RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-07-16_08:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.59 18.7302 0.655764 2 to 25 15.71 14.0999 0.339980 3 to 26 15.62 19.9469 0.723043 4 to 27 15.95 13.6609 0.309059 5 to 28 15.80 22.5466 0.835397 6 to 29 15.63 14.6477 0.379158 7 to 30 15.78 26.2854 0.930585 8 to 31 15.64 9.8354 0.089630 9 to 32 15.99 22.4501 0.831978 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.784955 Tough bday spacings test for dh-ranFile-2015-07-16_08:31: 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 11 36 80 96 92 83 53 31 8 4 6 (O-E)^2/E 0.4 0.0 0.6 0.0 0.3 0.3 0.0 0.1 3.2 1.0 0.9 Birthday Spacings: Sum(O-E)^2/E= 6.867, p= 0.262 RESULTS OF GCD FOR dh-ranFile-2015-07-16_08:31 Euclid's algorithm: p-value, steps to gcd: 0.734134 p-value, dist. of gcd's: 0.197627 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-07-16_08:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.827 0.140 0.987 0.468 0.718 0.317 0.122 0.216 Bits 8 to 15---> 0.007 0.941 0.288 0.450 0.136 0.113 0.345 0.824 Bits 16 to 23---> 0.335 0.141 0.541 0.966 0.591 0.139 0.701 0.809 Bits 24 to 31---> 0.907 0.888 0.630 0.643 0.300 0.585 0.174 0.675 KS test for the above 32 p values: 0.061 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-07-16_08:31, p-values for 5 runs: 0.6859, 0.0003, 0.1317, 0.8271, 0.8702 Rank test for binary matrices (31x31) for dh-ranFile-2015-07-16_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 181 211.4 4.376 4.376 r= 29 5121 5134.0 0.033 4.409 r= 30 23145 23103.0 0.076 4.486 r= 31 11553 11551.5 0.000 4.486 chi-square = 4.486 with df = 3; p-value = 0.786 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-07-16_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 201 211.4 0.513 0.513 r= 30 5064 5134.0 0.955 1.468 r= 31 23157 23103.0 0.126 1.594 r= 32 11578 11551.5 0.061 1.655 chi-square = 1.655 with df = 3; p-value = 0.353 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-07-16_08:31 b-rank test for bits 1 to 8, p=0.87353 b-rank test for bits 2 to 9, p=0.62384 b-rank test for bits 3 to 10, p=0.85684 b-rank test for bits 4 to 11, p=0.37014 b-rank test for bits 5 to 12, p=0.26052 b-rank test for bits 6 to 13, p=0.17689 b-rank test for bits 7 to 14, p=0.53406 b-rank test for bits 8 to 15, p=0.73130 b-rank test for bits 9 to 16, p=0.37694 b-rank test for bits 10 to 17, p=0.43887 b-rank test for bits 11 to 18, p=0.42825 b-rank test for bits 12 to 19, p=0.24368 b-rank test for bits 13 to 20, p=0.19496 b-rank test for bits 14 to 21, p=0.82198 b-rank test for bits 15 to 22, p=0.78432 b-rank test for bits 16 to 23, p=0.77212 b-rank test for bits 17 to 24, p=0.45447 b-rank test for bits 18 to 25, p=0.22591 b-rank test for bits 19 to 26, p=0.40036 b-rank test for bits 20 to 27, p=0.96336 b-rank test for bits 21 to 28, p=0.95007 b-rank test for bits 22 to 29, p=0.25187 b-rank test for bits 23 to 30, p=0.19313 b-rank test for bits 24 to 31, p=0.33887 b-rank test for bits 25 to 32, p=0.13238 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 = 0.608900 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-07-16_08:31 (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 142220 0.73 0.766039 2 142390 1.12 0.869294 3 142653 1.74 0.958855 4 141349 -1.31 0.095236 5 141264 -1.51 0.065805 6 141612 -0.69 0.243623 7 142119 0.49 0.687892 8 140926 -2.30 0.010795 9 141086 -1.92 0.027198 10 141618 -0.68 0.248038 11 141899 -0.02 0.490372 12 141938 0.07 0.526704 13 142589 1.59 0.943858 14 141578 -0.77 0.219425 15 142117 0.49 0.686236 16 142001 0.21 0.584798 17 141865 -0.10 0.458753 18 141651 -0.60 0.273063 19 142138 0.53 0.703425 20 142276 0.86 0.804196 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-07-16_08:31 Bits used No. missing words z-score p-value 23 to 32 142507 2.0609 0.980345 22 to 31 142371 1.5920 0.944304 21 to 30 142231 1.1092 0.866330 20 to 29 142001 0.3161 0.624038 19 to 28 142202 1.0092 0.843562 18 to 27 142070 0.5540 0.710222 17 to 26 142067 0.5437 0.706673 16 to 25 142495 2.0196 0.978285 15 to 24 142110 0.6920 0.755521 14 to 23 141987 0.2678 0.605584 13 to 22 142023 0.3920 0.652458 12 to 21 141839 -0.2425 0.404190 11 to 20 142415 1.7437 0.959393 10 to 19 141357 -1.9046 0.028417 9 to 18 141797 -0.3873 0.349251 8 to 17 141895 -0.0494 0.480295 7 to 16 141886 -0.0804 0.467940 6 to 15 142349 1.5161 0.935253 5 to 14 142444 1.8437 0.967386 4 to 13 141822 -0.3011 0.381655 3 to 12 142204 1.0161 0.845210 2 to 11 141785 -0.4287 0.334062 1 to 10 141727 -0.6287 0.264765 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-07-16_08:31 Bits used No. missing words z-score p-value 28 to 32 141290 -2.0994 0.017890 27 to 31 142055 0.4938 0.689275 26 to 30 141846 -0.2147 0.415009 25 to 29 141892 -0.0587 0.476577 24 to 28 141574 -1.1367 0.127829 23 to 27 141904 -0.0181 0.492792 22 to 26 141291 -2.0960 0.018040 21 to 25 141993 0.2836 0.611652 20 to 24 141886 -0.0791 0.468483 19 to 23 141896 -0.0452 0.481979 18 to 22 141285 -2.1164 0.017157 17 to 21 141536 -1.2655 0.102842 16 to 20 141816 -0.3164 0.375860 15 to 19 141730 -0.6079 0.271628 14 to 18 141691 -0.7401 0.229619 13 to 17 141833 -0.2587 0.397916 12 to 16 141947 0.1277 0.550805 11 to 15 142607 2.3650 0.990985 10 to 14 141974 0.2192 0.586761 9 to 13 141893 -0.0554 0.477928 8 to 12 142188 0.9446 0.827580 7 to 11 142402 1.6701 0.952547 6 to 10 142080 0.5785 0.718551 5 to 9 141818 -0.3096 0.378435 4 to 8 142315 1.3752 0.915458 3 to 7 141848 -0.2079 0.417654 2 to 6 142204 0.9989 0.841074 1 to 5 141481 -1.4520 0.073256 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-07-16_08:31 Bits used No. missing words z-score p-value 31 to 32 141797 -0.3314 0.370187 30 to 31 142084 0.5153 0.696811 29 to 30 142128 0.6450 0.740551 28 to 29 141607 -0.8918 0.186242 27 to 28 142156 0.7276 0.766583 26 to 27 141686 -0.6588 0.255015 25 to 26 141765 -0.4258 0.335144 24 to 25 142051 0.4179 0.661992 23 to 24 142237 0.9666 0.833123 22 to 23 142089 0.5300 0.701944 21 to 22 141520 -1.1485 0.125388 20 to 21 142077 0.4946 0.689559 19 to 20 141363 -1.6116 0.053525 18 to 19 142327 1.2321 0.891038 17 to 18 142128 0.6450 0.740551 16 to 17 142308 1.1760 0.880206 15 to 16 142405 1.4622 0.928150 14 to 15 141228 -2.0098 0.022225 13 to 14 142045 0.4002 0.655498 12 to 13 142372 1.3648 0.913843 11 to 12 142273 1.0728 0.858314 10 to 11 141709 -0.5909 0.277279 9 to 10 142262 1.0403 0.850905 8 to 9 141200 -2.0924 0.018201 7 to 8 141447 -1.3638 0.086314 6 to 7 141891 -0.0541 0.478439 5 to 6 142112 0.5978 0.725029 4 to 5 141987 0.2291 0.590610 3 to 4 141213 -2.0541 0.019984 2 to 3 142101 0.5654 0.714099 1 to 2 141557 -1.0393 0.149328 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-07-16_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2443.84 -0.794 0.213553 Test results for specific bytes for dh-ranFile-2015-07-16_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2626.86 1.794 0.963597 2 to 9 2458.52 -0.587 0.278727 3 to 10 2444.94 -0.779 0.218087 4 to 11 2618.73 1.679 0.953437 5 to 12 2533.26 0.470 0.680941 6 to 13 2656.53 2.214 0.986576 7 to 14 2445.21 -0.775 0.219217 8 to 15 2524.10 0.341 0.633375 9 to 16 2577.33 1.094 0.862952 10 to 17 2506.16 0.087 0.534727 11 to 18 2604.02 1.471 0.929368 12 to 19 2544.63 0.631 0.736030 13 to 20 2633.71 1.891 0.970686 14 to 21 2605.19 1.488 0.931573 15 to 22 2554.36 0.769 0.778987 16 to 23 2592.74 1.312 0.905159 17 to 24 2453.18 -0.662 0.253956 18 to 25 2482.08 -0.253 0.399986 19 to 26 2524.39 0.345 0.634918 20 to 27 2582.25 1.163 0.877612 21 to 28 2733.09 3.296 0.999510 22 to 29 2439.21 -0.860 0.194965 23 to 30 2579.93 1.130 0.870847 24 to 31 2500.60 0.009 0.503401 25 to 32 2574.81 1.058 0.854951 CDPARK for dh-ranFile-2015-07-16_08:31: 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 3494 -1.3242 0.092718 3575 2.3744 0.991212 3511 -0.5479 0.291865 3524 0.0457 0.518210 3511 -0.5479 0.291865 3508 -0.6849 0.246694 3550 1.2329 0.891189 3521 -0.0913 0.463617 3569 2.1005 0.982156 3531 0.3653 0.642555 Square side=100, avg. no. parked=3529.40 sample std.=25.62 p-value of the KSTEST for those 10 p-values: 0.458943 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-07-16_08:31 0.5791,0.8518,0.7646,0.6273,0.0835,0.9033,0.7424,0.0118,0.2442,0.1397, The KS test for those 10 p-values: 0.746841 The 3DSPHERES test for dh-ranFile-2015-07-16_08:31 sample no r^3 equiv. uni. 1 47.960 0.797831 2 12.633 0.343677 3 32.012 0.655985 4 31.805 0.653604 5 7.835 0.229859 6 32.559 0.662196 7 3.795 0.118828 8 45.414 0.779927 9 15.234 0.398176 10 107.044 0.971792 11 1.918 0.061933 12 8.124 0.237239 13 54.552 0.837712 14 18.355 0.457642 15 62.682 0.876239 16 36.337 0.702166 17 8.690 0.251487 18 0.762 0.025078 19 11.062 0.308388 20 17.226 0.436850 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.995463 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-07-16_08:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 0.1 -1.1 0.2 1.5 -2.7 -1.5 0.3 -0.1 -0.3 -0.0 -0.5 0.3 1.6 1.3 -0.9 1.3 -0.7 0.2 -0.4 0.3 -1.1 -0.7 0.0 0.3 -0.8 -1.4 0.4 0.8 2.2 0.9 -1.7 -0.0 -0.8 0.2 -0.5 -1.4 -1.3 -0.8 -1.3 -0.6 0.0 -0.1 Chi-square with 42 degrees of freedom:42.656038 z-score=0.071580, p-value=0.557225 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-07-16_08:31 Test no p-value 1 0.078594 2 0.621073 3 0.003262 4 0.412126 5 0.067431 6 0.104697 7 0.490694 8 0.091765 9 0.006695 10 0.260228 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000746 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-07-16_08:31: (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 66799 0.26 66709 0.03 3 25000.00 24974 0.03 24861 0.77 4 6666.67 6578 1.18 6694 0.11 5 1388.89 1374 0.16 1433 1.40 6 238.10 238 0.00 254 1.06 7 34.72 32 0.21 43 1.97 8 4.96 4 0.19 5 0.00 p=0.08286 p=0.50024 Number of rngs required: 688191, p-value: 0.404 RESULTS OF CRAPS TEST for dh-ranFile-2015-07-16_08:31 No. of wins: Observed Expected 98448 98585.9 z-score=-0.617, pvalue=0.26875 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66617 66666.7 0.037 0.037 2 37799 37654.3 0.556 0.593 3 26807 26954.7 0.810 1.403 4 19199 19313.5 0.678 2.081 5 13850 13851.4 0.000 2.081 6 10123 9943.5 3.239 5.320 7 7140 7145.0 0.004 5.323 8 5076 5139.1 0.774 6.097 9 3744 3699.9 0.526 6.624 10 2625 2666.3 0.640 7.264 11 1920 1923.3 0.006 7.269 12 1365 1388.7 0.406 7.675 13 1018 1003.7 0.203 7.879 14 718 726.1 0.091 7.970 15 583 525.8 6.214 14.184 16 365 381.2 0.684 14.868 17 277 276.5 0.001 14.869 18 200 200.8 0.003 14.873 19 178 146.0 7.021 21.894 20 105 106.2 0.014 21.908 21 291 287.1 0.053 21.960 Chisq= 21.96 for 20 degrees of freedom, p= 0.65734 SUMMARY of craptest p-value for no. of wins: 0.268755 p-value for throws/game: 0.657342 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-07-16_08:31 No. of wins: Observed Expected 98687 98585.9 z-score= 0.452, pvalue=0.67450 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66431 66666.7 0.833 0.833 2 37706 37654.3 0.071 0.904 3 27155 26954.7 1.488 2.392 4 19173 19313.5 1.022 3.413 5 13799 13851.4 0.198 3.612 6 10116 9943.5 2.991 6.603 7 7223 7145.0 0.851 7.454 8 5076 5139.1 0.774 8.228 9 3686 3699.9 0.052 8.280 10 2758 2666.3 3.154 11.434 11 1855 1923.3 2.427 13.861 12 1348 1388.7 1.195 15.057 13 975 1003.7 0.822 15.878 14 739 726.1 0.228 16.106 15 530 525.8 0.033 16.139 16 397 381.2 0.659 16.798 17 264 276.5 0.569 17.366 18 205 200.8 0.087 17.453 19 162 146.0 1.757 19.210 20 104 106.2 0.046 19.256 21 298 287.1 0.413 19.669 Chisq= 19.67 for 20 degrees of freedom, p= 0.52120 SUMMARY of craptest p-value for no. of wins: 0.674496 p-value for throws/game: 0.521197 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0003,0.0007,0.0033,0.0067,0.0067,0.0108,0.0118,0.0172,0.0179,0.0180, 0.0182,0.0200,0.0222,0.0251,0.0272,0.0284,0.0535,0.0607,0.0619,0.0658, 0.0674,0.0733,0.0786,0.0829,0.0835,0.0863,0.0896,0.0918,0.0927,0.0952, 0.1028,0.1047,0.1132,0.1188,0.1221,0.1254,0.1278,0.1317,0.1324,0.1362, 0.1390,0.1397,0.1401,0.1412,0.1493,0.1735,0.1769,0.1862,0.1931,0.1950, 0.1950,0.1976,0.2136,0.2163,0.2181,0.2192,0.2194,0.2259,0.2296,0.2299, 0.2372,0.2436,0.2437,0.2442,0.2467,0.2480,0.2515,0.2519,0.2540,0.2550, 0.2602,0.2605,0.2621,0.2648,0.2688,0.2716,0.2731,0.2773,0.2787,0.2877, 0.2919,0.2919,0.3005,0.3084,0.3091,0.3170,0.3341,0.3347,0.3351,0.3389, 0.3400,0.3437,0.3447,0.3493,0.3530,0.3701,0.3702,0.3759,0.3769,0.3784, 0.3792,0.3817,0.3979,0.3982,0.4000,0.4004,0.4036,0.4042,0.4121,0.4150, 0.4177,0.4283,0.4368,0.4389,0.4501,0.4545,0.4576,0.4588,0.4589,0.4636, 0.4679,0.4682,0.4685,0.4766,0.4779,0.4784,0.4803,0.4820,0.4904,0.4907, 0.4928,0.5002,0.5034,0.5182,0.5212,0.5267,0.5341,0.5347,0.5405,0.5508, 0.5572,0.5791,0.5848,0.5854,0.5868,0.5906,0.5910,0.6056,0.6089,0.6117, 0.6211,0.6238,0.6240,0.6273,0.6302,0.6334,0.6349,0.6426,0.6431,0.6525, 0.6536,0.6555,0.6558,0.6560,0.6573,0.6620,0.6622,0.6745,0.6755,0.6809, 0.6859,0.6862,0.6879,0.6893,0.6896,0.6968,0.7013,0.7019,0.7022,0.7034, 0.7067,0.7102,0.7141,0.7184,0.7186,0.7230,0.7250,0.7313,0.7341,0.7360, 0.7406,0.7406,0.7424,0.7468,0.7555,0.7646,0.7660,0.7666,0.7721,0.7790, 0.7799,0.7843,0.7850,0.7864,0.7978,0.8042,0.8094,0.8220,0.8243,0.8271, 0.8275,0.8276,0.8320,0.8331,0.8354,0.8377,0.8411,0.8436,0.8452,0.8509, 0.8518,0.8550,0.8568,0.8583,0.8630,0.8663,0.8693,0.8702,0.8708,0.8735, 0.8762,0.8776,0.8802,0.8883,0.8910,0.8912,0.9033,0.9052,0.9066,0.9138, 0.9155,0.9282,0.9294,0.9306,0.9316,0.9353,0.9409,0.9439,0.9443,0.9501, 0.9525,0.9534,0.9589,0.9594,0.9634,0.9636,0.9661,0.9674,0.9707,0.9718, 0.9783,0.9803,0.9822,0.9866,0.9875,0.9910,0.9912,0.9955,0.9995, Overall p-value after applying KStest on 269 p-values = 0.219647 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.