RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-11-07_09:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.66 24.1546 0.884705 2 to 25 15.68 12.2576 0.215706 3 to 26 15.87 10.8485 0.135671 4 to 27 15.72 23.1298 0.854927 5 to 28 15.88 17.2696 0.563753 6 to 29 15.97 6.2075 0.008320 7 to 30 15.76 35.3074 0.994332 8 to 31 15.40 31.4789 0.982547 9 to 32 15.55 20.2160 0.736672 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.119383 Tough bday spacings test for dh-ranFile-2016-11-07_09:31: 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 31 90 98 82 81 51 28 17 7 4 (O-E)^2/E 0.4 0.9 3.8 0.0 2.5 0.1 0.0 0.1 0.3 0.0 0.0 Birthday Spacings: Sum(O-E)^2/E= 8.136, p= 0.384 RESULTS OF GCD FOR dh-ranFile-2016-11-07_09:31 Euclid's algorithm: p-value, steps to gcd: 0.073011 p-value, dist. of gcd's: 0.814877 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-11-07_09:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.074 0.824 0.331 0.089 0.682 0.302 0.423 0.156 Bits 8 to 15---> 0.599 0.588 0.456 0.395 0.674 0.540 0.909 0.093 Bits 16 to 23---> 0.109 0.307 0.048 0.425 0.643 0.759 0.836 0.818 Bits 24 to 31---> 0.416 0.637 0.109 0.402 0.285 0.788 0.348 0.382 KS test for the above 32 p values: 0.633 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-11-07_09:31, p-values for 5 runs: 0.3729, 0.5313, 0.8170, 0.9628, 0.6335 Rank test for binary matrices (31x31) for dh-ranFile-2016-11-07_09:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 210 211.4 0.010 0.010 r= 29 5201 5134.0 0.874 0.884 r= 30 23145 23103.0 0.076 0.960 r= 31 11444 11551.5 1.001 1.961 chi-square = 1.961 with df = 3; p-value = 0.419 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-11-07_09:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 227 211.4 1.148 1.148 r= 30 5203 5134.0 0.927 2.075 r= 31 22932 23103.0 1.266 3.342 r= 32 11638 11551.5 0.647 3.989 chi-square = 3.989 with df = 3; p-value = 0.737 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-11-07_09:31 b-rank test for bits 1 to 8, p=0.13806 b-rank test for bits 2 to 9, p=0.81372 b-rank test for bits 3 to 10, p=0.93040 b-rank test for bits 4 to 11, p=0.76794 b-rank test for bits 5 to 12, p=0.58299 b-rank test for bits 6 to 13, p=0.24177 b-rank test for bits 7 to 14, p=0.79695 b-rank test for bits 8 to 15, p=0.40533 b-rank test for bits 9 to 16, p=0.91741 b-rank test for bits 10 to 17, p=0.58746 b-rank test for bits 11 to 18, p=0.34094 b-rank test for bits 12 to 19, p=0.84765 b-rank test for bits 13 to 20, p=0.50151 b-rank test for bits 14 to 21, p=0.12325 b-rank test for bits 15 to 22, p=0.34379 b-rank test for bits 16 to 23, p=0.39441 b-rank test for bits 17 to 24, p=0.04103 b-rank test for bits 18 to 25, p=0.41924 b-rank test for bits 19 to 26, p=0.19331 b-rank test for bits 20 to 27, p=0.50250 b-rank test for bits 21 to 28, p=0.51819 b-rank test for bits 22 to 29, p=0.18054 b-rank test for bits 23 to 30, p=0.62557 b-rank test for bits 24 to 31, p=0.85186 b-rank test for bits 25 to 32, p=0.06556 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 = 0.975787 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-11-07_09:31 (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 141514 -0.92 0.177830 2 141096 -1.90 0.028697 3 142052 0.33 0.630562 4 141969 0.14 0.555439 5 140980 -2.17 0.014953 6 142703 1.85 0.968157 7 142320 0.96 0.831349 8 141725 -0.43 0.333351 9 141325 -1.37 0.086086 10 142353 1.04 0.850042 11 142446 1.25 0.895061 12 141743 -0.39 0.348778 13 141987 0.18 0.572001 14 142492 1.36 0.913303 15 141842 -0.16 0.437499 16 142431 1.22 0.888550 17 141556 -0.83 0.204533 18 141611 -0.70 0.242891 19 141748 -0.38 0.353109 20 141964 0.13 0.550820 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-11-07_09:31 Bits used No. missing words z-score p-value 23 to 32 141676 -0.8046 0.210529 22 to 31 142148 0.8230 0.794746 21 to 30 141437 -1.6287 0.051686 20 to 29 141957 0.1644 0.565284 19 to 28 141697 -0.7322 0.232032 18 to 27 141582 -1.1287 0.129507 17 to 26 141668 -0.8322 0.202656 16 to 25 141755 -0.5322 0.297303 15 to 24 141381 -1.8218 0.034241 14 to 23 141845 -0.2218 0.412224 13 to 22 142089 0.6196 0.732224 12 to 21 141564 -1.1908 0.116867 11 to 20 142038 0.4437 0.671367 10 to 19 141821 -0.3046 0.380341 9 to 18 141694 -0.7425 0.228887 8 to 17 141928 0.0644 0.525666 7 to 16 142489 1.9989 0.977188 6 to 15 141848 -0.2115 0.416255 5 to 14 141538 -1.2804 0.100194 4 to 13 141818 -0.3149 0.376407 3 to 12 142053 0.4954 0.689846 2 to 11 141871 -0.1322 0.447424 1 to 10 142282 1.2851 0.900616 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-11-07_09:31 Bits used No. missing words z-score p-value 28 to 32 141936 0.0904 0.536018 27 to 31 142578 2.2667 0.988295 26 to 30 142027 0.3989 0.655010 25 to 29 141578 -1.1232 0.130686 24 to 28 142194 0.9650 0.832723 23 to 27 141392 -1.7537 0.039744 22 to 26 142035 0.4260 0.664946 21 to 25 141632 -0.9401 0.173583 20 to 24 142210 1.0192 0.845951 19 to 23 141790 -0.4045 0.342919 18 to 22 141465 -1.5062 0.066008 17 to 21 141779 -0.4418 0.329318 16 to 20 142222 1.0599 0.855405 15 to 19 142149 0.8124 0.791731 14 to 18 141942 0.1107 0.544091 13 to 17 141520 -1.3198 0.093457 12 to 16 142125 0.7311 0.767636 11 to 15 141722 -0.6350 0.262709 10 to 14 141899 -0.0350 0.486033 9 to 13 142021 0.3785 0.647486 8 to 12 141467 -1.4994 0.066882 7 to 11 141989 0.2701 0.606446 6 to 10 141630 -0.9469 0.171850 5 to 9 141501 -1.3842 0.083153 4 to 8 141989 0.2701 0.606446 3 to 7 141379 -1.7977 0.036110 2 to 6 141810 -0.3367 0.368167 1 to 5 142151 0.8192 0.793670 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-11-07_09:31 Bits used No. missing words z-score p-value 31 to 32 141934 0.0728 0.529007 30 to 31 141536 -1.1013 0.135390 29 to 30 142001 0.2704 0.606579 28 to 29 141383 -1.5526 0.060260 27 to 28 142107 0.5831 0.720086 26 to 27 141842 -0.1986 0.421283 25 to 26 141522 -1.1426 0.126609 24 to 25 142281 1.0964 0.863542 23 to 24 141261 -1.9125 0.027907 22 to 23 142309 1.1790 0.880794 21 to 22 142025 0.3412 0.633527 20 to 21 141992 0.2439 0.596332 19 to 20 141721 -0.5555 0.289261 18 to 19 142066 0.4622 0.678014 17 to 18 141860 -0.1455 0.442152 16 to 17 142217 0.9076 0.817950 15 to 16 141906 -0.0098 0.496081 14 to 15 141641 -0.7915 0.214316 13 to 14 141796 -0.3343 0.369074 12 to 13 141671 -0.7030 0.241016 11 to 12 141773 -0.4022 0.343786 10 to 11 141655 -0.7502 0.226556 9 to 10 141731 -0.5260 0.299428 8 to 9 142269 1.0610 0.855649 7 to 8 142291 1.1259 0.869890 6 to 7 141811 -0.2901 0.385886 5 to 6 142280 1.0934 0.862896 4 to 5 141955 0.1347 0.553583 3 to 4 141703 -0.6086 0.271381 2 to 3 141917 0.0226 0.509025 1 to 2 141682 -0.6706 0.251241 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-11-07_09:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2637.26 1.941 0.973878 Test results for specific bytes for dh-ranFile-2016-11-07_09:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2517.20 0.243 0.596077 2 to 9 2602.09 1.444 0.925589 3 to 10 2507.95 0.112 0.544786 4 to 11 2632.51 1.874 0.969532 5 to 12 2495.78 -0.060 0.476204 6 to 13 2359.26 -1.990 0.023276 7 to 14 2596.68 1.367 0.914239 8 to 15 2558.48 0.827 0.795882 9 to 16 2532.46 0.459 0.676910 10 to 17 2482.06 -0.254 0.399839 11 to 18 2470.41 -0.418 0.337806 12 to 19 2505.66 0.080 0.531920 13 to 20 2512.20 0.173 0.568492 14 to 21 2403.89 -1.359 0.087041 15 to 22 2513.29 0.188 0.574569 16 to 23 2391.81 -1.530 0.063002 17 to 24 2383.21 -1.652 0.049302 18 to 25 2476.65 -0.330 0.370632 19 to 26 2495.68 -0.061 0.475643 20 to 27 2463.62 -0.515 0.303430 21 to 28 2477.22 -0.322 0.373669 22 to 29 2427.04 -1.032 0.151093 23 to 30 2550.70 0.717 0.763312 24 to 31 2564.38 0.911 0.818724 25 to 32 2483.84 -0.228 0.409639 CDPARK for dh-ranFile-2016-11-07_09:31: 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 3541 0.8219 0.794438 3489 -1.5525 0.060270 3555 1.4612 0.928018 3550 1.2329 0.891189 3538 0.6849 0.753306 3488 -1.5982 0.055002 3472 -2.3288 0.009936 3458 -2.9680 0.001499 3547 1.0959 0.863437 3511 -0.5479 0.291865 Square side=100, avg. no. parked=3514.90 sample std.=34.02 p-value of the KSTEST for those 10 p-values: 0.044802 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-11-07_09:31 0.2805,0.4809,0.3134,0.9309,0.1248,0.2973,0.8723,0.7852,0.1861,0.9278, The KS test for those 10 p-values: 0.695886 The 3DSPHERES test for dh-ranFile-2016-11-07_09:31 sample no r^3 equiv. uni. 1 28.915 0.618570 2 35.384 0.692562 3 2.202 0.070781 4 0.167 0.005565 5 26.056 0.580438 6 41.674 0.750711 7 1.442 0.046924 8 12.406 0.338687 9 51.872 0.822551 10 20.753 0.499305 11 0.442 0.014636 12 18.255 0.455841 13 10.639 0.298576 14 46.616 0.788574 15 4.080 0.127150 16 50.497 0.814231 17 30.970 0.643827 18 36.266 0.701460 19 5.528 0.168274 20 20.759 0.499414 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.337319 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-11-07_09:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 1.3 0.6 0.8 -0.5 -0.1 -0.0 2.1 1.5 1.2 -0.9 -0.1 0.3 1.3 1.0 1.3 0.4 -3.1 -0.3 -0.3 -0.7 -1.4 -1.3 0.1 1.3 -0.7 1.7 -0.3 -1.4 -0.1 0.9 0.9 0.4 -0.4 -0.1 0.2 0.0 0.8 1.7 -0.1 0.1 0.0 -1.1 Chi-square with 42 degrees of freedom:45.069827 z-score=0.334946, p-value=0.655240 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-11-07_09:31 Test no p-value 1 0.085729 2 0.249347 3 0.969181 4 0.924991 5 0.214251 6 0.921017 7 0.404655 8 0.406682 9 0.704181 10 0.368392 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.675230 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-11-07_09:31: (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 66653 0.00 66670 0.00 3 25000.00 25011 0.00 25008 0.00 4 6666.67 6707 0.24 6638 0.12 5 1388.89 1387 0.00 1397 0.05 6 238.10 208 3.80 242 0.06 7 34.72 32 0.21 37 0.15 8 4.96 1 3.16 7 0.84 p=0.71734 p=0.02443 Number of rngs required: 688214, p-value: 0.414 RESULTS OF CRAPS TEST for dh-ranFile-2016-11-07_09:31 No. of wins: Observed Expected 98717 98585.9 z-score= 0.587, pvalue=0.72124 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66691 66666.7 0.009 0.009 2 37537 37654.3 0.366 0.374 3 27209 26954.7 2.399 2.773 4 19155 19313.5 1.300 4.073 5 13928 13851.4 0.423 4.496 6 9878 9943.5 0.432 4.929 7 7186 7145.0 0.235 5.163 8 5041 5139.1 1.872 7.035 9 3692 3699.9 0.017 7.052 10 2693 2666.3 0.267 7.319 11 1950 1923.3 0.370 7.689 12 1361 1388.7 0.554 8.243 13 992 1003.7 0.137 8.380 14 696 726.1 1.251 9.631 15 568 525.8 3.381 13.012 16 388 381.2 0.123 13.135 17 251 276.5 2.359 15.494 18 229 200.8 3.951 19.445 19 146 146.0 0.000 19.445 20 115 106.2 0.727 20.172 21 294 287.1 0.165 20.337 Chisq= 20.34 for 20 degrees of freedom, p= 0.56295 SUMMARY of craptest p-value for no. of wins: 0.721244 p-value for throws/game: 0.562951 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-11-07_09:31 No. of wins: Observed Expected 98813 98585.9 z-score= 1.016, pvalue=0.84516 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66565 66666.7 0.155 0.155 2 37712 37654.3 0.088 0.243 3 26996 26954.7 0.063 0.307 4 19204 19313.5 0.620 0.927 5 13887 13851.4 0.091 1.018 6 9913 9943.5 0.094 1.112 7 7173 7145.0 0.110 1.222 8 5284 5139.1 4.087 5.309 9 3748 3699.9 0.626 5.935 10 2574 2666.3 3.195 9.130 11 1916 1923.3 0.028 9.158 12 1377 1388.7 0.099 9.257 13 976 1003.7 0.765 10.023 14 773 726.1 3.024 13.046 15 520 525.8 0.065 13.111 16 388 381.2 0.123 13.234 17 278 276.5 0.008 13.242 18 197 200.8 0.073 13.315 19 152 146.0 0.248 13.563 20 111 106.2 0.216 13.779 21 256 287.1 3.372 17.150 Chisq= 17.15 for 20 degrees of freedom, p= 0.35680 SUMMARY of craptest p-value for no. of wins: 0.845164 p-value for throws/game: 0.356804 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0015,0.0056,0.0083,0.0099,0.0146,0.0150,0.0233,0.0244,0.0279,0.0287, 0.0342,0.0361,0.0397,0.0410,0.0448,0.0469,0.0480,0.0493,0.0517,0.0550, 0.0603,0.0603,0.0630,0.0656,0.0660,0.0669,0.0708,0.0730,0.0738,0.0832, 0.0857,0.0861,0.0870,0.0887,0.0925,0.0935,0.1002,0.1087,0.1089,0.1169, 0.1194,0.1232,0.1248,0.1266,0.1271,0.1295,0.1307,0.1354,0.1357,0.1381, 0.1511,0.1559,0.1683,0.1718,0.1736,0.1778,0.1805,0.1861,0.1933,0.2027, 0.2045,0.2105,0.2143,0.2143,0.2157,0.2266,0.2289,0.2320,0.2410,0.2418, 0.2429,0.2493,0.2512,0.2627,0.2714,0.2805,0.2852,0.2893,0.2919,0.2973, 0.2973,0.2986,0.2994,0.3021,0.3034,0.3065,0.3134,0.3293,0.3308,0.3334, 0.3373,0.3378,0.3387,0.3409,0.3429,0.3438,0.3438,0.3482,0.3488,0.3531, 0.3568,0.3682,0.3684,0.3691,0.3706,0.3729,0.3737,0.3764,0.3803,0.3818, 0.3844,0.3859,0.3944,0.3949,0.3998,0.4017,0.4047,0.4053,0.4067,0.4096, 0.4122,0.4139,0.4163,0.4163,0.4192,0.4194,0.4213,0.4225,0.4254,0.4375, 0.4422,0.4474,0.4558,0.4560,0.4756,0.4762,0.4809,0.4860,0.4961,0.4993, 0.4994,0.5015,0.5025,0.5090,0.5182,0.5257,0.5290,0.5313,0.5319,0.5360, 0.5396,0.5441,0.5448,0.5508,0.5536,0.5554,0.5630,0.5638,0.5653,0.5685, 0.5720,0.5746,0.5804,0.5830,0.5875,0.5879,0.5961,0.5963,0.5993,0.6064, 0.6064,0.6066,0.6186,0.6256,0.6306,0.6335,0.6335,0.6335,0.6369,0.6426, 0.6438,0.6475,0.6550,0.6552,0.6649,0.6714,0.6735,0.6752,0.6769,0.6780, 0.6823,0.6898,0.6926,0.6959,0.7015,0.7042,0.7173,0.7201,0.7212,0.7322, 0.7367,0.7374,0.7507,0.7533,0.7587,0.7633,0.7676,0.7679,0.7852,0.7884, 0.7886,0.7917,0.7937,0.7944,0.7947,0.7959,0.7969,0.8137,0.8142,0.8149, 0.8170,0.8180,0.8180,0.8187,0.8226,0.8242,0.8313,0.8327,0.8360,0.8452, 0.8460,0.8476,0.8500,0.8519,0.8549,0.8554,0.8556,0.8629,0.8634,0.8635, 0.8699,0.8723,0.8808,0.8847,0.8886,0.8912,0.8951,0.9006,0.9087,0.9133, 0.9142,0.9174,0.9210,0.9250,0.9256,0.9278,0.9280,0.9304,0.9309,0.9628, 0.9682,0.9692,0.9695,0.9739,0.9758,0.9772,0.9825,0.9883,0.9943, Overall p-value after applying KStest on 269 p-values = 0.388150 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.