RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-11-02_10:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.67 17.3724 0.570573 2 to 25 15.54 19.8782 0.719493 3 to 26 15.81 28.6636 0.962243 4 to 27 15.87 19.1944 0.682513 5 to 28 15.96 25.2329 0.910384 6 to 29 15.72 27.7832 0.952464 7 to 30 15.74 17.1407 0.555125 8 to 31 15.74 28.7572 0.963168 9 to 32 15.69 20.2815 0.739917 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.003331 Tough bday spacings test for dh-ranFile-2016-11-02_10:31: 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 41 84 113 91 83 42 19 8 5 6 (O-E)^2/E 0.1 0.5 1.6 2.4 0.5 0.3 2.0 3.9 3.2 0.4 0.9 Birthday Spacings: Sum(O-E)^2/E= 15.754, p= 0.893 RESULTS OF GCD FOR dh-ranFile-2016-11-02_10:31 Euclid's algorithm: p-value, steps to gcd: 0.794773 p-value, dist. of gcd's: 0.035889 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-11-02_10:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.889 0.163 0.096 0.646 0.218 0.672 0.283 0.213 Bits 8 to 15---> 0.304 0.803 0.119 0.959 0.079 0.845 0.713 0.418 Bits 16 to 23---> 0.887 0.234 0.548 0.136 0.152 0.544 0.856 0.512 Bits 24 to 31---> 0.500 0.809 0.791 0.086 0.395 0.379 0.970 0.835 KS test for the above 32 p values: 0.114 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-11-02_10:31, p-values for 5 runs: 0.2220, 0.0878, 0.1024, 0.0539, 0.5646 Rank test for binary matrices (31x31) for dh-ranFile-2016-11-02_10:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 224 211.4 0.749 0.749 r= 29 5081 5134.0 0.547 1.296 r= 30 23212 23103.0 0.514 1.810 r= 31 11483 11551.5 0.406 2.216 chi-square = 2.216 with df = 3; p-value = 0.471 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-11-02_10:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 214 211.4 0.032 0.032 r= 30 5165 5134.0 0.187 0.219 r= 31 23160 23103.0 0.140 0.359 r= 32 11461 11551.5 0.709 1.068 chi-square = 1.068 with df = 3; p-value = 0.215 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-11-02_10:31 b-rank test for bits 1 to 8, p=0.09550 b-rank test for bits 2 to 9, p=0.74726 b-rank test for bits 3 to 10, p=0.76622 b-rank test for bits 4 to 11, p=0.60205 b-rank test for bits 5 to 12, p=0.10954 b-rank test for bits 6 to 13, p=0.30606 b-rank test for bits 7 to 14, p=0.63249 b-rank test for bits 8 to 15, p=0.85952 b-rank test for bits 9 to 16, p=0.40022 b-rank test for bits 10 to 17, p=0.07625 b-rank test for bits 11 to 18, p=0.27098 b-rank test for bits 12 to 19, p=0.91416 b-rank test for bits 13 to 20, p=0.25996 b-rank test for bits 14 to 21, p=0.25978 b-rank test for bits 15 to 22, p=0.06070 b-rank test for bits 16 to 23, p=0.15227 b-rank test for bits 17 to 24, p=0.17023 b-rank test for bits 18 to 25, p=0.10617 b-rank test for bits 19 to 26, p=0.61247 b-rank test for bits 20 to 27, p=0.95313 b-rank test for bits 21 to 28, p=0.37743 b-rank test for bits 22 to 29, p=0.95890 b-rank test for bits 23 to 30, p=0.95971 b-rank test for bits 24 to 31, p=0.05323 b-rank test for bits 25 to 32, p=0.55201 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 = 0.347600 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-11-02_10:31 (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 142118 0.49 0.687065 2 141876 -0.08 0.468964 3 141928 0.04 0.517397 4 142880 2.27 0.988333 5 141980 0.17 0.565574 6 142642 1.71 0.956537 7 141293 -1.44 0.074930 8 142142 0.54 0.706649 9 142429 1.21 0.887661 10 141745 -0.38 0.350508 11 141346 -1.32 0.094055 12 141745 -0.38 0.350508 13 141793 -0.27 0.392888 14 142131 0.52 0.697743 15 141747 -0.38 0.352242 16 142172 0.61 0.730298 17 141796 -0.26 0.395586 18 142220 0.73 0.766039 19 141756 -0.36 0.360079 20 142314 0.95 0.827796 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-11-02_10:31 Bits used No. missing words z-score p-value 23 to 32 141753 -0.5391 0.294920 22 to 31 141899 -0.0356 0.485792 21 to 30 141719 -0.6563 0.255812 20 to 29 141252 -2.2667 0.011706 19 to 28 142362 1.5609 0.940730 18 to 27 141705 -0.7046 0.240534 17 to 26 141672 -0.8184 0.206570 16 to 25 141780 -0.4460 0.327811 15 to 24 141998 0.3058 0.620106 14 to 23 141967 0.1989 0.578815 13 to 22 141761 -0.5115 0.304507 12 to 21 142069 0.5506 0.709041 11 to 20 142159 0.8609 0.805362 10 to 19 141913 0.0127 0.505049 9 to 18 142078 0.5816 0.719589 8 to 17 141843 -0.2287 0.409542 7 to 16 141873 -0.1253 0.450153 6 to 15 141760 -0.5149 0.303301 5 to 14 142199 0.9989 0.841069 4 to 13 141750 -0.5494 0.291361 3 to 12 142369 1.5851 0.943525 2 to 11 141885 -0.0839 0.466569 1 to 10 141629 -0.9667 0.166858 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-11-02_10:31 Bits used No. missing words z-score p-value 28 to 32 141956 0.1582 0.562852 27 to 31 142348 1.4870 0.931495 26 to 30 141657 -0.8554 0.196177 25 to 29 141520 -1.3198 0.093457 24 to 28 142064 0.5243 0.699967 23 to 27 141387 -1.7706 0.038313 22 to 26 142012 0.3480 0.636093 21 to 25 142080 0.5785 0.718551 20 to 24 141843 -0.2248 0.411049 19 to 23 141420 -1.6587 0.048584 18 to 22 141675 -0.7943 0.213499 17 to 21 141803 -0.3604 0.359259 16 to 20 142078 0.5718 0.716259 15 to 19 141185 -2.4554 0.007037 14 to 18 141238 -2.2757 0.011432 13 to 17 141862 -0.1604 0.436267 12 to 16 141960 0.1718 0.568188 11 to 15 142084 0.5921 0.723109 10 to 14 141990 0.2735 0.607749 9 to 13 141767 -0.4825 0.314734 8 to 12 142443 1.8091 0.964778 7 to 11 141888 -0.0723 0.471180 6 to 10 142116 0.7006 0.758216 5 to 9 142224 1.0667 0.856941 4 to 8 141707 -0.6859 0.246399 3 to 7 141732 -0.6011 0.273881 2 to 6 141835 -0.2520 0.400534 1 to 5 142182 0.9243 0.822336 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-11-02_10:31 Bits used No. missing words z-score p-value 31 to 32 141337 -1.6883 0.045678 30 to 31 141993 0.2468 0.597474 29 to 30 141300 -1.7974 0.036133 28 to 29 141813 -0.2842 0.388144 27 to 28 142088 0.5271 0.700921 26 to 27 141762 -0.4346 0.331926 25 to 26 142011 0.2999 0.617878 24 to 25 141860 -0.1455 0.442152 23 to 24 141974 0.1908 0.575646 22 to 23 142326 1.2291 0.890486 21 to 22 141822 -0.2576 0.398354 20 to 21 141705 -0.6027 0.273340 19 to 20 142190 0.8279 0.796146 18 to 19 141490 -1.2370 0.108051 17 to 18 142064 0.4563 0.675896 16 to 17 141952 0.1259 0.550083 15 to 16 142519 1.7984 0.963946 14 to 15 142914 2.9636 0.998480 13 to 14 142375 1.3737 0.915226 12 to 13 142325 1.2262 0.889932 11 to 12 141301 -1.7945 0.036368 10 to 11 142112 0.5978 0.725029 9 to 10 142455 1.6096 0.946262 8 to 9 141912 0.0079 0.503142 7 to 8 142186 0.8161 0.792789 6 to 7 141684 -0.6647 0.253124 5 to 6 141705 -0.6027 0.273340 4 to 5 141704 -0.6057 0.272359 3 to 4 141472 -1.2901 0.098515 2 to 3 141964 0.1613 0.564059 1 to 2 142061 0.4474 0.672708 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-11-02_10:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2503.22 0.046 0.518176 Test results for specific bytes for dh-ranFile-2016-11-02_10:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2600.13 1.416 0.921627 2 to 9 2445.96 -0.764 0.222369 3 to 10 2481.85 -0.257 0.398688 4 to 11 2454.45 -0.644 0.259715 5 to 12 2403.08 -1.371 0.085240 6 to 13 2477.94 -0.312 0.377504 7 to 14 2481.53 -0.261 0.396963 8 to 15 2426.19 -1.044 0.148290 9 to 16 2463.49 -0.516 0.302834 10 to 17 2415.44 -1.196 0.115866 11 to 18 2446.69 -0.754 0.225442 12 to 19 2506.27 0.089 0.535332 13 to 20 2417.57 -1.166 0.121847 14 to 21 2576.15 1.077 0.859257 15 to 22 2497.90 -0.030 0.488179 16 to 23 2566.61 0.942 0.826910 17 to 24 2495.30 -0.066 0.473511 18 to 25 2433.24 -0.944 0.172551 19 to 26 2611.61 1.578 0.942768 20 to 27 2493.61 -0.090 0.463997 21 to 28 2455.00 -0.636 0.262248 22 to 29 2630.13 1.840 0.967139 23 to 30 2413.79 -1.219 0.111389 24 to 31 2424.68 -1.065 0.143382 25 to 32 2525.68 0.363 0.641750 CDPARK for dh-ranFile-2016-11-02_10:31: 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 3527 0.1826 0.572463 3505 -0.8219 0.205562 3526 0.1370 0.554479 3510 -0.5936 0.276387 3534 0.5023 0.692266 3517 -0.2740 0.392053 3515 -0.3653 0.357445 3531 0.3653 0.642555 3498 -1.1416 0.126820 3549 1.1872 0.882429 Square side=100, avg. no. parked=3521.20 sample std.=14.39 p-value of the KSTEST for those 10 p-values: 0.799964 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-11-02_10:31 0.3346,0.8785,0.9133,0.2128,0.0583,0.0764,0.4980,0.4919,0.9770,0.6108, The KS test for those 10 p-values: 0.884220 The 3DSPHERES test for dh-ranFile-2016-11-02_10:31 sample no r^3 equiv. uni. 1 6.245 0.187923 2 27.764 0.603651 3 14.096 0.374910 4 30.283 0.635574 5 47.390 0.793953 6 0.430 0.014219 7 19.283 0.474162 8 10.947 0.305734 9 8.982 0.258730 10 12.038 0.330539 11 7.553 0.222587 12 78.061 0.925877 13 35.466 0.693397 14 30.169 0.634182 15 13.547 0.363374 16 30.385 0.636806 17 14.823 0.389877 18 76.311 0.921426 19 87.071 0.945107 20 20.203 0.490042 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.796244 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-11-02_10:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -0.3 -1.1 -1.0 0.1 -0.1 1.2 -1.6 1.3 1.0 0.1 0.8 -1.0 -0.5 -0.5 -1.5 0.3 1.1 0.9 -0.9 0.3 0.1 -0.5 -0.5 0.6 -0.4 1.1 -0.1 0.8 -0.5 -0.7 -1.0 1.9 0.1 0.2 0.2 2.8 0.8 0.1 -0.7 -0.6 1.0 -0.1 Chi-square with 42 degrees of freedom:36.277466 z-score=-0.624380, p-value=0.280435 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-11-02_10:31 Test no p-value 1 0.304726 2 0.019901 3 0.330202 4 0.238158 5 0.005613 6 0.196872 7 0.115338 8 0.838446 9 0.305532 10 0.016866 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.002184 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-11-02_10:31: (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 66628 0.02 66389 1.16 3 25000.00 25013 0.01 25262 2.75 4 6666.67 6717 0.38 6714 0.34 5 1388.89 1386 0.01 1383 0.02 6 238.10 225 0.72 218 1.70 7 34.72 24 3.31 31 0.40 8 4.96 6 0.22 2 1.77 p=0.41234 p=0.77086 Number of rngs required: 689351, p-value: 0.864 RESULTS OF CRAPS TEST for dh-ranFile-2016-11-02_10:31 No. of wins: Observed Expected 98123 98585.9 z-score=-2.070, pvalue=0.01922 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66366 66666.7 1.356 1.356 2 37630 37654.3 0.016 1.372 3 26999 26954.7 0.073 1.444 4 19347 19313.5 0.058 1.503 5 13751 13851.4 0.728 2.231 6 9993 9943.5 0.246 2.477 7 7205 7145.0 0.503 2.980 8 5189 5139.1 0.485 3.465 9 3767 3699.9 1.218 4.683 10 2724 2666.3 1.249 5.932 11 1957 1923.3 0.589 6.522 12 1389 1388.7 0.000 6.522 13 1015 1003.7 0.127 6.648 14 763 726.1 1.871 8.520 15 521 525.8 0.044 8.564 16 344 381.2 3.621 12.185 17 278 276.5 0.008 12.193 18 220 200.8 1.830 14.023 19 143 146.0 0.061 14.084 20 113 106.2 0.433 14.517 21 286 287.1 0.004 14.521 Chisq= 14.52 for 20 degrees of freedom, p= 0.19689 SUMMARY of craptest p-value for no. of wins: 0.019218 p-value for throws/game: 0.196890 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-11-02_10:31 No. of wins: Observed Expected 98372 98585.9 z-score=-0.957, pvalue=0.16941 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66602 66666.7 0.063 0.063 2 37739 37654.3 0.190 0.253 3 27093 26954.7 0.709 0.962 4 19340 19313.5 0.036 0.999 5 13778 13851.4 0.389 1.388 6 9848 9943.5 0.918 2.306 7 7127 7145.0 0.045 2.352 8 5064 5139.1 1.097 3.448 9 3814 3699.9 3.521 6.969 10 2648 2666.3 0.126 7.095 11 1917 1923.3 0.021 7.115 12 1415 1388.7 0.497 7.612 13 1023 1003.7 0.371 7.983 14 718 726.1 0.091 8.074 15 538 525.8 0.281 8.355 16 382 381.2 0.002 8.357 17 258 276.5 1.243 9.600 18 192 200.8 0.388 9.988 19 131 146.0 1.538 11.526 20 115 106.2 0.727 12.253 21 258 287.1 2.952 15.205 Chisq= 15.21 for 20 degrees of freedom, p= 0.23545 SUMMARY of craptest p-value for no. of wins: 0.169410 p-value for throws/game: 0.235446 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0022,0.0033,0.0056,0.0070,0.0114,0.0117,0.0142,0.0169,0.0192,0.0199, 0.0359,0.0361,0.0364,0.0383,0.0457,0.0486,0.0532,0.0539,0.0583,0.0607, 0.0749,0.0763,0.0764,0.0792,0.0852,0.0860,0.0878,0.0935,0.0941,0.0955, 0.0965,0.0985,0.1024,0.1062,0.1081,0.1095,0.1114,0.1142,0.1153,0.1159, 0.1194,0.1218,0.1268,0.1359,0.1434,0.1483,0.1517,0.1523,0.1627,0.1669, 0.1694,0.1702,0.1726,0.1879,0.1962,0.1969,0.1969,0.2056,0.2066,0.2127, 0.2128,0.2135,0.2153,0.2175,0.2220,0.2224,0.2226,0.2254,0.2337,0.2354, 0.2382,0.2405,0.2464,0.2531,0.2558,0.2587,0.2597,0.2598,0.2600,0.2622, 0.2710,0.2724,0.2733,0.2733,0.2739,0.2764,0.2804,0.2832,0.2914,0.2949, 0.3028,0.3033,0.3038,0.3045,0.3047,0.3055,0.3057,0.3061,0.3147,0.3278, 0.3302,0.3305,0.3319,0.3346,0.3476,0.3505,0.3505,0.3522,0.3574,0.3593, 0.3601,0.3634,0.3749,0.3774,0.3775,0.3793,0.3881,0.3899,0.3921,0.3929, 0.3951,0.3956,0.3970,0.3984,0.3987,0.4002,0.4005,0.4095,0.4110,0.4123, 0.4185,0.4363,0.4422,0.4502,0.4640,0.4666,0.4690,0.4712,0.4713,0.4735, 0.4742,0.4858,0.4882,0.4900,0.4919,0.4980,0.4999,0.5031,0.5050,0.5120, 0.5174,0.5182,0.5353,0.5436,0.5478,0.5501,0.5520,0.5545,0.5551,0.5629, 0.5641,0.5646,0.5656,0.5682,0.5706,0.5725,0.5756,0.5788,0.5975,0.6021, 0.6037,0.6077,0.6108,0.6125,0.6179,0.6201,0.6325,0.6342,0.6356,0.6361, 0.6368,0.6417,0.6426,0.6461,0.6715,0.6727,0.6759,0.6825,0.6871,0.6923, 0.6934,0.6977,0.7000,0.7009,0.7066,0.7090,0.7130,0.7163,0.7186,0.7195, 0.7196,0.7231,0.7250,0.7303,0.7399,0.7473,0.7582,0.7660,0.7662,0.7709, 0.7910,0.7928,0.7940,0.7948,0.7961,0.7962,0.8000,0.8025,0.8054,0.8095, 0.8223,0.8269,0.8278,0.8352,0.8384,0.8411,0.8453,0.8564,0.8569,0.8593, 0.8595,0.8643,0.8785,0.8824,0.8842,0.8870,0.8877,0.8890,0.8899,0.8905, 0.8931,0.9104,0.9133,0.9142,0.9152,0.9214,0.9216,0.9259,0.9315,0.9407, 0.9428,0.9435,0.9451,0.9463,0.9525,0.9531,0.9565,0.9589,0.9594,0.9597, 0.9622,0.9632,0.9639,0.9648,0.9671,0.9703,0.9770,0.9883,0.9985, Overall p-value after applying KStest on 269 p-values = 0.262984 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.