0.9545,0.9599,0.9624,0.9640,0.9664,0.9742,0.9915,0.9953, Overall p-value after applying KStest on 269 p-values = 0.479564 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.