RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-02-16_17:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.87 21.5039 0.795441 2 to 25 15.79 13.4896 0.297158 3 to 26 15.73 22.8544 0.845949 4 to 27 15.68 18.0644 0.615213 5 to 28 15.73 12.9122 0.257954 6 to 29 15.71 13.1442 0.273523 7 to 30 15.79 15.0036 0.404777 8 to 31 15.66 26.4461 0.933293 9 to 32 15.77 26.8811 0.940166 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.425117 Tough bday spacings test for dh-ranFile-2016-02-16_17:31: 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 5 34 73 90 118 75 57 25 14 4 5 (O-E)^2/E 1.9 0.2 0.0 0.6 4.2 0.1 0.5 0.8 0.1 1.0 0.2 Birthday Spacings: Sum(O-E)^2/E= 9.561, p= 0.520 RESULTS OF GCD FOR dh-ranFile-2016-02-16_17:31 Euclid's algorithm: p-value, steps to gcd: 0.912051 p-value, dist. of gcd's: 0.386870 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-02-16_17:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.418 0.252 0.205 0.335 0.563 0.261 0.116 0.818 Bits 8 to 15---> 0.439 0.869 0.289 0.041 0.341 0.257 0.794 0.263 Bits 16 to 23---> 0.485 0.723 0.652 0.301 0.735 0.837 0.662 0.229 Bits 24 to 31---> 0.674 0.596 0.528 0.002 0.366 0.658 0.487 0.496 KS test for the above 32 p values: 0.738 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-02-16_17:31, p-values for 5 runs: 0.6759, 0.2766, 0.7926, 0.9535, 0.9115 Rank test for binary matrices (31x31) for dh-ranFile-2016-02-16_17:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 206 211.4 0.139 0.139 r= 29 5154 5134.0 0.078 0.217 r= 30 23048 23103.0 0.131 0.348 r= 31 11592 11551.5 0.142 0.490 chi-square = 0.490 with df = 3; p-value = 0.079 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-02-16_17:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 215 211.4 0.061 0.061 r= 30 5169 5134.0 0.238 0.299 r= 31 23088 23103.0 0.010 0.309 r= 32 11528 11551.5 0.048 0.357 chi-square = 0.357 with df = 3; p-value = 0.051 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-02-16_17:31 b-rank test for bits 1 to 8, p=0.80972 b-rank test for bits 2 to 9, p=0.09712 b-rank test for bits 3 to 10, p=0.32785 b-rank test for bits 4 to 11, p=0.80047 b-rank test for bits 5 to 12, p=0.56877 b-rank test for bits 6 to 13, p=0.89153 b-rank test for bits 7 to 14, p=0.01901 b-rank test for bits 8 to 15, p=0.29782 b-rank test for bits 9 to 16, p=0.99267 b-rank test for bits 10 to 17, p=0.85132 b-rank test for bits 11 to 18, p=0.50139 b-rank test for bits 12 to 19, p=0.37175 b-rank test for bits 13 to 20, p=0.95183 b-rank test for bits 14 to 21, p=0.82877 b-rank test for bits 15 to 22, p=0.88640 b-rank test for bits 16 to 23, p=0.44493 b-rank test for bits 17 to 24, p=0.54408 b-rank test for bits 18 to 25, p=0.04882 b-rank test for bits 19 to 26, p=0.66761 b-rank test for bits 20 to 27, p=0.27035 b-rank test for bits 21 to 28, p=0.56708 b-rank test for bits 22 to 29, p=0.34567 b-rank test for bits 23 to 30, p=0.64192 b-rank test for bits 24 to 31, p=0.71318 b-rank test for bits 25 to 32, p=0.13363 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 = 0.830106 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-02-16_17:31 (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 141474 -1.02 0.154547 2 141642 -0.62 0.266116 3 142203 0.69 0.753689 4 142181 0.63 0.737202 5 142470 1.31 0.904898 6 141350 -1.31 0.095633 7 141450 -1.07 0.141591 8 141741 -0.39 0.347051 9 141864 -0.11 0.457826 10 142538 1.47 0.929064 11 142606 1.63 0.948209 12 142224 0.74 0.768894 13 141995 0.20 0.579324 14 142012 0.24 0.594790 15 140927 -2.30 0.010862 16 141891 -0.04 0.482920 17 142259 0.82 0.793032 18 142177 0.63 0.734145 19 141582 -0.76 0.222198 20 141945 0.08 0.533210 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-02-16_17:31 Bits used No. missing words z-score p-value 23 to 32 141660 -0.8598 0.194961 22 to 31 141758 -0.5218 0.300895 21 to 30 142450 1.8644 0.968866 20 to 29 141694 -0.7425 0.228887 19 to 28 141586 -1.1149 0.132440 18 to 27 141757 -0.5253 0.299696 17 to 26 141925 0.0540 0.521546 16 to 25 141347 -1.9391 0.026246 15 to 24 141754 -0.5356 0.296110 14 to 23 141625 -0.9804 0.163432 13 to 22 142265 1.2264 0.889985 12 to 21 141861 -0.1667 0.433821 11 to 20 141849 -0.2080 0.417601 10 to 19 142219 1.0678 0.857201 9 to 18 141825 -0.2908 0.385605 8 to 17 141852 -0.1977 0.421644 7 to 16 141821 -0.3046 0.380341 6 to 15 141933 0.0816 0.532526 5 to 14 141645 -0.9115 0.181021 4 to 13 141773 -0.4701 0.319141 3 to 12 141636 -0.9425 0.172964 2 to 11 141599 -1.0701 0.142286 1 to 10 141826 -0.2873 0.386924 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-02-16_17:31 Bits used No. missing words z-score p-value 28 to 32 142536 2.1243 0.983178 27 to 31 142116 0.7006 0.758216 26 to 30 141993 0.2836 0.611652 25 to 29 142328 1.4192 0.922083 24 to 28 141563 -1.1740 0.120198 23 to 27 141444 -1.5774 0.057353 22 to 26 142224 1.0667 0.856941 21 to 25 141585 -1.0994 0.135792 20 to 24 142230 1.0870 0.861485 19 to 23 141648 -0.8859 0.187845 18 to 22 141904 -0.0181 0.492792 17 to 21 141957 0.1616 0.564187 16 to 20 142022 0.3819 0.648744 15 to 19 141748 -0.5469 0.292230 14 to 18 142090 0.6124 0.729877 13 to 17 142129 0.7446 0.771757 12 to 16 141597 -1.0587 0.144858 11 to 15 141602 -1.0418 0.148753 10 to 14 141898 -0.0384 0.484682 9 to 13 142032 0.4158 0.661233 8 to 12 142057 0.5006 0.691665 7 to 11 141777 -0.4486 0.326869 6 to 10 142117 0.7040 0.759273 5 to 9 142088 0.6057 0.727630 4 to 8 141544 -1.2384 0.107783 3 to 7 141951 0.1413 0.556166 2 to 6 141687 -0.7537 0.225526 1 to 5 141731 -0.6045 0.272753 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-02-16_17:31 Bits used No. missing words z-score p-value 31 to 32 142032 0.3619 0.641271 30 to 31 142251 1.0079 0.843243 29 to 30 141973 0.1878 0.574490 28 to 29 142061 0.4474 0.672708 27 to 28 141838 -0.2104 0.416673 26 to 27 142633 2.1347 0.983608 25 to 26 142118 0.6155 0.730903 24 to 25 142235 0.9607 0.831643 23 to 24 142045 0.4002 0.655498 22 to 23 142318 1.2055 0.885998 21 to 22 141608 -0.8889 0.187034 20 to 21 142316 1.1996 0.884856 19 to 20 141917 0.0226 0.509025 18 to 19 142073 0.4828 0.685382 17 to 18 141735 -0.5142 0.303539 16 to 17 141953 0.1288 0.551250 15 to 16 142275 1.0787 0.859633 14 to 15 141622 -0.8476 0.198336 13 to 14 142010 0.2970 0.616752 12 to 13 142843 2.7542 0.997058 11 to 12 142100 0.5624 0.713095 10 to 11 142432 1.5418 0.938439 9 to 10 141674 -0.6942 0.243782 8 to 9 141685 -0.6617 0.254069 7 to 8 142792 2.6037 0.995389 6 to 7 141406 -1.4847 0.068805 5 to 6 142173 0.7778 0.781653 4 to 5 141946 0.1082 0.543070 3 to 4 142157 0.7306 0.767485 2 to 3 141951 0.1229 0.548915 1 to 2 141632 -0.8181 0.206655 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-02-16_17:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2675.93 2.488 0.993578 Test results for specific bytes for dh-ranFile-2016-02-16_17:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2498.05 -0.028 0.489017 2 to 9 2542.45 0.600 0.725839 3 to 10 2483.37 -0.235 0.407011 4 to 11 2403.37 -1.367 0.085878 5 to 12 2582.06 1.160 0.877077 6 to 13 2546.02 0.651 0.742426 7 to 14 2571.25 1.008 0.843192 8 to 15 2525.28 0.358 0.639664 9 to 16 2539.82 0.563 0.713349 10 to 17 2522.54 0.319 0.625069 11 to 18 2448.09 -0.734 0.231418 12 to 19 2430.61 -0.981 0.163215 13 to 20 2515.33 0.217 0.585818 14 to 21 2483.58 -0.232 0.408180 15 to 22 2486.30 -0.194 0.423178 16 to 23 2477.37 -0.320 0.374463 17 to 24 2517.50 0.247 0.597737 18 to 25 2565.45 0.926 0.822688 19 to 26 2474.56 -0.360 0.359482 20 to 27 2437.03 -0.890 0.186607 21 to 28 2488.91 -0.157 0.437714 22 to 29 2455.87 -0.624 0.266301 23 to 30 2518.61 0.263 0.603820 24 to 31 2557.35 0.811 0.791317 25 to 32 2509.30 0.132 0.552345 CDPARK for dh-ranFile-2016-02-16_17:31: 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 3516 -0.3196 0.374623 3498 -1.1416 0.126820 3516 -0.3196 0.374623 3513 -0.4566 0.323972 3465 -2.6484 0.004044 3513 -0.4566 0.323972 3517 -0.2740 0.392053 3564 1.8721 0.969407 3539 0.7306 0.767486 3526 0.1370 0.554479 Square side=100, avg. no. parked=3516.70 sample std.=24.23 p-value of the KSTEST for those 10 p-values: 0.408172 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-02-16_17:31 0.2250,0.4662,0.1455,0.4091,0.2162,0.5659,0.5827,0.2990,0.2894,0.6156, The KS test for those 10 p-values: 0.146221 The 3DSPHERES test for dh-ranFile-2016-02-16_17:31 sample no r^3 equiv. uni. 1 28.115 0.608268 2 6.167 0.185821 3 72.660 0.911255 4 44.927 0.776327 5 14.568 0.384662 6 5.767 0.174893 7 2.685 0.085599 8 12.186 0.333833 9 3.473 0.109315 10 0.150 0.004994 11 0.059 0.001965 12 40.980 0.744872 13 0.517 0.017083 14 17.394 0.439995 15 7.313 0.216334 16 29.813 0.629817 17 20.910 0.501930 18 35.455 0.693284 19 41.873 0.752357 20 14.174 0.376548 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.100713 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-02-16_17:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 2.7 -0.3 -1.1 -0.1 -0.9 0.8 0.4 -1.5 0.3 -0.0 -0.7 -0.8 -1.3 -0.7 0.4 -0.0 2.2 0.0 0.1 0.6 0.4 0.7 0.7 0.0 -2.2 -0.1 -0.5 -0.9 -0.4 2.2 -0.4 -0.3 -0.5 0.7 -0.5 -0.5 1.0 0.5 -0.4 0.4 -1.3 1.0 -0.1 Chi-square with 42 degrees of freedom:39.076884 z-score=-0.318938, p-value=0.399978 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-02-16_17:31 Test no p-value 1 0.010892 2 0.903619 3 0.261363 4 0.657722 5 0.581874 6 0.987401 7 0.595744 8 0.846301 9 0.118452 10 0.054701 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.577484 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-02-16_17:31: (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 66779 0.19 66479 0.53 3 25000.00 24785 1.85 25134 0.72 4 6666.67 6748 0.99 6689 0.07 5 1388.89 1415 0.49 1403 0.14 6 238.10 229 0.35 258 1.66 7 34.72 41 1.14 31 0.40 8 4.96 2 1.77 5 0.00 p=0.65746 p=0.25971 Number of rngs required: 688074, p-value: 0.352 RESULTS OF CRAPS TEST for dh-ranFile-2016-02-16_17:31 No. of wins: Observed Expected 98358 98585.9 z-score=-1.019, pvalue=0.15407 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66687 66666.7 0.006 0.006 2 37165 37654.3 6.359 6.365 3 27064 26954.7 0.443 6.808 4 19527 19313.5 2.361 9.169 5 14003 13851.4 1.659 10.828 6 9928 9943.5 0.024 10.852 7 7171 7145.0 0.094 10.946 8 5117 5139.1 0.095 11.041 9 3655 3699.9 0.544 11.585 10 2733 2666.3 1.669 13.254 11 1926 1923.3 0.004 13.258 12 1325 1388.7 2.926 16.183 13 1043 1003.7 1.538 17.721 14 741 726.1 0.304 18.025 15 513 525.8 0.313 18.338 16 383 381.2 0.009 18.347 17 266 276.5 0.402 18.749 18 207 200.8 0.190 18.938 19 148 146.0 0.028 18.966 20 109 106.2 0.073 19.039 21 289 287.1 0.012 19.052 Chisq= 19.05 for 20 degrees of freedom, p= 0.48153 SUMMARY of craptest p-value for no. of wins: 0.154074 p-value for throws/game: 0.481527 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-02-16_17:31 No. of wins: Observed Expected 98574 98585.9 z-score=-0.053, pvalue=0.47885 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66978 66666.7 1.454 1.454 2 37372 37654.3 2.117 3.571 3 26716 26954.7 2.114 5.685 4 19465 19313.5 1.189 6.874 5 13971 13851.4 1.032 7.906 6 9986 9943.5 0.181 8.088 7 7089 7145.0 0.439 8.527 8 5048 5139.1 1.614 10.141 9 3699 3699.9 0.000 10.141 10 2703 2666.3 0.505 10.646 11 1953 1923.3 0.458 11.104 12 1380 1388.7 0.055 11.159 13 990 1003.7 0.187 11.347 14 701 726.1 0.870 12.217 15 572 525.8 4.053 16.270 16 404 381.2 1.370 17.640 17 278 276.5 0.008 17.647 18 211 200.8 0.515 18.162 19 138 146.0 0.437 18.599 20 100 106.2 0.364 18.963 21 246 287.1 5.887 24.850 Chisq= 24.85 for 20 degrees of freedom, p= 0.79277 SUMMARY of craptest p-value for no. of wins: 0.478851 p-value for throws/game: 0.792774 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0017,0.0020,0.0040,0.0050,0.0109,0.0109,0.0171,0.0190,0.0262,0.0407, 0.0488,0.0510,0.0547,0.0574,0.0688,0.0788,0.0856,0.0859,0.0956,0.0971, 0.1007,0.1078,0.1093,0.1163,0.1185,0.1202,0.1268,0.1324,0.1336,0.1358, 0.1416,0.1423,0.1449,0.1455,0.1462,0.1488,0.1541,0.1545,0.1632,0.1634, 0.1730,0.1749,0.1810,0.1858,0.1866,0.1870,0.1878,0.1950,0.1983,0.2055, 0.2067,0.2162,0.2163,0.2222,0.2250,0.2255,0.2289,0.2291,0.2314,0.2438, 0.2517,0.2541,0.2568,0.2580,0.2597,0.2614,0.2614,0.2628,0.2661,0.2663, 0.2704,0.2728,0.2735,0.2766,0.2892,0.2894,0.2922,0.2961,0.2972,0.2978, 0.2990,0.2997,0.3007,0.3009,0.3035,0.3191,0.3240,0.3240,0.3269,0.3278, 0.3338,0.3350,0.3411,0.3457,0.3471,0.3524,0.3595,0.3660,0.3717,0.3745, 0.3746,0.3746,0.3765,0.3803,0.3847,0.3856,0.3869,0.3869,0.3921,0.4000, 0.4048,0.4070,0.4082,0.4082,0.4091,0.4167,0.4176,0.4178,0.4216,0.4232, 0.4251,0.4338,0.4377,0.4393,0.4400,0.4449,0.4578,0.4662,0.4789,0.4815, 0.4829,0.4847,0.4847,0.4869,0.4890,0.4928,0.4956,0.5014,0.5019,0.5090, 0.5202,0.5215,0.5280,0.5325,0.5332,0.5431,0.5441,0.5489,0.5513,0.5523, 0.5545,0.5562,0.5626,0.5642,0.5659,0.5671,0.5688,0.5745,0.5775,0.5793, 0.5819,0.5827,0.5858,0.5948,0.5957,0.5961,0.5977,0.6038,0.6083,0.6117, 0.6152,0.6156,0.6168,0.6251,0.6298,0.6397,0.6413,0.6419,0.6487,0.6520, 0.6555,0.6575,0.6575,0.6577,0.6612,0.6617,0.6676,0.6727,0.6739,0.6759, 0.6854,0.6917,0.6933,0.7131,0.7132,0.7133,0.7229,0.7258,0.7276,0.7299, 0.7309,0.7341,0.7348,0.7372,0.7380,0.7424,0.7449,0.7524,0.7537,0.7582, 0.7593,0.7675,0.7675,0.7689,0.7718,0.7763,0.7817,0.7913,0.7926,0.7928, 0.7930,0.7939,0.7954,0.8005,0.8097,0.8180,0.8227,0.8288,0.8301,0.8316, 0.8365,0.8432,0.8432,0.8459,0.8463,0.8513,0.8569,0.8572,0.8596,0.8615, 0.8688,0.8771,0.8849,0.8860,0.8864,0.8900,0.8915,0.9036,0.9049,0.9113, 0.9115,0.9121,0.9221,0.9291,0.9333,0.9384,0.9402,0.9482,0.9518,0.9535, 0.9689,0.9694,0.9832,0.9836,0.9874,0.9927,0.9936,0.9954,0.9971, Overall p-value after applying KStest on 269 p-values = 0.648483 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.