RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-11-10_15:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.91 20.2115 0.736446 2 to 25 15.85 19.1421 0.679561 3 to 26 15.64 27.3853 0.947347 4 to 27 15.74 21.6271 0.800512 5 to 28 15.58 15.6795 0.453342 6 to 29 15.63 19.3755 0.692588 7 to 30 15.72 18.2324 0.625680 8 to 31 15.97 11.2985 0.159366 9 to 32 15.79 16.7195 0.526480 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.261776 Tough bday spacings test for dh-ranFile-2015-11-10_15:31: 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 39 79 110 96 68 48 32 6 10 5 (O-E)^2/E 0.5 0.2 0.4 1.6 0.0 1.3 0.3 0.2 5.3 1.7 0.2 Birthday Spacings: Sum(O-E)^2/E= 11.749, p= 0.698 RESULTS OF GCD FOR dh-ranFile-2015-11-10_15:31 Euclid's algorithm: p-value, steps to gcd: 0.351579 p-value, dist. of gcd's: 0.618827 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-11-10_15:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.387 0.420 0.277 0.695 0.450 0.046 0.624 0.189 Bits 8 to 15---> 0.747 0.792 0.674 0.925 0.353 0.762 0.956 0.809 Bits 16 to 23---> 0.367 0.835 0.902 0.212 0.330 0.684 0.082 0.093 Bits 24 to 31---> 0.755 0.407 0.199 0.645 0.062 0.936 0.764 0.489 KS test for the above 32 p values: 0.146 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-11-10_15:31, p-values for 5 runs: 0.0910, 0.2897, 0.9037, 0.4280, 0.8563 Rank test for binary matrices (31x31) for dh-ranFile-2015-11-10_15:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 216 211.4 0.099 0.099 r= 29 5182 5134.0 0.449 0.548 r= 30 23215 23103.0 0.542 1.090 r= 31 11387 11551.5 2.343 3.434 chi-square = 3.434 with df = 3; p-value = 0.671 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-11-10_15:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 207 211.4 0.092 0.092 r= 30 5108 5134.0 0.132 0.224 r= 31 23099 23103.0 0.001 0.225 r= 32 11586 11551.5 0.103 0.328 chi-square = 0.328 with df = 3; p-value = 0.045 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-11-10_15:31 b-rank test for bits 1 to 8, p=0.04070 b-rank test for bits 2 to 9, p=0.03312 b-rank test for bits 3 to 10, p=0.36221 b-rank test for bits 4 to 11, p=0.27696 b-rank test for bits 5 to 12, p=0.01239 b-rank test for bits 6 to 13, p=0.37675 b-rank test for bits 7 to 14, p=0.14884 b-rank test for bits 8 to 15, p=0.91435 b-rank test for bits 9 to 16, p=0.02768 b-rank test for bits 10 to 17, p=0.46813 b-rank test for bits 11 to 18, p=0.15202 b-rank test for bits 12 to 19, p=0.25320 b-rank test for bits 13 to 20, p=0.93383 b-rank test for bits 14 to 21, p=0.99237 b-rank test for bits 15 to 22, p=0.69267 b-rank test for bits 16 to 23, p=0.76341 b-rank test for bits 17 to 24, p=0.60701 b-rank test for bits 18 to 25, p=0.75418 b-rank test for bits 19 to 26, p=0.96473 b-rank test for bits 20 to 27, p=0.56791 b-rank test for bits 21 to 28, p=0.91472 b-rank test for bits 22 to 29, p=0.54360 b-rank test for bits 23 to 30, p=0.24714 b-rank test for bits 24 to 31, p=0.91040 b-rank test for bits 25 to 32, p=0.53726 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 = 0.517945 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-11-10_15:31 (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 141612 -0.69 0.243623 2 141874 -0.08 0.467106 3 141796 -0.26 0.395586 4 142516 1.42 0.921825 5 141947 0.09 0.535067 6 142276 0.86 0.804196 7 141711 -0.46 0.321543 8 141441 -1.09 0.136927 9 141390 -1.21 0.112491 10 142167 0.60 0.726424 11 141834 -0.18 0.430145 12 141319 -1.38 0.083905 13 141920 0.02 0.509945 14 141321 -1.37 0.084627 15 141550 -0.84 0.200579 16 142026 0.27 0.607417 17 141205 -1.65 0.049920 18 141679 -0.54 0.295235 19 141644 -0.62 0.267652 20 141593 -0.74 0.229927 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-11-10_15:31 Bits used No. missing words z-score p-value 23 to 32 141485 -1.4632 0.071705 22 to 31 141646 -0.9080 0.181930 21 to 30 141800 -0.3770 0.353087 20 to 29 141809 -0.3460 0.364684 19 to 28 141677 -0.8011 0.211526 18 to 27 141916 0.0230 0.509175 17 to 26 141631 -0.9598 0.168588 16 to 25 142197 0.9920 0.839393 15 to 24 141602 -1.0598 0.144627 14 to 23 141761 -0.5115 0.304507 13 to 22 141746 -0.5632 0.286647 12 to 21 142125 0.7437 0.771468 11 to 20 141530 -1.3080 0.095431 10 to 19 141897 -0.0425 0.483043 9 to 18 142448 1.8575 0.968379 8 to 17 141768 -0.4873 0.313007 7 to 16 141594 -1.0873 0.138442 6 to 15 142426 1.7816 0.962594 5 to 14 142257 1.1989 0.884709 4 to 13 141999 0.3092 0.621418 3 to 12 142231 1.1092 0.866330 2 to 11 142319 1.4127 0.921121 1 to 10 141890 -0.0667 0.473428 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-11-10_15:31 Bits used No. missing words z-score p-value 28 to 32 141509 -1.3571 0.087383 27 to 31 141742 -0.5672 0.285282 26 to 30 142076 0.5650 0.713957 25 to 29 142213 1.0294 0.848352 24 to 28 142187 0.9413 0.826713 23 to 27 142172 0.8904 0.813376 22 to 26 142014 0.3548 0.638635 21 to 25 142614 2.3887 0.991546 20 to 24 141588 -1.0893 0.138021 19 to 23 142107 0.6701 0.748593 18 to 22 141669 -0.8147 0.207628 17 to 21 142198 0.9785 0.836097 16 to 20 141534 -1.2723 0.101632 15 to 19 142144 0.7955 0.786836 14 to 18 141707 -0.6859 0.246399 13 to 17 141913 0.0124 0.504963 12 to 16 142248 1.1480 0.874523 11 to 15 141821 -0.2994 0.382308 10 to 14 142093 0.6226 0.733230 9 to 13 141989 0.2701 0.606446 8 to 12 141884 -0.0859 0.465787 7 to 11 141855 -0.1842 0.426940 6 to 10 141955 0.1548 0.561516 5 to 9 141734 -0.5943 0.276143 4 to 8 141829 -0.2723 0.392694 3 to 7 141784 -0.4248 0.335474 2 to 6 142210 1.0192 0.845951 1 to 5 141724 -0.6282 0.264924 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-11-10_15:31 Bits used No. missing words z-score p-value 31 to 32 141612 -0.8771 0.190222 30 to 31 142169 0.7660 0.778158 29 to 30 142208 0.8810 0.810850 28 to 29 141896 -0.0393 0.484317 27 to 28 141672 -0.7001 0.241936 26 to 27 141958 0.1436 0.557080 25 to 26 142147 0.7011 0.758377 24 to 25 141533 -1.1101 0.133474 23 to 24 141046 -2.5467 0.005437 22 to 23 141785 -0.3668 0.356901 21 to 22 141654 -0.7532 0.225669 20 to 21 141988 0.2321 0.591756 19 to 20 141484 -1.2547 0.104801 18 to 19 142201 0.8604 0.805211 17 to 18 141705 -0.6027 0.273340 16 to 17 142150 0.7099 0.761130 15 to 16 141962 0.1554 0.561735 14 to 15 141497 -1.2163 0.111933 13 to 14 141639 -0.7974 0.212600 12 to 13 142012 0.3029 0.619002 11 to 12 141616 -0.8653 0.193443 10 to 11 141886 -0.0688 0.472566 9 to 10 141751 -0.4671 0.320232 8 to 9 141665 -0.7207 0.235536 7 to 8 142144 0.6922 0.755607 6 to 7 142118 0.6155 0.730903 5 to 6 142207 0.8781 0.810051 4 to 5 141764 -0.4287 0.334070 3 to 4 141844 -0.1927 0.423592 2 to 3 141518 -1.1544 0.124175 1 to 2 142080 0.5035 0.692677 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-11-10_15:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2499.72 -0.004 0.498416 Test results for specific bytes for dh-ranFile-2015-11-10_15:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2507.14 0.101 0.540232 2 to 9 2537.43 0.529 0.701730 3 to 10 2606.09 1.500 0.933245 4 to 11 2416.29 -1.184 0.118246 5 to 12 2591.95 1.300 0.903256 6 to 13 2362.58 -1.943 0.025985 7 to 14 2560.11 0.850 0.802367 8 to 15 2394.89 -1.486 0.068574 9 to 16 2620.55 1.705 0.955882 10 to 17 2375.99 -1.754 0.039735 11 to 18 2553.55 0.757 0.775580 12 to 19 2490.69 -0.132 0.447636 13 to 20 2396.32 -1.466 0.071286 14 to 21 2459.55 -0.572 0.283624 15 to 22 2433.93 -0.934 0.175039 16 to 23 2529.79 0.421 0.663238 17 to 24 2427.73 -1.022 0.153394 18 to 25 2518.64 0.264 0.603958 19 to 26 2581.75 1.156 0.876179 20 to 27 2561.13 0.865 0.806348 21 to 28 2639.56 1.974 0.975792 22 to 29 2494.04 -0.084 0.466426 23 to 30 2503.16 0.045 0.517817 24 to 31 2489.20 -0.153 0.439325 25 to 32 2596.24 1.361 0.913239 CDPARK for dh-ranFile-2015-11-10_15:31: 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 3493 -1.3699 0.085365 3512 -0.5023 0.307734 3545 1.0046 0.842447 3557 1.5525 0.939730 3501 -1.0046 0.157553 3547 1.0959 0.863437 3526 0.1370 0.554479 3546 1.0502 0.853193 3520 -0.1370 0.445521 3531 0.3653 0.642555 Square side=100, avg. no. parked=3527.80 sample std.=20.25 p-value of the KSTEST for those 10 p-values: 0.718966 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-11-10_15:31 0.2541,0.4912,0.0843,0.6715,0.9496,0.1342,0.2490,0.5308,0.8078,0.1051, The KS test for those 10 p-values: 0.693828 The 3DSPHERES test for dh-ranFile-2015-11-10_15:31 sample no r^3 equiv. uni. 1 18.979 0.468814 2 4.876 0.150007 3 20.628 0.497223 4 4.212 0.130980 5 102.851 0.967560 6 26.506 0.586674 7 1.278 0.041702 8 8.553 0.248063 9 56.916 0.850014 10 22.906 0.533982 11 59.519 0.862479 12 2.627 0.083851 13 17.760 0.446771 14 24.180 0.553362 15 77.438 0.924323 16 7.477 0.220597 17 21.943 0.518774 18 7.524 0.221835 19 35.339 0.692098 20 3.216 0.101662 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.743321 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-11-10_15:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 0.1 -0.4 -0.7 0.1 -0.1 -1.6 0.2 -1.1 -0.6 -0.0 0.7 1.5 -1.5 0.8 -0.1 0.7 -0.7 0.2 0.5 -1.3 -0.5 1.2 -1.1 1.5 -0.6 -0.8 0.6 1.9 -2.3 1.2 -0.9 0.6 0.4 1.2 1.0 0.7 -0.4 0.5 -0.7 0.1 -1.0 -0.1 Chi-square with 42 degrees of freedom:38.487927 z-score=-0.383199, p-value=0.374069 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-11-10_15:31 Test no p-value 1 0.021795 2 0.084807 3 0.532759 4 0.318895 5 0.016104 6 0.778629 7 0.034017 8 0.354856 9 0.825190 10 0.889849 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.094939 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-11-10_15:31: (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 66408 1.00 66509 0.37 3 25000.00 25157 0.99 25150 0.90 4 6666.67 6781 1.96 6647 0.06 5 1388.89 1385 0.01 1400 0.09 6 238.10 232 0.16 247 0.33 7 34.72 33 0.09 42 1.53 8 4.96 3 0.77 4 0.19 p=0.45323 p=0.25139 Number of rngs required: 687862, p-value: 0.266 RESULTS OF CRAPS TEST for dh-ranFile-2015-11-10_15:31 No. of wins: Observed Expected 98454 98585.9 z-score=-0.590, pvalue=0.27768 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66839 66666.7 0.445 0.445 2 37536 37654.3 0.372 0.817 3 26877 26954.7 0.224 1.041 4 19158 19313.5 1.251 2.293 5 13943 13851.4 0.605 2.898 6 9867 9943.5 0.589 3.488 7 7134 7145.0 0.017 3.505 8 5182 5139.1 0.359 3.863 9 3709 3699.9 0.023 3.886 10 2718 2666.3 1.003 4.888 11 1944 1923.3 0.222 5.110 12 1401 1388.7 0.108 5.219 13 1020 1003.7 0.264 5.483 14 754 726.1 1.069 6.552 15 542 525.8 0.497 7.049 16 356 381.2 1.660 8.708 17 277 276.5 0.001 8.709 18 208 200.8 0.256 8.965 19 145 146.0 0.007 8.972 20 107 106.2 0.006 8.977 21 283 287.1 0.059 9.036 Chisq= 9.04 for 20 degrees of freedom, p= 0.01752 SUMMARY of craptest p-value for no. of wins: 0.277680 p-value for throws/game: 0.017517 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-11-10_15:31 No. of wins: Observed Expected 98085 98585.9 z-score=-2.240, pvalue=0.01254 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66722 66666.7 0.046 0.046 2 37561 37654.3 0.231 0.277 3 26975 26954.7 0.015 0.292 4 19298 19313.5 0.012 0.305 5 13914 13851.4 0.283 0.588 6 9992 9943.5 0.236 0.824 7 7067 7145.0 0.852 1.676 8 5210 5139.1 0.979 2.655 9 3602 3699.9 2.589 5.243 10 2680 2666.3 0.070 5.314 11 1922 1923.3 0.001 5.315 12 1457 1388.7 3.355 8.670 13 967 1003.7 1.343 10.013 14 698 726.1 1.091 11.103 15 524 525.8 0.006 11.110 16 366 381.2 0.602 11.712 17 300 276.5 1.990 13.702 18 202 200.8 0.007 13.709 19 149 146.0 0.062 13.771 20 103 106.2 0.097 13.869 21 291 287.1 0.053 13.921 Chisq= 13.92 for 20 degrees of freedom, p= 0.16554 SUMMARY of craptest p-value for no. of wins: 0.012541 p-value for throws/game: 0.165536 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0054,0.0124,0.0125,0.0161,0.0175,0.0218,0.0260,0.0277,0.0331,0.0340, 0.0397,0.0407,0.0417,0.0453,0.0455,0.0499,0.0619,0.0686,0.0713,0.0717, 0.0816,0.0839,0.0839,0.0843,0.0846,0.0848,0.0854,0.0874,0.0910,0.0933, 0.0949,0.0954,0.1016,0.1017,0.1048,0.1051,0.1119,0.1125,0.1182,0.1242, 0.1310,0.1335,0.1342,0.1369,0.1380,0.1384,0.1446,0.1456,0.1488,0.1500, 0.1520,0.1534,0.1576,0.1594,0.1655,0.1686,0.1750,0.1819,0.1888,0.1902, 0.1934,0.1994,0.2006,0.2076,0.2115,0.2120,0.2126,0.2206,0.2218,0.2257, 0.2299,0.2355,0.2419,0.2436,0.2464,0.2471,0.2481,0.2490,0.2514,0.2532, 0.2541,0.2618,0.2649,0.2663,0.2677,0.2733,0.2761,0.2770,0.2773,0.2777, 0.2836,0.2853,0.2866,0.2897,0.2952,0.3045,0.3077,0.3130,0.3189,0.3202, 0.3215,0.3301,0.3341,0.3355,0.3516,0.3530,0.3531,0.3549,0.3569,0.3622, 0.3647,0.3666,0.3741,0.3767,0.3823,0.3874,0.3927,0.3956,0.4074,0.4196, 0.4236,0.4269,0.4280,0.4301,0.4393,0.4455,0.4468,0.4476,0.4501,0.4532, 0.4533,0.4658,0.4664,0.4671,0.4681,0.4688,0.4726,0.4734,0.4830,0.4843, 0.4889,0.4912,0.4972,0.4984,0.5050,0.5092,0.5099,0.5178,0.5179,0.5188, 0.5265,0.5308,0.5328,0.5340,0.5351,0.5373,0.5402,0.5436,0.5534,0.5545, 0.5571,0.5615,0.5617,0.5679,0.5867,0.5918,0.6040,0.6064,0.6070,0.6074, 0.6188,0.6190,0.6214,0.6242,0.6257,0.6386,0.6426,0.6450,0.6632,0.6705, 0.6715,0.6739,0.6796,0.6837,0.6921,0.6926,0.6927,0.6927,0.6938,0.6948, 0.6978,0.7017,0.7140,0.7190,0.7264,0.7309,0.7332,0.7364,0.7433,0.7468, 0.7486,0.7542,0.7552,0.7556,0.7584,0.7611,0.7619,0.7634,0.7643,0.7715, 0.7756,0.7782,0.7786,0.7868,0.7921,0.8005,0.8024,0.8042,0.8052,0.8063, 0.8078,0.8089,0.8101,0.8108,0.8134,0.8252,0.8267,0.8348,0.8361,0.8394, 0.8424,0.8460,0.8484,0.8500,0.8532,0.8563,0.8625,0.8634,0.8663,0.8745, 0.8762,0.8847,0.8898,0.9017,0.9033,0.9037,0.9104,0.9132,0.9144,0.9147, 0.9211,0.9218,0.9243,0.9249,0.9332,0.9338,0.9365,0.9397,0.9473,0.9496, 0.9559,0.9561,0.9626,0.9647,0.9676,0.9684,0.9758,0.9915,0.9924, Overall p-value after applying KStest on 269 p-values = 0.294814 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.