RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-11-08_08:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.71 28.9273 0.964798 2 to 25 15.64 17.9191 0.606037 3 to 26 15.70 15.1751 0.417130 4 to 27 15.67 35.3775 0.994452 5 to 28 15.79 10.5743 0.122180 6 to 29 15.86 18.2990 0.629782 7 to 30 15.58 13.7060 0.312209 8 to 31 16.03 15.6666 0.452420 9 to 32 15.80 25.8304 0.922393 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.275216 Tough bday spacings test for dh-ranFile-2015-11-08_08:31: 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 17 32 74 83 103 77 49 29 24 7 5 (O-E)^2/E 6.7 0.6 0.0 2.2 0.3 0.0 0.2 0.0 5.6 0.0 0.2 Birthday Spacings: Sum(O-E)^2/E= 15.844, p= 0.896 RESULTS OF GCD FOR dh-ranFile-2015-11-08_08:31 Euclid's algorithm: p-value, steps to gcd: 0.345364 p-value, dist. of gcd's: 0.943446 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-11-08_08:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.620 0.104 0.568 0.662 0.085 0.517 0.735 0.307 Bits 8 to 15---> 0.828 0.087 0.813 0.214 0.315 0.043 0.637 0.422 Bits 16 to 23---> 0.382 0.076 0.578 0.205 0.482 0.087 0.106 0.177 Bits 24 to 31---> 0.158 0.569 0.165 0.034 0.284 0.946 0.678 0.826 KS test for the above 32 p values: 0.941 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-11-08_08:31, p-values for 5 runs: 0.5324, 0.4323, 0.9322, 0.7942, 0.8519 Rank test for binary matrices (31x31) for dh-ranFile-2015-11-08_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 196 211.4 1.124 1.124 r= 29 5111 5134.0 0.103 1.228 r= 30 23160 23103.0 0.140 1.368 r= 31 11533 11551.5 0.030 1.398 chi-square = 1.398 with df = 3; p-value = 0.294 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-11-08_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 209 211.4 0.028 0.028 r= 30 5206 5134.0 1.009 1.037 r= 31 23062 23103.0 0.073 1.110 r= 32 11523 11551.5 0.070 1.180 chi-square = 1.180 with df = 3; p-value = 0.242 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-11-08_08:31 b-rank test for bits 1 to 8, p=0.44934 b-rank test for bits 2 to 9, p=0.79077 b-rank test for bits 3 to 10, p=0.55283 b-rank test for bits 4 to 11, p=0.70535 b-rank test for bits 5 to 12, p=0.11030 b-rank test for bits 6 to 13, p=0.06962 b-rank test for bits 7 to 14, p=0.76276 b-rank test for bits 8 to 15, p=0.33517 b-rank test for bits 9 to 16, p=0.78099 b-rank test for bits 10 to 17, p=0.35383 b-rank test for bits 11 to 18, p=0.66677 b-rank test for bits 12 to 19, p=0.77711 b-rank test for bits 13 to 20, p=0.82678 b-rank test for bits 14 to 21, p=0.38950 b-rank test for bits 15 to 22, p=0.54859 b-rank test for bits 16 to 23, p=0.18393 b-rank test for bits 17 to 24, p=0.15620 b-rank test for bits 18 to 25, p=0.56064 b-rank test for bits 19 to 26, p=0.76070 b-rank test for bits 20 to 27, p=0.38240 b-rank test for bits 21 to 28, p=0.38064 b-rank test for bits 22 to 29, p=0.29914 b-rank test for bits 23 to 30, p=0.71015 b-rank test for bits 24 to 31, p=0.32814 b-rank test for bits 25 to 32, p=0.58993 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 = 0.385496 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-11-08_08:31 (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 141543 -0.86 0.196023 2 141843 -0.15 0.438420 3 141532 -0.88 0.188993 4 141508 -0.94 0.174203 5 141822 -0.20 0.419160 6 141660 -0.58 0.280099 7 141313 -1.39 0.081765 8 142259 0.82 0.793032 9 141438 -1.10 0.135396 10 141269 -1.50 0.067314 11 142253 0.80 0.789003 12 141372 -1.26 0.104659 13 142623 1.67 0.952288 14 141363 -1.28 0.100894 15 143002 2.55 0.994660 16 141498 -0.96 0.168263 17 141829 -0.19 0.425561 18 141787 -0.29 0.387509 19 142064 0.36 0.641092 20 141922 0.03 0.511808 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-11-08_08:31 Bits used No. missing words z-score p-value 23 to 32 141961 0.1782 0.570706 22 to 31 142037 0.4402 0.670119 21 to 30 142156 0.8506 0.802500 20 to 29 142283 1.2885 0.901217 19 to 28 141903 -0.0218 0.491293 18 to 27 141679 -0.7942 0.213528 17 to 26 141840 -0.2391 0.405526 16 to 25 141937 0.0954 0.538007 15 to 24 141699 -0.7253 0.234141 14 to 23 141994 0.2920 0.614844 13 to 22 142200 1.0023 0.841903 12 to 21 141956 0.1609 0.563926 11 to 20 142232 1.1127 0.867072 10 to 19 142103 0.6678 0.747878 9 to 18 141752 -0.5425 0.293731 8 to 17 141492 -1.4391 0.075066 7 to 16 141737 -0.5942 0.276175 6 to 15 141578 -1.1425 0.126620 5 to 14 141672 -0.8184 0.206570 4 to 13 141326 -2.0115 0.022137 3 to 12 141748 -0.5563 0.288999 2 to 11 141860 -0.1701 0.432464 1 to 10 142021 0.3851 0.649907 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-11-08_08:31 Bits used No. missing words z-score p-value 28 to 32 141859 -0.1706 0.432265 27 to 31 141860 -0.1672 0.433598 26 to 30 142125 0.7311 0.767636 25 to 29 142091 0.6158 0.730997 24 to 28 141853 -0.1909 0.424283 23 to 27 141532 -1.2791 0.100434 22 to 26 142090 0.6124 0.729877 21 to 25 142205 1.0023 0.841894 20 to 24 142046 0.4633 0.678421 19 to 23 141746 -0.5537 0.289905 18 to 22 141629 -0.9503 0.170987 17 to 21 141609 -1.0181 0.154323 16 to 20 141771 -0.4689 0.319565 15 to 19 142320 1.3921 0.918054 14 to 18 141521 -1.3164 0.094024 13 to 17 141855 -0.1842 0.426940 12 to 16 142184 0.9311 0.824095 11 to 15 142307 1.3480 0.911176 10 to 14 141932 0.0768 0.530628 9 to 13 142343 1.4701 0.929228 8 to 12 141706 -0.6893 0.245332 7 to 11 141475 -1.4723 0.070469 6 to 10 141944 0.1175 0.546778 5 to 9 142308 1.3514 0.911720 4 to 8 142168 0.8768 0.809715 3 to 7 141612 -1.0079 0.156752 2 to 6 141808 -0.3435 0.365614 1 to 5 141455 -1.5401 0.061768 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-11-08_08:31 Bits used No. missing words z-score p-value 31 to 32 142175 0.7837 0.783388 30 to 31 141470 -1.2960 0.097495 29 to 30 142247 0.9961 0.840394 28 to 29 141824 -0.2517 0.400632 27 to 28 142020 0.3265 0.627962 26 to 27 142195 0.8427 0.800298 25 to 26 141487 -1.2458 0.106417 24 to 25 141469 -1.2989 0.096988 23 to 24 142176 0.7866 0.784253 22 to 23 142259 1.0315 0.848841 21 to 22 141763 -0.4317 0.332997 20 to 21 141589 -0.9449 0.172348 19 to 20 142018 0.3206 0.625728 18 to 19 141916 0.0197 0.507849 17 to 18 142241 0.9784 0.836056 16 to 17 141622 -0.8476 0.198336 15 to 16 142288 1.1170 0.868007 14 to 15 141812 -0.2871 0.387014 13 to 14 142652 2.1908 0.985766 12 to 13 142218 0.9105 0.818729 11 to 12 141578 -0.9774 0.164192 10 to 11 141998 0.2616 0.603171 9 to 10 142102 0.5683 0.715101 8 to 9 141985 0.2232 0.588316 7 to 8 142101 0.5654 0.714099 6 to 7 141887 -0.0659 0.473741 5 to 6 142101 0.5654 0.714099 4 to 5 141578 -0.9774 0.164192 3 to 4 141905 -0.0128 0.494905 2 to 3 141493 -1.2281 0.109702 1 to 2 141675 -0.6912 0.244708 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-11-08_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2548.15 0.681 0.752061 Test results for specific bytes for dh-ranFile-2015-11-08_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2483.75 -0.230 0.409105 2 to 9 2552.98 0.749 0.773167 3 to 10 2447.93 -0.736 0.230737 4 to 11 2499.10 -0.013 0.494913 5 to 12 2460.68 -0.556 0.289070 6 to 13 2477.74 -0.315 0.376465 7 to 14 2494.05 -0.084 0.466448 8 to 15 2503.84 0.054 0.521640 9 to 16 2523.44 0.332 0.629879 10 to 17 2427.34 -1.028 0.152078 11 to 18 2477.84 -0.313 0.376983 12 to 19 2436.83 -0.893 0.185835 13 to 20 2508.42 0.119 0.547408 14 to 21 2460.69 -0.556 0.289151 15 to 22 2531.91 0.451 0.674102 16 to 23 2509.46 0.134 0.553211 17 to 24 2528.88 0.408 0.658541 18 to 25 2573.42 1.038 0.850431 19 to 26 2390.29 -1.552 0.060386 20 to 27 2496.00 -0.057 0.477443 21 to 28 2436.96 -0.891 0.186331 22 to 29 2389.22 -1.567 0.058594 23 to 30 2522.35 0.316 0.624033 24 to 31 2385.85 -1.614 0.053226 25 to 32 2471.11 -0.409 0.341424 CDPARK for dh-ranFile-2015-11-08_08:31: 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 3539 0.7306 0.767486 3521 -0.0913 0.463617 3520 -0.1370 0.445521 3531 0.3653 0.642555 3529 0.2740 0.607947 3527 0.1826 0.572463 3494 -1.3242 0.092718 3516 -0.3196 0.374623 3503 -0.9132 0.180558 3544 0.9589 0.831196 Square side=100, avg. no. parked=3522.40 sample std.=14.53 p-value of the KSTEST for those 10 p-values: 0.793266 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-11-08_08:31 0.0717,0.0080,0.4048,0.2776,0.5078,0.6715,0.1865,0.7771,0.2300,0.1357, The KS test for those 10 p-values: 0.099026 The 3DSPHERES test for dh-ranFile-2015-11-08_08:31 sample no r^3 equiv. uni. 1 22.918 0.534162 2 14.626 0.385854 3 53.404 0.831383 4 5.045 0.154793 5 114.334 0.977877 6 16.854 0.429823 7 74.707 0.917108 8 6.081 0.183475 9 50.561 0.814621 10 69.121 0.900144 11 0.319 0.010563 12 18.633 0.462643 13 29.912 0.631044 14 57.659 0.853682 15 5.696 0.172939 16 80.293 0.931193 17 26.447 0.585867 18 4.522 0.139919 19 63.569 0.879844 20 7.191 0.213148 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.461409 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-11-08_08:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 0.1 0.1 -1.1 0.3 0.4 0.1 1.3 -0.2 1.0 1.5 -1.4 -0.1 1.0 1.9 0.3 0.3 -0.5 -1.2 -1.3 0.4 -1.3 0.9 -1.6 0.5 -0.2 0.9 -0.9 0.4 -0.3 0.0 0.5 1.3 -1.5 -1.9 -1.2 -2.3 -0.1 0.5 -0.1 -1.3 -1.0 0.8 Chi-square with 42 degrees of freedom:42.617357 z-score=0.067359, p-value=0.555577 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-11-08_08:31 Test no p-value 1 0.000286 2 0.030332 3 0.655008 4 0.741999 5 0.656728 6 0.011621 7 0.602085 8 0.041618 9 0.032489 10 0.100277 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000822 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-11-08_08:31: (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 66786 0.21 66807 0.30 3 25000.00 24837 1.06 24926 0.22 4 6666.67 6650 0.04 6589 0.90 5 1388.89 1436 1.60 1397 0.05 6 238.10 253 0.93 228 0.43 7 34.72 33 0.09 44 2.48 8 4.96 4 0.19 8 1.86 p=0.33956 p=0.60297 Number of rngs required: 687358, p-value: 0.112 RESULTS OF CRAPS TEST for dh-ranFile-2015-11-08_08:31 No. of wins: Observed Expected 98557 98585.9 z-score=-0.129, pvalue=0.44865 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66601 66666.7 0.065 0.065 2 37590 37654.3 0.110 0.175 3 26850 26954.7 0.407 0.581 4 19313 19313.5 0.000 0.582 5 13869 13851.4 0.022 0.604 6 9912 9943.5 0.100 0.704 7 7180 7145.0 0.171 0.875 8 5238 5139.1 1.904 2.779 9 3680 3699.9 0.107 2.886 10 2770 2666.3 4.033 6.920 11 1967 1923.3 0.992 7.911 12 1419 1388.7 0.659 8.570 13 965 1003.7 1.493 10.064 14 710 726.1 0.359 10.423 15 559 525.8 2.092 12.514 16 355 381.2 1.794 14.308 17 276 276.5 0.001 14.309 18 203 200.8 0.023 14.333 19 135 146.0 0.827 15.159 20 104 106.2 0.046 15.206 21 304 287.1 0.993 16.199 Chisq= 16.20 for 20 degrees of freedom, p= 0.29577 SUMMARY of craptest p-value for no. of wins: 0.448650 p-value for throws/game: 0.295774 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-11-08_08:31 No. of wins: Observed Expected 98653 98585.9 z-score= 0.300, pvalue=0.61802 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66594 66666.7 0.079 0.079 2 37669 37654.3 0.006 0.085 3 26861 26954.7 0.326 0.411 4 19488 19313.5 1.577 1.988 5 13708 13851.4 1.485 3.473 6 9978 9943.5 0.119 3.593 7 7109 7145.0 0.182 3.774 8 5212 5139.1 1.035 4.809 9 3686 3699.9 0.052 4.861 10 2644 2666.3 0.186 5.048 11 1912 1923.3 0.067 5.114 12 1406 1388.7 0.215 5.329 13 1055 1003.7 2.620 7.949 14 725 726.1 0.002 7.951 15 527 525.8 0.003 7.954 16 378 381.2 0.026 7.980 17 250 276.5 2.547 10.527 18 213 200.8 0.737 11.264 19 145 146.0 0.007 11.271 20 135 106.2 7.801 19.072 21 305 287.1 1.114 20.186 Chisq= 20.19 for 20 degrees of freedom, p= 0.55364 SUMMARY of craptest p-value for no. of wins: 0.618024 p-value for throws/game: 0.553636 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0003,0.0008,0.0080,0.0106,0.0116,0.0221,0.0303,0.0325,0.0336,0.0416, 0.0429,0.0532,0.0586,0.0604,0.0618,0.0673,0.0696,0.0705,0.0717,0.0751, 0.0757,0.0818,0.0847,0.0873,0.0875,0.0927,0.0940,0.0970,0.0975,0.0990, 0.1003,0.1004,0.1009,0.1039,0.1047,0.1059,0.1064,0.1097,0.1103,0.1122, 0.1222,0.1266,0.1354,0.1357,0.1399,0.1521,0.1543,0.1548,0.1562,0.1568, 0.1578,0.1642,0.1642,0.1655,0.1683,0.1710,0.1723,0.1729,0.1742,0.1766, 0.1806,0.1835,0.1839,0.1858,0.1863,0.1865,0.1890,0.1960,0.1983,0.2052, 0.2066,0.2131,0.2135,0.2144,0.2300,0.2307,0.2341,0.2423,0.2447,0.2453, 0.2752,0.2762,0.2776,0.2801,0.2837,0.2890,0.2891,0.2892,0.2899,0.2937, 0.2939,0.2958,0.2991,0.3068,0.3122,0.3147,0.3196,0.3281,0.3330,0.3352, 0.3396,0.3414,0.3454,0.3538,0.3656,0.3746,0.3765,0.3770,0.3806,0.3817, 0.3824,0.3855,0.3859,0.3870,0.3875,0.3895,0.4006,0.4048,0.4055,0.4091, 0.4171,0.4192,0.4216,0.4243,0.4256,0.4269,0.4298,0.4323,0.4323,0.4325, 0.4336,0.4384,0.4455,0.4487,0.4493,0.4524,0.4614,0.4626,0.4636,0.4664, 0.4737,0.4774,0.4824,0.4913,0.4949,0.4949,0.5078,0.5078,0.5118,0.5171, 0.5216,0.5306,0.5324,0.5342,0.5380,0.5468,0.5474,0.5486,0.5528,0.5532, 0.5536,0.5556,0.5606,0.5639,0.5684,0.5694,0.5707,0.5725,0.5784,0.5859, 0.5883,0.5899,0.6021,0.6030,0.6032,0.6060,0.6079,0.6148,0.6180,0.6204, 0.6240,0.6257,0.6280,0.6298,0.6299,0.6310,0.6370,0.6411,0.6426,0.6499, 0.6550,0.6567,0.6585,0.6624,0.6668,0.6701,0.6715,0.6741,0.6782,0.6784, 0.7054,0.7102,0.7141,0.7141,0.7151,0.7299,0.7310,0.7350,0.7420,0.7479, 0.7521,0.7607,0.7628,0.7675,0.7676,0.7732,0.7771,0.7771,0.7810,0.7834, 0.7843,0.7890,0.7908,0.7930,0.7933,0.7942,0.8003,0.8025,0.8097,0.8132, 0.8146,0.8187,0.8241,0.8255,0.8268,0.8284,0.8312,0.8314,0.8361,0.8404, 0.8419,0.8419,0.8488,0.8504,0.8519,0.8537,0.8671,0.8680,0.8798,0.8958, 0.9001,0.9012,0.9112,0.9117,0.9171,0.9181,0.9224,0.9292,0.9312,0.9322, 0.9409,0.9434,0.9457,0.9523,0.9648,0.9779,0.9858,0.9945,0.9947, Overall p-value after applying KStest on 269 p-values = 0.057932 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.