RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-08-24_04:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.85 32.6052 0.987358 2 to 25 15.77 15.8284 0.463971 3 to 26 15.86 11.2339 0.155848 4 to 27 15.87 20.4496 0.748119 5 to 28 15.82 16.5651 0.515812 6 to 29 15.83 26.1460 0.928158 7 to 30 15.85 21.9965 0.815146 8 to 31 15.67 29.5997 0.970619 9 to 32 15.49 23.1253 0.854786 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.026144 Tough bday spacings test for dh-ranFile-2015-08-24_04:31: 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 41 81 108 88 69 48 34 11 8 5 (O-E)^2/E 0.5 0.5 0.8 1.1 1.0 1.1 0.3 0.6 1.0 0.3 0.2 Birthday Spacings: Sum(O-E)^2/E= 7.408, p= 0.314 RESULTS OF GCD FOR dh-ranFile-2015-08-24_04:31 Euclid's algorithm: p-value, steps to gcd: 0.501156 p-value, dist. of gcd's: 0.407949 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-08-24_04:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.925 0.921 0.647 0.592 0.464 0.008 0.362 0.376 Bits 8 to 15---> 0.068 0.289 0.572 0.554 0.058 0.077 0.439 0.235 Bits 16 to 23---> 0.921 0.137 0.246 0.645 0.438 0.593 0.050 0.376 Bits 24 to 31---> 0.594 0.261 0.769 0.120 0.453 0.320 0.443 0.522 KS test for the above 32 p values: 0.852 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-08-24_04:31, p-values for 5 runs: 0.0248, 0.4297, 0.5610, 0.0965, 0.7446 Rank test for binary matrices (31x31) for dh-ranFile-2015-08-24_04:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 225 211.4 0.873 0.873 r= 29 5148 5134.0 0.038 0.911 r= 30 23108 23103.0 0.001 0.912 r= 31 11519 11551.5 0.092 1.003 chi-square = 1.003 with df = 3; p-value = 0.200 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-08-24_04:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 195 211.4 1.275 1.275 r= 30 5023 5134.0 2.400 3.675 r= 31 23135 23103.0 0.044 3.719 r= 32 11647 11551.5 0.789 4.509 chi-square = 4.509 with df = 3; p-value = 0.788 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-08-24_04:31 b-rank test for bits 1 to 8, p=0.09125 b-rank test for bits 2 to 9, p=0.27327 b-rank test for bits 3 to 10, p=0.09567 b-rank test for bits 4 to 11, p=0.49546 b-rank test for bits 5 to 12, p=0.33094 b-rank test for bits 6 to 13, p=0.46730 b-rank test for bits 7 to 14, p=0.77256 b-rank test for bits 8 to 15, p=0.80062 b-rank test for bits 9 to 16, p=0.96757 b-rank test for bits 10 to 17, p=0.46082 b-rank test for bits 11 to 18, p=0.78433 b-rank test for bits 12 to 19, p=0.86487 b-rank test for bits 13 to 20, p=0.20201 b-rank test for bits 14 to 21, p=0.47659 b-rank test for bits 15 to 22, p=0.73683 b-rank test for bits 16 to 23, p=0.93205 b-rank test for bits 17 to 24, p=0.45516 b-rank test for bits 18 to 25, p=0.89227 b-rank test for bits 19 to 26, p=0.06995 b-rank test for bits 20 to 27, p=0.10235 b-rank test for bits 21 to 28, p=0.45010 b-rank test for bits 22 to 29, p=0.61184 b-rank test for bits 23 to 30, p=0.54195 b-rank test for bits 24 to 31, p=0.17890 b-rank test for bits 25 to 32, p=0.06604 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 = 0.916679 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-08-24_04:31 (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 142307 0.93 0.823591 2 142092 0.43 0.665237 3 142192 0.66 0.745516 4 141848 -0.14 0.443029 5 142156 0.58 0.717805 6 141579 -0.77 0.220117 7 142363 1.06 0.855422 8 142261 0.82 0.794364 9 141520 -0.91 0.181504 10 141435 -1.11 0.133877 11 141369 -1.26 0.103393 12 142438 1.24 0.891624 13 142373 1.08 0.860672 14 142491 1.36 0.912933 15 142006 0.23 0.589347 16 141481 -1.00 0.158469 17 142121 0.49 0.689543 18 141366 -1.27 0.102138 19 141506 -0.94 0.173004 20 142225 0.74 0.769605 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-08-24_04:31 Bits used No. missing words z-score p-value 23 to 32 141399 -1.7598 0.039224 22 to 31 141630 -0.9632 0.167722 21 to 30 141492 -1.4391 0.075066 20 to 29 142162 0.8713 0.808198 19 to 28 141456 -1.5632 0.059002 18 to 27 141635 -0.9460 0.172083 17 to 26 141731 -0.6149 0.269300 16 to 25 141825 -0.2908 0.385605 15 to 24 141708 -0.6942 0.243765 14 to 23 142087 0.6127 0.729948 13 to 22 141981 0.2471 0.597599 12 to 21 141873 -0.1253 0.450153 11 to 20 142338 1.4782 0.930319 10 to 19 141698 -0.7287 0.233085 9 to 18 142014 0.3609 0.640925 8 to 17 142158 0.8575 0.804411 7 to 16 141836 -0.2529 0.400187 6 to 15 142044 0.4644 0.678812 5 to 14 142081 0.5920 0.723063 4 to 13 141853 -0.1942 0.422994 3 to 12 141512 -1.3701 0.085327 2 to 11 142220 1.0713 0.857977 1 to 10 141940 0.1058 0.542113 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-08-24_04:31 Bits used No. missing words z-score p-value 28 to 32 141824 -0.2893 0.386193 27 to 31 142086 0.5989 0.725374 26 to 30 141942 0.1107 0.544091 25 to 29 141779 -0.4418 0.329318 24 to 28 141558 -1.1909 0.116837 23 to 27 141958 0.1650 0.565521 22 to 26 141323 -1.9876 0.023430 21 to 25 141943 0.1141 0.545435 20 to 24 142182 0.9243 0.822336 19 to 23 141974 0.2192 0.586761 18 to 22 141613 -1.0045 0.157567 17 to 21 141673 -0.8011 0.211532 16 to 20 142122 0.7209 0.764519 15 to 19 141866 -0.1469 0.441613 14 to 18 141775 -0.4554 0.324427 13 to 17 141860 -0.1672 0.433598 12 to 16 142258 1.1819 0.881384 11 to 15 141735 -0.5909 0.277277 10 to 14 141587 -1.0926 0.137275 9 to 13 141560 -1.1842 0.118173 8 to 12 141020 -3.0147 0.001286 7 to 11 142485 1.9514 0.974497 6 to 10 141988 0.2667 0.605141 5 to 9 142157 0.8396 0.799422 4 to 8 141895 -0.0486 0.480629 3 to 7 141962 0.1785 0.570852 2 to 6 141674 -0.7977 0.212514 1 to 5 141893 -0.0554 0.477928 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-08-24_04:31 Bits used No. missing words z-score p-value 31 to 32 141648 -0.7709 0.220388 30 to 31 142086 0.5212 0.698869 29 to 30 141834 -0.2222 0.412074 28 to 29 141566 -1.0128 0.155584 27 to 28 141771 -0.4081 0.341617 26 to 27 141656 -0.7473 0.227445 25 to 26 141611 -0.8800 0.189422 24 to 25 141628 -0.8299 0.203303 23 to 24 142275 1.0787 0.859633 22 to 23 142007 0.2881 0.613370 21 to 22 142215 0.9017 0.816387 20 to 21 141891 -0.0541 0.478439 19 to 20 141550 -1.0600 0.144579 18 to 19 141590 -0.9420 0.173102 17 to 18 142189 0.8250 0.795310 16 to 17 141376 -1.5732 0.057831 15 to 16 142122 0.6273 0.734784 14 to 15 141790 -0.3520 0.362417 13 to 14 141992 0.2439 0.596332 12 to 13 141620 -0.8535 0.196696 11 to 12 142185 0.8132 0.791944 10 to 11 141646 -0.7768 0.218643 9 to 10 141644 -0.7827 0.216906 8 to 9 141835 -0.2193 0.413223 7 to 8 141587 -0.9508 0.170846 6 to 7 141575 -0.9862 0.162012 5 to 6 141812 -0.2871 0.387014 4 to 5 142241 0.9784 0.836056 3 to 4 141592 -0.9361 0.174617 2 to 3 141686 -0.6588 0.255015 1 to 2 141653 -0.7561 0.224784 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-08-24_04:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2579.85 1.129 0.870616 Test results for specific bytes for dh-ranFile-2015-08-24_04:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2437.40 -0.885 0.187980 2 to 9 2480.82 -0.271 0.393081 3 to 10 2593.98 1.329 0.908088 4 to 11 2559.37 0.840 0.799421 5 to 12 2495.44 -0.064 0.474316 6 to 13 2651.61 2.144 0.983987 7 to 14 2437.75 -0.880 0.189341 8 to 15 2525.15 0.356 0.638954 9 to 16 2455.59 -0.628 0.264974 10 to 17 2478.08 -0.310 0.378306 11 to 18 2552.26 0.739 0.770088 12 to 19 2468.58 -0.444 0.328385 13 to 20 2555.57 0.786 0.784045 14 to 21 2559.25 0.838 0.798971 15 to 22 2566.15 0.936 0.825239 16 to 23 2534.69 0.491 0.688166 17 to 24 2625.16 1.770 0.961641 18 to 25 2540.38 0.571 0.716032 19 to 26 2515.35 0.217 0.585901 20 to 27 2615.82 1.638 0.949287 21 to 28 2483.89 -0.228 0.409875 22 to 29 2566.28 0.937 0.825722 23 to 30 2510.07 0.142 0.556618 24 to 31 2509.95 0.141 0.555937 25 to 32 2577.49 1.096 0.863427 CDPARK for dh-ranFile-2015-08-24_04:31: 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 3543 0.9132 0.819442 3482 -1.8721 0.030593 3524 0.0457 0.518210 3567 2.0091 0.977738 3569 2.1005 0.982156 3531 0.3653 0.642555 3578 2.5114 0.993988 3540 0.7763 0.781201 3512 -0.5023 0.307734 3515 -0.3653 0.357445 Square side=100, avg. no. parked=3536.10 sample std.=28.25 p-value of the KSTEST for those 10 p-values: 0.063419 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-08-24_04:31 0.2372,0.1276,0.4021,0.6432,0.7187,0.0353,0.2540,0.6573,0.8194,0.6300, The KS test for those 10 p-values: 0.789246 The 3DSPHERES test for dh-ranFile-2015-08-24_04:31 sample no r^3 equiv. uni. 1 15.209 0.397675 2 72.682 0.911322 3 48.340 0.800380 4 21.350 0.509170 5 23.117 0.537250 6 2.321 0.074456 7 108.375 0.973016 8 19.597 0.479641 9 8.742 0.252779 10 23.050 0.536208 11 31.141 0.645854 12 4.095 0.127591 13 18.453 0.459421 14 35.050 0.689117 15 8.747 0.252916 16 12.968 0.350966 17 3.594 0.112897 18 9.287 0.266239 19 18.508 0.460399 20 17.566 0.443184 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.554438 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-08-24_04:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 2.7 0.5 0.8 -0.5 1.2 1.1 -0.0 0.8 0.6 -0.9 -2.6 2.1 -0.9 1.5 -0.1 0.3 0.2 0.8 -0.4 0.0 -0.9 -0.9 0.5 0.1 0.1 -0.4 -0.2 -0.0 -1.0 1.0 -1.2 0.3 -1.4 -0.6 -0.4 0.2 2.1 -0.1 0.1 -0.7 -1.3 -1.0 -1.1 Chi-square with 42 degrees of freedom:45.121552 z-score=0.340589, p-value=0.657218 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-08-24_04:31 Test no p-value 1 0.628177 2 0.065797 3 0.804541 4 0.427064 5 0.181758 6 0.995922 7 0.445363 8 0.610002 9 0.735407 10 0.794547 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.635071 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-08-24_04:31: (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 66794 0.24 66703 0.02 3 25000.00 24928 0.21 24887 0.51 4 6666.67 6655 0.02 6745 0.92 5 1388.89 1346 1.32 1395 0.03 6 238.10 234 0.07 228 0.43 7 34.72 40 0.80 37 0.15 8 4.96 2 1.77 4 0.19 p=0.38201 p=0.10378 Number of rngs required: 687977, p-value: 0.312 RESULTS OF CRAPS TEST for dh-ranFile-2015-08-24_04:31 No. of wins: Observed Expected 98522 98585.9 z-score=-0.286, pvalue=0.38759 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66613 66666.7 0.043 0.043 2 37388 37654.3 1.884 1.927 3 27125 26954.7 1.076 3.002 4 19316 19313.5 0.000 3.003 5 13931 13851.4 0.457 3.460 6 10112 9943.5 2.854 6.314 7 7113 7145.0 0.144 6.457 8 5038 5139.1 1.988 8.445 9 3608 3699.9 2.281 10.726 10 2709 2666.3 0.684 11.410 11 1915 1923.3 0.036 11.446 12 1451 1388.7 2.791 14.237 13 989 1003.7 0.216 14.453 14 745 726.1 0.490 14.943 15 519 525.8 0.089 15.032 16 409 381.2 2.035 17.067 17 275 276.5 0.009 17.075 18 192 200.8 0.388 17.463 19 134 146.0 0.984 18.447 20 118 106.2 1.308 19.755 21 300 287.1 0.578 20.333 Chisq= 20.33 for 20 degrees of freedom, p= 0.56273 SUMMARY of craptest p-value for no. of wins: 0.387587 p-value for throws/game: 0.562727 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-08-24_04:31 No. of wins: Observed Expected 98447 98585.9 z-score=-0.621, pvalue=0.26728 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66467 66666.7 0.598 0.598 2 37937 37654.3 2.122 2.720 3 26700 26954.7 2.407 5.127 4 19295 19313.5 0.018 5.145 5 13930 13851.4 0.446 5.591 6 9824 9943.5 1.437 7.028 7 7237 7145.0 1.184 8.212 8 5194 5139.1 0.587 8.799 9 3716 3699.9 0.070 8.869 10 2660 2666.3 0.015 8.884 11 1955 1923.3 0.522 9.406 12 1415 1388.7 0.497 9.902 13 1066 1003.7 3.865 13.767 14 708 726.1 0.453 14.221 15 531 525.8 0.051 14.271 16 377 381.2 0.045 14.317 17 268 276.5 0.264 14.580 18 194 200.8 0.232 14.813 19 166 146.0 2.744 17.557 20 89 106.2 2.790 20.347 21 271 287.1 0.904 21.251 Chisq= 21.25 for 20 degrees of freedom, p= 0.61753 SUMMARY of craptest p-value for no. of wins: 0.267281 p-value for throws/game: 0.617530 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0013,0.0076,0.0234,0.0248,0.0261,0.0306,0.0353,0.0392,0.0504,0.0578, 0.0582,0.0590,0.0634,0.0658,0.0660,0.0676,0.0699,0.0745,0.0751,0.0767, 0.0853,0.0912,0.0957,0.0965,0.1021,0.1023,0.1034,0.1038,0.1129,0.1168, 0.1182,0.1200,0.1276,0.1276,0.1339,0.1371,0.1373,0.1446,0.1556,0.1558, 0.1576,0.1585,0.1620,0.1677,0.1708,0.1721,0.1730,0.1731,0.1746,0.1789, 0.1815,0.1818,0.1880,0.1893,0.1894,0.1967,0.1995,0.2020,0.2033,0.2115, 0.2125,0.2169,0.2186,0.2201,0.2204,0.2248,0.2274,0.2331,0.2348,0.2372, 0.2438,0.2460,0.2528,0.2529,0.2540,0.2550,0.2608,0.2650,0.2662,0.2673, 0.2693,0.2733,0.2773,0.2892,0.3077,0.3117,0.3136,0.3205,0.3244,0.3284, 0.3293,0.3309,0.3416,0.3510,0.3574,0.3621,0.3624,0.3763,0.3763,0.3783, 0.3820,0.3856,0.3862,0.3870,0.3876,0.3931,0.3977,0.4002,0.4021,0.4079, 0.4099,0.4121,0.4132,0.4230,0.4271,0.4297,0.4336,0.4384,0.4387,0.4416, 0.4430,0.4431,0.4432,0.4454,0.4501,0.4502,0.4532,0.4552,0.4594,0.4604, 0.4608,0.4640,0.4643,0.4673,0.4743,0.4766,0.4779,0.4784,0.4796,0.4806, 0.4955,0.5012,0.5092,0.5158,0.5182,0.5224,0.5362,0.5373,0.5420,0.5421, 0.5441,0.5454,0.5537,0.5544,0.5559,0.5566,0.5610,0.5627,0.5655,0.5709, 0.5717,0.5859,0.5868,0.5893,0.5917,0.5931,0.5941,0.5963,0.5976,0.6051, 0.6100,0.6118,0.6134,0.6175,0.6282,0.6300,0.6351,0.6390,0.6409,0.6426, 0.6432,0.6451,0.6459,0.6469,0.6572,0.6573,0.6652,0.6788,0.6882,0.6891, 0.6895,0.6989,0.7160,0.7178,0.7187,0.7231,0.7254,0.7299,0.7348,0.7354, 0.7368,0.7446,0.7455,0.7481,0.7645,0.7688,0.7696,0.7701,0.7726,0.7812, 0.7840,0.7843,0.7885,0.7892,0.7919,0.7944,0.7945,0.7953,0.7990,0.7994, 0.7994,0.8004,0.8006,0.8044,0.8045,0.8082,0.8151,0.8164,0.8194,0.8194, 0.8223,0.8236,0.8252,0.8257,0.8361,0.8518,0.8548,0.8554,0.8580,0.8596, 0.8607,0.8634,0.8649,0.8706,0.8814,0.8916,0.8923,0.9081,0.9113,0.9129, 0.9167,0.9206,0.9214,0.9246,0.9282,0.9303,0.9321,0.9493,0.9616,0.9676, 0.9706,0.9730,0.9745,0.9777,0.9822,0.9840,0.9874,0.9940,0.9959, Overall p-value after applying KStest on 269 p-values = 0.664202 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.