RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-06-07_20:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.97 15.7838 0.460790 2 to 25 15.89 17.3671 0.570223 3 to 26 15.44 26.3822 0.932227 4 to 27 15.75 15.7838 0.460789 5 to 28 16.03 21.1509 0.780388 6 to 29 15.65 15.5583 0.444667 7 to 30 15.52 23.5605 0.868124 8 to 31 16.12 18.6161 0.648995 9 to 32 15.92 14.2844 0.353122 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.282793 Tough bday spacings test for dh-ranFile-2016-06-07_20:31: 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 5 31 66 103 92 91 43 36 17 10 6 (O-E)^2/E 1.9 0.9 0.7 0.3 0.3 2.1 1.6 1.3 0.3 1.7 0.9 Birthday Spacings: Sum(O-E)^2/E= 12.052, p= 0.718 RESULTS OF GCD FOR dh-ranFile-2016-06-07_20:31 Euclid's algorithm: p-value, steps to gcd: 0.029932 p-value, dist. of gcd's: 0.799884 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-06-07_20:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.656 0.341 0.549 0.321 0.107 0.705 0.280 0.226 Bits 8 to 15---> 0.903 0.213 0.756 0.541 0.296 0.692 0.623 0.792 Bits 16 to 23---> 0.481 0.928 0.100 0.194 0.981 0.041 0.508 0.564 Bits 24 to 31---> 0.563 0.035 0.835 0.254 0.450 0.718 0.138 0.464 KS test for the above 32 p values: 0.063 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-06-07_20:31, p-values for 5 runs: 0.4777, 0.7278, 0.9665, 0.1113, 0.2299 Rank test for binary matrices (31x31) for dh-ranFile-2016-06-07_20:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 188 211.4 2.594 2.594 r= 29 5065 5134.0 0.928 3.522 r= 30 23391 23103.0 3.589 7.111 r= 31 11356 11551.5 3.309 10.420 chi-square = 10.420 with df = 3; p-value = 0.985 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-06-07_20:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 225 211.4 0.873 0.873 r= 30 5108 5134.0 0.132 1.004 r= 31 23045 23103.0 0.146 1.150 r= 32 11622 11551.5 0.430 1.580 chi-square = 1.580 with df = 3; p-value = 0.336 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-06-07_20:31 b-rank test for bits 1 to 8, p=0.82402 b-rank test for bits 2 to 9, p=0.29425 b-rank test for bits 3 to 10, p=0.53495 b-rank test for bits 4 to 11, p=0.73300 b-rank test for bits 5 to 12, p=0.25752 b-rank test for bits 6 to 13, p=0.93566 b-rank test for bits 7 to 14, p=0.70462 b-rank test for bits 8 to 15, p=0.18288 b-rank test for bits 9 to 16, p=0.88983 b-rank test for bits 10 to 17, p=0.89369 b-rank test for bits 11 to 18, p=0.53399 b-rank test for bits 12 to 19, p=0.22772 b-rank test for bits 13 to 20, p=0.87518 b-rank test for bits 14 to 21, p=0.87864 b-rank test for bits 15 to 22, p=0.86740 b-rank test for bits 16 to 23, p=0.19642 b-rank test for bits 17 to 24, p=0.56477 b-rank test for bits 18 to 25, p=0.84415 b-rank test for bits 19 to 26, p=0.03268 b-rank test for bits 20 to 27, p=0.24416 b-rank test for bits 21 to 28, p=0.64940 b-rank test for bits 22 to 29, p=0.34933 b-rank test for bits 23 to 30, p=0.45827 b-rank test for bits 24 to 31, p=0.35669 b-rank test for bits 25 to 32, p=0.39764 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 = 0.499390 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-06-07_20:31 (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 141866 -0.10 0.459681 2 141451 -1.07 0.142115 3 141564 -0.81 0.209878 4 141686 -0.52 0.300905 5 141989 0.19 0.573834 6 141837 -0.17 0.432900 7 141736 -0.40 0.342747 8 141760 -0.35 0.363582 9 142014 0.24 0.596600 10 141678 -0.54 0.294429 11 142090 0.42 0.663534 12 142254 0.81 0.789678 13 142052 0.33 0.630562 14 141144 -1.79 0.036876 15 142051 0.33 0.629680 16 141660 -0.58 0.280099 17 141012 -2.10 0.018016 18 141644 -0.62 0.267652 19 141448 -1.08 0.140545 20 141876 -0.08 0.468964 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-06-07_20:31 Bits used No. missing words z-score p-value 23 to 32 141394 -1.7770 0.037784 22 to 31 141741 -0.5804 0.280806 21 to 30 141904 -0.0184 0.492668 20 to 29 142267 1.2333 0.891276 19 to 28 142060 0.5196 0.698312 18 to 27 141818 -0.3149 0.376407 17 to 26 142003 0.3230 0.626652 16 to 25 142028 0.4092 0.658806 15 to 24 141547 -1.2494 0.105757 14 to 23 142031 0.4196 0.662594 13 to 22 141349 -1.9322 0.026669 12 to 21 142111 0.6954 0.756602 11 to 20 141660 -0.8598 0.194961 10 to 19 142016 0.3678 0.643499 9 to 18 141427 -1.6632 0.048136 8 to 17 142127 0.7506 0.773549 7 to 16 141605 -1.0494 0.146994 6 to 15 142025 0.3989 0.655003 5 to 14 141609 -1.0356 0.150190 4 to 13 141735 -0.6011 0.273874 3 to 12 141744 -0.5701 0.284304 2 to 11 142111 0.6954 0.756602 1 to 10 142091 0.6264 0.734490 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-06-07_20:31 Bits used No. missing words z-score p-value 28 to 32 141283 -2.1232 0.016871 27 to 31 141499 -1.3909 0.082120 26 to 30 142119 0.7107 0.761379 25 to 29 142614 2.3887 0.991546 24 to 28 142413 1.7074 0.956122 23 to 27 141734 -0.5943 0.276143 22 to 26 142387 1.6192 0.947300 21 to 25 141815 -0.3198 0.374574 20 to 24 141719 -0.6452 0.259403 19 to 23 142010 0.3413 0.633544 18 to 22 141752 -0.5333 0.296905 17 to 21 142175 0.9006 0.816093 16 to 20 141665 -0.8282 0.203768 15 to 19 141946 0.1243 0.549463 14 to 18 141850 -0.2011 0.420303 13 to 17 141792 -0.3977 0.345415 12 to 16 142156 0.8362 0.798470 11 to 15 142169 0.8802 0.810635 10 to 14 141844 -0.2215 0.412368 9 to 13 142200 0.9853 0.837767 8 to 12 141652 -0.8723 0.191521 7 to 11 141734 -0.5943 0.276143 6 to 10 141847 -0.2113 0.416331 5 to 9 142390 1.6294 0.948385 4 to 8 142085 0.5955 0.724243 3 to 7 142303 1.3345 0.908976 2 to 6 141432 -1.6181 0.052824 1 to 5 141669 -0.8147 0.207628 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-06-07_20:31 Bits used No. missing words z-score p-value 31 to 32 141445 -1.3697 0.085390 30 to 31 142323 1.2203 0.888818 29 to 30 142034 0.3678 0.643473 28 to 29 141900 -0.0275 0.489022 27 to 28 142281 1.0964 0.863542 26 to 27 141874 -0.1042 0.458498 25 to 26 141405 -1.4877 0.068415 24 to 25 142215 0.9017 0.816387 23 to 24 141440 -1.3845 0.083110 22 to 23 142407 1.4681 0.928955 21 to 22 141569 -1.0039 0.157708 20 to 21 142539 1.8574 0.968375 19 to 20 142115 0.6067 0.727974 18 to 19 141562 -1.0246 0.152783 17 to 18 142052 0.4209 0.663070 16 to 17 141779 -0.3845 0.350321 15 to 16 141656 -0.7473 0.227445 14 to 15 141322 -1.7325 0.041589 13 to 14 141824 -0.2517 0.400632 12 to 13 142458 1.6185 0.947222 11 to 12 141809 -0.2960 0.383631 10 to 11 141458 -1.3314 0.091536 9 to 10 142162 0.7453 0.771967 8 to 9 141482 -1.2606 0.103734 7 to 8 141518 -1.1544 0.124175 6 to 7 142069 0.4710 0.681181 5 to 6 141771 -0.4081 0.341617 4 to 5 141873 -0.1072 0.457328 3 to 4 142051 0.4179 0.661992 2 to 3 141670 -0.7060 0.240098 1 to 2 142560 1.9194 0.972532 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-06-07_20:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2432.68 -0.952 0.170530 Test results for specific bytes for dh-ranFile-2016-06-07_20:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2571.17 1.007 0.842925 2 to 9 2507.97 0.113 0.544879 3 to 10 2495.15 -0.069 0.472643 4 to 11 2483.25 -0.237 0.406389 5 to 12 2585.15 1.204 0.885756 6 to 13 2482.09 -0.253 0.400030 7 to 14 2423.72 -1.079 0.140359 8 to 15 2530.46 0.431 0.666679 9 to 16 2423.55 -1.081 0.139817 10 to 17 2544.56 0.630 0.735705 11 to 18 2428.91 -1.005 0.157349 12 to 19 2592.54 1.309 0.904680 13 to 20 2450.73 -0.697 0.242962 14 to 21 2509.11 0.129 0.551262 15 to 22 2592.03 1.302 0.903464 16 to 23 2418.86 -1.147 0.125595 17 to 24 2390.99 -1.542 0.061584 18 to 25 2408.07 -1.300 0.096789 19 to 26 2465.85 -0.483 0.314546 20 to 27 2492.61 -0.104 0.458402 21 to 28 2472.78 -0.385 0.350129 22 to 29 2359.63 -1.985 0.023564 23 to 30 2591.44 1.293 0.902026 24 to 31 2570.77 1.001 0.841551 25 to 32 2547.53 0.672 0.749251 CDPARK for dh-ranFile-2016-06-07_20:31: 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 3509 -0.6393 0.261324 3541 0.8219 0.794438 3514 -0.4110 0.340551 3506 -0.7763 0.218799 3525 0.0913 0.536383 3581 2.6484 0.995956 3552 1.3242 0.907282 3516 -0.3196 0.374623 3525 0.0913 0.536383 3527 0.1826 0.572463 Square side=100, avg. no. parked=3529.60 sample std.=21.75 p-value of the KSTEST for those 10 p-values: 0.578938 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-06-07_20:31 0.1038,0.7430,0.1922,0.6742,0.1930,0.8257,0.7096,0.4775,0.1959,0.6568, The KS test for those 10 p-values: 0.699471 The 3DSPHERES test for dh-ranFile-2016-06-07_20:31 sample no r^3 equiv. uni. 1 3.437 0.108245 2 45.171 0.778137 3 31.978 0.655589 4 4.316 0.133997 5 19.188 0.472491 6 9.661 0.275335 7 46.813 0.789957 8 56.213 0.846454 9 38.847 0.726072 10 43.007 0.761539 11 30.553 0.638837 12 1.708 0.055332 13 24.025 0.551048 14 0.723 0.023825 15 5.052 0.154977 16 27.579 0.601206 17 8.716 0.252144 18 41.017 0.745191 19 5.803 0.175886 20 5.522 0.168128 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.414834 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-06-07_20:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 3.0 -0.6 0.8 -1.5 -1.4 0.6 -0.8 -0.9 0.7 0.2 -0.6 -0.2 -0.4 -1.6 0.5 0.3 1.1 1.6 -0.9 -1.0 0.3 -0.5 -0.5 1.0 1.4 -0.5 -0.2 0.3 1.2 0.6 -0.4 -1.0 1.7 -0.8 0.4 -0.5 0.8 0.1 -0.7 0.1 0.0 0.8 Chi-square with 42 degrees of freedom:39.164320 z-score=-0.309398, p-value=0.403843 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-06-07_20:31 Test no p-value 1 0.690158 2 0.782893 3 0.325511 4 0.689303 5 0.074317 6 0.020710 7 0.162821 8 0.507065 9 0.111365 10 0.268026 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.215943 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-06-07_20:31: (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 66577 0.12 66508 0.38 3 25000.00 25114 0.52 25197 1.55 4 6666.67 6681 0.03 6646 0.06 5 1388.89 1329 2.58 1362 0.52 6 238.10 261 2.20 240 0.02 7 34.72 31 0.40 38 0.31 8 4.96 6 0.22 8 1.86 p=0.58503 p=0.41757 Number of rngs required: 687624, p-value: 0.184 RESULTS OF CRAPS TEST for dh-ranFile-2016-06-07_20:31 No. of wins: Observed Expected 98365 98585.9 z-score=-0.988, pvalue=0.16162 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66278 66666.7 2.266 2.266 2 37688 37654.3 0.030 2.296 3 26897 26954.7 0.124 2.420 4 19255 19313.5 0.177 2.597 5 13850 13851.4 0.000 2.597 6 10311 9943.5 13.579 16.176 7 7176 7145.0 0.134 16.310 8 5190 5139.1 0.505 16.815 9 3768 3699.9 1.255 18.070 10 2639 2666.3 0.279 18.349 11 1927 1923.3 0.007 18.356 12 1464 1388.7 4.079 22.435 13 1024 1003.7 0.410 22.845 14 667 726.1 4.817 27.661 15 489 525.8 2.580 30.242 16 393 381.2 0.368 30.610 17 301 276.5 2.164 32.774 18 185 200.8 1.248 34.021 19 125 146.0 3.016 37.038 20 96 106.2 0.982 38.020 21 277 287.1 0.356 38.377 Chisq= 38.38 for 20 degrees of freedom, p= 0.99204 SUMMARY of craptest p-value for no. of wins: 0.161623 p-value for throws/game: 0.992037 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-06-07_20:31 No. of wins: Observed Expected 98655 98585.9 z-score= 0.309, pvalue=0.62143 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66882 66666.7 0.696 0.696 2 37819 37654.3 0.720 1.416 3 26719 26954.7 2.062 3.477 4 19226 19313.5 0.396 3.873 5 13864 13851.4 0.011 3.885 6 9973 9943.5 0.087 3.972 7 7118 7145.0 0.102 4.074 8 5189 5139.1 0.485 4.559 9 3717 3699.9 0.079 4.639 10 2704 2666.3 0.533 5.172 11 1859 1923.3 2.152 7.323 12 1379 1388.7 0.068 7.392 13 979 1003.7 0.609 8.000 14 760 726.1 1.579 9.579 15 522 525.8 0.028 9.607 16 364 381.2 0.772 10.379 17 229 276.5 8.172 18.551 18 184 200.8 1.410 19.962 19 162 146.0 1.757 21.719 20 109 106.2 0.073 21.792 21 242 287.1 7.089 28.881 Chisq= 28.88 for 20 degrees of freedom, p= 0.90986 SUMMARY of craptest p-value for no. of wins: 0.621431 p-value for throws/game: 0.909861 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0169,0.0180,0.0207,0.0236,0.0238,0.0267,0.0299,0.0327,0.0349,0.0369, 0.0378,0.0411,0.0416,0.0481,0.0528,0.0553,0.0616,0.0629,0.0684,0.0743, 0.0821,0.0831,0.0854,0.0915,0.0968,0.1000,0.1037,0.1038,0.1058,0.1072, 0.1082,0.1113,0.1114,0.1242,0.1256,0.1340,0.1379,0.1398,0.1404,0.1405, 0.1421,0.1470,0.1502,0.1528,0.1550,0.1573,0.1577,0.1616,0.1628,0.1681, 0.1705,0.1759,0.1829,0.1837,0.1915,0.1922,0.1930,0.1936,0.1950,0.1959, 0.1964,0.2038,0.2076,0.2099,0.2135,0.2159,0.2188,0.2257,0.2274,0.2277, 0.2299,0.2401,0.2430,0.2442,0.2521,0.2543,0.2575,0.2594,0.2613,0.2677, 0.2680,0.2739,0.2753,0.2761,0.2761,0.2801,0.2801,0.2808,0.2828,0.2843, 0.2942,0.2944,0.2961,0.2969,0.3009,0.3145,0.3214,0.3255,0.3361,0.3406, 0.3409,0.3416,0.3427,0.3454,0.3493,0.3501,0.3503,0.3531,0.3567,0.3636, 0.3746,0.3746,0.3764,0.3836,0.3976,0.4000,0.4006,0.4038,0.4064,0.4124, 0.4148,0.4163,0.4176,0.4203,0.4329,0.4447,0.4501,0.4573,0.4583,0.4584, 0.4585,0.4597,0.4608,0.4608,0.4643,0.4690,0.4725,0.4726,0.4775,0.4777, 0.4808,0.4890,0.4927,0.4994,0.5071,0.5079,0.5340,0.5350,0.5364,0.5364, 0.5409,0.5449,0.5488,0.5495,0.5510,0.5513,0.5626,0.5635,0.5648,0.5702, 0.5725,0.5738,0.5789,0.5850,0.5966,0.6012,0.6214,0.6228,0.6267,0.6297, 0.6306,0.6335,0.6388,0.6435,0.6435,0.6490,0.6494,0.6550,0.6556,0.6562, 0.6568,0.6588,0.6620,0.6626,0.6631,0.6635,0.6667,0.6742,0.6812,0.6893, 0.6902,0.6921,0.6983,0.6995,0.7046,0.7049,0.7096,0.7180,0.7184,0.7242, 0.7261,0.7278,0.7280,0.7330,0.7345,0.7357,0.7430,0.7452,0.7493,0.7562, 0.7566,0.7566,0.7614,0.7615,0.7720,0.7735,0.7781,0.7804,0.7829,0.7897, 0.7900,0.7925,0.7944,0.7985,0.7999,0.8106,0.8161,0.8164,0.8240,0.8257, 0.8354,0.8378,0.8416,0.8429,0.8441,0.8465,0.8635,0.8674,0.8681,0.8752, 0.8786,0.8858,0.8888,0.8898,0.8913,0.8937,0.9020,0.9033,0.9035,0.9047, 0.9073,0.9090,0.9099,0.9277,0.9290,0.9322,0.9357,0.9472,0.9473,0.9484, 0.9561,0.9665,0.9684,0.9725,0.9811,0.9847,0.9915,0.9920,0.9960, Overall p-value after applying KStest on 269 p-values = 0.402722 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.