RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-01-09_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 15.96 20.5695 0.753861 2 to 25 15.65 14.0847 0.338904 3 to 26 15.67 16.7424 0.528050 4 to 27 15.85 9.8728 0.091140 5 to 28 16.17 14.9513 0.401008 6 to 29 15.81 29.3592 0.968646 7 to 30 15.65 11.3556 0.162510 8 to 31 15.72 16.5085 0.511884 9 to 32 15.50 18.0118 0.611906 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.968407 Tough bday spacings test for dh-ranFile-2016-01-09_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 8 33 78 98 96 71 66 30 12 5 3 (O-E)^2/E 0.1 0.4 0.3 0.0 0.0 0.7 3.7 0.0 0.6 0.4 0.3 Birthday Spacings: Sum(O-E)^2/E= 6.441, p= 0.223 RESULTS OF GCD FOR dh-ranFile-2016-01-09_15:31 Euclid's algorithm: p-value, steps to gcd: 0.134946 p-value, dist. of gcd's: 0.624651 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-01-09_15:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.319 0.427 0.847 0.683 0.944 0.983 0.528 0.937 Bits 8 to 15---> 0.165 0.028 0.001 0.414 0.819 0.816 0.644 0.887 Bits 16 to 23---> 0.763 0.924 0.430 0.642 0.204 0.958 0.752 0.192 Bits 24 to 31---> 0.128 0.996 0.810 0.644 0.634 0.665 0.592 0.906 KS test for the above 32 p values: 0.974 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-01-09_15:31, p-values for 5 runs: 0.5573, 0.7016, 0.6202, 0.8671, 0.4653 Rank test for binary matrices (31x31) for dh-ranFile-2016-01-09_15:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 236 211.4 2.858 2.858 r= 29 5033 5134.0 1.987 4.846 r= 30 23191 23103.0 0.335 5.180 r= 31 11540 11551.5 0.011 5.192 chi-square = 5.192 with df = 3; p-value = 0.842 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-01-09_15:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 184 211.4 3.556 3.556 r= 30 5122 5134.0 0.028 3.584 r= 31 23028 23103.0 0.244 3.828 r= 32 11666 11551.5 1.134 4.962 chi-square = 4.962 with df = 3; p-value = 0.825 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-01-09_15:31 b-rank test for bits 1 to 8, p=0.79544 b-rank test for bits 2 to 9, p=0.93162 b-rank test for bits 3 to 10, p=0.57109 b-rank test for bits 4 to 11, p=0.87406 b-rank test for bits 5 to 12, p=0.04652 b-rank test for bits 6 to 13, p=0.63558 b-rank test for bits 7 to 14, p=0.53021 b-rank test for bits 8 to 15, p=0.96119 b-rank test for bits 9 to 16, p=0.59920 b-rank test for bits 10 to 17, p=0.42601 b-rank test for bits 11 to 18, p=0.59552 b-rank test for bits 12 to 19, p=0.81945 b-rank test for bits 13 to 20, p=0.10412 b-rank test for bits 14 to 21, p=0.83554 b-rank test for bits 15 to 22, p=0.00032 b-rank test for bits 16 to 23, p=0.40753 b-rank test for bits 17 to 24, p=0.19995 b-rank test for bits 18 to 25, p=0.01991 b-rank test for bits 19 to 26, p=0.41022 b-rank test for bits 20 to 27, p=0.18803 b-rank test for bits 21 to 28, p=0.16486 b-rank test for bits 22 to 29, p=0.08451 b-rank test for bits 23 to 30, p=0.23790 b-rank test for bits 24 to 31, p=0.51757 b-rank test for bits 25 to 32, p=0.46249 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 = 0.571545 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-01-09_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 141989 0.19 0.573834 2 141845 -0.15 0.440263 3 141515 -0.92 0.178439 4 142162 0.59 0.722522 5 141825 -0.20 0.421901 6 141507 -0.94 0.173603 7 141867 -0.10 0.460608 8 142694 1.83 0.966624 9 142105 0.46 0.676227 10 142083 0.41 0.657545 11 141860 -0.12 0.454121 12 141883 -0.06 0.475473 13 141539 -0.87 0.193449 14 142244 0.78 0.782875 15 141880 -0.07 0.472683 16 142207 0.70 0.756626 17 141772 -0.32 0.374157 18 141303 -1.42 0.078291 19 142340 1.01 0.842850 20 141879 -0.07 0.471753 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-01-09_15:31 Bits used No. missing words z-score p-value 23 to 32 141759 -0.5184 0.302097 22 to 31 142066 0.5402 0.705485 21 to 30 141677 -0.8011 0.211526 20 to 29 141717 -0.6632 0.253599 19 to 28 142391 1.6609 0.951636 18 to 27 141829 -0.2770 0.390890 17 to 26 141677 -0.8011 0.211526 16 to 25 141705 -0.7046 0.240534 15 to 24 142083 0.5989 0.725368 14 to 23 141631 -0.9598 0.168588 13 to 22 141420 -1.6873 0.045769 12 to 21 141787 -0.4218 0.336575 11 to 20 141692 -0.7494 0.226804 10 to 19 141150 -2.6184 0.004417 9 to 18 141877 -0.1115 0.455617 8 to 17 141866 -0.1494 0.440614 7 to 16 141587 -1.1115 0.133180 6 to 15 141926 0.0575 0.522920 5 to 14 142375 1.6058 0.945837 4 to 13 141580 -1.1356 0.128058 3 to 12 141637 -0.9391 0.173848 2 to 11 141475 -1.4977 0.067107 1 to 10 141552 -1.2322 0.108942 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-01-09_15:31 Bits used No. missing words z-score p-value 28 to 32 141760 -0.5062 0.306357 27 to 31 141988 0.2667 0.605141 26 to 30 141215 -2.3537 0.009295 25 to 29 141107 -2.7198 0.003266 24 to 28 141953 0.1480 0.558842 23 to 27 141739 -0.5774 0.281838 22 to 26 142173 0.8938 0.814285 21 to 25 142180 0.9175 0.820566 20 to 24 141541 -1.2486 0.105910 19 to 23 141974 0.2192 0.586761 18 to 22 141825 -0.2859 0.387491 17 to 21 141566 -1.1638 0.122246 16 to 20 141779 -0.4418 0.329318 15 to 19 141698 -0.7164 0.236881 14 to 18 141933 0.0802 0.531976 13 to 17 141660 -0.8452 0.199003 12 to 16 142039 0.4396 0.669872 11 to 15 141928 0.0633 0.525232 10 to 14 142402 1.6701 0.952547 9 to 13 142243 1.1311 0.870990 8 to 12 141619 -0.9842 0.162516 7 to 11 142232 1.0938 0.862978 6 to 10 141581 -1.1130 0.132858 5 to 9 142304 1.3379 0.909530 4 to 8 141670 -0.8113 0.208600 3 to 7 141529 -1.2893 0.098655 2 to 6 141831 -0.2655 0.395302 1 to 5 141708 -0.6825 0.247470 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-01-09_15:31 Bits used No. missing words z-score p-value 31 to 32 142097 0.5536 0.710073 30 to 31 141924 0.0433 0.517259 29 to 30 141479 -1.2694 0.102147 28 to 29 141899 -0.0305 0.487845 27 to 28 141242 -1.9685 0.024504 26 to 27 141588 -0.9479 0.171596 25 to 26 142246 0.9931 0.839676 24 to 25 141926 0.0492 0.519610 23 to 24 141891 -0.0541 0.478439 22 to 23 142044 0.3973 0.654411 21 to 22 141651 -0.7620 0.223019 20 to 21 141933 0.0698 0.527833 19 to 20 141176 -2.1632 0.015262 18 to 19 141721 -0.5555 0.289261 17 to 18 141868 -0.1219 0.451482 16 to 17 142175 0.7837 0.783388 15 to 16 141838 -0.2104 0.416673 14 to 15 141665 -0.7207 0.235536 13 to 14 141208 -2.0688 0.019281 12 to 13 142097 0.5536 0.710073 11 to 12 142420 1.5064 0.934018 10 to 11 141867 -0.1249 0.450314 9 to 10 141729 -0.5319 0.297381 8 to 9 141077 -2.4553 0.007039 7 to 8 141855 -0.1603 0.436336 6 to 7 142077 0.4946 0.689559 5 to 6 141635 -0.8092 0.209191 4 to 5 141153 -2.2311 0.012839 3 to 4 142213 0.8958 0.814815 2 to 3 142092 0.5388 0.705005 1 to 2 141772 -0.4051 0.342701 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-01-09_15:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2502.44 0.034 0.513742 Test results for specific bytes for dh-ranFile-2016-01-09_15:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2390.94 -1.542 0.061493 2 to 9 2483.87 -0.228 0.409760 3 to 10 2365.30 -1.905 0.028395 4 to 11 2516.88 0.239 0.594317 5 to 12 2584.86 1.200 0.884949 6 to 13 2451.01 -0.693 0.244205 7 to 14 2700.04 2.829 0.997666 8 to 15 2413.07 -1.229 0.109463 9 to 16 2606.70 1.509 0.934344 10 to 17 2475.27 -0.350 0.363278 11 to 18 2485.92 -0.199 0.421062 12 to 19 2470.27 -0.420 0.337071 13 to 20 2570.61 0.999 0.840987 14 to 21 2508.41 0.119 0.547328 15 to 22 2529.56 0.418 0.662018 16 to 23 2448.64 -0.726 0.233818 17 to 24 2662.68 2.301 0.989294 18 to 25 2420.82 -1.120 0.131414 19 to 26 2488.89 -0.157 0.437560 20 to 27 2538.29 0.542 0.705936 21 to 28 2439.38 -0.857 0.195647 22 to 29 2516.77 0.237 0.593733 23 to 30 2507.90 0.112 0.544488 24 to 31 2532.64 0.462 0.677801 25 to 32 2419.39 -1.140 0.127141 CDPARK for dh-ranFile-2016-01-09_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 3468 -2.5114 0.006012 3507 -0.7306 0.232514 3527 0.1826 0.572463 3573 2.2831 0.988788 3542 0.8676 0.807188 3546 1.0502 0.853193 3523 0.0000 0.500000 3522 -0.0457 0.481790 3534 0.5023 0.692266 3541 0.8219 0.794438 Square side=100, avg. no. parked=3528.30 sample std.=26.18 p-value of the KSTEST for those 10 p-values: 0.404009 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-01-09_15:31 0.6768,0.0406,0.5963,0.8557,0.4863,0.4233,0.4716,0.5715,0.0354,0.4623, The KS test for those 10 p-values: 0.446758 The 3DSPHERES test for dh-ranFile-2016-01-09_15:31 sample no r^3 equiv. uni. 1 6.599 0.197460 2 6.610 0.197751 3 65.444 0.887125 4 14.468 0.382612 5 73.196 0.912828 6 63.455 0.879386 7 0.398 0.013188 8 48.931 0.804271 9 17.486 0.441710 10 5.187 0.158775 11 49.110 0.805435 12 1.143 0.037373 13 8.180 0.238645 14 30.169 0.634183 15 28.053 0.607459 16 7.954 0.232900 17 13.129 0.354436 18 13.000 0.351654 19 0.407 0.013479 20 18.425 0.458899 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.357485 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-01-09_15:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -1.2 -0.1 -0.7 -0.3 -0.4 -0.7 -0.2 1.0 -0.7 0.5 0.3 -0.5 0.2 1.5 -1.4 0.3 -1.5 0.2 -0.3 0.0 0.5 -0.1 -0.3 1.9 0.9 -1.2 -0.4 1.5 1.8 -1.1 -0.7 -0.3 -1.4 0.5 -0.1 -1.2 -0.7 -0.8 -0.1 0.9 3.0 -0.1 Chi-square with 42 degrees of freedom:40.187407 z-score=-0.197770, p-value=0.449231 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-01-09_15:31 Test no p-value 1 0.000062 2 0.087236 3 0.618634 4 0.378976 5 0.864714 6 0.310948 7 0.838673 8 0.479773 9 0.540341 10 0.806321 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.467658 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-01-09_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 66426 0.87 66583 0.11 3 25000.00 25212 1.80 25168 1.13 4 6666.67 6772 1.66 6589 0.90 5 1388.89 1353 0.93 1385 0.01 6 238.10 201 5.78 241 0.04 7 34.72 30 0.64 33 0.09 8 4.96 5 0.00 0 4.96 p=0.93049 p=0.69994 Number of rngs required: 688183, p-value: 0.400 RESULTS OF CRAPS TEST for dh-ranFile-2016-01-09_15:31 No. of wins: Observed Expected 98538 98585.9 z-score=-0.214, pvalue=0.41525 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66749 66666.7 0.102 0.102 2 37668 37654.3 0.005 0.107 3 26789 26954.7 1.019 1.126 4 19371 19313.5 0.171 1.297 5 13840 13851.4 0.009 1.306 6 9818 9943.5 1.585 2.892 7 7130 7145.0 0.032 2.923 8 5153 5139.1 0.038 2.961 9 3684 3699.9 0.068 3.029 10 2709 2666.3 0.684 3.713 11 1953 1923.3 0.458 4.171 12 1441 1388.7 1.967 6.137 13 981 1003.7 0.514 6.651 14 723 726.1 0.014 6.665 15 525 525.8 0.001 6.666 16 375 381.2 0.099 6.765 17 282 276.5 0.108 6.873 18 231 200.8 4.532 11.406 19 166 146.0 2.744 14.150 20 118 106.2 1.308 15.457 21 294 287.1 0.165 15.623 Chisq= 15.62 for 20 degrees of freedom, p= 0.26025 SUMMARY of craptest p-value for no. of wins: 0.415253 p-value for throws/game: 0.260253 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-01-09_15:31 No. of wins: Observed Expected 98646 98585.9 z-score= 0.269, pvalue=0.60603 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66615 66666.7 0.040 0.040 2 37877 37654.3 1.317 1.357 3 26829 26954.7 0.586 1.943 4 19370 19313.5 0.166 2.109 5 13922 13851.4 0.360 2.469 6 9956 9943.5 0.016 2.484 7 7195 7145.0 0.350 2.834 8 5110 5139.1 0.164 2.998 9 3665 3699.9 0.329 3.327 10 2637 2666.3 0.322 3.649 11 1922 1923.3 0.001 3.650 12 1364 1388.7 0.441 4.090 13 997 1003.7 0.045 4.135 14 678 726.1 3.192 7.327 15 498 525.8 1.474 8.800 16 375 381.2 0.099 8.900 17 268 276.5 0.264 9.163 18 229 200.8 3.951 13.115 19 149 146.0 0.062 13.177 20 92 106.2 1.902 15.079 21 252 287.1 4.294 19.374 Chisq= 19.37 for 20 degrees of freedom, p= 0.50234 SUMMARY of craptest p-value for no. of wins: 0.606030 p-value for throws/game: 0.502341 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0001,0.0003,0.0007,0.0033,0.0044,0.0060,0.0070,0.0093,0.0128,0.0132, 0.0135,0.0153,0.0193,0.0199,0.0245,0.0282,0.0284,0.0354,0.0374,0.0406, 0.0458,0.0465,0.0615,0.0671,0.0783,0.0845,0.0872,0.0911,0.0987,0.1021, 0.1041,0.1059,0.1089,0.1095,0.1222,0.1271,0.1279,0.1281,0.1314,0.1329, 0.1332,0.1349,0.1588,0.1625,0.1625,0.1649,0.1650,0.1686,0.1716,0.1736, 0.1738,0.1784,0.1880,0.1918,0.1934,0.1956,0.1975,0.1978,0.1990,0.2000, 0.2042,0.2086,0.2092,0.2115,0.2115,0.2230,0.2231,0.2268,0.2325,0.2329, 0.2338,0.2355,0.2369,0.2379,0.2386,0.2405,0.2442,0.2475,0.2536,0.2603, 0.2818,0.2893,0.2974,0.3021,0.3064,0.3109,0.3194,0.3293,0.3366,0.3371, 0.3389,0.3427,0.3517,0.3544,0.3575,0.3633,0.3742,0.3790,0.3826,0.3875, 0.3909,0.3953,0.4001,0.4010,0.4040,0.4075,0.4098,0.4102,0.4139,0.4153, 0.4167,0.4211,0.4219,0.4233,0.4260,0.4269,0.4302,0.4363,0.4376,0.4403, 0.4406,0.4417,0.4468,0.4492,0.4503,0.4515,0.4541,0.4556,0.4589,0.4606, 0.4623,0.4625,0.4653,0.4677,0.4716,0.4718,0.4727,0.4755,0.4784,0.4798, 0.4818,0.4863,0.4878,0.5000,0.5023,0.5119,0.5137,0.5173,0.5176,0.5196, 0.5229,0.5252,0.5278,0.5281,0.5281,0.5302,0.5320,0.5403,0.5445,0.5473, 0.5573,0.5588,0.5711,0.5715,0.5715,0.5725,0.5738,0.5868,0.5917,0.5937, 0.5943,0.5955,0.5963,0.5992,0.6051,0.6060,0.6075,0.6119,0.6186,0.6202, 0.6247,0.6335,0.6342,0.6356,0.6424,0.6440,0.6441,0.6544,0.6575,0.6620, 0.6649,0.6699,0.6762,0.6768,0.6778,0.6830,0.6896,0.6923,0.6999,0.7016, 0.7050,0.7055,0.7059,0.7101,0.7101,0.7225,0.7254,0.7521,0.7539,0.7566, 0.7626,0.7829,0.7834,0.7944,0.7954,0.8043,0.8054,0.8063,0.8072,0.8096, 0.8143,0.8148,0.8163,0.8191,0.8194,0.8206,0.8254,0.8355,0.8387,0.8397, 0.8410,0.8417,0.8428,0.8469,0.8532,0.8557,0.8630,0.8647,0.8671,0.8710, 0.8741,0.8794,0.8849,0.8871,0.8873,0.9061,0.9095,0.9128,0.9239,0.9305, 0.9316,0.9340,0.9343,0.9367,0.9444,0.9458,0.9516,0.9525,0.9577,0.9612, 0.9666,0.9684,0.9686,0.9742,0.9825,0.9888,0.9893,0.9956,0.9977, Overall p-value after applying KStest on 269 p-values = 0.216944 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.