RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-07-18_07:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.74 18.9408 0.668059 2 to 25 15.59 16.6105 0.518956 3 to 26 15.85 21.5553 0.797567 4 to 27 15.80 9.4960 0.076593 5 to 28 15.77 24.8812 0.902599 6 to 29 15.92 14.7582 0.387103 7 to 30 15.87 9.1293 0.063883 8 to 31 15.92 6.0936 0.007465 9 to 32 15.81 5.8355 0.005775 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.062107 Tough bday spacings test for dh-ranFile-2015-07-18_07:31: 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 32 56 89 101 88 67 25 25 5 5 (O-E)^2/E 0.5 0.6 4.1 0.8 0.1 1.2 4.3 0.8 6.9 0.4 0.2 Birthday Spacings: Sum(O-E)^2/E= 19.798, p= 0.969 RESULTS OF GCD FOR dh-ranFile-2015-07-18_07:31 Euclid's algorithm: p-value, steps to gcd: 0.745441 p-value, dist. of gcd's: 0.402730 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-07-18_07:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.735 0.076 0.533 0.766 0.769 0.030 0.241 0.061 Bits 8 to 15---> 0.894 0.719 0.509 0.896 0.384 0.974 0.011 0.663 Bits 16 to 23---> 0.806 0.325 0.002 0.902 0.648 0.642 0.635 0.924 Bits 24 to 31---> 0.728 0.895 0.332 0.006 0.288 0.664 0.108 0.824 KS test for the above 32 p values: 0.823 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-07-18_07:31, p-values for 5 runs: 0.0318, 0.1267, 0.3187, 0.6459, 0.8008 Rank test for binary matrices (31x31) for dh-ranFile-2015-07-18_07:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 220 211.4 0.348 0.348 r= 29 5119 5134.0 0.044 0.392 r= 30 23022 23103.0 0.284 0.677 r= 31 11639 11551.5 0.662 1.339 chi-square = 1.339 with df = 3; p-value = 0.280 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-07-18_07:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 187 211.4 2.820 2.820 r= 30 5130 5134.0 0.003 2.823 r= 31 23094 23103.0 0.004 2.827 r= 32 11589 11551.5 0.122 2.948 chi-square = 2.948 with df = 3; p-value = 0.600 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-07-18_07:31 b-rank test for bits 1 to 8, p=0.86166 b-rank test for bits 2 to 9, p=0.30696 b-rank test for bits 3 to 10, p=0.23003 b-rank test for bits 4 to 11, p=0.18202 b-rank test for bits 5 to 12, p=0.95791 b-rank test for bits 6 to 13, p=0.89211 b-rank test for bits 7 to 14, p=0.29403 b-rank test for bits 8 to 15, p=0.49866 b-rank test for bits 9 to 16, p=0.22434 b-rank test for bits 10 to 17, p=0.65882 b-rank test for bits 11 to 18, p=0.60407 b-rank test for bits 12 to 19, p=0.13157 b-rank test for bits 13 to 20, p=0.59079 b-rank test for bits 14 to 21, p=0.74609 b-rank test for bits 15 to 22, p=0.11300 b-rank test for bits 16 to 23, p=0.01153 b-rank test for bits 17 to 24, p=0.42748 b-rank test for bits 18 to 25, p=0.35433 b-rank test for bits 19 to 26, p=0.32984 b-rank test for bits 20 to 27, p=0.08057 b-rank test for bits 21 to 28, p=0.51111 b-rank test for bits 22 to 29, p=0.47572 b-rank test for bits 23 to 30, p=0.80418 b-rank test for bits 24 to 31, p=0.36122 b-rank test for bits 25 to 32, p=0.73931 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 = 0.795902 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-07-18_07:31 (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 142842 2.18 0.985339 2 142238 0.77 0.778733 3 142123 0.50 0.691191 4 142254 0.81 0.789678 5 140800 -2.59 0.004772 6 142140 0.54 0.705039 7 142054 0.34 0.632324 8 142591 1.59 0.944385 9 141907 -0.01 0.497828 10 141692 -0.51 0.305804 11 142728 1.91 0.972112 12 141691 -0.51 0.304985 13 142305 0.92 0.822377 14 142643 1.71 0.956752 15 141438 -1.10 0.135396 16 142085 0.41 0.659260 17 142963 2.46 0.993089 18 141452 -1.07 0.142641 19 141839 -0.16 0.434739 20 141460 -1.05 0.146897 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-07-18_07:31 Bits used No. missing words z-score p-value 23 to 32 141886 -0.0804 0.467940 22 to 31 141932 0.0782 0.531155 21 to 30 142004 0.3264 0.627957 20 to 29 141777 -0.4563 0.324083 19 to 28 142410 1.7264 0.957867 18 to 27 141721 -0.6494 0.258036 17 to 26 141697 -0.7322 0.232032 16 to 25 142119 0.7230 0.765160 15 to 24 142020 0.3816 0.648629 14 to 23 141234 -2.3287 0.009937 13 to 22 141470 -1.5149 0.064895 12 to 21 141796 -0.3908 0.347975 11 to 20 142024 0.3954 0.653731 10 to 19 141459 -1.5529 0.060228 9 to 18 141940 0.1058 0.542113 8 to 17 142040 0.4506 0.673856 7 to 16 141840 -0.2391 0.405526 6 to 15 141804 -0.3632 0.358225 5 to 14 141723 -0.6425 0.260269 4 to 13 141739 -0.5873 0.278486 3 to 12 142603 2.3920 0.991621 2 to 11 142271 1.2471 0.893827 1 to 10 141594 -1.0873 0.138442 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-07-18_07:31 Bits used No. missing words z-score p-value 28 to 32 141489 -1.4248 0.077101 27 to 31 141547 -1.2282 0.109679 26 to 30 141800 -0.3706 0.355464 25 to 29 141934 0.0836 0.533324 24 to 28 141898 -0.0384 0.484682 23 to 27 141870 -0.1333 0.446969 22 to 26 141820 -0.3028 0.381016 21 to 25 142092 0.6192 0.732114 20 to 24 141713 -0.6655 0.252857 19 to 23 142105 0.6633 0.746427 18 to 22 142039 0.4396 0.669872 17 to 21 141826 -0.2825 0.388790 16 to 20 141895 -0.0486 0.480629 15 to 19 142185 0.9345 0.824970 14 to 18 141922 0.0429 0.517129 13 to 17 141928 0.0633 0.525232 12 to 16 142058 0.5040 0.692857 11 to 15 141722 -0.6350 0.262709 10 to 14 141397 -1.7367 0.041219 9 to 13 141754 -0.5265 0.299256 8 to 12 141805 -0.3537 0.361797 7 to 11 141673 -0.8011 0.211532 6 to 10 141313 -2.0215 0.021616 5 to 9 141864 -0.1537 0.438939 4 to 8 142061 0.5141 0.696421 3 to 7 142083 0.5887 0.721973 2 to 6 141628 -0.9537 0.170128 1 to 5 141781 -0.4350 0.331775 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-07-18_07:31 Bits used No. missing words z-score p-value 31 to 32 141488 -1.2429 0.106959 30 to 31 142301 1.1554 0.876030 29 to 30 140894 -2.9951 0.001372 28 to 29 142013 0.3058 0.620126 27 to 28 141465 -1.3107 0.094978 26 to 27 141569 -1.0039 0.157708 25 to 26 142055 0.4297 0.666295 24 to 25 142456 1.6126 0.946584 23 to 24 141681 -0.6735 0.250302 22 to 23 141677 -0.6853 0.246565 21 to 22 141677 -0.6853 0.246565 20 to 21 141081 -2.4435 0.007274 19 to 20 141898 -0.0334 0.486669 18 to 19 141463 -1.3166 0.093985 17 to 18 142085 0.5182 0.697841 16 to 17 141186 -2.1337 0.016433 15 to 16 142085 0.5182 0.697841 14 to 15 142264 1.0462 0.852271 13 to 14 141655 -0.7502 0.226556 12 to 13 141780 -0.3815 0.351415 11 to 12 142016 0.3147 0.623490 10 to 11 141610 -0.8830 0.188624 9 to 10 141954 0.1318 0.552417 8 to 9 141746 -0.4818 0.314974 7 to 8 142070 0.4740 0.682233 6 to 7 142035 0.3707 0.644573 5 to 6 142107 0.5831 0.720086 4 to 5 142180 0.7984 0.787691 3 to 4 141873 -0.1072 0.457328 2 to 3 142373 1.3678 0.914306 1 to 2 142055 0.4297 0.666295 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-07-18_07:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2493.09 -0.098 0.461103 Test results for specific bytes for dh-ranFile-2015-07-18_07:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2516.76 0.237 0.593663 2 to 9 2510.81 0.153 0.560778 3 to 10 2420.46 -1.125 0.130338 4 to 11 2452.51 -0.672 0.250932 5 to 12 2512.90 0.182 0.572371 6 to 13 2469.83 -0.427 0.334798 7 to 14 2420.97 -1.118 0.131851 8 to 15 2585.72 1.212 0.887295 9 to 16 2331.95 -2.377 0.008737 10 to 17 2499.95 -0.001 0.499722 11 to 18 2439.49 -0.856 0.196083 12 to 19 2502.79 0.039 0.515716 13 to 20 2432.16 -0.959 0.168683 14 to 21 2658.68 2.244 0.987584 15 to 22 2534.66 0.490 0.687976 16 to 23 2464.52 -0.502 0.307931 17 to 24 2384.75 -1.630 0.051567 18 to 25 2575.13 1.063 0.855996 19 to 26 2468.61 -0.444 0.328536 20 to 27 2433.30 -0.943 0.172771 21 to 28 2443.23 -0.803 0.211050 22 to 29 2431.39 -0.970 0.165963 23 to 30 2395.80 -1.474 0.070287 24 to 31 2500.45 0.006 0.502532 25 to 32 2493.03 -0.099 0.460714 CDPARK for dh-ranFile-2015-07-18_07:31: 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 3505 -0.8219 0.205562 3560 1.6895 0.954438 3551 1.2785 0.899470 3556 1.5068 0.934075 3525 0.0913 0.536383 3541 0.8219 0.794438 3519 -0.1826 0.427537 3585 2.8311 0.997680 3532 0.4110 0.659449 3560 1.6895 0.954438 Square side=100, avg. no. parked=3543.40 sample std.=22.46 p-value of the KSTEST for those 10 p-values: 0.006167 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-07-18_07:31 0.9597,0.5382,0.1540,0.8336,0.3557,0.2867,0.4400,0.3965,0.2701,0.5837, The KS test for those 10 p-values: 0.735554 The 3DSPHERES test for dh-ranFile-2015-07-18_07:31 sample no r^3 equiv. uni. 1 5.392 0.164509 2 15.058 0.394646 3 48.478 0.801292 4 18.471 0.459745 5 18.347 0.457495 6 0.825 0.027132 7 0.423 0.014014 8 17.593 0.443697 9 12.686 0.344840 10 13.994 0.372793 11 51.409 0.819792 12 12.385 0.338237 13 13.609 0.364687 14 69.015 0.899790 15 6.294 0.189261 16 26.736 0.589836 17 19.618 0.480000 18 5.174 0.158412 19 25.515 0.572795 20 2.390 0.076575 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.151709 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-07-18_07:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 0.1 1.1 0.5 -2.6 -0.3 0.3 1.2 -0.2 0.2 0.8 1.0 0.3 0.1 -0.7 1.2 -0.8 0.5 -0.5 -0.2 0.6 -1.1 -0.3 0.4 -0.9 0.3 -0.8 -0.8 -0.3 1.1 -0.7 0.8 -1.7 2.3 1.2 0.1 -0.2 -0.7 0.1 1.0 0.1 -1.0 -1.1 Chi-square with 42 degrees of freedom:36.592337 z-score=-0.590024, p-value=0.293287 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-07-18_07:31 Test no p-value 1 0.174365 2 0.051762 3 0.307925 4 0.948739 5 0.284527 6 0.812016 7 0.038819 8 0.936753 9 0.997691 10 0.000907 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.055002 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-07-18_07:31: (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 66768 0.15 66721 0.04 3 25000.00 24833 1.12 25089 0.32 4 6666.67 6742 0.85 6548 2.11 5 1388.89 1369 0.28 1381 0.04 6 238.10 249 0.50 216 2.05 7 34.72 33 0.09 41 1.14 8 4.96 5 0.00 3 0.77 p=0.18997 p=0.62830 Number of rngs required: 687357, p-value: 0.112 RESULTS OF CRAPS TEST for dh-ranFile-2015-07-18_07:31 No. of wins: Observed Expected 98342 98585.9 z-score=-1.091, pvalue=0.13771 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66744 66666.7 0.090 0.090 2 37451 37654.3 1.098 1.188 3 26930 26954.7 0.023 1.210 4 19401 19313.5 0.397 1.607 5 13789 13851.4 0.281 1.888 6 9922 9943.5 0.047 1.935 7 7342 7145.0 5.430 7.365 8 5129 5139.1 0.020 7.385 9 3797 3699.9 2.550 9.935 10 2711 2666.3 0.749 10.685 11 1785 1923.3 9.949 20.633 12 1372 1388.7 0.202 20.835 13 985 1003.7 0.349 21.184 14 716 726.1 0.142 21.326 15 497 525.8 1.581 22.907 16 360 381.2 1.174 24.081 17 290 276.5 0.655 24.736 18 212 200.8 0.621 25.357 19 161 146.0 1.544 26.902 20 103 106.2 0.097 26.999 21 303 287.1 0.879 27.878 Chisq= 27.88 for 20 degrees of freedom, p= 0.88768 SUMMARY of craptest p-value for no. of wins: 0.137707 p-value for throws/game: 0.887681 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-07-18_07:31 No. of wins: Observed Expected 98506 98585.9 z-score=-0.357, pvalue=0.36048 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66606 66666.7 0.055 0.055 2 37589 37654.3 0.113 0.169 3 27135 26954.7 1.206 1.374 4 19304 19313.5 0.005 1.379 5 13938 13851.4 0.541 1.920 6 9895 9943.5 0.237 2.157 7 7045 7145.0 1.400 3.557 8 5034 5139.1 2.148 5.705 9 3810 3699.9 3.278 8.984 10 2632 2666.3 0.441 9.425 11 1982 1923.3 1.790 11.215 12 1382 1388.7 0.033 11.248 13 994 1003.7 0.094 11.342 14 778 726.1 3.704 15.045 15 537 525.8 0.237 15.282 16 353 381.2 2.079 17.361 17 280 276.5 0.043 17.405 18 181 200.8 1.958 19.363 19 133 146.0 1.155 20.518 20 109 106.2 0.073 20.591 21 283 287.1 0.059 20.650 Chisq= 20.65 for 20 degrees of freedom, p= 0.58199 SUMMARY of craptest p-value for no. of wins: 0.360481 p-value for throws/game: 0.581989 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0009,0.0014,0.0015,0.0048,0.0058,0.0062,0.0065,0.0073,0.0075,0.0087, 0.0099,0.0110,0.0115,0.0140,0.0164,0.0216,0.0271,0.0300,0.0318,0.0388, 0.0412,0.0516,0.0518,0.0550,0.0602,0.0611,0.0621,0.0639,0.0649,0.0703, 0.0760,0.0766,0.0766,0.0771,0.0806,0.0940,0.0950,0.1070,0.1083,0.1097, 0.1120,0.1130,0.1267,0.1303,0.1316,0.1319,0.1354,0.1377,0.1384,0.1426, 0.1469,0.1517,0.1540,0.1577,0.1584,0.1645,0.1660,0.1687,0.1701,0.1728, 0.1744,0.1820,0.1886,0.1893,0.1900,0.1961,0.2056,0.2110,0.2115,0.2243, 0.2266,0.2300,0.2320,0.2411,0.2466,0.2466,0.2503,0.2509,0.2529,0.2580, 0.2603,0.2627,0.2701,0.2785,0.2801,0.2845,0.2867,0.2881,0.2933,0.2940, 0.2993,0.3050,0.3058,0.3070,0.3079,0.3079,0.3150,0.3187,0.3241,0.3250, 0.3285,0.3298,0.3318,0.3321,0.3348,0.3382,0.3448,0.3480,0.3514,0.3543, 0.3555,0.3557,0.3582,0.3605,0.3612,0.3618,0.3647,0.3728,0.3810,0.3839, 0.3871,0.3888,0.3946,0.3965,0.4027,0.4055,0.4275,0.4275,0.4347,0.4389, 0.4400,0.4437,0.4470,0.4573,0.4575,0.4597,0.4607,0.4611,0.4679,0.4757, 0.4800,0.4806,0.4847,0.4867,0.4978,0.4987,0.4997,0.5025,0.5090,0.5111, 0.5157,0.5171,0.5190,0.5252,0.5312,0.5327,0.5333,0.5364,0.5382,0.5421, 0.5524,0.5608,0.5724,0.5728,0.5820,0.5837,0.5898,0.5908,0.5937,0.6004, 0.6041,0.6201,0.6235,0.6280,0.6283,0.6323,0.6352,0.6423,0.6446,0.6459, 0.6478,0.6486,0.6537,0.6588,0.6593,0.6594,0.6633,0.6644,0.6663,0.6663, 0.6681,0.6699,0.6739,0.6822,0.6880,0.6912,0.6929,0.6964,0.6978,0.6978, 0.7050,0.7193,0.7201,0.7220,0.7282,0.7321,0.7345,0.7356,0.7393,0.7454, 0.7461,0.7464,0.7652,0.7660,0.7694,0.7787,0.7877,0.7897,0.7944,0.7959, 0.7976,0.8008,0.8013,0.8042,0.8063,0.8120,0.8198,0.8224,0.8231,0.8241, 0.8250,0.8336,0.8523,0.8560,0.8617,0.8760,0.8873,0.8877,0.8921,0.8938, 0.8943,0.8955,0.8958,0.8995,0.8998,0.9016,0.9026,0.9143,0.9235,0.9341, 0.9368,0.9444,0.9466,0.9487,0.9544,0.9544,0.9568,0.9579,0.9579,0.9597, 0.9688,0.9721,0.9743,0.9853,0.9876,0.9916,0.9931,0.9977,0.9977, Overall p-value after applying KStest on 269 p-values = 0.042444 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.