RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-02-18_21:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.49 35.0320 0.993839 2 to 25 15.85 14.5895 0.374974 3 to 26 16.26 9.9585 0.094657 4 to 27 16.20 12.3837 0.223633 5 to 28 15.97 14.4034 0.361631 6 to 29 15.73 29.5825 0.970482 7 to 30 15.81 21.7185 0.804211 8 to 31 15.71 19.4509 0.696727 9 to 32 15.50 19.6043 0.705035 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.429932 Tough bday spacings test for dh-ranFile-2016-02-18_21:31: 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 13 29 85 99 90 74 56 25 23 2 4 (O-E)^2/E 1.6 1.6 1.9 0.0 0.6 0.2 0.3 0.8 4.4 3.2 0.0 Birthday Spacings: Sum(O-E)^2/E= 14.626, p= 0.854 RESULTS OF GCD FOR dh-ranFile-2016-02-18_21:31 Euclid's algorithm: p-value, steps to gcd: 0.421733 p-value, dist. of gcd's: 0.203159 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-02-18_21:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.088 0.519 0.343 0.559 0.343 0.291 0.145 0.506 Bits 8 to 15---> 0.534 0.966 0.202 0.751 0.453 0.890 0.093 0.690 Bits 16 to 23---> 0.785 0.623 0.909 0.286 0.351 0.879 0.760 0.003 Bits 24 to 31---> 0.414 0.811 0.187 0.559 0.039 0.361 0.831 0.453 KS test for the above 32 p values: 0.019 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-02-18_21:31, p-values for 5 runs: 0.7212, 0.6375, 0.2131, 0.5370, 0.7217 Rank test for binary matrices (31x31) for dh-ranFile-2016-02-18_21:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 219 211.4 0.272 0.272 r= 29 5169 5134.0 0.238 0.510 r= 30 22981 23103.0 0.645 1.155 r= 31 11631 11551.5 0.547 1.702 chi-square = 1.702 with df = 3; p-value = 0.363 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-02-18_21:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 207 211.4 0.092 0.092 r= 30 5087 5134.0 0.430 0.523 r= 31 22971 23103.0 0.755 1.278 r= 32 11735 11551.5 2.914 4.192 chi-square = 4.192 with df = 3; p-value = 0.759 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-02-18_21:31 b-rank test for bits 1 to 8, p=0.95453 b-rank test for bits 2 to 9, p=0.11691 b-rank test for bits 3 to 10, p=0.32993 b-rank test for bits 4 to 11, p=0.29790 b-rank test for bits 5 to 12, p=0.78433 b-rank test for bits 6 to 13, p=0.60403 b-rank test for bits 7 to 14, p=0.27838 b-rank test for bits 8 to 15, p=0.41665 b-rank test for bits 9 to 16, p=0.47611 b-rank test for bits 10 to 17, p=0.33703 b-rank test for bits 11 to 18, p=0.65178 b-rank test for bits 12 to 19, p=0.48351 b-rank test for bits 13 to 20, p=0.76053 b-rank test for bits 14 to 21, p=0.71477 b-rank test for bits 15 to 22, p=0.77166 b-rank test for bits 16 to 23, p=0.21704 b-rank test for bits 17 to 24, p=0.27112 b-rank test for bits 18 to 25, p=0.90924 b-rank test for bits 19 to 26, p=0.25258 b-rank test for bits 20 to 27, p=0.26034 b-rank test for bits 21 to 28, p=0.65093 b-rank test for bits 22 to 29, p=0.31506 b-rank test for bits 23 to 30, p=0.63376 b-rank test for bits 24 to 31, p=0.37491 b-rank test for bits 25 to 32, p=0.02342 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 = 0.540168 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-02-18_21:31 (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 141218 -1.62 0.053128 2 141247 -1.55 0.060871 3 140954 -2.23 0.012805 4 141363 -1.28 0.100894 5 141372 -1.26 0.104659 6 141418 -1.15 0.125491 7 142850 2.20 0.986019 8 142011 0.24 0.593884 9 142403 1.15 0.875634 10 141927 0.04 0.516466 11 141587 -0.75 0.225693 12 141937 0.06 0.525774 13 142573 1.55 0.939505 14 141912 0.01 0.502489 15 142137 0.53 0.702616 16 142514 1.41 0.921140 17 140896 -2.37 0.008952 18 140641 -2.96 0.001521 19 141704 -0.48 0.315705 20 141916 0.02 0.506217 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-02-18_21:31 Bits used No. missing words z-score p-value 23 to 32 141756 -0.5287 0.298498 22 to 31 141441 -1.6149 0.053163 21 to 30 141499 -1.4149 0.078544 20 to 29 141243 -2.2977 0.010790 19 to 28 141648 -0.9011 0.183758 18 to 27 141618 -1.0046 0.157548 17 to 26 141353 -1.9184 0.027531 16 to 25 141534 -1.2942 0.097791 15 to 24 141830 -0.2736 0.392215 14 to 23 142365 1.5713 0.941941 13 to 22 142675 2.6402 0.995858 12 to 21 142099 0.6540 0.743455 11 to 20 141756 -0.5287 0.298498 10 to 19 141679 -0.7942 0.213528 9 to 18 141613 -1.0218 0.153431 8 to 17 141753 -0.5391 0.294920 7 to 16 141290 -2.1356 0.016355 6 to 15 141783 -0.4356 0.331556 5 to 14 142217 1.0609 0.855639 4 to 13 142474 1.9471 0.974241 3 to 12 142045 0.4678 0.680046 2 to 11 141870 -0.1356 0.446061 1 to 10 141890 -0.0667 0.473428 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-02-18_21:31 Bits used No. missing words z-score p-value 28 to 32 142181 0.9209 0.821453 27 to 31 141669 -0.8147 0.207628 26 to 30 141978 0.2328 0.592034 25 to 29 142014 0.3548 0.638635 24 to 28 141990 0.2735 0.607749 23 to 27 141359 -1.8655 0.031054 22 to 26 141479 -1.4587 0.072318 21 to 25 141635 -0.9299 0.176203 20 to 24 141916 0.0226 0.509019 19 to 23 142103 0.6565 0.744252 18 to 22 142080 0.5785 0.718551 17 to 21 141625 -0.9638 0.167565 16 to 20 142151 0.8192 0.793670 15 to 19 141995 0.2904 0.614248 14 to 18 141673 -0.8011 0.211532 13 to 17 141910 0.0023 0.500906 12 to 16 141723 -0.6316 0.263815 11 to 15 141768 -0.4791 0.315939 10 to 14 142363 1.5379 0.937959 9 to 13 142448 1.8260 0.966075 8 to 12 141996 0.2938 0.615543 7 to 11 141811 -0.3333 0.369446 6 to 10 141874 -0.1198 0.452336 5 to 9 141509 -1.3571 0.087383 4 to 8 142083 0.5887 0.721973 3 to 7 141723 -0.6316 0.263815 2 to 6 141944 0.1175 0.546778 1 to 5 142519 2.0667 0.980618 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-02-18_21:31 Bits used No. missing words z-score p-value 31 to 32 142446 1.5831 0.943300 30 to 31 142161 0.7424 0.771074 29 to 30 141855 -0.1603 0.436336 28 to 29 141606 -0.8948 0.185453 27 to 28 141620 -0.8535 0.196696 26 to 27 142066 0.4622 0.678014 25 to 26 141892 -0.0511 0.479615 24 to 25 142437 1.5565 0.940211 23 to 24 141748 -0.4759 0.317073 22 to 23 142043 0.3943 0.653323 21 to 22 141807 -0.3019 0.381380 20 to 21 142090 0.5329 0.702966 19 to 20 142441 1.5683 0.941600 18 to 19 142294 1.1347 0.871754 17 to 18 141940 0.0905 0.536044 16 to 17 141621 -0.8505 0.197515 15 to 16 141617 -0.8623 0.194253 14 to 15 141906 -0.0098 0.496081 13 to 14 141908 -0.0039 0.498435 12 to 13 142487 1.7040 0.955813 11 to 12 141924 0.0433 0.517259 10 to 11 142183 0.8073 0.790249 9 to 10 142243 0.9843 0.837510 8 to 9 142077 0.4946 0.689559 7 to 8 142131 0.6539 0.743410 6 to 7 142557 1.9105 0.971968 5 to 6 141763 -0.4317 0.332997 4 to 5 141706 -0.5998 0.274322 3 to 4 142107 0.5831 0.720086 2 to 3 142251 1.0079 0.843243 1 to 2 141999 0.2645 0.604308 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-02-18_21:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2508.16 0.115 0.545923 Test results for specific bytes for dh-ranFile-2016-02-18_21:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2424.09 -1.074 0.141521 2 to 9 2559.87 0.847 0.801434 3 to 10 2445.17 -0.775 0.219057 4 to 11 2519.46 0.275 0.608395 5 to 12 2516.24 0.230 0.590837 6 to 13 2463.69 -0.514 0.303779 7 to 14 2497.56 -0.034 0.486246 8 to 15 2656.13 2.208 0.986377 9 to 16 2629.54 1.832 0.966524 10 to 17 2442.42 -0.814 0.207726 11 to 18 2568.58 0.970 0.833937 12 to 19 2445.29 -0.774 0.219552 13 to 20 2508.83 0.125 0.549716 14 to 21 2596.13 1.360 0.913010 15 to 22 2609.97 1.555 0.940048 16 to 23 2574.94 1.060 0.855399 17 to 24 2594.44 1.336 0.909153 18 to 25 2423.89 -1.076 0.140881 19 to 26 2392.27 -1.524 0.063809 20 to 27 2496.39 -0.051 0.479666 21 to 28 2506.44 0.091 0.536307 22 to 29 2491.32 -0.123 0.451134 23 to 30 2400.98 -1.400 0.080709 24 to 31 2443.86 -0.794 0.213597 25 to 32 2577.73 1.099 0.864182 CDPARK for dh-ranFile-2016-02-18_21:31: 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 3519 -0.1826 0.427537 3500 -1.0502 0.146807 3486 -1.6895 0.045562 3498 -1.1416 0.126820 3513 -0.4566 0.323972 3506 -0.7763 0.218799 3514 -0.4110 0.340551 3513 -0.4566 0.323972 3556 1.5068 0.934075 3545 1.0046 0.842447 Square side=100, avg. no. parked=3515.00 sample std.=20.10 p-value of the KSTEST for those 10 p-values: 0.213776 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-02-18_21:31 0.6252,0.9924,0.9273,0.2904,0.2920,0.2962,0.5397,0.0836,0.5848,0.8985, The KS test for those 10 p-values: 0.630134 The 3DSPHERES test for dh-ranFile-2016-02-18_21:31 sample no r^3 equiv. uni. 1 54.598 0.837962 2 6.737 0.201129 3 68.129 0.896789 4 52.781 0.827849 5 29.000 0.619654 6 5.341 0.163081 7 134.742 0.988795 8 17.447 0.440977 9 8.359 0.243181 10 15.342 0.400347 11 31.336 0.648143 12 61.808 0.872582 13 3.368 0.106186 14 22.294 0.524385 15 24.702 0.561067 16 36.121 0.700013 17 27.962 0.606260 18 22.911 0.534058 19 96.791 0.960298 20 36.730 0.706044 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.272979 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-02-18_21:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 1.3 -1.3 -0.8 -1.1 -0.1 -0.3 0.8 -1.1 -0.1 0.8 1.6 0.6 -1.0 1.1 0.4 -0.1 -1.5 -1.7 0.8 0.7 -0.7 -1.1 1.2 -0.8 0.4 0.2 0.9 0.3 0.0 -0.3 1.6 -1.2 -0.8 1.5 0.8 0.0 -0.1 0.9 -0.7 -0.6 1.0 1.8 Chi-square with 42 degrees of freedom:37.679716 z-score=-0.471382, p-value=0.339024 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-02-18_21:31 Test no p-value 1 0.069097 2 0.113433 3 0.482165 4 0.695760 5 0.204091 6 0.833975 7 0.797894 8 0.010429 9 0.278281 10 0.051415 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.104340 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-02-18_21:31: (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 66677 0.00 66586 0.10 3 25000.00 24955 0.08 25135 0.73 4 6666.67 6696 0.13 6682 0.04 5 1388.89 1406 0.21 1329 2.58 6 238.10 224 0.83 221 1.23 7 34.72 37 0.15 39 0.53 8 4.96 4 0.19 7 0.84 p=0.04688 p=0.58110 Number of rngs required: 688484, p-value: 0.537 RESULTS OF CRAPS TEST for dh-ranFile-2016-02-18_21:31 No. of wins: Observed Expected 98186 98585.9 z-score=-1.788, pvalue=0.03686 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66406 66666.7 1.019 1.019 2 37610 37654.3 0.052 1.071 3 26904 26954.7 0.095 1.167 4 19558 19313.5 3.096 4.263 5 14006 13851.4 1.725 5.988 6 9930 9943.5 0.018 6.007 7 7163 7145.0 0.045 6.052 8 5125 5139.1 0.039 6.090 9 3676 3699.9 0.154 6.244 10 2686 2666.3 0.146 6.390 11 1908 1923.3 0.122 6.512 12 1391 1388.7 0.004 6.516 13 970 1003.7 1.132 7.648 14 729 726.1 0.011 7.660 15 521 525.8 0.044 7.704 16 383 381.2 0.009 7.713 17 305 276.5 2.929 10.642 18 197 200.8 0.073 10.715 19 146 146.0 0.000 10.715 20 111 106.2 0.216 10.931 21 275 287.1 0.511 11.442 Chisq= 11.44 for 20 degrees of freedom, p= 0.06605 SUMMARY of craptest p-value for no. of wins: 0.036856 p-value for throws/game: 0.066046 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-02-18_21:31 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 66573 66666.7 0.132 0.132 2 37577 37654.3 0.159 0.290 3 27028 26954.7 0.199 0.490 4 19331 19313.5 0.016 0.505 5 13958 13851.4 0.820 1.326 6 9913 9943.5 0.094 1.419 7 7185 7145.0 0.224 1.643 8 5085 5139.1 0.569 2.212 9 3696 3699.9 0.004 2.216 10 2643 2666.3 0.204 2.420 11 1970 1923.3 1.133 3.552 12 1361 1388.7 0.554 4.106 13 986 1003.7 0.313 4.419 14 742 726.1 0.346 4.765 15 525 525.8 0.001 4.767 16 387 381.2 0.090 4.856 17 290 276.5 0.655 5.511 18 207 200.8 0.190 5.701 19 143 146.0 0.061 5.762 20 120 106.2 1.789 7.551 21 280 287.1 0.176 7.727 Chisq= 7.73 for 20 degrees of freedom, p= 0.00648 SUMMARY of craptest p-value for no. of wins: 0.569485 p-value for throws/game: 0.006477 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0015,0.0027,0.0065,0.0090,0.0104,0.0108,0.0128,0.0164,0.0189,0.0234, 0.0275,0.0311,0.0369,0.0390,0.0456,0.0469,0.0514,0.0531,0.0532,0.0609, 0.0638,0.0660,0.0691,0.0723,0.0785,0.0807,0.0836,0.0874,0.0883,0.0925, 0.0947,0.0978,0.1009,0.1043,0.1047,0.1062,0.1134,0.1169,0.1255,0.1268, 0.1409,0.1415,0.1448,0.1468,0.1534,0.1575,0.1631,0.1676,0.1762,0.1838, 0.1855,0.1873,0.1943,0.1967,0.1975,0.2011,0.2017,0.2032,0.2041,0.2076, 0.2077,0.2115,0.2131,0.2135,0.2136,0.2138,0.2170,0.2188,0.2191,0.2196, 0.2236,0.2257,0.2432,0.2526,0.2603,0.2638,0.2638,0.2711,0.2730,0.2743, 0.2783,0.2784,0.2862,0.2904,0.2910,0.2920,0.2949,0.2962,0.2979,0.2985, 0.2985,0.3038,0.3151,0.3157,0.3159,0.3171,0.3240,0.3240,0.3299,0.3316, 0.3330,0.3370,0.3390,0.3406,0.3426,0.3431,0.3508,0.3611,0.3616,0.3635, 0.3694,0.3749,0.3750,0.3814,0.3922,0.4003,0.4145,0.4166,0.4217,0.4275, 0.4299,0.4363,0.4410,0.4461,0.4511,0.4523,0.4526,0.4529,0.4734,0.4761, 0.4796,0.4797,0.4822,0.4835,0.4862,0.4961,0.4984,0.5009,0.5025,0.5062, 0.5062,0.5090,0.5165,0.5173,0.5188,0.5244,0.5258,0.5339,0.5341,0.5360, 0.5363,0.5370,0.5371,0.5397,0.5402,0.5459,0.5468,0.5497,0.5588,0.5589, 0.5611,0.5695,0.5811,0.5848,0.5908,0.5920,0.5939,0.6040,0.6043,0.6063, 0.6077,0.6084,0.6142,0.6155,0.6197,0.6229,0.6252,0.6301,0.6338,0.6375, 0.6386,0.6481,0.6509,0.6518,0.6533,0.6780,0.6800,0.6896,0.6898,0.6958, 0.6967,0.7000,0.7026,0.7030,0.7050,0.7060,0.7148,0.7186,0.7201,0.7212, 0.7217,0.7220,0.7434,0.7435,0.7443,0.7509,0.7585,0.7599,0.7605,0.7711, 0.7717,0.7843,0.7846,0.7902,0.7937,0.7979,0.8014,0.8042,0.8112,0.8215, 0.8278,0.8315,0.8339,0.8340,0.8375,0.8380,0.8424,0.8432,0.8537,0.8554, 0.8556,0.8642,0.8718,0.8726,0.8756,0.8788,0.8901,0.8968,0.8985,0.9092, 0.9092,0.9094,0.9130,0.9211,0.9273,0.9341,0.9380,0.9395,0.9400,0.9402, 0.9416,0.9419,0.9433,0.9545,0.9558,0.9603,0.9658,0.9661,0.9665,0.9705, 0.9720,0.9742,0.9806,0.9860,0.9864,0.9888,0.9924,0.9938,0.9959, Overall p-value after applying KStest on 269 p-values = 0.551265 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.