RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-12-15_05:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.94 12.0005 0.199896 2 to 25 15.83 15.5202 0.441936 3 to 26 15.48 20.6988 0.759944 4 to 27 15.77 17.0730 0.550567 5 to 28 15.76 15.7115 0.455625 6 to 29 15.47 17.3405 0.568461 7 to 30 15.69 20.0119 0.726381 8 to 31 15.67 19.9084 0.721059 9 to 32 15.63 17.9609 0.608689 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.280529 Tough bday spacings test for dh-ranFile-2015-12-15_05:31: 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 7 33 69 102 111 72 56 28 16 6 0 (O-E)^2/E 0.5 0.4 0.2 0.2 1.8 0.5 0.3 0.1 0.1 0.1 4.1 Birthday Spacings: Sum(O-E)^2/E= 8.210, p= 0.392 RESULTS OF GCD FOR dh-ranFile-2015-12-15_05:31 Euclid's algorithm: p-value, steps to gcd: 0.058958 p-value, dist. of gcd's: 0.858195 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-12-15_05:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.382 0.221 0.135 0.901 0.465 0.612 0.647 0.017 Bits 8 to 15---> 0.065 0.543 0.029 0.241 0.296 0.572 0.541 0.949 Bits 16 to 23---> 0.534 0.788 0.331 0.314 0.317 0.147 0.249 0.930 Bits 24 to 31---> 0.483 0.447 0.542 0.114 0.098 0.500 0.443 0.400 KS test for the above 32 p values: 0.887 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-12-15_05:31, p-values for 5 runs: 0.8113, 0.5605, 0.4492, 0.5842, 0.7636 Rank test for binary matrices (31x31) for dh-ranFile-2015-12-15_05:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 190 211.4 2.170 2.170 r= 29 5065 5134.0 0.928 3.097 r= 30 23156 23103.0 0.121 3.219 r= 31 11589 11551.5 0.122 3.340 chi-square = 3.340 with df = 3; p-value = 0.658 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-12-15_05:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 196 211.4 1.124 1.124 r= 30 5209 5134.0 1.095 2.220 r= 31 22998 23103.0 0.478 2.697 r= 32 11597 11551.5 0.179 2.876 chi-square = 2.876 with df = 3; p-value = 0.589 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-12-15_05:31 b-rank test for bits 1 to 8, p=0.28597 b-rank test for bits 2 to 9, p=0.71852 b-rank test for bits 3 to 10, p=0.46003 b-rank test for bits 4 to 11, p=0.73843 b-rank test for bits 5 to 12, p=0.79354 b-rank test for bits 6 to 13, p=0.88893 b-rank test for bits 7 to 14, p=0.38553 b-rank test for bits 8 to 15, p=0.07543 b-rank test for bits 9 to 16, p=0.36259 b-rank test for bits 10 to 17, p=0.32761 b-rank test for bits 11 to 18, p=0.38049 b-rank test for bits 12 to 19, p=0.80485 b-rank test for bits 13 to 20, p=0.70204 b-rank test for bits 14 to 21, p=0.48712 b-rank test for bits 15 to 22, p=0.70948 b-rank test for bits 16 to 23, p=0.62905 b-rank test for bits 17 to 24, p=0.98543 b-rank test for bits 18 to 25, p=0.43421 b-rank test for bits 19 to 26, p=0.33161 b-rank test for bits 20 to 27, p=0.42646 b-rank test for bits 21 to 28, p=0.06209 b-rank test for bits 22 to 29, p=0.61670 b-rank test for bits 23 to 30, p=0.54676 b-rank test for bits 24 to 31, p=0.45186 b-rank test for bits 25 to 32, p=0.06034 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 = 0.570424 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-12-15_05:31 (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 142604 1.62 0.947712 2 142091 0.42 0.664386 3 142030 0.28 0.611005 4 141429 -1.12 0.130875 5 141796 -0.26 0.395586 6 141168 -1.73 0.041630 7 143427 3.55 0.999804 8 141573 -0.79 0.215987 9 141936 0.06 0.524843 10 141760 -0.35 0.363582 11 142487 1.35 0.911443 12 142674 1.79 0.963000 13 141096 -1.90 0.028697 14 141474 -1.02 0.154547 15 141063 -1.98 0.023998 16 141579 -0.77 0.220117 17 141867 -0.10 0.460608 18 142399 1.14 0.873707 19 142113 0.48 0.682915 20 141813 -0.23 0.410962 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-12-15_05:31 Bits used No. missing words z-score p-value 23 to 32 141644 -0.9149 0.180114 22 to 31 141985 0.2609 0.602927 21 to 30 141983 0.2540 0.600266 20 to 29 141904 -0.0184 0.492668 19 to 28 141267 -2.2149 0.013382 18 to 27 142397 1.6816 0.953679 17 to 26 141623 -0.9873 0.161737 16 to 25 141942 0.1127 0.544848 15 to 24 141804 -0.3632 0.358225 14 to 23 141535 -1.2908 0.098388 13 to 22 141988 0.2713 0.606911 12 to 21 141968 0.2023 0.580163 11 to 20 142305 1.3644 0.913776 10 to 19 142236 1.1264 0.870012 9 to 18 141758 -0.5218 0.300895 8 to 17 141914 0.0161 0.506424 7 to 16 141553 -1.2287 0.109588 6 to 15 141712 -0.6804 0.248110 5 to 14 142102 0.6644 0.746776 4 to 13 141890 -0.0667 0.473428 3 to 12 141583 -1.1253 0.130236 2 to 11 141839 -0.2425 0.404190 1 to 10 142233 1.1161 0.867811 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-12-15_05:31 Bits used No. missing words z-score p-value 28 to 32 141807 -0.3469 0.364340 27 to 31 141538 -1.2587 0.104061 26 to 30 141668 -0.8181 0.206659 25 to 29 142154 0.8294 0.796558 24 to 28 142031 0.4124 0.659992 23 to 27 141463 -1.5130 0.065142 22 to 26 142264 1.2023 0.885371 21 to 25 141209 -2.3740 0.008798 20 to 24 141771 -0.4689 0.319565 19 to 23 142002 0.3141 0.623291 18 to 22 141890 -0.0655 0.473878 17 to 21 142197 0.9752 0.835258 16 to 20 141698 -0.7164 0.236881 15 to 19 141696 -0.7232 0.234793 14 to 18 142466 1.8870 0.970421 13 to 17 141858 -0.1740 0.430933 12 to 16 141080 -2.8113 0.002467 11 to 15 141943 0.1141 0.545435 10 to 14 141910 0.0023 0.500906 9 to 13 141905 -0.0147 0.494145 8 to 12 141977 0.2294 0.590717 7 to 11 142091 0.6158 0.730997 6 to 10 142039 0.4396 0.669872 5 to 9 141968 0.1989 0.578822 4 to 8 142411 1.7006 0.955489 3 to 7 141337 -1.9401 0.026184 2 to 6 142194 0.9650 0.832723 1 to 5 141989 0.2701 0.606446 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-12-15_05:31 Bits used No. missing words z-score p-value 31 to 32 141940 0.0905 0.536044 30 to 31 141274 -1.8741 0.030456 29 to 30 141826 -0.2458 0.402914 28 to 29 142072 0.4799 0.684334 27 to 28 141327 -1.7178 0.042918 26 to 27 141946 0.1082 0.543070 25 to 26 141634 -0.8122 0.208343 24 to 25 141773 -0.4022 0.343786 23 to 24 141594 -0.9302 0.176140 22 to 23 141727 -0.5378 0.295342 21 to 22 142259 1.0315 0.848841 20 to 21 141987 0.2291 0.590610 19 to 20 142346 1.2881 0.901147 18 to 19 141554 -1.0482 0.147280 17 to 18 141802 -0.3166 0.375771 16 to 17 142519 1.7984 0.963946 15 to 16 141548 -1.0659 0.143241 14 to 15 141381 -1.5585 0.059558 13 to 14 141996 0.2557 0.600895 12 to 13 141821 -0.2606 0.397216 11 to 12 142348 1.2940 0.902169 10 to 11 141943 0.0993 0.539559 9 to 10 142554 1.9017 0.971394 8 to 9 141716 -0.5703 0.284239 7 to 8 142128 0.6450 0.740551 6 to 7 141845 -0.1898 0.424747 5 to 6 141529 -1.1219 0.130949 4 to 5 142140 0.6804 0.751888 3 to 4 141759 -0.4435 0.328720 2 to 3 141800 -0.3225 0.373534 1 to 2 141753 -0.4612 0.322345 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-12-15_05:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2497.89 -0.030 0.488091 Test results for specific bytes for dh-ranFile-2015-12-15_05:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2480.40 -0.277 0.390812 2 to 9 2476.56 -0.331 0.370136 3 to 10 2493.84 -0.087 0.465307 4 to 11 2510.26 0.145 0.557660 5 to 12 2425.29 -1.057 0.145355 6 to 13 2533.46 0.473 0.681954 7 to 14 2553.57 0.758 0.775644 8 to 15 2560.82 0.860 0.805140 9 to 16 2599.42 1.406 0.920145 10 to 17 2462.66 -0.528 0.298738 11 to 18 2471.75 -0.399 0.344781 12 to 19 2579.63 1.126 0.869934 13 to 20 2608.72 1.537 0.937912 14 to 21 2595.26 1.347 0.911045 15 to 22 2537.15 0.525 0.700357 16 to 23 2478.12 -0.309 0.378520 17 to 24 2419.42 -1.140 0.127237 18 to 25 2404.32 -1.353 0.088006 19 to 26 2540.69 0.576 0.717525 20 to 27 2477.47 -0.319 0.375030 21 to 28 2402.87 -1.374 0.084771 22 to 29 2349.42 -2.129 0.016607 23 to 30 2422.17 -1.101 0.135518 24 to 31 2614.07 1.613 0.946653 25 to 32 2448.75 -0.725 0.234277 CDPARK for dh-ranFile-2015-12-15_05:31: 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 3506 -0.7763 0.218799 3498 -1.1416 0.126820 3526 0.1370 0.554479 3498 -1.1416 0.126820 3520 -0.1370 0.445521 3536 0.5936 0.723613 3524 0.0457 0.518210 3485 -1.7352 0.041356 3539 0.7306 0.767486 3525 0.0913 0.536383 Square side=100, avg. no. parked=3515.70 sample std.=17.02 p-value of the KSTEST for those 10 p-values: 0.448049 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-12-15_05:31 0.5417,0.8795,0.8139,0.4865,0.3215,0.6010,0.6214,0.5272,0.7613,0.0794, The KS test for those 10 p-values: 0.539760 The 3DSPHERES test for dh-ranFile-2015-12-15_05:31 sample no r^3 equiv. uni. 1 3.636 0.114140 2 12.048 0.330744 3 33.060 0.667796 4 20.093 0.488169 5 5.443 0.165939 6 16.200 0.417244 7 45.615 0.781399 8 16.193 0.417106 9 58.345 0.856991 10 8.584 0.248831 11 6.945 0.206652 12 10.009 0.283677 13 38.872 0.726301 14 1.702 0.055158 15 9.647 0.274977 16 41.340 0.747916 17 9.063 0.260736 18 3.857 0.120632 19 3.255 0.102814 20 142.863 0.991452 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.241601 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-12-15_05:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 -2.0 0.1 1.2 0.7 2.0 1.0 -0.9 -0.6 0.0 -0.2 -1.4 -1.9 0.9 0.6 -0.8 -0.7 -0.7 2.4 -0.3 0.5 1.7 -0.4 -2.0 0.5 -0.4 1.3 -0.8 0.1 0.6 0.3 0.6 1.0 0.5 -0.1 0.1 0.0 1.8 0.1 -1.3 -1.3 2.0 -1.1 Chi-square with 42 degrees of freedom:51.662182 z-score=1.054230, p-value=0.854123 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-12-15_05:31 Test no p-value 1 0.092746 2 0.142441 3 0.134048 4 0.024064 5 0.032820 6 0.418703 7 0.087154 8 0.209488 9 0.004755 10 0.657206 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000188 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-12-15_05:31: (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 66625 0.03 66624 0.03 3 25000.00 25070 0.20 25091 0.33 4 6666.67 6644 0.08 6681 0.03 5 1388.89 1386 0.01 1360 0.60 6 238.10 237 0.01 205 4.60 7 34.72 35 0.00 33 0.09 8 4.96 2 1.77 5 0.00 p=0.08770 p=0.53956 Number of rngs required: 687488, p-value: 0.144 RESULTS OF CRAPS TEST for dh-ranFile-2015-12-15_05:31 No. of wins: Observed Expected 98691 98585.9 z-score= 0.470, pvalue=0.68091 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67081 66666.7 2.575 2.575 2 37516 37654.3 0.508 3.083 3 26779 26954.7 1.146 4.229 4 19403 19313.5 0.415 4.644 5 13880 13851.4 0.059 4.703 6 9745 9943.5 3.964 8.667 7 7168 7145.0 0.074 8.741 8 5186 5139.1 0.429 9.170 9 3598 3699.9 2.805 11.974 10 2620 2666.3 0.804 12.778 11 1952 1923.3 0.427 13.206 12 1362 1388.7 0.515 13.720 13 1037 1003.7 1.104 14.824 14 731 726.1 0.033 14.857 15 526 525.8 0.000 14.857 16 354 381.2 1.934 16.791 17 259 276.5 1.112 17.903 18 214 200.8 0.864 18.767 19 155 146.0 0.557 19.324 20 104 106.2 0.046 19.370 21 330 287.1 6.406 25.776 Chisq= 25.78 for 20 degrees of freedom, p= 0.82665 SUMMARY of craptest p-value for no. of wins: 0.680913 p-value for throws/game: 0.826653 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-12-15_05:31 No. of wins: Observed Expected 98819 98585.9 z-score= 1.043, pvalue=0.85147 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66655 66666.7 0.002 0.002 2 37688 37654.3 0.030 0.032 3 27111 26954.7 0.906 0.938 4 19260 19313.5 0.148 1.086 5 13945 13851.4 0.632 1.718 6 9953 9943.5 0.009 1.727 7 7059 7145.0 1.036 2.763 8 5070 5139.1 0.928 3.691 9 3681 3699.9 0.096 3.788 10 2684 2666.3 0.118 3.905 11 1888 1923.3 0.649 4.554 12 1326 1388.7 2.834 7.389 13 1025 1003.7 0.451 7.840 14 674 726.1 3.744 11.584 15 535 525.8 0.160 11.744 16 418 381.2 3.563 15.306 17 285 276.5 0.259 15.565 18 194 200.8 0.232 15.797 19 160 146.0 1.346 17.143 20 102 106.2 0.167 17.310 21 287 287.1 0.000 17.310 Chisq= 17.31 for 20 degrees of freedom, p= 0.36725 SUMMARY of craptest p-value for no. of wins: 0.851467 p-value for throws/game: 0.367255 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0002,0.0025,0.0048,0.0088,0.0134,0.0166,0.0171,0.0240,0.0241,0.0262, 0.0287,0.0287,0.0305,0.0328,0.0414,0.0416,0.0429,0.0552,0.0590,0.0596, 0.0603,0.0621,0.0650,0.0651,0.0754,0.0794,0.0848,0.0872,0.0877,0.0880, 0.0927,0.0977,0.0984,0.1028,0.1041,0.1096,0.1141,0.1145,0.1206,0.1268, 0.1268,0.1272,0.1302,0.1309,0.1309,0.1340,0.1354,0.1355,0.1424,0.1432, 0.1443,0.1454,0.1473,0.1475,0.1545,0.1617,0.1659,0.1761,0.1801,0.1999, 0.2067,0.2067,0.2083,0.2095,0.2160,0.2188,0.2201,0.2213,0.2343,0.2348, 0.2369,0.2412,0.2416,0.2481,0.2488,0.2488,0.2607,0.2750,0.2805,0.2837, 0.2842,0.2860,0.2953,0.2961,0.2987,0.3009,0.3141,0.3170,0.3196,0.3215, 0.3223,0.3276,0.3287,0.3307,0.3314,0.3316,0.3438,0.3448,0.3582,0.3626, 0.3636,0.3643,0.3673,0.3701,0.3735,0.3750,0.3758,0.3785,0.3805,0.3821, 0.3855,0.3908,0.3917,0.3956,0.3972,0.3999,0.4029,0.4042,0.4110,0.4171, 0.4172,0.4187,0.4247,0.4265,0.4309,0.4342,0.4419,0.4425,0.4455,0.4467, 0.4480,0.4492,0.4519,0.4556,0.4600,0.4606,0.4646,0.4653,0.4734,0.4739, 0.4829,0.4865,0.4871,0.4881,0.4882,0.4927,0.4941,0.5004,0.5009,0.5064, 0.5182,0.5248,0.5272,0.5339,0.5360,0.5364,0.5396,0.5396,0.5398,0.5413, 0.5417,0.5423,0.5429,0.5431,0.5448,0.5454,0.5468,0.5506,0.5545,0.5577, 0.5605,0.5685,0.5704,0.5724,0.5788,0.5802,0.5842,0.5889,0.5906,0.5907, 0.6003,0.6009,0.6010,0.6029,0.6064,0.6069,0.6087,0.6110,0.6120,0.6167, 0.6214,0.6233,0.6290,0.6467,0.6572,0.6579,0.6600,0.6644,0.6678,0.6699, 0.6809,0.6820,0.6829,0.6843,0.7004,0.7020,0.7095,0.7175,0.7185,0.7211, 0.7236,0.7263,0.7264,0.7310,0.7384,0.7406,0.7468,0.7479,0.7519,0.7599, 0.7613,0.7636,0.7675,0.7756,0.7814,0.7879,0.7935,0.7966,0.8049,0.8051, 0.8113,0.8139,0.8267,0.8327,0.8353,0.8488,0.8515,0.8541,0.8570,0.8582, 0.8678,0.8699,0.8700,0.8737,0.8795,0.8854,0.8866,0.8889,0.9007,0.9011, 0.9022,0.9110,0.9114,0.9138,0.9201,0.9299,0.9379,0.9467,0.9477,0.9492, 0.9537,0.9555,0.9630,0.9639,0.9704,0.9714,0.9854,0.9915,0.9998, Overall p-value after applying KStest on 269 p-values = 0.043531 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.