RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-03-19_12:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.81 9.9618 0.094794 2 to 25 15.80 17.8263 0.600125 3 to 26 15.66 19.2672 0.686587 4 to 27 15.67 22.2778 0.825731 5 to 28 15.86 16.3164 0.498473 6 to 29 15.58 20.3630 0.743915 7 to 30 15.54 12.6548 0.241031 8 to 31 15.87 23.0803 0.853345 9 to 32 15.82 18.4088 0.636498 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.551204 Tough bday spacings test for dh-ranFile-2016-03-19_12:31: 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 8 41 61 99 93 95 50 24 15 11 3 (O-E)^2/E 0.1 0.5 2.1 0.0 0.2 3.6 0.1 1.1 0.0 2.9 0.3 Birthday Spacings: Sum(O-E)^2/E= 10.986, p= 0.641 RESULTS OF GCD FOR dh-ranFile-2016-03-19_12:31 Euclid's algorithm: p-value, steps to gcd: 0.784843 p-value, dist. of gcd's: 0.195001 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-03-19_12:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.368 0.859 0.933 0.035 0.773 0.422 0.788 0.837 Bits 8 to 15---> 0.651 0.431 0.877 0.430 0.861 0.771 0.589 0.476 Bits 16 to 23---> 0.228 0.779 0.713 0.778 0.906 0.705 0.758 0.976 Bits 24 to 31---> 0.763 0.821 0.736 0.823 0.099 0.259 0.933 0.712 KS test for the above 32 p values: 0.998 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-03-19_12:31, p-values for 5 runs: 0.7155, 0.7257, 0.3227, 0.3664, 0.7064 Rank test for binary matrices (31x31) for dh-ranFile-2016-03-19_12:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 193 211.4 1.605 1.605 r= 29 5053 5134.0 1.278 2.883 r= 30 23158 23103.0 0.131 3.014 r= 31 11596 11551.5 0.171 3.185 chi-square = 3.185 with df = 3; p-value = 0.636 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-03-19_12:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 212 211.4 0.002 0.002 r= 30 4960 5134.0 5.898 5.899 r= 31 23339 23103.0 2.410 8.309 r= 32 11489 11551.5 0.338 8.648 chi-square = 8.648 with df = 3; p-value = 0.966 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-03-19_12:31 b-rank test for bits 1 to 8, p=0.92908 b-rank test for bits 2 to 9, p=0.41834 b-rank test for bits 3 to 10, p=0.39797 b-rank test for bits 4 to 11, p=0.16138 b-rank test for bits 5 to 12, p=0.24239 b-rank test for bits 6 to 13, p=0.57127 b-rank test for bits 7 to 14, p=0.65850 b-rank test for bits 8 to 15, p=0.05987 b-rank test for bits 9 to 16, p=0.54446 b-rank test for bits 10 to 17, p=0.10702 b-rank test for bits 11 to 18, p=0.27407 b-rank test for bits 12 to 19, p=0.92213 b-rank test for bits 13 to 20, p=0.09189 b-rank test for bits 14 to 21, p=0.09691 b-rank test for bits 15 to 22, p=0.38505 b-rank test for bits 16 to 23, p=0.72796 b-rank test for bits 17 to 24, p=0.77672 b-rank test for bits 18 to 25, p=0.37833 b-rank test for bits 19 to 26, p=0.15254 b-rank test for bits 20 to 27, p=0.14110 b-rank test for bits 21 to 28, p=0.37458 b-rank test for bits 22 to 29, p=0.20192 b-rank test for bits 23 to 30, p=0.32518 b-rank test for bits 24 to 31, p=0.00754 b-rank test for bits 25 to 32, p=0.20100 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 = 0.029890 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-03-19_12:31 (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 141821 -0.21 0.418248 2 141718 -0.45 0.327426 3 141973 0.15 0.559129 4 141986 0.18 0.571084 5 141678 -0.54 0.294429 6 142114 0.48 0.683746 7 141808 -0.24 0.406425 8 142382 1.10 0.865284 9 142262 0.82 0.795029 10 141643 -0.62 0.266883 11 141706 -0.48 0.317369 12 142218 0.72 0.764604 13 141986 0.18 0.571084 14 141566 -0.80 0.211227 15 142222 0.73 0.767469 16 141799 -0.26 0.398288 17 141615 -0.69 0.245825 18 141341 -1.33 0.092110 19 142136 0.53 0.701806 20 142061 0.35 0.638469 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-03-19_12:31 Bits used No. missing words z-score p-value 23 to 32 142292 1.3196 0.906508 22 to 31 141918 0.0299 0.511925 21 to 30 141686 -0.7701 0.220619 20 to 29 142142 0.8023 0.788813 19 to 28 141492 -1.4391 0.075066 18 to 27 141801 -0.3736 0.354369 17 to 26 142168 0.8920 0.813794 16 to 25 141774 -0.4667 0.320373 15 to 24 142023 0.3920 0.652458 14 to 23 141921 0.0402 0.516050 13 to 22 142374 1.6023 0.945457 12 to 21 142125 0.7437 0.771468 11 to 20 142252 1.1816 0.881322 10 to 19 142211 1.0402 0.850886 9 to 18 141627 -0.9736 0.165140 8 to 17 142369 1.5851 0.943525 7 to 16 142150 0.8299 0.796701 6 to 15 141777 -0.4563 0.324083 5 to 14 141683 -0.7804 0.217564 4 to 13 142030 0.4161 0.661333 3 to 12 142066 0.5402 0.705485 2 to 11 142111 0.6954 0.756602 1 to 10 142039 0.4471 0.672612 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-03-19_12:31 Bits used No. missing words z-score p-value 28 to 32 142260 1.1887 0.882723 27 to 31 141744 -0.5604 0.287589 26 to 30 141677 -0.7876 0.215477 25 to 29 141872 -0.1265 0.449651 24 to 28 141759 -0.5096 0.305168 23 to 27 141875 -0.1164 0.453679 22 to 26 141739 -0.5774 0.281838 21 to 25 141616 -0.9943 0.160029 20 to 24 141732 -0.6011 0.273881 19 to 23 141601 -1.0452 0.147968 18 to 22 142298 1.3175 0.906169 17 to 21 141882 -0.0926 0.463093 16 to 20 141778 -0.4452 0.328093 15 to 19 142017 0.3650 0.642438 14 to 18 141691 -0.7401 0.229619 13 to 17 141600 -1.0486 0.147187 12 to 16 141877 -0.1096 0.456366 11 to 15 141375 -1.8113 0.035048 10 to 14 141549 -1.2215 0.110956 9 to 13 141376 -1.8079 0.035311 8 to 12 141676 -0.7909 0.214487 7 to 11 142287 1.2802 0.899769 6 to 10 142135 0.7650 0.777859 5 to 9 141977 0.2294 0.590717 4 to 8 141777 -0.4486 0.326869 3 to 7 142028 0.4023 0.656258 2 to 6 141827 -0.2791 0.390090 1 to 5 142281 1.2599 0.896147 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-03-19_12:31 Bits used No. missing words z-score p-value 31 to 32 142126 0.6391 0.738636 30 to 31 142059 0.4415 0.670576 29 to 30 141489 -1.2399 0.107504 28 to 29 141446 -1.3668 0.085851 27 to 28 141899 -0.0305 0.487845 26 to 27 141457 -1.3343 0.091052 25 to 26 141525 -1.1337 0.128457 24 to 25 141541 -1.0865 0.138625 23 to 24 142001 0.2704 0.606579 22 to 23 142017 0.3176 0.624610 21 to 22 141677 -0.6853 0.246565 20 to 21 141706 -0.5998 0.274322 19 to 20 141970 0.1790 0.571018 18 to 19 141960 0.1495 0.559408 17 to 18 142576 1.9666 0.975384 16 to 17 142497 1.7335 0.958500 15 to 16 141463 -1.3166 0.093985 14 to 15 142361 1.3324 0.908629 13 to 14 142290 1.1229 0.869264 12 to 13 141143 -2.2606 0.011893 11 to 12 142083 0.5123 0.695780 10 to 11 142277 1.0846 0.860944 9 to 10 141766 -0.4228 0.336220 8 to 9 142215 0.9017 0.816387 7 to 8 142319 1.2085 0.886566 6 to 7 142004 0.2793 0.609978 5 to 6 141953 0.1288 0.551250 4 to 5 141875 -0.1013 0.459669 3 to 4 142166 0.7571 0.775517 2 to 3 141777 -0.3904 0.348137 1 to 2 141842 -0.1986 0.421283 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-03-19_12:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2413.88 -1.218 0.111614 Test results for specific bytes for dh-ranFile-2016-03-19_12:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2526.60 0.376 0.646631 2 to 9 2443.86 -0.794 0.213610 3 to 10 2520.21 0.286 0.612490 4 to 11 2488.35 -0.165 0.434593 5 to 12 2580.66 1.141 0.872989 6 to 13 2480.53 -0.275 0.391532 7 to 14 2558.19 0.823 0.794719 8 to 15 2474.13 -0.366 0.357236 9 to 16 2569.67 0.985 0.837764 10 to 17 2550.29 0.711 0.761506 11 to 18 2431.61 -0.967 0.166724 12 to 19 2409.81 -1.275 0.101078 13 to 20 2404.16 -1.355 0.087656 14 to 21 2519.89 0.281 0.610770 15 to 22 2455.22 -0.633 0.263287 16 to 23 2384.89 -1.628 0.051778 17 to 24 2626.62 1.791 0.963323 18 to 25 2535.03 0.495 0.689850 19 to 26 2487.97 -0.170 0.432446 20 to 27 2499.66 -0.005 0.498098 21 to 28 2496.04 -0.056 0.477660 22 to 29 2401.69 -1.390 0.082227 23 to 30 2677.57 2.511 0.993985 24 to 31 2481.25 -0.265 0.395459 25 to 32 2487.71 -0.174 0.430991 CDPARK for dh-ranFile-2016-03-19_12:31: 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 3560 1.6895 0.954438 3501 -1.0046 0.157553 3519 -0.1826 0.427537 3523 0.0000 0.500000 3508 -0.6849 0.246694 3509 -0.6393 0.261324 3536 0.5936 0.723613 3521 -0.0913 0.463617 3526 0.1370 0.554479 3492 -1.4155 0.078457 Square side=100, avg. no. parked=3519.50 sample std.=18.19 p-value of the KSTEST for those 10 p-values: 0.740288 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-03-19_12:31 0.0276,0.2139,0.9841,0.4105,0.7734,0.1489,0.8889,0.4212,0.0058,0.6938, The KS test for those 10 p-values: 0.481915 The 3DSPHERES test for dh-ranFile-2016-03-19_12:31 sample no r^3 equiv. uni. 1 30.962 0.643731 2 49.115 0.805471 3 21.957 0.519003 4 5.539 0.168582 5 22.786 0.532121 6 18.553 0.461212 7 92.934 0.954852 8 18.130 0.453566 9 4.776 0.147184 10 3.182 0.100637 11 15.629 0.406062 12 60.005 0.864689 13 10.965 0.306152 14 21.744 0.515584 15 24.674 0.560656 16 107.020 0.971769 17 9.389 0.268724 18 16.356 0.420272 19 49.402 0.807320 20 105.352 0.970154 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.588244 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-03-19_12:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -1.2 -1.3 -1.1 1.4 -0.1 -1.0 -0.6 0.4 0.5 -0.6 1.4 0.5 -0.1 0.4 0.2 -1.3 -0.3 -0.1 1.1 1.5 -0.0 -0.7 0.2 -1.2 -0.1 -0.5 -0.3 -0.6 0.8 -1.5 -0.3 -1.6 0.7 -0.9 -1.0 -0.5 -1.0 -0.4 1.0 0.1 0.0 -0.1 Chi-square with 42 degrees of freedom:29.180469 z-score=-1.398725, p-value=0.066996 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-03-19_12:31 Test no p-value 1 0.042968 2 0.747958 3 0.036798 4 0.265741 5 0.016952 6 0.310121 7 0.013139 8 0.707353 9 0.230945 10 0.263318 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.004687 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-03-19_12:31: (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 66558 0.18 66726 0.05 3 25000.00 25136 0.74 24974 0.03 4 6666.67 6647 0.06 6631 0.19 5 1388.89 1378 0.09 1377 0.10 6 238.10 241 0.04 249 0.50 7 34.72 31 0.40 37 0.15 8 4.96 8 1.86 5 0.00 p=0.23720 p=0.01523 Number of rngs required: 688093, p-value: 0.361 RESULTS OF CRAPS TEST for dh-ranFile-2016-03-19_12:31 No. of wins: Observed Expected 98531 98585.9 z-score=-0.245, pvalue=0.40309 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66473 66666.7 0.563 0.563 2 37628 37654.3 0.018 0.581 3 27132 26954.7 1.166 1.747 4 19326 19313.5 0.008 1.755 5 14001 13851.4 1.615 3.370 6 9985 9943.5 0.173 3.543 7 7091 7145.0 0.409 3.952 8 5071 5139.1 0.902 4.853 9 3832 3699.9 4.719 9.572 10 2612 2666.3 1.106 10.678 11 1863 1923.3 1.892 12.570 12 1324 1388.7 3.018 15.588 13 1001 1003.7 0.007 15.596 14 725 726.1 0.002 15.598 15 540 525.8 0.382 15.979 16 389 381.2 0.162 16.141 17 256 276.5 1.526 17.666 18 197 200.8 0.073 17.739 19 157 146.0 0.831 18.571 20 101 106.2 0.256 18.827 21 296 287.1 0.275 19.102 Chisq= 19.10 for 20 degrees of freedom, p= 0.48477 SUMMARY of craptest p-value for no. of wins: 0.403089 p-value for throws/game: 0.484769 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-03-19_12:31 No. of wins: Observed Expected 98690 98585.9 z-score= 0.466, pvalue=0.67931 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66550 66666.7 0.204 0.204 2 37629 37654.3 0.017 0.221 3 26972 26954.7 0.011 0.232 4 19522 19313.5 2.252 2.484 5 13681 13851.4 2.097 4.581 6 9976 9943.5 0.106 4.687 7 7088 7145.0 0.455 5.142 8 5238 5139.1 1.904 7.046 9 3696 3699.9 0.004 7.050 10 2726 2666.3 1.337 8.387 11 1851 1923.3 2.720 11.107 12 1385 1388.7 0.010 11.117 13 996 1003.7 0.059 11.176 14 746 726.1 0.543 11.720 15 529 525.8 0.019 11.739 16 386 381.2 0.062 11.800 17 287 276.5 0.396 12.196 18 215 200.8 1.000 13.196 19 140 146.0 0.245 13.441 20 111 106.2 0.216 13.657 21 276 287.1 0.430 14.087 Chisq= 14.09 for 20 degrees of freedom, p= 0.17394 SUMMARY of craptest p-value for no. of wins: 0.679314 p-value for throws/game: 0.173936 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0047,0.0058,0.0075,0.0119,0.0131,0.0152,0.0170,0.0276,0.0299,0.0350, 0.0352,0.0353,0.0368,0.0430,0.0518,0.0599,0.0670,0.0751,0.0785,0.0822, 0.0859,0.0877,0.0911,0.0919,0.0921,0.0940,0.0948,0.0969,0.0992,0.1006, 0.1011,0.1070,0.1075,0.1110,0.1116,0.1285,0.1386,0.1411,0.1472,0.1472, 0.1480,0.1489,0.1525,0.1576,0.1600,0.1614,0.1651,0.1667,0.1686,0.1739, 0.1950,0.2010,0.2019,0.2112,0.2136,0.2139,0.2145,0.2155,0.2176,0.2206, 0.2280,0.2296,0.2309,0.2372,0.2410,0.2424,0.2458,0.2466,0.2467,0.2589, 0.2613,0.2633,0.2633,0.2657,0.2669,0.2687,0.2739,0.2741,0.2743,0.2818, 0.2876,0.2944,0.3052,0.3062,0.3101,0.3174,0.3204,0.3227,0.3241,0.3252, 0.3269,0.3274,0.3281,0.3362,0.3481,0.3544,0.3572,0.3606,0.3664,0.3677, 0.3746,0.3783,0.3851,0.3901,0.3915,0.3955,0.3980,0.3983,0.4031,0.4061, 0.4064,0.4105,0.4182,0.4183,0.4203,0.4212,0.4213,0.4218,0.4275,0.4299, 0.4306,0.4310,0.4324,0.4346,0.4497,0.4536,0.4537,0.4564,0.4597,0.4612, 0.4631,0.4636,0.4762,0.4777,0.4819,0.4848,0.4878,0.4981,0.4985,0.5000, 0.5119,0.5156,0.5160,0.5190,0.5321,0.5445,0.5512,0.5513,0.5545,0.5591, 0.5594,0.5607,0.5710,0.5711,0.5711,0.5713,0.5882,0.5890,0.5907,0.6001, 0.6066,0.6100,0.6108,0.6125,0.6246,0.6360,0.6365,0.6385,0.6414,0.6424, 0.6437,0.6466,0.6513,0.6525,0.6563,0.6585,0.6613,0.6706,0.6726,0.6793, 0.6837,0.6866,0.6899,0.6938,0.6958,0.7018,0.7047,0.7055,0.7064,0.7074, 0.7118,0.7130,0.7155,0.7236,0.7257,0.7280,0.7358,0.7386,0.7403,0.7439, 0.7480,0.7566,0.7576,0.7615,0.7629,0.7646,0.7675,0.7709,0.7715,0.7728, 0.7734,0.7755,0.7767,0.7777,0.7779,0.7792,0.7848,0.7881,0.7888,0.7947, 0.7950,0.7967,0.8055,0.8073,0.8138,0.8164,0.8213,0.8229,0.8257,0.8366, 0.8378,0.8509,0.8533,0.8586,0.8609,0.8611,0.8647,0.8653,0.8693,0.8730, 0.8768,0.8813,0.8827,0.8866,0.8889,0.8961,0.8998,0.9062,0.9062,0.9065, 0.9086,0.9221,0.9291,0.9325,0.9334,0.9435,0.9455,0.9544,0.9549,0.9585, 0.9633,0.9656,0.9702,0.9718,0.9754,0.9755,0.9841,0.9940,0.9984, Overall p-value after applying KStest on 269 p-values = 0.967675 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.