RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-04-02_18:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.92 17.7415 0.594676 2 to 25 15.57 33.7403 0.990932 3 to 26 15.41 23.4363 0.864421 4 to 27 15.67 14.5090 0.369196 5 to 28 15.91 27.1230 0.943711 6 to 29 15.75 15.7641 0.459388 7 to 30 15.56 17.0555 0.549387 8 to 31 15.32 23.1912 0.856872 9 to 32 15.91 18.1059 0.617808 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.061852 Tough bday spacings test for dh-ranFile-2016-04-02_18:31: 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 34 76 114 108 77 43 22 10 4 4 (O-E)^2/E 0.1 0.2 0.1 2.7 1.1 0.0 1.6 2.0 1.6 1.0 0.0 Birthday Spacings: Sum(O-E)^2/E= 10.525, p= 0.604 RESULTS OF GCD FOR dh-ranFile-2016-04-02_18:31 Euclid's algorithm: p-value, steps to gcd: 0.454204 p-value, dist. of gcd's: 0.407349 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-04-02_18:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.371 0.932 0.853 0.282 0.809 0.592 0.849 0.563 Bits 8 to 15---> 0.136 0.055 0.446 0.186 0.839 0.764 0.486 0.481 Bits 16 to 23---> 0.961 0.080 0.153 0.691 0.994 0.121 0.659 0.556 Bits 24 to 31---> 0.009 0.159 0.070 0.702 0.065 0.657 0.520 0.105 KS test for the above 32 p values: 0.407 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-04-02_18:31, p-values for 5 runs: 0.7219, 0.8901, 0.3099, 0.0072, 0.6783 Rank test for binary matrices (31x31) for dh-ranFile-2016-04-02_18:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 204 211.4 0.260 0.260 r= 29 5126 5134.0 0.012 0.273 r= 30 23066 23103.0 0.059 0.332 r= 31 11604 11551.5 0.238 0.571 chi-square = 0.571 with df = 3; p-value = 0.097 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-04-02_18:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 202 211.4 0.420 0.420 r= 30 5112 5134.0 0.094 0.514 r= 31 23185 23103.0 0.291 0.805 r= 32 11501 11551.5 0.221 1.026 chi-square = 1.026 with df = 3; p-value = 0.205 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-04-02_18:31 b-rank test for bits 1 to 8, p=0.51745 b-rank test for bits 2 to 9, p=0.08330 b-rank test for bits 3 to 10, p=0.52286 b-rank test for bits 4 to 11, p=0.88678 b-rank test for bits 5 to 12, p=0.66618 b-rank test for bits 6 to 13, p=0.51005 b-rank test for bits 7 to 14, p=0.32678 b-rank test for bits 8 to 15, p=0.77942 b-rank test for bits 9 to 16, p=0.37370 b-rank test for bits 10 to 17, p=0.78727 b-rank test for bits 11 to 18, p=0.05599 b-rank test for bits 12 to 19, p=0.59320 b-rank test for bits 13 to 20, p=0.12488 b-rank test for bits 14 to 21, p=0.14623 b-rank test for bits 15 to 22, p=0.83603 b-rank test for bits 16 to 23, p=0.67470 b-rank test for bits 17 to 24, p=0.76824 b-rank test for bits 18 to 25, p=0.18300 b-rank test for bits 19 to 26, p=0.17059 b-rank test for bits 20 to 27, p=0.69657 b-rank test for bits 21 to 28, p=0.11215 b-rank test for bits 22 to 29, p=0.40032 b-rank test for bits 23 to 30, p=0.15057 b-rank test for bits 24 to 31, p=0.40694 b-rank test for bits 25 to 32, p=0.51477 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 = 0.497280 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-04-02_18:31 (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 142251 0.80 0.787650 2 141650 -0.61 0.272287 3 141811 -0.23 0.409146 4 142186 0.65 0.740998 5 141487 -0.99 0.161882 6 141942 0.08 0.530422 7 142091 0.42 0.664386 8 141994 0.20 0.578410 9 142294 0.90 0.815610 10 142150 0.56 0.713049 11 142131 0.52 0.697743 12 141654 -0.60 0.275399 13 142045 0.32 0.624373 14 141650 -0.61 0.272287 15 142045 0.32 0.624373 16 142652 1.74 0.958648 17 141722 -0.44 0.330807 18 142061 0.35 0.638469 19 141164 -1.74 0.040805 20 141877 -0.08 0.469894 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-04-02_18:31 Bits used No. missing words z-score p-value 23 to 32 142064 0.5333 0.703103 22 to 31 142001 0.3161 0.624038 21 to 30 142342 1.4920 0.932146 20 to 29 141968 0.2023 0.580163 19 to 28 141636 -0.9425 0.172964 18 to 27 141934 0.0851 0.533897 17 to 26 142137 0.7851 0.783793 16 to 25 142050 0.4851 0.686186 15 to 24 141523 -1.3322 0.091402 14 to 23 141976 0.2299 0.590914 13 to 22 141594 -1.0873 0.138442 12 to 21 141905 -0.0149 0.494044 11 to 20 141894 -0.0529 0.478921 10 to 19 141879 -0.1046 0.458352 9 to 18 141485 -1.4632 0.071705 8 to 17 141949 0.1368 0.554403 7 to 16 142062 0.5264 0.700712 6 to 15 142116 0.7127 0.761970 5 to 14 142327 1.4402 0.925100 4 to 13 142239 1.1368 0.872188 3 to 12 141213 -2.4011 0.008172 2 to 11 141989 0.2747 0.608236 1 to 10 141711 -0.6839 0.247020 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-04-02_18:31 Bits used No. missing words z-score p-value 28 to 32 141891 -0.0621 0.475227 27 to 31 142006 0.3277 0.628429 26 to 30 142433 1.7752 0.962064 25 to 29 141862 -0.1604 0.436267 24 to 28 141830 -0.2689 0.393998 23 to 27 141885 -0.0825 0.467135 22 to 26 142458 1.8599 0.968550 21 to 25 142520 2.0701 0.980777 20 to 24 142109 0.6768 0.750749 19 to 23 141538 -1.2587 0.104061 18 to 22 142456 1.8531 0.968067 17 to 21 141696 -0.7232 0.234793 16 to 20 142318 1.3853 0.917023 15 to 19 140818 -3.6994 0.000108 14 to 18 141878 -0.1062 0.457711 13 to 17 142122 0.7209 0.764519 12 to 16 141706 -0.6893 0.245332 11 to 15 141724 -0.6282 0.264924 10 to 14 141893 -0.0554 0.477928 9 to 13 141870 -0.1333 0.446969 8 to 12 141698 -0.7164 0.236881 7 to 11 142178 0.9107 0.818785 6 to 10 141738 -0.5808 0.280695 5 to 9 142126 0.7345 0.768670 4 to 8 142055 0.4938 0.689275 3 to 7 141808 -0.3435 0.365614 2 to 6 142503 2.0124 0.977913 1 to 5 142093 0.6226 0.733230 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-04-02_18:31 Bits used No. missing words z-score p-value 31 to 32 142419 1.5035 0.933639 30 to 31 142304 1.1642 0.877832 29 to 30 141858 -0.1514 0.439824 28 to 29 141536 -1.1013 0.135390 27 to 28 142015 0.3117 0.622370 26 to 27 141793 -0.3432 0.365740 25 to 26 141222 -2.0275 0.021305 24 to 25 141436 -1.3963 0.081319 23 to 24 142345 1.2852 0.900632 22 to 23 142078 0.4976 0.690600 21 to 22 142123 0.6303 0.735749 20 to 21 142525 1.8161 0.965325 19 to 20 142010 0.2970 0.616752 18 to 19 141238 -1.9803 0.023834 17 to 18 141559 -1.0334 0.150703 16 to 17 141672 -0.7001 0.241936 15 to 16 142353 1.3088 0.904692 14 to 15 142012 0.3029 0.619002 13 to 14 141751 -0.4671 0.320232 12 to 13 141611 -0.8800 0.189422 11 to 12 141982 0.2144 0.584869 10 to 11 142082 0.5094 0.694747 9 to 10 142414 1.4887 0.931717 8 to 9 141476 -1.2783 0.100579 7 to 8 142270 1.0639 0.856318 6 to 7 142126 0.6391 0.738636 5 to 6 142085 0.5182 0.697841 4 to 5 142302 1.1583 0.876633 3 to 4 141755 -0.4553 0.324464 2 to 3 141828 -0.2399 0.405199 1 to 2 142118 0.6155 0.730903 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-04-02_18:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2459.26 -0.576 0.282259 Test results for specific bytes for dh-ranFile-2016-04-02_18:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2535.92 0.508 0.694277 2 to 9 2474.93 -0.354 0.361491 3 to 10 2544.64 0.631 0.736092 4 to 11 2378.82 -1.714 0.043285 5 to 12 2509.04 0.128 0.550846 6 to 13 2538.71 0.547 0.707980 7 to 14 2477.05 -0.325 0.372767 8 to 15 2528.75 0.407 0.657837 9 to 16 2600.43 1.420 0.922236 10 to 17 2642.45 2.015 0.978026 11 to 18 2439.26 -0.859 0.195165 12 to 19 2589.12 1.260 0.896217 13 to 20 2542.11 0.595 0.724237 14 to 21 2449.74 -0.711 0.238628 15 to 22 2430.73 -0.980 0.163622 16 to 23 2398.87 -1.430 0.076329 17 to 24 2553.95 0.763 0.777265 18 to 25 2455.14 -0.634 0.262889 19 to 26 2389.33 -1.565 0.058785 20 to 27 2474.09 -0.366 0.357009 21 to 28 2420.71 -1.121 0.131068 22 to 29 2519.59 0.277 0.609149 23 to 30 2493.48 -0.092 0.463240 24 to 31 2451.67 -0.683 0.247146 25 to 32 2490.37 -0.136 0.445827 CDPARK for dh-ranFile-2016-04-02_18:31: 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 3500 -1.0502 0.146807 3512 -0.5023 0.307734 3534 0.5023 0.692266 3553 1.3699 0.914635 3514 -0.4110 0.340551 3494 -1.3242 0.092718 3519 -0.1826 0.427537 3556 1.5068 0.934075 3518 -0.2283 0.409702 3511 -0.5479 0.291865 Square side=100, avg. no. parked=3521.10 sample std.=19.57 p-value of the KSTEST for those 10 p-values: 0.730915 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-04-02_18:31 0.8583,0.6047,0.7771,0.6017,0.1062,0.6916,0.6788,0.1421,0.5307,0.8103, The KS test for those 10 p-values: 0.366222 The 3DSPHERES test for dh-ranFile-2016-04-02_18:31 sample no r^3 equiv. uni. 1 41.550 0.749680 2 70.171 0.903580 3 7.803 0.229026 4 32.652 0.663246 5 39.664 0.733431 6 16.189 0.417030 7 5.565 0.169304 8 23.135 0.537527 9 54.232 0.835972 10 22.900 0.533891 11 53.181 0.830125 12 19.271 0.473957 13 0.634 0.020919 14 2.614 0.083460 15 65.280 0.886505 16 44.905 0.776162 17 14.276 0.378652 18 12.230 0.334794 19 3.444 0.108441 20 15.077 0.395028 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.983305 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-04-02_18:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 -0.7 3.0 0.6 -1.5 0.6 -1.0 -0.6 -1.8 -0.3 0.6 0.6 1.7 -1.3 1.6 -1.4 -2.0 -0.1 0.3 -0.3 2.3 -0.7 -0.4 0.7 -0.4 1.5 0.6 -0.6 1.0 -0.6 -0.9 -0.2 -0.1 -0.4 -0.1 1.1 0.3 -1.0 0.1 1.0 -0.6 -1.0 -1.1 Chi-square with 42 degrees of freedom:49.770796 z-score=0.847863, p-value=0.808490 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-04-02_18:31 Test no p-value 1 0.125694 2 0.950482 3 0.339323 4 0.052971 5 0.308275 6 0.662630 7 0.665898 8 0.208442 9 0.094074 10 0.039599 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.104400 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-04-02_18:31: (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 66562 0.16 67006 1.73 3 25000.00 25116 0.54 24755 2.40 4 6666.67 6703 0.20 6622 0.30 5 1388.89 1347 1.26 1365 0.41 6 238.10 235 0.04 226 0.61 7 34.72 33 0.09 19 7.12 8 4.96 3 0.77 6 0.22 p=0.19922 p=0.95348 Number of rngs required: 688611, p-value: 0.595 RESULTS OF CRAPS TEST for dh-ranFile-2016-04-02_18:31 No. of wins: Observed Expected 98496 98585.9 z-score=-0.402, pvalue=0.34388 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66555 66666.7 0.187 0.187 2 37637 37654.3 0.008 0.195 3 26825 26954.7 0.624 0.819 4 19530 19313.5 2.428 3.247 5 13845 13851.4 0.003 3.250 6 9883 9943.5 0.369 3.619 7 7229 7145.0 0.987 4.606 8 5075 5139.1 0.799 5.405 9 3696 3699.9 0.004 5.409 10 2778 2666.3 4.680 10.088 11 1962 1923.3 0.778 10.866 12 1379 1388.7 0.068 10.934 13 996 1003.7 0.059 10.993 14 706 726.1 0.559 11.552 15 551 525.8 1.204 12.756 16 387 381.2 0.090 12.846 17 280 276.5 0.043 12.889 18 197 200.8 0.073 12.962 19 137 146.0 0.553 13.515 20 102 106.2 0.167 13.683 21 250 287.1 4.798 18.480 Chisq= 18.48 for 20 degrees of freedom, p= 0.44419 SUMMARY of craptest p-value for no. of wins: 0.343879 p-value for throws/game: 0.444193 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-04-02_18:31 No. of wins: Observed Expected 98634 98585.9 z-score= 0.215, pvalue=0.58524 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66358 66666.7 1.429 1.429 2 37667 37654.3 0.004 1.433 3 26932 26954.7 0.019 1.453 4 19418 19313.5 0.566 2.018 5 13923 13851.4 0.370 2.388 6 9859 9943.5 0.719 3.107 7 7224 7145.0 0.873 3.980 8 5108 5139.1 0.188 4.168 9 3814 3699.9 3.521 7.689 10 2734 2666.3 1.719 9.408 11 1937 1923.3 0.097 9.505 12 1392 1388.7 0.008 9.513 13 998 1003.7 0.033 9.545 14 750 726.1 0.784 10.329 15 523 525.8 0.015 10.345 16 369 381.2 0.387 10.732 17 284 276.5 0.201 10.933 18 191 200.8 0.481 11.414 19 143 146.0 0.061 11.475 20 112 106.2 0.315 11.790 21 264 287.1 1.861 13.651 Chisq= 13.65 for 20 degrees of freedom, p= 0.15226 SUMMARY of craptest p-value for no. of wins: 0.585240 p-value for throws/game: 0.152265 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0001,0.0072,0.0082,0.0087,0.0209,0.0213,0.0238,0.0396,0.0408,0.0433, 0.0530,0.0546,0.0560,0.0588,0.0619,0.0651,0.0698,0.0717,0.0763,0.0805, 0.0813,0.0833,0.0835,0.0914,0.0927,0.0941,0.0969,0.1006,0.1041,0.1044, 0.1046,0.1062,0.1084,0.1121,0.1208,0.1249,0.1257,0.1311,0.1354,0.1360, 0.1384,0.1421,0.1462,0.1468,0.1506,0.1507,0.1523,0.1529,0.1586,0.1619, 0.1636,0.1693,0.1706,0.1730,0.1830,0.1858,0.1894,0.1952,0.1992,0.2049, 0.2084,0.2290,0.2348,0.2369,0.2386,0.2419,0.2453,0.2470,0.2471,0.2629, 0.2649,0.2723,0.2723,0.2754,0.2807,0.2817,0.2823,0.2919,0.3077,0.3083, 0.3099,0.3202,0.3245,0.3268,0.3308,0.3348,0.3393,0.3406,0.3439,0.3570, 0.3615,0.3656,0.3657,0.3662,0.3692,0.3714,0.3728,0.3737,0.3787,0.3940, 0.3950,0.4003,0.4052,0.4067,0.4069,0.4073,0.4091,0.4097,0.4170,0.4275, 0.4363,0.4398,0.4442,0.4455,0.4458,0.4470,0.4542,0.4577,0.4584,0.4594, 0.4632,0.4671,0.4699,0.4740,0.4752,0.4779,0.4789,0.4806,0.4860,0.4940, 0.4973,0.5100,0.5148,0.5174,0.5198,0.5229,0.5304,0.5307,0.5339,0.5339, 0.5375,0.5494,0.5508,0.5544,0.5556,0.5634,0.5784,0.5802,0.5849,0.5852, 0.5909,0.5920,0.5932,0.5946,0.5947,0.6017,0.6043,0.6047,0.6082,0.6091, 0.6168,0.6178,0.6190,0.6224,0.6240,0.6244,0.6244,0.6284,0.6385,0.6570, 0.6578,0.6586,0.6626,0.6632,0.6644,0.6659,0.6662,0.6747,0.6783,0.6788, 0.6862,0.6893,0.6906,0.6915,0.6916,0.6923,0.6943,0.6947,0.6966,0.6977, 0.6978,0.7007,0.7017,0.7031,0.7080,0.7130,0.7219,0.7242,0.7309,0.7309, 0.7332,0.7334,0.7357,0.7361,0.7386,0.7410,0.7497,0.7507,0.7620,0.7641, 0.7645,0.7682,0.7687,0.7762,0.7771,0.7773,0.7794,0.7838,0.7873,0.7877, 0.8085,0.8094,0.8103,0.8156,0.8188,0.8301,0.8360,0.8360,0.8393,0.8493, 0.8531,0.8563,0.8569,0.8583,0.8644,0.8722,0.8766,0.8778,0.8865,0.8868, 0.8901,0.8962,0.9006,0.9036,0.9047,0.9146,0.9170,0.9222,0.9251,0.9317, 0.9319,0.9321,0.9336,0.9341,0.9437,0.9505,0.9535,0.9586,0.9614,0.9621, 0.9653,0.9681,0.9686,0.9779,0.9780,0.9808,0.9833,0.9909,0.9939, Overall p-value after applying KStest on 269 p-values = 0.892599 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.