RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-12-21_19:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 16.00 15.7326 0.457133 2 to 25 15.87 8.7788 0.053054 3 to 26 15.65 15.5151 0.441571 4 to 27 15.58 9.0254 0.060538 5 to 28 15.38 29.7762 0.971995 6 to 29 15.67 14.8273 0.392084 7 to 30 15.56 24.2753 0.887855 8 to 31 15.96 15.4314 0.435561 9 to 32 15.97 16.9478 0.542093 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.665634 Tough bday spacings test for dh-ranFile-2015-12-21_19:31: 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 9 40 73 95 95 72 51 37 13 8 7 (O-E)^2/E 0.0 0.3 0.0 0.1 0.1 0.5 0.0 1.8 0.2 0.3 2.1 Birthday Spacings: Sum(O-E)^2/E= 5.369, p= 0.135 RESULTS OF GCD FOR dh-ranFile-2015-12-21_19:31 Euclid's algorithm: p-value, steps to gcd: 0.360657 p-value, dist. of gcd's: 0.949451 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-12-21_19:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.240 0.367 0.119 0.419 0.997 0.773 0.955 0.131 Bits 8 to 15---> 0.647 0.520 0.265 0.907 0.091 0.487 0.170 0.135 Bits 16 to 23---> 0.164 0.459 0.100 0.853 0.897 0.501 0.873 0.920 Bits 24 to 31---> 0.922 0.863 0.985 0.217 0.210 0.490 0.188 0.022 KS test for the above 32 p values: 0.731 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-12-21_19:31, p-values for 5 runs: 0.8272, 0.3433, 0.9664, 0.3245, 0.4710 Rank test for binary matrices (31x31) for dh-ranFile-2015-12-21_19:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 214 211.4 0.032 0.032 r= 29 5124 5134.0 0.020 0.051 r= 30 23113 23103.0 0.004 0.055 r= 31 11549 11551.5 0.001 0.056 chi-square = 0.056 with df = 3; p-value = 0.003 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-12-21_19:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 232 211.4 2.004 2.004 r= 30 5258 5134.0 2.994 4.998 r= 31 23068 23103.0 0.053 5.051 r= 32 11442 11551.5 1.038 6.090 chi-square = 6.090 with df = 3; p-value = 0.893 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-12-21_19:31 b-rank test for bits 1 to 8, p=0.77680 b-rank test for bits 2 to 9, p=0.81134 b-rank test for bits 3 to 10, p=0.78704 b-rank test for bits 4 to 11, p=0.70879 b-rank test for bits 5 to 12, p=0.70296 b-rank test for bits 6 to 13, p=0.14350 b-rank test for bits 7 to 14, p=0.34794 b-rank test for bits 8 to 15, p=0.04379 b-rank test for bits 9 to 16, p=0.76043 b-rank test for bits 10 to 17, p=0.30750 b-rank test for bits 11 to 18, p=0.54754 b-rank test for bits 12 to 19, p=0.03727 b-rank test for bits 13 to 20, p=0.35961 b-rank test for bits 14 to 21, p=0.91767 b-rank test for bits 15 to 22, p=0.55142 b-rank test for bits 16 to 23, p=0.82958 b-rank test for bits 17 to 24, p=0.61420 b-rank test for bits 18 to 25, p=0.75622 b-rank test for bits 19 to 26, p=0.69627 b-rank test for bits 20 to 27, p=0.46983 b-rank test for bits 21 to 28, p=0.50944 b-rank test for bits 22 to 29, p=0.39394 b-rank test for bits 23 to 30, p=0.01048 b-rank test for bits 24 to 31, p=0.03912 b-rank test for bits 25 to 32, p=0.96739 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 = 0.551729 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-12-21_19:31 (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 142383 1.11 0.865789 2 142217 0.72 0.763885 3 141611 -0.70 0.242891 4 141660 -0.58 0.280099 5 141894 -0.04 0.485714 6 141997 0.20 0.581150 7 142701 1.85 0.967821 8 141495 -0.97 0.166507 9 142091 0.42 0.664386 10 141373 -1.25 0.105083 11 142111 0.47 0.681248 12 141574 -0.78 0.216672 13 141008 -2.11 0.017606 14 142087 0.42 0.660972 15 141610 -0.70 0.242161 16 142521 1.43 0.923517 17 142420 1.19 0.883596 18 141114 -1.86 0.031567 19 141447 -1.08 0.140024 20 141953 0.10 0.540635 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-12-21_19:31 Bits used No. missing words z-score p-value 23 to 32 141718 -0.6598 0.254704 22 to 31 141647 -0.9046 0.182842 21 to 30 142418 1.7540 0.960288 20 to 29 142316 1.4023 0.919589 19 to 28 142165 0.8816 0.811009 18 to 27 142278 1.2713 0.898185 17 to 26 141851 -0.2011 0.420295 16 to 25 141634 -0.9494 0.171205 15 to 24 141989 0.2747 0.608236 14 to 23 141660 -0.8598 0.194961 13 to 22 141753 -0.5391 0.294920 12 to 21 141769 -0.4839 0.314230 11 to 20 142230 1.1058 0.865585 10 to 19 141660 -0.8598 0.194961 9 to 18 142106 0.6782 0.751169 8 to 17 141896 -0.0460 0.481669 7 to 16 142027 0.4058 0.657540 6 to 15 142605 2.3989 0.991777 5 to 14 141840 -0.2391 0.405526 4 to 13 142202 1.0092 0.843562 3 to 12 141667 -0.8356 0.201684 2 to 11 141561 -1.2011 0.114849 1 to 10 141451 -1.5804 0.057002 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-12-21_19:31 Bits used No. missing words z-score p-value 28 to 32 141737 -0.5842 0.279553 27 to 31 141718 -0.6486 0.258306 26 to 30 141960 0.1718 0.568188 25 to 29 142003 0.3175 0.624578 24 to 28 142422 1.7379 0.958883 23 to 27 141576 -1.1299 0.129252 22 to 26 142072 0.5514 0.709328 21 to 25 142199 0.9819 0.836933 20 to 24 142243 1.1311 0.870990 19 to 23 141643 -0.9028 0.183312 18 to 22 141942 0.1107 0.544091 17 to 21 142083 0.5887 0.721973 16 to 20 141926 0.0565 0.522532 15 to 19 141648 -0.8859 0.187845 14 to 18 141856 -0.1808 0.428270 13 to 17 141958 0.1650 0.565521 12 to 16 141917 0.0260 0.510371 11 to 15 141255 -2.2181 0.013275 10 to 14 141728 -0.6147 0.269384 9 to 13 141232 -2.2960 0.010837 8 to 12 141889 -0.0689 0.472529 7 to 11 141631 -0.9435 0.172715 6 to 10 141694 -0.7299 0.232716 5 to 9 142373 1.5718 0.941997 4 to 8 142137 0.7718 0.779873 3 to 7 142423 1.7413 0.959181 2 to 6 142415 1.7141 0.956748 1 to 5 142564 2.2192 0.986764 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-12-21_19:31 Bits used No. missing words z-score p-value 31 to 32 142165 0.7542 0.774632 30 to 31 142256 1.0226 0.846758 29 to 30 142300 1.1524 0.875426 28 to 29 141870 -0.1160 0.453819 27 to 28 141785 -0.3668 0.356901 26 to 27 141955 0.1347 0.553583 25 to 26 141179 -2.1544 0.015606 24 to 25 141769 -0.4140 0.339454 23 to 24 142028 0.3501 0.636853 22 to 23 141061 -2.5024 0.006167 21 to 22 142223 0.9253 0.822590 20 to 21 141986 0.2262 0.589464 19 to 20 142050 0.4150 0.660913 18 to 19 141909 -0.0010 0.499612 17 to 18 141529 -1.1219 0.130949 16 to 17 141807 -0.3019 0.381380 15 to 16 141774 -0.3992 0.344872 14 to 15 142026 0.3442 0.634637 13 to 14 142305 1.1672 0.878429 12 to 13 141613 -0.8741 0.191024 11 to 12 141344 -1.6676 0.047694 10 to 11 141934 0.0728 0.529007 9 to 10 141725 -0.5437 0.293308 8 to 9 141488 -1.2429 0.106959 7 to 8 142463 1.6332 0.948791 6 to 7 141598 -0.9184 0.179211 5 to 6 141768 -0.4169 0.338375 4 to 5 141340 -1.6794 0.046533 3 to 4 141936 0.0787 0.531354 2 to 3 141441 -1.3815 0.083562 1 to 2 142303 1.1613 0.877234 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-12-21_19:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2436.92 -0.892 0.186156 Test results for specific bytes for dh-ranFile-2015-12-21_19:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2486.72 -0.188 0.425541 2 to 9 2558.60 0.829 0.796372 3 to 10 2498.30 -0.024 0.490384 4 to 11 2603.60 1.465 0.928551 5 to 12 2613.15 1.600 0.945220 6 to 13 2517.62 0.249 0.598411 7 to 14 2520.60 0.291 0.614607 8 to 15 2528.02 0.396 0.654034 9 to 16 2433.13 -0.946 0.172146 10 to 17 2596.18 1.360 0.913116 11 to 18 2447.98 -0.736 0.230957 12 to 19 2475.12 -0.352 0.362486 13 to 20 2545.07 0.637 0.738042 14 to 21 2434.40 -0.928 0.176762 15 to 22 2529.20 0.413 0.660177 16 to 23 2360.13 -1.978 0.023963 17 to 24 2435.83 -0.907 0.182089 18 to 25 2583.21 1.177 0.880359 19 to 26 2499.07 -0.013 0.494755 20 to 27 2614.56 1.620 0.947399 21 to 28 2490.05 -0.141 0.444046 22 to 29 2539.84 0.563 0.713409 23 to 30 2553.07 0.750 0.773515 24 to 31 2533.10 0.468 0.680157 25 to 32 2469.42 -0.432 0.332720 CDPARK for dh-ranFile-2015-12-21_19:31: 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 3541 0.8219 0.794438 3528 0.2283 0.590298 3559 1.6438 0.949895 3536 0.5936 0.723613 3492 -1.4155 0.078457 3526 0.1370 0.554479 3490 -1.5068 0.065925 3571 2.1918 0.985802 3533 0.4566 0.676028 3554 1.4155 0.921543 Square side=100, avg. no. parked=3533.00 sample std.=24.98 p-value of the KSTEST for those 10 p-values: 0.137559 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-12-21_19:31 0.0354,0.1970,0.8439,0.1576,0.7922,0.9831,0.1558,0.2974,0.0373,0.0209, The KS test for those 10 p-values: 0.034808 The 3DSPHERES test for dh-ranFile-2015-12-21_19:31 sample no r^3 equiv. uni. 1 83.259 0.937669 2 14.752 0.388430 3 31.134 0.645766 4 7.314 0.216352 5 8.659 0.250703 6 21.317 0.508633 7 108.090 0.972758 8 2.984 0.094683 9 41.298 0.747562 10 2.508 0.080203 11 2.341 0.075079 12 40.669 0.742220 13 9.580 0.273369 14 10.734 0.300787 15 38.471 0.722624 16 70.492 0.904606 17 21.113 0.505287 18 6.400 0.192100 19 45.999 0.784175 20 27.498 0.600125 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.990549 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-12-21_19:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -1.2 -1.1 -0.1 1.0 -1.2 0.2 0.1 0.7 1.7 -1.3 -0.0 0.8 -1.1 -0.8 1.7 -0.2 0.6 0.0 -1.9 0.6 0.8 -0.0 -0.3 1.0 -0.8 0.6 -0.9 0.2 -1.1 -1.1 -0.8 -0.1 1.0 -1.2 0.4 0.5 1.1 -0.4 -0.7 0.1 -1.0 -0.1 Chi-square with 42 degrees of freedom:32.426267 z-score=-1.044580, p-value=0.144066 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-12-21_19:31 Test no p-value 1 0.494404 2 0.687445 3 0.174050 4 0.391966 5 0.103465 6 0.791629 7 0.085195 8 0.620438 9 0.305701 10 0.007112 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.233816 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-12-21_19:31: (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 66671 0.00 66589 0.09 3 25000.00 24953 0.09 24977 0.02 4 6666.67 6626 0.25 6659 0.01 5 1388.89 1464 4.06 1500 8.89 6 238.10 258 1.66 233 0.11 7 34.72 25 2.72 34 0.01 8 4.96 2 1.77 7 0.84 p=0.89669 p=0.87417 Number of rngs required: 688344, p-value: 0.473 RESULTS OF CRAPS TEST for dh-ranFile-2015-12-21_19:31 No. of wins: Observed Expected 98626 98585.9 z-score= 0.180, pvalue=0.57124 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67102 66666.7 2.843 2.843 2 37704 37654.3 0.066 2.908 3 26754 26954.7 1.495 4.403 4 19238 19313.5 0.295 4.698 5 13574 13851.4 5.556 10.254 6 9899 9943.5 0.200 10.454 7 7090 7145.0 0.424 10.878 8 5151 5139.1 0.028 10.905 9 3723 3699.9 0.145 11.050 10 2693 2666.3 0.267 11.317 11 1933 1923.3 0.049 11.366 12 1415 1388.7 0.497 11.862 13 1058 1003.7 2.936 14.798 14 759 726.1 1.487 16.285 15 559 525.8 2.092 18.377 16 361 381.2 1.065 19.442 17 269 276.5 0.206 19.648 18 184 200.8 1.410 21.058 19 140 146.0 0.245 21.304 20 107 106.2 0.006 21.309 21 287 287.1 0.000 21.309 Chisq= 21.31 for 20 degrees of freedom, p= 0.62087 SUMMARY of craptest p-value for no. of wins: 0.571242 p-value for throws/game: 0.620874 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-12-21_19:31 No. of wins: Observed Expected 98276 98585.9 z-score=-1.386, pvalue=0.08289 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66605 66666.7 0.057 0.057 2 37941 37654.3 2.183 2.240 3 26672 26954.7 2.966 5.205 4 19271 19313.5 0.093 5.299 5 13800 13851.4 0.191 5.490 6 10004 9943.5 0.368 5.857 7 7199 7145.0 0.408 6.265 8 5172 5139.1 0.211 6.476 9 3722 3699.9 0.132 6.608 10 2716 2666.3 0.927 7.535 11 1876 1923.3 1.165 8.699 12 1383 1388.7 0.024 8.723 13 995 1003.7 0.076 8.799 14 690 726.1 1.799 10.598 15 551 525.8 1.204 11.802 16 408 381.2 1.891 13.693 17 274 276.5 0.023 13.716 18 180 200.8 2.160 15.877 19 140 146.0 0.245 16.122 20 101 106.2 0.256 16.378 21 300 287.1 0.578 16.957 Chisq= 16.96 for 20 degrees of freedom, p= 0.34421 SUMMARY of craptest p-value for no. of wins: 0.082894 p-value for throws/game: 0.344214 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0035,0.0062,0.0071,0.0105,0.0108,0.0133,0.0156,0.0176,0.0209,0.0216, 0.0240,0.0316,0.0348,0.0354,0.0373,0.0373,0.0391,0.0438,0.0465,0.0477, 0.0531,0.0570,0.0605,0.0659,0.0751,0.0785,0.0802,0.0829,0.0836,0.0852, 0.0914,0.0947,0.1003,0.1035,0.1051,0.1070,0.1148,0.1188,0.1293,0.1308, 0.1309,0.1348,0.1354,0.1376,0.1400,0.1435,0.1441,0.1558,0.1576,0.1644, 0.1665,0.1697,0.1712,0.1721,0.1727,0.1741,0.1768,0.1792,0.1821,0.1828, 0.1833,0.1862,0.1878,0.1882,0.1910,0.1921,0.1950,0.1950,0.1970,0.2017, 0.2101,0.2164,0.2167,0.2175,0.2310,0.2327,0.2338,0.2396,0.2422,0.2429, 0.2507,0.2547,0.2583,0.2654,0.2694,0.2734,0.2796,0.2801,0.2933,0.2949, 0.2974,0.3008,0.3057,0.3075,0.3142,0.3245,0.3327,0.3384,0.3395,0.3433, 0.3442,0.3449,0.3479,0.3569,0.3596,0.3607,0.3625,0.3669,0.3814,0.3884, 0.3920,0.3921,0.3939,0.4055,0.4194,0.4203,0.4255,0.4283,0.4356,0.4416, 0.4440,0.4538,0.4571,0.4595,0.4698,0.4710,0.4725,0.4729,0.4817,0.4857, 0.4875,0.4896,0.4904,0.4944,0.4948,0.4996,0.5006,0.5053,0.5086,0.5094, 0.5104,0.5200,0.5225,0.5290,0.5314,0.5406,0.5421,0.5441,0.5475,0.5514, 0.5517,0.5536,0.5545,0.5655,0.5682,0.5712,0.5812,0.5895,0.5903,0.5984, 0.6001,0.6082,0.6142,0.6146,0.6204,0.6209,0.6246,0.6346,0.6369,0.6458, 0.6466,0.6540,0.6575,0.6602,0.6609,0.6610,0.6644,0.6656,0.6760,0.6802, 0.6812,0.6874,0.6963,0.7030,0.7088,0.7093,0.7134,0.7220,0.7226,0.7236, 0.7307,0.7380,0.7422,0.7476,0.7512,0.7562,0.7604,0.7639,0.7730,0.7735, 0.7746,0.7768,0.7799,0.7842,0.7870,0.7916,0.7922,0.7944,0.7964,0.8110, 0.8113,0.8226,0.8272,0.8296,0.8369,0.8436,0.8439,0.8468,0.8530,0.8631, 0.8656,0.8658,0.8710,0.8734,0.8742,0.8754,0.8772,0.8784,0.8804,0.8836, 0.8879,0.8927,0.8967,0.8969,0.8982,0.9046,0.9072,0.9131,0.9177,0.9196, 0.9198,0.9215,0.9218,0.9235,0.9286,0.9377,0.9420,0.9452,0.9474,0.9488, 0.9495,0.9499,0.9554,0.9567,0.9589,0.9592,0.9603,0.9664,0.9674,0.9678, 0.9720,0.9728,0.9831,0.9847,0.9858,0.9868,0.9905,0.9918,0.9968, Overall p-value after applying KStest on 269 p-values = 0.210569 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.