RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-09-11_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 15.80 18.1910 0.623114 2 to 25 15.78 23.1843 0.856653 3 to 26 15.78 17.5173 0.580116 4 to 27 15.65 15.8878 0.468196 5 to 28 15.73 17.4214 0.573809 6 to 29 15.65 14.8361 0.392712 7 to 30 15.81 19.2033 0.683012 8 to 31 15.69 13.7152 0.312851 9 to 32 15.72 7.7917 0.029199 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.682965 Tough bday spacings test for dh-ranFile-2015-09-11_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 45 79 88 89 84 53 28 17 7 1 (O-E)^2/E 0.0 1.9 0.4 1.0 0.8 0.4 0.0 0.1 0.3 0.0 2.3 Birthday Spacings: Sum(O-E)^2/E= 7.290, p= 0.302 RESULTS OF GCD FOR dh-ranFile-2015-09-11_14:31 Euclid's algorithm: p-value, steps to gcd: 0.041430 p-value, dist. of gcd's: 0.962186 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-09-11_14:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.446 0.744 0.343 0.046 0.005 0.472 0.400 0.148 Bits 8 to 15---> 0.673 0.418 0.042 0.245 0.928 0.271 0.740 0.344 Bits 16 to 23---> 0.787 0.768 0.512 0.205 0.179 0.390 0.484 0.296 Bits 24 to 31---> 0.540 0.164 0.717 0.596 0.991 0.686 0.329 0.285 KS test for the above 32 p values: 0.650 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-09-11_14:31, p-values for 5 runs: 0.4028, 0.7415, 0.6705, 0.1090, 0.4796 Rank test for binary matrices (31x31) for dh-ranFile-2015-09-11_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 222 211.4 0.530 0.530 r= 29 5217 5134.0 1.341 1.871 r= 30 23034 23103.0 0.206 2.078 r= 31 11527 11551.5 0.052 2.130 chi-square = 2.130 with df = 3; p-value = 0.454 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-09-11_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 225 211.4 0.873 0.873 r= 30 5326 5134.0 7.180 8.052 r= 31 22933 23103.0 1.252 9.304 r= 32 11516 11551.5 0.109 9.413 chi-square = 9.413 with df = 3; p-value = 0.976 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-09-11_14:31 b-rank test for bits 1 to 8, p=0.80592 b-rank test for bits 2 to 9, p=0.02342 b-rank test for bits 3 to 10, p=0.79974 b-rank test for bits 4 to 11, p=0.89130 b-rank test for bits 5 to 12, p=0.49010 b-rank test for bits 6 to 13, p=0.97954 b-rank test for bits 7 to 14, p=0.20194 b-rank test for bits 8 to 15, p=0.55081 b-rank test for bits 9 to 16, p=0.98009 b-rank test for bits 10 to 17, p=0.56378 b-rank test for bits 11 to 18, p=0.26920 b-rank test for bits 12 to 19, p=0.55189 b-rank test for bits 13 to 20, p=0.46804 b-rank test for bits 14 to 21, p=0.15649 b-rank test for bits 15 to 22, p=0.16557 b-rank test for bits 16 to 23, p=0.59469 b-rank test for bits 17 to 24, p=0.75207 b-rank test for bits 18 to 25, p=0.82242 b-rank test for bits 19 to 26, p=0.84606 b-rank test for bits 20 to 27, p=0.46701 b-rank test for bits 21 to 28, p=0.81107 b-rank test for bits 22 to 29, p=0.99864 b-rank test for bits 23 to 30, p=0.93553 b-rank test for bits 24 to 31, p=0.64193 b-rank test for bits 25 to 32, p=0.60597 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 = 0.059344 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-09-11_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 141199 -1.66 0.048492 2 141277 -1.48 0.069783 3 141979 0.16 0.564654 4 141427 -1.13 0.129884 5 142038 0.30 0.618152 6 141391 -1.21 0.112938 7 141642 -0.62 0.266116 8 142617 1.65 0.950879 9 141444 -1.09 0.138470 10 142002 0.22 0.585708 11 142057 0.35 0.634962 12 141330 -1.35 0.087936 13 142123 0.50 0.691191 14 142460 1.29 0.900885 15 141890 -0.05 0.481989 16 142139 0.54 0.704232 17 140731 -2.75 0.002952 18 141313 -1.39 0.081765 19 142157 0.58 0.718594 20 141811 -0.23 0.409146 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-09-11_14:31 Bits used No. missing words z-score p-value 23 to 32 141853 -0.1942 0.422994 22 to 31 141967 0.1989 0.578815 21 to 30 141693 -0.7460 0.227844 20 to 29 141659 -0.8632 0.194012 19 to 28 141319 -2.0356 0.020894 18 to 27 141996 0.2989 0.617477 17 to 26 141988 0.2713 0.606911 16 to 25 142265 1.2264 0.889985 15 to 24 141709 -0.6908 0.244848 14 to 23 141759 -0.5184 0.302097 13 to 22 142240 1.1402 0.872907 12 to 21 142054 0.4989 0.691062 11 to 20 141840 -0.2391 0.405526 10 to 19 142116 0.7127 0.761970 9 to 18 141824 -0.2942 0.384287 8 to 17 142331 1.4540 0.927032 7 to 16 141856 -0.1839 0.427047 6 to 15 142615 2.4333 0.992520 5 to 14 142095 0.6402 0.738992 4 to 13 141920 0.0368 0.514675 3 to 12 141595 -1.0839 0.139205 2 to 11 141947 0.1299 0.551676 1 to 10 141555 -1.2218 0.110886 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-09-11_14:31 Bits used No. missing words z-score p-value 28 to 32 141962 0.1785 0.570852 27 to 31 141995 0.2904 0.614248 26 to 30 141779 -0.4418 0.329318 25 to 29 142240 1.1209 0.868838 24 to 28 142524 2.0836 0.981403 23 to 27 141590 -1.0825 0.139521 22 to 26 141649 -0.8825 0.188760 21 to 25 142334 1.4396 0.925004 20 to 24 141888 -0.0723 0.471180 19 to 23 141701 -0.7062 0.240031 18 to 22 141581 -1.1130 0.132858 17 to 21 142094 0.6260 0.734343 16 to 20 141518 -1.3265 0.092330 15 to 19 142130 0.7480 0.772780 14 to 18 141750 -0.5401 0.294564 13 to 17 141909 -0.0011 0.499554 12 to 16 142175 0.9006 0.816093 11 to 15 142511 2.0396 0.979303 10 to 14 142053 0.4870 0.686877 9 to 13 142157 0.8396 0.799422 8 to 12 141198 -2.4113 0.007948 7 to 11 142252 1.1616 0.877300 6 to 10 142728 2.7752 0.997241 5 to 9 141994 0.2870 0.612950 4 to 8 142173 0.8938 0.814285 3 to 7 142078 0.5718 0.716259 2 to 6 142252 1.1616 0.877300 1 to 5 142391 1.6328 0.948742 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-09-11_14:31 Bits used No. missing words z-score p-value 31 to 32 142104 0.5742 0.717100 30 to 31 141904 -0.0157 0.493728 29 to 30 142438 1.5595 0.940561 28 to 29 141535 -1.1042 0.134749 27 to 28 141991 0.2409 0.595189 26 to 27 142079 0.5005 0.691639 25 to 26 141710 -0.5880 0.278268 24 to 25 142129 0.6480 0.741506 23 to 24 141513 -1.1691 0.121179 22 to 23 142006 0.2852 0.612240 21 to 22 141984 0.2203 0.587168 20 to 21 141321 -1.7355 0.041327 19 to 20 141564 -1.0187 0.154179 18 to 19 141531 -1.1160 0.132207 17 to 18 142118 0.6155 0.730903 16 to 17 142281 1.0964 0.863542 15 to 16 142158 0.7335 0.768385 14 to 15 142052 0.4209 0.663070 13 to 14 141892 -0.0511 0.479615 12 to 13 142369 1.3560 0.912444 11 to 12 142251 1.0079 0.843243 10 to 11 141263 -1.9066 0.028288 9 to 10 142365 1.3442 0.910552 8 to 9 141590 -0.9420 0.173102 7 to 8 141771 -0.4081 0.341617 6 to 7 141891 -0.0541 0.478439 5 to 6 141545 -1.0747 0.141250 4 to 5 141412 -1.4671 0.071181 3 to 4 142037 0.3766 0.646767 2 to 3 142664 2.2262 0.986998 1 to 2 142051 0.4179 0.661992 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-09-11_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2537.79 0.534 0.703494 Test results for specific bytes for dh-ranFile-2015-09-11_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2566.36 0.939 0.826008 2 to 9 2597.94 1.385 0.916975 3 to 10 2556.96 0.806 0.789738 4 to 11 2465.95 -0.482 0.315046 5 to 12 2415.30 -1.198 0.115495 6 to 13 2459.03 -0.579 0.281144 7 to 14 2517.86 0.253 0.599688 8 to 15 2480.27 -0.279 0.390098 9 to 16 2524.13 0.341 0.633562 10 to 17 2599.73 1.410 0.920795 11 to 18 2515.64 0.221 0.587500 12 to 19 2457.96 -0.594 0.276100 13 to 20 2532.28 0.457 0.676010 14 to 21 2556.89 0.804 0.789443 15 to 22 2549.11 0.695 0.756328 16 to 23 2568.98 0.976 0.835356 17 to 24 2491.69 -0.117 0.453244 18 to 25 2455.52 -0.629 0.264649 19 to 26 2502.45 0.035 0.513837 20 to 27 2516.81 0.238 0.593976 21 to 28 2543.71 0.618 0.731772 22 to 29 2550.26 0.711 0.761402 23 to 30 2446.70 -0.754 0.225482 24 to 31 2546.07 0.651 0.742625 25 to 32 2546.54 0.658 0.744786 CDPARK for dh-ranFile-2015-09-11_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 3555 1.4612 0.928018 3535 0.5479 0.708135 3553 1.3699 0.914635 3507 -0.7306 0.232514 3500 -1.0502 0.146807 3537 0.6393 0.738676 3526 0.1370 0.554479 3495 -1.2785 0.100530 3496 -1.2329 0.108811 3558 1.5982 0.944998 Square side=100, avg. no. parked=3526.20 sample std.=23.86 p-value of the KSTEST for those 10 p-values: 0.499800 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-09-11_14:31 0.0335,0.4597,0.9876,0.5904,0.0098,0.6963,0.9582,0.2774,0.1331,0.9347, The KS test for those 10 p-values: 0.300810 The 3DSPHERES test for dh-ranFile-2015-09-11_14:31 sample no r^3 equiv. uni. 1 9.361 0.268035 2 3.815 0.119408 3 64.395 0.883108 4 7.363 0.217624 5 57.712 0.853937 6 87.440 0.945779 7 7.177 0.212765 8 83.404 0.937970 9 17.249 0.437282 10 5.402 0.164772 11 22.275 0.524083 12 0.083 0.002771 13 7.448 0.219861 14 8.848 0.255425 15 22.841 0.532965 16 3.736 0.117084 17 23.487 0.542916 18 18.929 0.467923 19 6.119 0.184499 20 9.070 0.260918 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.139489 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-09-11_14:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 0.9 -0.4 0.5 -0.4 -0.1 -1.8 1.0 -0.5 0.4 0.8 -0.9 1.0 1.0 -1.0 -1.7 0.4 -1.0 1.6 -0.6 0.4 0.4 0.9 0.8 -0.5 -0.8 1.3 -0.3 -1.2 0.8 0.1 -1.3 -0.0 -2.2 0.1 -3.0 -0.5 0.8 -0.8 -0.7 -0.6 -1.0 0.8 Chi-square with 42 degrees of freedom:43.642326 z-score=0.179192, p-value=0.598512 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-09-11_14:31 Test no p-value 1 0.135548 2 0.007039 3 0.055554 4 0.012245 5 0.799847 6 0.208275 7 0.495394 8 0.353432 9 0.330511 10 0.438763 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.017539 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-09-11_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 66804 0.28 66723 0.05 3 25000.00 24953 0.09 24957 0.07 4 6666.67 6569 1.43 6649 0.05 5 1388.89 1411 0.35 1383 0.02 6 238.10 223 0.96 230 0.28 7 34.72 34 0.01 50 6.72 8 4.96 5 0.00 7 0.84 p=0.20718 p=0.76425 Number of rngs required: 687387, p-value: 0.119 RESULTS OF CRAPS TEST for dh-ranFile-2015-09-11_14:31 No. of wins: Observed Expected 98026 98585.9 z-score=-2.504, pvalue=0.00614 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66107 66666.7 4.698 4.698 2 37993 37654.3 3.046 7.745 3 26844 26954.7 0.455 8.200 4 19356 19313.5 0.094 8.293 5 13949 13851.4 0.687 8.981 6 10058 9943.5 1.317 10.298 7 7184 7145.0 0.213 10.511 8 5178 5139.1 0.295 10.806 9 3745 3699.9 0.551 11.356 10 2565 2666.3 3.848 15.205 11 1958 1923.3 0.625 15.830 12 1337 1388.7 1.928 17.757 13 1053 1003.7 2.420 20.177 14 750 726.1 0.784 20.961 15 505 525.8 0.826 21.787 16 391 381.2 0.255 22.041 17 286 276.5 0.324 22.365 18 208 200.8 0.256 22.621 19 150 146.0 0.110 22.732 20 90 106.2 2.475 25.207 21 293 287.1 0.121 25.328 Chisq= 25.33 for 20 degrees of freedom, p= 0.81082 SUMMARY of craptest p-value for no. of wins: 0.006140 p-value for throws/game: 0.810819 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-09-11_14:31 No. of wins: Observed Expected 98420 98585.9 z-score=-0.742, pvalue=0.22910 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66634 66666.7 0.016 0.016 2 37932 37654.3 2.048 2.064 3 27019 26954.7 0.153 2.217 4 19224 19313.5 0.414 2.631 5 13799 13851.4 0.198 2.830 6 9915 9943.5 0.082 2.912 7 7124 7145.0 0.062 2.974 8 5141 5139.1 0.001 2.974 9 3609 3699.9 2.232 5.206 10 2654 2666.3 0.057 5.263 11 1905 1923.3 0.175 5.437 12 1436 1388.7 1.608 7.045 13 983 1003.7 0.428 7.473 14 721 726.1 0.036 7.509 15 534 525.8 0.127 7.636 16 370 381.2 0.326 7.962 17 286 276.5 0.324 8.286 18 184 200.8 1.410 9.696 19 126 146.0 2.736 12.432 20 92 106.2 1.902 14.335 21 312 287.1 2.157 16.492 Chisq= 16.49 for 20 degrees of freedom, p= 0.31431 SUMMARY of craptest p-value for no. of wins: 0.229099 p-value for throws/game: 0.314307 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0028,0.0030,0.0053,0.0061,0.0070,0.0079,0.0098,0.0122,0.0175,0.0209, 0.0234,0.0283,0.0292,0.0335,0.0413,0.0414,0.0422,0.0463,0.0485,0.0556, 0.0593,0.0698,0.0712,0.0818,0.0879,0.0923,0.1005,0.1088,0.1090,0.1109, 0.1129,0.1155,0.1171,0.1189,0.1194,0.1212,0.1299,0.1322,0.1329,0.1331, 0.1347,0.1355,0.1385,0.1392,0.1395,0.1395,0.1413,0.1468,0.1480,0.1542, 0.1565,0.1645,0.1648,0.1656,0.1731,0.1788,0.1845,0.1888,0.1940,0.2019, 0.2054,0.2072,0.2083,0.2128,0.2176,0.2199,0.2255,0.2278,0.2291,0.2325, 0.2400,0.2448,0.2448,0.2554,0.2609,0.2646,0.2661,0.2680,0.2692,0.2715, 0.2761,0.2774,0.2783,0.2811,0.2851,0.2946,0.2964,0.3008,0.3021,0.3022, 0.3129,0.3143,0.3150,0.3287,0.3293,0.3305,0.3416,0.3432,0.3441,0.3534, 0.3843,0.3901,0.3903,0.3927,0.4001,0.4028,0.4055,0.4091,0.4183,0.4230, 0.4270,0.4373,0.4388,0.4465,0.4532,0.4540,0.4597,0.4670,0.4679,0.4680, 0.4682,0.4712,0.4723,0.4784,0.4796,0.4796,0.4820,0.4841,0.4901,0.4937, 0.4954,0.4996,0.4998,0.5124,0.5138,0.5147,0.5241,0.5330,0.5402,0.5429, 0.5508,0.5517,0.5519,0.5545,0.5638,0.5647,0.5709,0.5738,0.5788,0.5801, 0.5857,0.5872,0.5875,0.5904,0.5940,0.5947,0.5952,0.5962,0.5985,0.5997, 0.6060,0.6069,0.6122,0.6130,0.6142,0.6175,0.6182,0.6231,0.6336,0.6350, 0.6419,0.6468,0.6495,0.6620,0.6631,0.6705,0.6730,0.6760,0.6830,0.6830, 0.6855,0.6869,0.6911,0.6912,0.6916,0.6963,0.7035,0.7042,0.7081,0.7163, 0.7171,0.7171,0.7186,0.7309,0.7318,0.7343,0.7387,0.7390,0.7402,0.7415, 0.7415,0.7426,0.7439,0.7448,0.7521,0.7563,0.7614,0.7620,0.7642,0.7682, 0.7684,0.7728,0.7870,0.7894,0.7897,0.7994,0.7997,0.7998,0.8059,0.8108, 0.8111,0.8143,0.8161,0.8224,0.8260,0.8354,0.8432,0.8461,0.8539,0.8567, 0.8635,0.8688,0.8729,0.8773,0.8773,0.8831,0.8900,0.8913,0.9009,0.9106, 0.9124,0.9146,0.9170,0.9208,0.9250,0.9270,0.9279,0.9280,0.9347,0.9355, 0.9380,0.9406,0.9450,0.9458,0.9487,0.9509,0.9582,0.9622,0.9757,0.9793, 0.9795,0.9801,0.9814,0.9870,0.9876,0.9907,0.9925,0.9972,0.9986, Overall p-value after applying KStest on 269 p-values = 0.667197 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.