RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-05-08_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 15.64 18.4818 0.640926 2 to 25 15.51 19.8516 0.718113 3 to 26 15.68 14.2554 0.351056 4 to 27 15.93 20.9869 0.773121 5 to 28 15.56 27.3807 0.947285 6 to 29 15.70 14.9309 0.399542 7 to 30 15.57 21.3978 0.791000 8 to 31 15.63 17.0211 0.547060 9 to 32 15.86 12.3716 0.222868 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.486376 Tough bday spacings test for dh-ranFile-2016-05-08_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 49 77 87 110 64 55 28 8 7 4 (O-E)^2/E 0.4 4.2 0.2 1.2 1.6 2.6 0.2 0.1 3.2 0.0 0.0 Birthday Spacings: Sum(O-E)^2/E= 13.495, p= 0.803 RESULTS OF GCD FOR dh-ranFile-2016-05-08_08:31 Euclid's algorithm: p-value, steps to gcd: 0.596657 p-value, dist. of gcd's: 0.578777 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-05-08_08:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.777 1.000 0.626 0.565 0.655 0.041 0.253 0.108 Bits 8 to 15---> 0.950 0.775 0.012 0.793 0.120 0.146 0.840 0.916 Bits 16 to 23---> 0.556 0.019 0.629 0.230 0.475 0.416 0.375 0.181 Bits 24 to 31---> 0.814 0.814 0.343 0.375 0.075 0.418 0.240 0.828 KS test for the above 32 p values: 0.243 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-05-08_08:31, p-values for 5 runs: 0.4893, 0.6889, 0.3622, 0.4877, 0.5004 Rank test for binary matrices (31x31) for dh-ranFile-2016-05-08_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 199 211.4 0.729 0.729 r= 29 5106 5134.0 0.153 0.882 r= 30 23155 23103.0 0.117 0.999 r= 31 11540 11551.5 0.011 1.011 chi-square = 1.011 with df = 3; p-value = 0.201 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-05-08_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 227 211.4 1.148 1.148 r= 30 5023 5134.0 2.400 3.549 r= 31 23230 23103.0 0.698 4.246 r= 32 11520 11551.5 0.086 4.332 chi-square = 4.332 with df = 3; p-value = 0.772 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-05-08_08:31 b-rank test for bits 1 to 8, p=0.12397 b-rank test for bits 2 to 9, p=0.46192 b-rank test for bits 3 to 10, p=0.88995 b-rank test for bits 4 to 11, p=0.87375 b-rank test for bits 5 to 12, p=0.59328 b-rank test for bits 6 to 13, p=0.25006 b-rank test for bits 7 to 14, p=0.32227 b-rank test for bits 8 to 15, p=0.28219 b-rank test for bits 9 to 16, p=0.20276 b-rank test for bits 10 to 17, p=0.77379 b-rank test for bits 11 to 18, p=0.56874 b-rank test for bits 12 to 19, p=0.86627 b-rank test for bits 13 to 20, p=0.89715 b-rank test for bits 14 to 21, p=0.11910 b-rank test for bits 15 to 22, p=0.20940 b-rank test for bits 16 to 23, p=0.50036 b-rank test for bits 17 to 24, p=0.41473 b-rank test for bits 18 to 25, p=0.56632 b-rank test for bits 19 to 26, p=0.15517 b-rank test for bits 20 to 27, p=0.61082 b-rank test for bits 21 to 28, p=0.20621 b-rank test for bits 22 to 29, p=0.19701 b-rank test for bits 23 to 30, p=0.50707 b-rank test for bits 24 to 31, p=0.90884 b-rank test for bits 25 to 32, p=0.75876 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 = 0.714241 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-05-08_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 141692 -0.51 0.305804 2 141975 0.15 0.560972 3 142355 1.04 0.851128 4 142003 0.22 0.586619 5 142234 0.76 0.775947 6 142116 0.48 0.685407 7 142398 1.14 0.873222 8 141870 -0.09 0.463392 9 141930 0.05 0.519259 10 141126 -1.83 0.033609 11 142219 0.72 0.765322 12 142368 1.07 0.858063 13 141890 -0.05 0.481989 14 141716 -0.45 0.325741 15 141765 -0.34 0.367976 16 141969 0.14 0.555439 17 141336 -1.34 0.090195 18 142528 1.45 0.925840 19 141739 -0.40 0.345327 20 142264 0.83 0.796354 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-05-08_08:31 Bits used No. missing words z-score p-value 23 to 32 141985 0.2609 0.602927 22 to 31 141822 -0.3011 0.381655 21 to 30 141405 -1.7391 0.041011 20 to 29 141709 -0.6908 0.244848 19 to 28 142323 1.4264 0.923131 18 to 27 142515 2.0885 0.981624 17 to 26 141848 -0.2115 0.416255 16 to 25 142238 1.1333 0.871465 15 to 24 141911 0.0058 0.502297 14 to 23 141667 -0.8356 0.201684 13 to 22 141672 -0.8184 0.206570 12 to 21 142334 1.4644 0.928455 11 to 20 142101 0.6609 0.745672 10 to 19 142012 0.3540 0.638344 9 to 18 141845 -0.2218 0.412224 8 to 17 141625 -0.9804 0.163432 7 to 16 142117 0.7161 0.763036 6 to 15 142086 0.6092 0.728806 5 to 14 142017 0.3713 0.644784 4 to 13 141609 -1.0356 0.150190 3 to 12 141705 -0.7046 0.240534 2 to 11 142216 1.0575 0.854854 1 to 10 142340 1.4851 0.931237 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-05-08_08:31 Bits used No. missing words z-score p-value 28 to 32 142073 0.5548 0.710489 27 to 31 142128 0.7413 0.770730 26 to 30 142314 1.3718 0.914931 25 to 29 141665 -0.8282 0.203768 24 to 28 141880 -0.0994 0.460401 23 to 27 141477 -1.4655 0.071389 22 to 26 142070 0.5446 0.707001 21 to 25 142378 1.5887 0.943937 20 to 24 142137 0.7718 0.779873 19 to 23 142219 1.0497 0.853079 18 to 22 142766 2.9040 0.998158 17 to 21 142138 0.7752 0.780875 16 to 20 141955 0.1548 0.561516 15 to 19 141976 0.2260 0.589399 14 to 18 141495 -1.4045 0.080084 13 to 17 142097 0.6362 0.737667 12 to 16 142100 0.6463 0.740970 11 to 15 141778 -0.4452 0.328093 10 to 14 141336 -1.9435 0.025978 9 to 13 141838 -0.2418 0.404469 8 to 12 141896 -0.0452 0.481979 7 to 11 141960 0.1718 0.568188 6 to 10 141966 0.1921 0.576169 5 to 9 142189 0.9480 0.828444 4 to 8 141899 -0.0350 0.486033 3 to 7 141815 -0.3198 0.374574 2 to 6 141981 0.2429 0.595978 1 to 5 141733 -0.5977 0.275010 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-05-08_08:31 Bits used No. missing words z-score p-value 31 to 32 142341 1.2734 0.898555 30 to 31 142056 0.4327 0.667367 29 to 30 141848 -0.1809 0.428217 28 to 29 142027 0.3471 0.635745 27 to 28 141520 -1.1485 0.125388 26 to 27 141535 -1.1042 0.134749 25 to 26 141728 -0.5349 0.296361 24 to 25 141841 -0.2016 0.420129 23 to 24 142585 1.9931 0.976876 22 to 23 141999 0.2645 0.604308 21 to 22 142342 1.2763 0.899078 20 to 21 141779 -0.3845 0.350321 19 to 20 142758 2.5035 0.993851 18 to 19 142166 0.7571 0.775517 17 to 18 142150 0.7099 0.761130 16 to 17 142084 0.5153 0.696811 15 to 16 142055 0.4297 0.666295 14 to 15 141545 -1.0747 0.141250 13 to 14 141828 -0.2399 0.405199 12 to 13 142166 0.7571 0.775517 11 to 12 141849 -0.1780 0.429375 10 to 11 141896 -0.0393 0.484317 9 to 10 141914 0.0138 0.505496 8 to 9 141677 -0.6853 0.246565 7 to 8 142008 0.2911 0.614498 6 to 7 141408 -1.4788 0.069590 5 to 6 141213 -2.0541 0.019984 4 to 5 141510 -1.1780 0.119405 3 to 4 142055 0.4297 0.666295 2 to 3 141945 0.1052 0.541900 1 to 2 141563 -1.0216 0.153480 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-05-08_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2528.83 0.408 0.658283 Test results for specific bytes for dh-ranFile-2016-05-08_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2417.08 -1.173 0.120470 2 to 9 2418.95 -1.146 0.125864 3 to 10 2494.89 -0.072 0.471169 4 to 11 2463.29 -0.519 0.301811 5 to 12 2418.23 -1.156 0.123748 6 to 13 2427.14 -1.030 0.151397 7 to 14 2443.48 -0.799 0.212055 8 to 15 2611.14 1.572 0.941992 9 to 16 2530.00 0.424 0.664318 10 to 17 2459.76 -0.569 0.284647 11 to 18 2502.85 0.040 0.516068 12 to 19 2522.28 0.315 0.623636 13 to 20 2431.95 -0.962 0.167935 14 to 21 2359.16 -1.992 0.023197 15 to 22 2446.68 -0.754 0.225395 16 to 23 2534.09 0.482 0.685134 17 to 24 2524.95 0.353 0.637910 18 to 25 2376.81 -1.742 0.040736 19 to 26 2551.53 0.729 0.766939 20 to 27 2554.33 0.768 0.778860 21 to 28 2607.22 1.516 0.935275 22 to 29 2391.70 -1.532 0.062807 23 to 30 2506.34 0.090 0.535737 24 to 31 2516.83 0.238 0.594057 25 to 32 2465.65 -0.486 0.313542 CDPARK for dh-ranFile-2016-05-08_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 3522 -0.0457 0.481790 3535 0.5479 0.708135 3530 0.3196 0.625377 3523 0.0000 0.500000 3532 0.4110 0.659449 3548 1.1416 0.873180 3528 0.2283 0.590298 3488 -1.5982 0.055002 3547 1.0959 0.863437 3557 1.5525 0.939730 Square side=100, avg. no. parked=3531.00 sample std.=18.01 p-value of the KSTEST for those 10 p-values: 0.215182 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-05-08_08:31 0.5358,0.9530,0.9606,0.4702,0.4244,0.3915,0.7604,0.4271,0.0334,0.0458, The KS test for those 10 p-values: 0.653432 The 3DSPHERES test for dh-ranFile-2016-05-08_08:31 sample no r^3 equiv. uni. 1 26.501 0.586607 2 5.006 0.153692 3 51.907 0.822757 4 53.713 0.833112 5 0.636 0.020990 6 17.312 0.438463 7 44.228 0.771050 8 45.185 0.778239 9 13.513 0.362643 10 46.830 0.790077 11 1.188 0.038816 12 30.723 0.640875 13 36.770 0.706443 14 29.867 0.630486 15 20.287 0.491473 16 5.345 0.163210 17 33.281 0.670233 18 52.791 0.827903 19 74.970 0.917832 20 20.794 0.499986 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.354854 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-05-08_08:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 -1.6 -0.1 0.8 -0.4 0.4 -0.7 2.9 1.1 -0.2 1.4 0.4 1.2 -0.2 1.1 -0.0 -0.4 0.3 0.4 0.1 0.6 0.2 -1.0 -2.2 -2.1 -0.3 -0.4 -1.1 -0.2 -1.3 -2.1 0.3 -0.8 -0.4 -0.5 -0.7 0.3 0.2 2.5 -1.3 -1.3 -1.0 -0.1 Chi-square with 42 degrees of freedom:49.903259 z-score=0.862316, p-value=0.811984 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-05-08_08:31 Test no p-value 1 0.197791 2 0.896011 3 0.280317 4 0.436921 5 0.249574 6 0.299256 7 0.150349 8 0.529782 9 0.179133 10 0.973424 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.318651 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-05-08_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 66608 0.05 66859 0.55 3 25000.00 24935 0.17 24954 0.08 4 6666.67 6761 1.33 6503 4.02 5 1388.89 1394 0.02 1382 0.03 6 238.10 259 1.84 258 1.66 7 34.72 37 0.15 33 0.09 8 4.96 5 0.00 10 5.12 p=0.26398 p=0.92753 Number of rngs required: 687966, p-value: 0.307 RESULTS OF CRAPS TEST for dh-ranFile-2016-05-08_08:31 No. of wins: Observed Expected 98445 98585.9 z-score=-0.630, pvalue=0.26435 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66674 66666.7 0.001 0.001 2 37427 37654.3 1.372 1.373 3 26943 26954.7 0.005 1.378 4 19496 19313.5 1.725 3.103 5 13943 13851.4 0.605 3.709 6 9944 9943.5 0.000 3.709 7 7080 7145.0 0.592 4.301 8 5218 5139.1 1.212 5.513 9 3710 3699.9 0.028 5.541 10 2624 2666.3 0.671 6.212 11 1955 1923.3 0.522 6.733 12 1380 1388.7 0.055 6.788 13 999 1003.7 0.022 6.810 14 713 726.1 0.238 7.048 15 493 525.8 2.050 9.099 16 412 381.2 2.497 11.596 17 286 276.5 0.324 11.919 18 193 200.8 0.305 12.224 19 152 146.0 0.248 12.472 20 98 106.2 0.635 13.108 21 260 287.1 2.561 15.668 Chisq= 15.67 for 20 degrees of freedom, p= 0.26302 SUMMARY of craptest p-value for no. of wins: 0.264347 p-value for throws/game: 0.263022 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-05-08_08:31 No. of wins: Observed Expected 99045 98585.9 z-score= 2.054, pvalue=0.97999 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67204 66666.7 4.331 4.331 2 37377 37654.3 2.042 6.373 3 26853 26954.7 0.384 6.757 4 19300 19313.5 0.009 6.767 5 13886 13851.4 0.086 6.853 6 9900 9943.5 0.191 7.044 7 7221 7145.0 0.808 7.852 8 5060 5139.1 1.217 9.068 9 3690 3699.9 0.026 9.094 10 2629 2666.3 0.522 9.616 11 1905 1923.3 0.175 9.791 12 1373 1388.7 0.178 9.969 13 1004 1003.7 0.000 9.969 14 682 726.1 2.683 12.653 15 511 525.8 0.419 13.071 16 355 381.2 1.794 14.865 17 294 276.5 1.102 15.968 18 215 200.8 1.000 16.968 19 166 146.0 2.744 19.712 20 95 106.2 1.184 20.896 21 280 287.1 0.176 21.072 Chisq= 21.07 for 20 degrees of freedom, p= 0.60712 SUMMARY of craptest p-value for no. of wins: 0.979990 p-value for throws/game: 0.607118 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0118,0.0186,0.0200,0.0210,0.0232,0.0260,0.0334,0.0336,0.0388,0.0407, 0.0408,0.0410,0.0458,0.0550,0.0628,0.0696,0.0714,0.0753,0.0801,0.0902, 0.1078,0.1191,0.1194,0.1196,0.1205,0.1237,0.1240,0.1254,0.1259,0.1347, 0.1413,0.1458,0.1502,0.1503,0.1514,0.1535,0.1537,0.1552,0.1632,0.1634, 0.1679,0.1791,0.1812,0.1970,0.1978,0.2013,0.2017,0.2028,0.2038,0.2062, 0.2066,0.2094,0.2121,0.2152,0.2229,0.2254,0.2302,0.2396,0.2405,0.2428, 0.2448,0.2466,0.2496,0.2501,0.2528,0.2630,0.2640,0.2643,0.2750,0.2803, 0.2822,0.2846,0.2964,0.2993,0.3018,0.3058,0.3073,0.3135,0.3187,0.3223, 0.3257,0.3281,0.3433,0.3453,0.3503,0.3511,0.3549,0.3622,0.3626,0.3680, 0.3746,0.3750,0.3752,0.3817,0.3915,0.3995,0.4045,0.4052,0.4122,0.4147, 0.4163,0.4164,0.4181,0.4201,0.4244,0.4271,0.4282,0.4294,0.4369,0.4385, 0.4604,0.4619,0.4634,0.4702,0.4712,0.4754,0.4818,0.4820,0.4820,0.4843, 0.4860,0.4864,0.4877,0.4893,0.4915,0.5000,0.5000,0.5004,0.5004,0.5023, 0.5055,0.5071,0.5161,0.5193,0.5298,0.5357,0.5358,0.5419,0.5471,0.5554, 0.5559,0.5610,0.5615,0.5652,0.5663,0.5682,0.5687,0.5762,0.5788,0.5866, 0.5866,0.5894,0.5903,0.5933,0.5941,0.5960,0.5967,0.6029,0.6043,0.6071, 0.6108,0.6145,0.6236,0.6254,0.6262,0.6293,0.6305,0.6357,0.6379,0.6383, 0.6409,0.6409,0.6448,0.6534,0.6547,0.6583,0.6594,0.6643,0.6663,0.6663, 0.6674,0.6702,0.6851,0.6854,0.6889,0.6968,0.7064,0.7070,0.7081,0.7105, 0.7142,0.7181,0.7288,0.7377,0.7410,0.7457,0.7588,0.7604,0.7611,0.7630, 0.7653,0.7669,0.7707,0.7711,0.7723,0.7731,0.7738,0.7751,0.7755,0.7755, 0.7759,0.7771,0.7782,0.7789,0.7799,0.7809,0.7901,0.7910,0.7929,0.7964, 0.8027,0.8120,0.8141,0.8142,0.8228,0.8279,0.8283,0.8284,0.8331,0.8396, 0.8511,0.8531,0.8549,0.8581,0.8634,0.8663,0.8715,0.8732,0.8732,0.8738, 0.8900,0.8960,0.8972,0.8986,0.8991,0.9088,0.9149,0.9165,0.9178,0.9231, 0.9258,0.9275,0.9285,0.9312,0.9353,0.9397,0.9420,0.9439,0.9473,0.9495, 0.9530,0.9606,0.9734,0.9769,0.9800,0.9816,0.9939,0.9982,0.9999, Overall p-value after applying KStest on 269 p-values = 0.460768 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.