RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-04-20_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 15.87 24.2602 0.887463 2 to 25 15.71 15.5142 0.441505 3 to 26 15.94 26.4836 0.933911 4 to 27 16.05 18.8877 0.664985 5 to 28 15.74 14.2914 0.353625 6 to 29 15.77 13.4272 0.292847 7 to 30 15.63 14.2300 0.349240 8 to 31 15.61 17.3284 0.567662 9 to 32 15.54 20.5520 0.753028 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.548703 Tough bday spacings test for dh-ranFile-2016-04-20_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 12 42 75 93 102 73 46 30 16 7 4 (O-E)^2/E 0.9 0.8 0.0 0.2 0.2 0.3 0.7 0.0 0.1 0.0 0.0 Birthday Spacings: Sum(O-E)^2/E= 3.287, p= 0.026 RESULTS OF GCD FOR dh-ranFile-2016-04-20_10:31 Euclid's algorithm: p-value, steps to gcd: 0.347591 p-value, dist. of gcd's: 0.218126 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-04-20_10:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.919 0.419 0.368 0.163 0.746 0.860 0.252 0.645 Bits 8 to 15---> 0.754 0.624 0.272 0.335 0.664 0.441 0.995 0.578 Bits 16 to 23---> 0.272 0.360 0.934 0.907 0.789 0.493 0.601 0.585 Bits 24 to 31---> 0.794 0.993 0.203 0.151 0.393 0.288 0.572 0.292 KS test for the above 32 p values: 0.710 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-04-20_10:31, p-values for 5 runs: 0.6920, 0.3068, 0.7752, 0.0566, 0.0126 Rank test for binary matrices (31x31) for dh-ranFile-2016-04-20_10:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 213 211.4 0.012 0.012 r= 29 5159 5134.0 0.122 0.133 r= 30 23053 23103.0 0.108 0.242 r= 31 11575 11551.5 0.048 0.290 chi-square = 0.290 with df = 3; p-value = 0.038 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-04-20_10:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 209 211.4 0.028 0.028 r= 30 5258 5134.0 2.994 3.022 r= 31 22986 23103.0 0.593 3.615 r= 32 11547 11551.5 0.002 3.617 chi-square = 3.617 with df = 3; p-value = 0.694 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-04-20_10:31 b-rank test for bits 1 to 8, p=0.76262 b-rank test for bits 2 to 9, p=0.50589 b-rank test for bits 3 to 10, p=0.55891 b-rank test for bits 4 to 11, p=0.56143 b-rank test for bits 5 to 12, p=0.66954 b-rank test for bits 6 to 13, p=0.29474 b-rank test for bits 7 to 14, p=0.61382 b-rank test for bits 8 to 15, p=0.19647 b-rank test for bits 9 to 16, p=0.90669 b-rank test for bits 10 to 17, p=0.90385 b-rank test for bits 11 to 18, p=0.74093 b-rank test for bits 12 to 19, p=0.85434 b-rank test for bits 13 to 20, p=0.88944 b-rank test for bits 14 to 21, p=0.20521 b-rank test for bits 15 to 22, p=0.81150 b-rank test for bits 16 to 23, p=0.34655 b-rank test for bits 17 to 24, p=0.58106 b-rank test for bits 18 to 25, p=0.28824 b-rank test for bits 19 to 26, p=0.19597 b-rank test for bits 20 to 27, p=0.37625 b-rank test for bits 21 to 28, p=0.01013 b-rank test for bits 22 to 29, p=0.22198 b-rank test for bits 23 to 30, p=0.77349 b-rank test for bits 24 to 31, p=0.08109 b-rank test for bits 25 to 32, p=0.48117 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 = 0.929832 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-04-20_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 141770 -0.33 0.372387 2 142716 1.88 0.970268 3 141514 -0.92 0.177830 4 141655 -0.59 0.276180 5 141745 -0.38 0.350508 6 142358 1.05 0.852749 7 142162 0.59 0.722522 8 141923 0.03 0.512740 9 141446 -1.08 0.139505 10 142770 2.01 0.977833 11 141885 -0.06 0.477334 12 141865 -0.10 0.458753 13 140982 -2.17 0.015130 14 142609 1.63 0.948949 15 141916 0.02 0.506217 16 142018 0.25 0.600214 17 141790 -0.28 0.390196 18 141788 -0.28 0.388404 19 141991 0.19 0.575666 20 142185 0.64 0.740241 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-04-20_10:31 Bits used No. missing words z-score p-value 23 to 32 141630 -0.9632 0.167722 22 to 31 141726 -0.6322 0.263637 21 to 30 142252 1.1816 0.881322 20 to 29 141784 -0.4322 0.332808 19 to 28 141591 -1.0977 0.136170 18 to 27 141814 -0.3287 0.371182 17 to 26 142341 1.4885 0.931693 16 to 25 142611 2.4196 0.992230 15 to 24 141880 -0.1011 0.459721 14 to 23 141873 -0.1253 0.450153 13 to 22 141426 -1.6667 0.047792 12 to 21 141657 -0.8701 0.192122 11 to 20 142409 1.7230 0.957556 10 to 19 142093 0.6333 0.736746 9 to 18 141102 -2.7839 0.002686 8 to 17 141745 -0.5667 0.285474 7 to 16 142173 0.9092 0.818380 6 to 15 142358 1.5471 0.939085 5 to 14 141997 0.3023 0.618792 4 to 13 141669 -0.8287 0.203630 3 to 12 141687 -0.7667 0.221643 2 to 11 141824 -0.2942 0.384287 1 to 10 142427 1.7851 0.962875 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-04-20_10:31 Bits used No. missing words z-score p-value 28 to 32 142166 0.8701 0.807868 27 to 31 141810 -0.3367 0.368167 26 to 30 142508 2.0294 0.978791 25 to 29 142307 1.3480 0.911176 24 to 28 142400 1.6633 0.951873 23 to 27 142043 0.4531 0.674768 22 to 26 141872 -0.1265 0.449651 21 to 25 141831 -0.2655 0.395302 20 to 24 141836 -0.2486 0.401844 19 to 23 142046 0.4633 0.678421 18 to 22 142161 0.8531 0.803203 17 to 21 143005 3.7141 0.999898 16 to 20 141971 0.2091 0.582796 15 to 19 142068 0.5379 0.704665 14 to 18 141943 0.1141 0.545435 13 to 17 141737 -0.5842 0.279553 12 to 16 141678 -0.7842 0.216470 11 to 15 142008 0.3345 0.630989 10 to 14 142133 0.7582 0.775835 9 to 13 142015 0.3582 0.639905 8 to 12 142254 1.1684 0.878672 7 to 11 141734 -0.5943 0.276143 6 to 10 142393 1.6396 0.949452 5 to 9 141637 -0.9232 0.177964 4 to 8 141638 -0.9198 0.178848 3 to 7 141820 -0.3028 0.381016 2 to 6 141710 -0.6757 0.249617 1 to 5 142174 0.8972 0.815190 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-04-20_10:31 Bits used No. missing words z-score p-value 31 to 32 141924 0.0433 0.517259 30 to 31 141553 -1.0511 0.146602 29 to 30 141596 -0.9243 0.177671 28 to 29 141690 -0.6470 0.258819 27 to 28 141766 -0.4228 0.336220 26 to 27 141966 0.1672 0.566381 25 to 26 141928 0.0551 0.521960 24 to 25 141421 -1.4405 0.074863 23 to 24 141433 -1.4051 0.079995 22 to 23 142007 0.2881 0.613370 21 to 22 142054 0.4268 0.665221 20 to 21 142016 0.3147 0.623490 19 to 20 142486 1.7011 0.955537 18 to 19 142113 0.6008 0.726012 17 to 18 142118 0.6155 0.730903 16 to 17 142270 1.0639 0.856318 15 to 16 142111 0.5949 0.724044 14 to 15 141762 -0.4346 0.331926 13 to 14 141812 -0.2871 0.387014 12 to 13 141573 -0.9921 0.160569 11 to 12 141560 -1.0305 0.151394 10 to 11 141394 -1.5201 0.064237 9 to 10 141808 -0.2989 0.382505 8 to 9 141722 -0.5526 0.290270 7 to 8 141209 -2.0659 0.019420 6 to 7 141825 -0.2488 0.401773 5 to 6 141812 -0.2871 0.387014 4 to 5 141236 -1.9862 0.023504 3 to 4 142013 0.3058 0.620126 2 to 3 142083 0.5123 0.695780 1 to 2 141696 -0.6293 0.264579 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-04-20_10:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2509.53 0.135 0.553581 Test results for specific bytes for dh-ranFile-2016-04-20_10:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2374.57 -1.774 0.038040 2 to 9 2616.44 1.647 0.950185 3 to 10 2465.69 -0.485 0.313738 4 to 11 2599.61 1.409 0.920537 5 to 12 2572.70 1.028 0.848067 6 to 13 2609.29 1.546 0.938900 7 to 14 2514.37 0.203 0.580531 8 to 15 2406.23 -1.326 0.092412 9 to 16 2440.13 -0.847 0.198590 10 to 17 2495.95 -0.057 0.477164 11 to 18 2396.82 -1.459 0.072252 12 to 19 2401.56 -1.392 0.081944 13 to 20 2528.19 0.399 0.654913 14 to 21 2546.91 0.663 0.746482 15 to 22 2561.09 0.864 0.806182 16 to 23 2416.70 -1.178 0.119381 17 to 24 2468.82 -0.441 0.329633 18 to 25 2444.07 -0.791 0.214484 19 to 26 2523.27 0.329 0.628981 20 to 27 2454.74 -0.640 0.261063 21 to 28 2597.40 1.377 0.915808 22 to 29 2501.56 0.022 0.508822 23 to 30 2443.01 -0.806 0.210141 24 to 31 2491.56 -0.119 0.452488 25 to 32 2496.05 -0.056 0.477712 CDPARK for dh-ranFile-2016-04-20_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 3495 -1.2785 0.100530 3544 0.9589 0.831196 3484 -1.7808 0.037471 3507 -0.7306 0.232514 3489 -1.5525 0.060270 3487 -1.6438 0.050105 3517 -0.2740 0.392053 3532 0.4110 0.659449 3569 2.1005 0.982156 3540 0.7763 0.781201 Square side=100, avg. no. parked=3516.40 sample std.=27.46 p-value of the KSTEST for those 10 p-values: 0.196083 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-04-20_10:31 0.7002,0.1025,0.5945,0.5322,0.5636,0.9995,0.5342,0.7334,0.2832,0.9918, The KS test for those 10 p-values: 0.129863 The 3DSPHERES test for dh-ranFile-2016-04-20_10:31 sample no r^3 equiv. uni. 1 6.121 0.184556 2 68.116 0.896743 3 2.473 0.079124 4 4.926 0.151441 5 11.341 0.314800 6 32.074 0.656697 7 51.301 0.819141 8 3.734 0.117029 9 8.943 0.257764 10 10.739 0.300897 11 34.559 0.683984 12 77.868 0.925398 13 72.127 0.909666 14 14.961 0.392675 15 56.950 0.850183 16 38.672 0.724471 17 31.153 0.645987 18 35.699 0.695773 19 76.196 0.921122 20 51.647 0.821212 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.347729 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-04-20_10:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -0.7 0.8 0.5 2.4 -0.6 -0.2 1.7 -0.7 -2.1 -0.1 0.0 0.6 -0.4 0.6 -1.7 -0.7 -0.2 0.5 -0.9 0.1 -0.4 2.8 1.0 0.5 -0.4 1.1 0.8 0.7 -1.0 -1.4 0.4 -1.1 -0.3 0.6 -1.0 0.0 -0.1 1.3 -0.1 -0.6 0.0 0.8 Chi-square with 42 degrees of freedom:41.588089 z-score=-0.044943, p-value=0.511085 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-04-20_10:31 Test no p-value 1 0.582933 2 0.036835 3 0.780214 4 0.628476 5 0.941221 6 0.909029 7 0.703066 8 0.771031 9 0.706703 10 0.642224 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.060803 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-04-20_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 66694 0.01 66614 0.04 3 25000.00 25050 0.10 25100 0.40 4 6666.67 6637 0.13 6612 0.45 5 1388.89 1328 2.67 1387 0.00 6 238.10 252 0.81 242 0.06 7 34.72 33 0.09 38 0.31 8 4.96 5 0.00 6 0.22 p=0.29767 p=0.03948 Number of rngs required: 688564, p-value: 0.573 RESULTS OF CRAPS TEST for dh-ranFile-2016-04-20_10:31 No. of wins: Observed Expected 98488 98585.9 z-score=-0.438, pvalue=0.33081 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66515 66666.7 0.345 0.345 2 37633 37654.3 0.012 0.357 3 27219 26954.7 2.591 2.948 4 19320 19313.5 0.002 2.950 5 13948 13851.4 0.673 3.624 6 9879 9943.5 0.419 4.043 7 7040 7145.0 1.544 5.586 8 4991 5139.1 4.266 9.853 9 3688 3699.9 0.038 9.891 10 2698 2666.3 0.377 10.268 11 1986 1923.3 2.042 12.310 12 1421 1388.7 0.749 13.059 13 990 1003.7 0.187 13.247 14 712 726.1 0.275 13.522 15 528 525.8 0.009 13.531 16 377 381.2 0.045 13.576 17 288 276.5 0.475 14.051 18 203 200.8 0.023 14.075 19 169 146.0 3.629 17.703 20 114 106.2 0.571 18.274 21 281 287.1 0.130 18.404 Chisq= 18.40 for 20 degrees of freedom, p= 0.43918 SUMMARY of craptest p-value for no. of wins: 0.330809 p-value for throws/game: 0.439181 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-04-20_10:31 No. of wins: Observed Expected 98406 98585.9 z-score=-0.804, pvalue=0.21057 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66439 66666.7 0.777 0.777 2 37827 37654.3 0.792 1.569 3 27101 26954.7 0.794 2.363 4 19560 19313.5 3.147 5.510 5 13712 13851.4 1.403 6.913 6 9877 9943.5 0.445 7.359 7 7067 7145.0 0.852 8.211 8 5082 5139.1 0.634 8.845 9 3707 3699.9 0.014 8.858 10 2631 2666.3 0.467 9.326 11 1916 1923.3 0.028 9.354 12 1399 1388.7 0.076 9.429 13 1038 1003.7 1.171 10.601 14 706 726.1 0.559 11.159 15 531 525.8 0.051 11.210 16 380 381.2 0.003 11.213 17 279 276.5 0.022 11.235 18 200 200.8 0.003 11.239 19 150 146.0 0.110 11.349 20 111 106.2 0.216 11.565 21 287 287.1 0.000 11.565 Chisq= 11.56 for 20 degrees of freedom, p= 0.06976 SUMMARY of craptest p-value for no. of wins: 0.210574 p-value for throws/game: 0.069756 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0027,0.0101,0.0126,0.0151,0.0194,0.0235,0.0262,0.0368,0.0375,0.0380, 0.0380,0.0395,0.0478,0.0501,0.0566,0.0603,0.0608,0.0642,0.0698,0.0723, 0.0749,0.0791,0.0800,0.0811,0.0819,0.0924,0.1005,0.1025,0.1170,0.1194, 0.1299,0.1362,0.1395,0.1466,0.1512,0.1514,0.1514,0.1606,0.1630,0.1677, 0.1777,0.1778,0.1780,0.1788,0.1846,0.1921,0.1960,0.1961,0.1965,0.1986, 0.2030,0.2036,0.2052,0.2101,0.2106,0.2145,0.2165,0.2181,0.2216,0.2220, 0.2325,0.2496,0.2519,0.2578,0.2588,0.2611,0.2636,0.2646,0.2719,0.2720, 0.2761,0.2762,0.2796,0.2832,0.2855,0.2876,0.2882,0.2903,0.2923,0.2928, 0.2947,0.2977,0.3009,0.3068,0.3137,0.3148,0.3296,0.3308,0.3319,0.3328, 0.3351,0.3362,0.3466,0.3476,0.3477,0.3492,0.3505,0.3536,0.3604,0.3680, 0.3682,0.3712,0.3724,0.3762,0.3810,0.3825,0.3843,0.3870,0.3870,0.3884, 0.3902,0.3921,0.3927,0.3931,0.3953,0.4018,0.4018,0.4191,0.4392,0.4411, 0.4415,0.4497,0.4502,0.4525,0.4588,0.4597,0.4772,0.4773,0.4777,0.4812, 0.4933,0.5059,0.5062,0.5088,0.5111,0.5127,0.5173,0.5220,0.5322,0.5342, 0.5454,0.5487,0.5536,0.5589,0.5614,0.5636,0.5664,0.5677,0.5720,0.5735, 0.5757,0.5780,0.5805,0.5811,0.5828,0.5829,0.5845,0.5945,0.6002,0.6008, 0.6134,0.6138,0.6188,0.6201,0.6235,0.6243,0.6285,0.6290,0.6310,0.6399, 0.6422,0.6446,0.6460,0.6549,0.6567,0.6594,0.6638,0.6650,0.6652,0.6695, 0.6748,0.6784,0.6840,0.6920,0.6941,0.6958,0.6958,0.7002,0.7031,0.7047, 0.7067,0.7098,0.7225,0.7240,0.7245,0.7260,0.7309,0.7334,0.7367,0.7402, 0.7409,0.7456,0.7465,0.7530,0.7536,0.7626,0.7710,0.7735,0.7752,0.7758, 0.7802,0.7812,0.7888,0.7937,0.8032,0.8062,0.8079,0.8115,0.8152,0.8184, 0.8191,0.8212,0.8312,0.8481,0.8502,0.8527,0.8543,0.8563,0.8598,0.8787, 0.8813,0.8875,0.8894,0.8967,0.9038,0.9067,0.9070,0.9090,0.9097,0.9112, 0.9158,0.9189,0.9205,0.9211,0.9254,0.9298,0.9317,0.9339,0.9345,0.9389, 0.9391,0.9412,0.9489,0.9495,0.9502,0.9519,0.9555,0.9576,0.9629,0.9703, 0.9778,0.9788,0.9822,0.9918,0.9922,0.9932,0.9954,0.9995,0.9999, Overall p-value after applying KStest on 269 p-values = 0.877258 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.