RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-08-06_05:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.77 12.4457 0.227568 2 to 25 15.81 20.0195 0.726768 3 to 26 15.77 12.0855 0.205067 4 to 27 15.66 19.2877 0.687729 5 to 28 15.74 18.3121 0.630590 6 to 29 15.67 24.0722 0.882514 7 to 30 15.86 13.4394 0.293691 8 to 31 15.98 11.1491 0.151293 9 to 32 15.81 18.6712 0.652272 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.818353 Tough bday spacings test for dh-ranFile-2015-08-06_05:31: 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 43 82 87 107 86 41 26 12 6 3 (O-E)^2/E 0.5 1.1 1.0 1.2 0.9 0.8 2.4 0.5 0.6 0.1 0.3 Birthday Spacings: Sum(O-E)^2/E= 9.241, p= 0.491 RESULTS OF GCD FOR dh-ranFile-2015-08-06_05:31 Euclid's algorithm: p-value, steps to gcd: 0.009325 p-value, dist. of gcd's: 0.292478 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-08-06_05:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.326 0.166 0.212 0.174 0.398 0.492 0.589 0.131 Bits 8 to 15---> 0.535 0.864 0.440 0.928 0.658 0.145 0.243 0.484 Bits 16 to 23---> 0.926 0.834 0.198 0.284 0.448 0.867 0.079 0.616 Bits 24 to 31---> 0.437 0.594 0.582 0.126 0.396 0.145 0.295 0.785 KS test for the above 32 p values: 0.670 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-08-06_05:31, p-values for 5 runs: 0.2309, 0.7003, 0.8615, 0.4346, 0.9949 Rank test for binary matrices (31x31) for dh-ranFile-2015-08-06_05:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 193 211.4 1.605 1.605 r= 29 5178 5134.0 0.377 1.981 r= 30 23018 23103.0 0.313 2.295 r= 31 11611 11551.5 0.306 2.601 chi-square = 2.601 with df = 3; p-value = 0.543 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-08-06_05:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 180 211.4 4.669 4.669 r= 30 5073 5134.0 0.725 5.394 r= 31 23195 23103.0 0.366 5.760 r= 32 11552 11551.5 0.000 5.760 chi-square = 5.760 with df = 3; p-value = 0.876 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-08-06_05:31 b-rank test for bits 1 to 8, p=0.51559 b-rank test for bits 2 to 9, p=0.08588 b-rank test for bits 3 to 10, p=0.84452 b-rank test for bits 4 to 11, p=0.85663 b-rank test for bits 5 to 12, p=0.18169 b-rank test for bits 6 to 13, p=0.33363 b-rank test for bits 7 to 14, p=0.49449 b-rank test for bits 8 to 15, p=0.41347 b-rank test for bits 9 to 16, p=0.64133 b-rank test for bits 10 to 17, p=0.03406 b-rank test for bits 11 to 18, p=0.32222 b-rank test for bits 12 to 19, p=0.26569 b-rank test for bits 13 to 20, p=0.58928 b-rank test for bits 14 to 21, p=0.69230 b-rank test for bits 15 to 22, p=0.56211 b-rank test for bits 16 to 23, p=0.18749 b-rank test for bits 17 to 24, p=0.88645 b-rank test for bits 18 to 25, p=0.64605 b-rank test for bits 19 to 26, p=0.78536 b-rank test for bits 20 to 27, p=0.77681 b-rank test for bits 21 to 28, p=0.25669 b-rank test for bits 22 to 29, p=0.24816 b-rank test for bits 23 to 30, p=0.20225 b-rank test for bits 24 to 31, p=0.33660 b-rank test for bits 25 to 32, p=0.68145 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 = 0.713564 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-08-06_05:31 (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 142142 0.54 0.706649 2 142354 1.04 0.850586 3 141831 -0.18 0.427394 4 141898 -0.03 0.489440 5 142205 0.69 0.755160 6 141320 -1.38 0.084266 7 141841 -0.16 0.436579 8 142188 0.65 0.742508 9 141673 -0.55 0.290415 10 141835 -0.17 0.431063 11 141936 0.06 0.524843 12 142576 1.56 0.940341 13 141949 0.09 0.536924 14 141677 -0.54 0.293624 15 142515 1.42 0.921483 16 141821 -0.21 0.418248 17 142022 0.26 0.603820 18 141790 -0.28 0.390196 19 142204 0.69 0.754425 20 142090 0.42 0.663534 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-08-06_05:31 Bits used No. missing words z-score p-value 23 to 32 142469 1.9299 0.973190 22 to 31 141926 0.0575 0.522920 21 to 30 141419 -1.6908 0.045438 20 to 29 141857 -0.1804 0.428400 19 to 28 142365 1.5713 0.941941 18 to 27 141934 0.0851 0.533897 17 to 26 141421 -1.6839 0.046101 16 to 25 141986 0.2644 0.604256 15 to 24 142064 0.5333 0.703103 14 to 23 141864 -0.1563 0.437894 13 to 22 142084 0.6023 0.726516 12 to 21 142174 0.9127 0.819288 11 to 20 142119 0.7230 0.765160 10 to 19 142127 0.7506 0.773549 9 to 18 142080 0.5885 0.721907 8 to 17 141261 -2.2356 0.012688 7 to 16 141795 -0.3942 0.346701 6 to 15 141924 0.0506 0.520172 5 to 14 141278 -2.1770 0.014740 4 to 13 141778 -0.4529 0.325324 3 to 12 141550 -1.2391 0.107660 2 to 11 141756 -0.5287 0.298498 1 to 10 141773 -0.4701 0.319141 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-08-06_05:31 Bits used No. missing words z-score p-value 28 to 32 142537 2.1277 0.983319 27 to 31 141898 -0.0384 0.484682 26 to 30 141819 -0.3062 0.379725 25 to 29 141704 -0.6960 0.243204 24 to 28 142061 0.5141 0.696421 23 to 27 141963 0.1819 0.572182 22 to 26 141664 -0.8316 0.202810 21 to 25 142143 0.7921 0.785849 20 to 24 141848 -0.2079 0.417654 19 to 23 142061 0.5141 0.696421 18 to 22 141380 -1.7943 0.036380 17 to 21 141994 0.2870 0.612950 16 to 20 142020 0.3752 0.646227 15 to 19 141700 -0.7096 0.238978 14 to 18 141959 0.1684 0.566855 13 to 17 142140 0.7819 0.782873 12 to 16 141725 -0.6248 0.266036 11 to 15 142178 0.9107 0.818785 10 to 14 142016 0.3616 0.641172 9 to 13 141363 -1.8520 0.032015 8 to 12 142051 0.4802 0.684471 7 to 11 141519 -1.3232 0.092892 6 to 10 141506 -1.3672 0.085778 5 to 9 141956 0.1582 0.562852 4 to 8 141693 -0.7333 0.231681 3 to 7 141737 -0.5842 0.279553 2 to 6 141605 -1.0316 0.151123 1 to 5 142032 0.4158 0.661233 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-08-06_05:31 Bits used No. missing words z-score p-value 31 to 32 141530 -1.1190 0.131577 30 to 31 141902 -0.0216 0.491375 29 to 30 141403 -1.4936 0.067640 28 to 29 141653 -0.7561 0.224784 27 to 28 142319 1.2085 0.886566 26 to 27 141889 -0.0600 0.476090 25 to 26 142249 1.0020 0.841823 24 to 25 141482 -1.2606 0.103734 23 to 24 142495 1.7276 0.957974 22 to 23 142028 0.3501 0.636853 21 to 22 142146 0.6981 0.757456 20 to 21 141852 -0.1691 0.432853 19 to 20 141576 -0.9833 0.162736 18 to 19 141867 -0.1249 0.450314 17 to 18 141839 -0.2075 0.417824 16 to 17 142282 1.0993 0.864186 15 to 16 142557 1.9105 0.971968 14 to 15 142187 0.8191 0.793631 13 to 14 142564 1.9312 0.973270 12 to 13 142320 1.2114 0.887132 11 to 12 142496 1.7306 0.958238 10 to 11 141638 -0.8004 0.211744 9 to 10 142546 1.8781 0.969815 8 to 9 142051 0.4179 0.661992 7 to 8 141934 0.0728 0.529007 6 to 7 141614 -0.8712 0.191828 5 to 6 142361 1.3324 0.908629 4 to 5 142225 0.9312 0.824120 3 to 4 142750 2.4799 0.993428 2 to 3 142140 0.6804 0.751888 1 to 2 142148 0.7040 0.759297 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-08-06_05:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2502.49 0.035 0.514027 Test results for specific bytes for dh-ranFile-2015-08-06_05:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2573.43 1.038 0.850476 2 to 9 2404.17 -1.355 0.087672 3 to 10 2417.24 -1.170 0.120908 4 to 11 2424.72 -1.065 0.143532 5 to 12 2586.92 1.229 0.890509 6 to 13 2485.03 -0.212 0.416157 7 to 14 2482.87 -0.242 0.404279 8 to 15 2398.23 -1.439 0.075043 9 to 16 2504.04 0.057 0.522769 10 to 17 2483.09 -0.239 0.405513 11 to 18 2447.24 -0.746 0.227809 12 to 19 2561.17 0.865 0.806495 13 to 20 2445.56 -0.770 0.220684 14 to 21 2527.68 0.391 0.652253 15 to 22 2468.14 -0.451 0.326138 16 to 23 2427.14 -1.030 0.151420 17 to 24 2444.69 -0.782 0.217030 18 to 25 2461.74 -0.541 0.294206 19 to 26 2458.47 -0.587 0.278514 20 to 27 2552.95 0.749 0.773038 21 to 28 2366.07 -1.894 0.029113 22 to 29 2585.90 1.215 0.887794 23 to 30 2513.13 0.186 0.573653 24 to 31 2557.42 0.812 0.791635 25 to 32 2406.14 -1.327 0.092187 CDPARK for dh-ranFile-2015-08-06_05:31: 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 3530 0.3196 0.625377 3520 -0.1370 0.445521 3515 -0.3653 0.357445 3485 -1.7352 0.041356 3554 1.4155 0.921543 3499 -1.0959 0.136563 3541 0.8219 0.794438 3559 1.6438 0.949895 3533 0.4566 0.676028 3497 -1.1872 0.117571 Square side=100, avg. no. parked=3523.30 sample std.=23.45 p-value of the KSTEST for those 10 p-values: 0.955997 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-08-06_05:31 0.8253,0.1169,0.6445,0.6299,0.6424,0.2424,0.9314,0.7587,0.2843,0.2487, The KS test for those 10 p-values: 0.865821 The 3DSPHERES test for dh-ranFile-2015-08-06_05:31 sample no r^3 equiv. uni. 1 32.249 0.658690 2 18.827 0.466106 3 86.821 0.944647 4 19.846 0.483935 5 4.542 0.140503 6 8.397 0.244142 7 23.193 0.538421 8 7.048 0.209384 9 15.785 0.409130 10 26.908 0.592184 11 1.313 0.042814 12 2.315 0.074273 13 57.013 0.850496 14 1.553 0.050444 15 1.738 0.056297 16 7.271 0.215220 17 17.718 0.446000 18 0.252 0.008350 19 1.120 0.036640 20 3.694 0.115846 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.007472 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-08-06_05:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 0.1 -0.4 -0.1 0.3 0.6 -0.3 0.4 1.6 -2.0 -0.1 -0.0 -0.7 -1.4 -0.7 1.5 1.5 0.3 0.7 0.5 -0.1 0.6 0.6 -1.2 -0.1 -1.3 -0.3 0.4 -2.1 -0.4 -1.6 -0.3 -0.6 -0.4 -0.6 -0.1 0.7 -0.4 0.5 -0.7 0.9 1.0 -1.1 Chi-square with 42 degrees of freedom:32.870861 z-score=-0.996071, p-value=0.157492 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-08-06_05:31 Test no p-value 1 0.052579 2 0.395678 3 0.286878 4 0.597368 5 0.049706 6 0.000199 7 0.374449 8 0.659338 9 0.377190 10 0.789376 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.088674 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-08-06_05:31: (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 66576 0.12 66704 0.02 3 25000.00 25123 0.61 25099 0.39 4 6666.67 6614 0.42 6613 0.43 5 1388.89 1420 0.70 1326 2.85 6 238.10 228 0.43 208 3.80 7 34.72 33 0.09 41 1.14 8 4.96 5 0.00 8 1.86 p=0.11567 p=0.89474 Number of rngs required: 687332, p-value: 0.106 RESULTS OF CRAPS TEST for dh-ranFile-2015-08-06_05:31 No. of wins: Observed Expected 98489 98585.9 z-score=-0.433, pvalue=0.33243 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66759 66666.7 0.128 0.128 2 37567 37654.3 0.202 0.330 3 26999 26954.7 0.073 0.403 4 19206 19313.5 0.598 1.001 5 13812 13851.4 0.112 1.113 6 9978 9943.5 0.119 1.233 7 7202 7145.0 0.454 1.687 8 5152 5139.1 0.033 1.719 9 3696 3699.9 0.004 1.723 10 2618 2666.3 0.875 2.598 11 1930 1923.3 0.023 2.621 12 1386 1388.7 0.005 2.627 13 1002 1003.7 0.003 2.630 14 750 726.1 0.784 3.414 15 525 525.8 0.001 3.415 16 385 381.2 0.039 3.454 17 283 276.5 0.151 3.605 18 208 200.8 0.256 3.861 19 127 146.0 2.469 6.330 20 104 106.2 0.046 6.376 21 311 287.1 1.987 8.363 Chisq= 8.36 for 20 degrees of freedom, p= 0.01082 SUMMARY of craptest p-value for no. of wins: 0.332432 p-value for throws/game: 0.010820 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-08-06_05:31 No. of wins: Observed Expected 98749 98585.9 z-score= 0.730, pvalue=0.76720 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67052 66666.7 2.227 2.227 2 37412 37654.3 1.559 3.787 3 26752 26954.7 1.525 5.311 4 19298 19313.5 0.012 5.324 5 13935 13851.4 0.504 5.828 6 9981 9943.5 0.141 5.969 7 7179 7145.0 0.162 6.131 8 5215 5139.1 1.122 7.253 9 3689 3699.9 0.032 7.285 10 2665 2666.3 0.001 7.285 11 1871 1923.3 1.424 8.709 12 1342 1388.7 1.573 10.282 13 1001 1003.7 0.007 10.289 14 725 726.1 0.002 10.291 15 520 525.8 0.065 10.356 16 378 381.2 0.026 10.382 17 252 276.5 2.178 12.560 18 209 200.8 0.332 12.892 19 146 146.0 0.000 12.892 20 96 106.2 0.982 13.874 21 282 287.1 0.091 13.965 Chisq= 13.97 for 20 degrees of freedom, p= 0.16776 SUMMARY of craptest p-value for no. of wins: 0.767202 p-value for throws/game: 0.167757 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0002,0.0075,0.0083,0.0093,0.0108,0.0127,0.0147,0.0291,0.0320,0.0341, 0.0364,0.0366,0.0414,0.0428,0.0454,0.0461,0.0497,0.0504,0.0526,0.0563, 0.0676,0.0743,0.0750,0.0791,0.0843,0.0858,0.0859,0.0877,0.0887,0.0922, 0.0929,0.1037,0.1065,0.1077,0.1157,0.1158,0.1169,0.1176,0.1209,0.1259, 0.1309,0.1316,0.1366,0.1405,0.1435,0.1446,0.1452,0.1511,0.1513,0.1514, 0.1575,0.1627,0.1664,0.1678,0.1745,0.1817,0.1875,0.1918,0.1978,0.2023, 0.2028,0.2051,0.2094,0.2117,0.2121,0.2152,0.2170,0.2207,0.2248,0.2276, 0.2278,0.2309,0.2317,0.2390,0.2424,0.2426,0.2432,0.2441,0.2482,0.2487, 0.2567,0.2657,0.2660,0.2785,0.2796,0.2837,0.2843,0.2869,0.2904,0.2925, 0.2936,0.2937,0.2942,0.2945,0.2985,0.3191,0.3222,0.3253,0.3261,0.3265, 0.3324,0.3336,0.3366,0.3467,0.3574,0.3744,0.3772,0.3797,0.3902,0.3957, 0.3957,0.3975,0.4043,0.4055,0.4091,0.4135,0.4162,0.4177,0.4178,0.4182, 0.4274,0.4284,0.4311,0.4329,0.4346,0.4366,0.4373,0.4379,0.4402,0.4455, 0.4460,0.4477,0.4503,0.4661,0.4761,0.4835,0.4839,0.4847,0.4894,0.4906, 0.4914,0.4920,0.4945,0.5140,0.5156,0.5202,0.5228,0.5229,0.5248,0.5290, 0.5339,0.5348,0.5369,0.5384,0.5426,0.5621,0.5629,0.5669,0.5722,0.5737, 0.5821,0.5890,0.5893,0.5922,0.5939,0.5974,0.6038,0.6043,0.6130,0.6160, 0.6254,0.6299,0.6306,0.6369,0.6412,0.6413,0.6424,0.6445,0.6461,0.6462, 0.6523,0.6523,0.6579,0.6587,0.6593,0.6612,0.6620,0.6635,0.6700,0.6760, 0.6814,0.6845,0.6877,0.6923,0.6964,0.6964,0.7003,0.7031,0.7066,0.7136, 0.7219,0.7265,0.7268,0.7425,0.7519,0.7544,0.7552,0.7575,0.7587,0.7593, 0.7652,0.7672,0.7730,0.7735,0.7768,0.7829,0.7854,0.7855,0.7858,0.7894, 0.7916,0.7936,0.7944,0.8065,0.8184,0.8188,0.8193,0.8241,0.8253,0.8343, 0.8418,0.8445,0.8505,0.8505,0.8506,0.8566,0.8615,0.8642,0.8645,0.8658, 0.8668,0.8761,0.8825,0.8864,0.8866,0.8871,0.8878,0.8905,0.8947,0.9086, 0.9215,0.9215,0.9259,0.9277,0.9314,0.9403,0.9419,0.9446,0.9499,0.9560, 0.9580,0.9582,0.9698,0.9720,0.9732,0.9733,0.9833,0.9934,0.9949, Overall p-value after applying KStest on 269 p-values = 0.368937 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.