RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-01-24_17:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.81 21.1939 0.782263 2 to 25 15.47 22.2296 0.823951 3 to 26 15.95 8.4924 0.045146 4 to 27 15.74 14.1866 0.346145 5 to 28 16.00 19.3560 0.691513 6 to 29 15.44 22.1220 0.819928 7 to 30 15.86 18.9461 0.668364 8 to 31 15.80 17.5267 0.580731 9 to 32 15.72 16.9131 0.539729 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.369654 Tough bday spacings test for dh-ranFile-2016-01-24_17:31: 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 11 40 73 111 75 78 49 29 15 10 9 (O-E)^2/E 0.4 0.3 0.0 1.8 5.3 0.0 0.2 0.0 0.0 1.7 6.0 Birthday Spacings: Sum(O-E)^2/E= 15.688, p= 0.891 RESULTS OF GCD FOR dh-ranFile-2016-01-24_17:31 Euclid's algorithm: p-value, steps to gcd: 0.693283 p-value, dist. of gcd's: 0.418521 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-01-24_17:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.697 0.573 0.711 0.936 0.864 0.682 0.527 0.276 Bits 8 to 15---> 0.026 0.961 0.558 0.011 0.081 0.469 0.190 0.803 Bits 16 to 23---> 0.883 0.849 0.009 0.759 0.456 0.793 0.372 0.262 Bits 24 to 31---> 0.361 0.477 0.974 0.646 0.363 0.196 0.007 0.226 KS test for the above 32 p values: 0.308 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-01-24_17:31, p-values for 5 runs: 0.9864, 0.1200, 0.6718, 0.0943, 0.4393 Rank test for binary matrices (31x31) for dh-ranFile-2016-01-24_17:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 223 211.4 0.634 0.634 r= 29 5156 5134.0 0.094 0.729 r= 30 23033 23103.0 0.212 0.941 r= 31 11588 11551.5 0.115 1.056 chi-square = 1.056 with df = 3; p-value = 0.212 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-01-24_17:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 208 211.4 0.055 0.055 r= 30 5113 5134.0 0.086 0.141 r= 31 23026 23103.0 0.257 0.398 r= 32 11653 11551.5 0.891 1.290 chi-square = 1.290 with df = 3; p-value = 0.268 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-01-24_17:31 b-rank test for bits 1 to 8, p=0.34754 b-rank test for bits 2 to 9, p=0.21409 b-rank test for bits 3 to 10, p=0.77497 b-rank test for bits 4 to 11, p=0.15356 b-rank test for bits 5 to 12, p=0.94367 b-rank test for bits 6 to 13, p=0.66914 b-rank test for bits 7 to 14, p=0.64278 b-rank test for bits 8 to 15, p=0.82087 b-rank test for bits 9 to 16, p=0.80580 b-rank test for bits 10 to 17, p=0.65410 b-rank test for bits 11 to 18, p=0.17766 b-rank test for bits 12 to 19, p=0.17084 b-rank test for bits 13 to 20, p=0.09171 b-rank test for bits 14 to 21, p=0.17850 b-rank test for bits 15 to 22, p=0.36525 b-rank test for bits 16 to 23, p=0.93884 b-rank test for bits 17 to 24, p=0.63534 b-rank test for bits 18 to 25, p=0.18992 b-rank test for bits 19 to 26, p=0.04725 b-rank test for bits 20 to 27, p=0.55415 b-rank test for bits 21 to 28, p=0.31708 b-rank test for bits 22 to 29, p=0.66474 b-rank test for bits 23 to 30, p=0.59728 b-rank test for bits 24 to 31, p=0.39798 b-rank test for bits 25 to 32, p=0.78071 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 = 0.847770 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-01-24_17:31 (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 141953 0.10 0.540635 2 142054 0.34 0.632324 3 141944 0.08 0.532281 4 142236 0.76 0.777342 5 141786 -0.29 0.386614 6 141678 -0.54 0.294429 7 141824 -0.20 0.420987 8 141597 -0.73 0.232774 9 142363 1.06 0.855422 10 142747 1.96 0.974836 11 142167 0.60 0.726424 12 142319 0.96 0.830760 13 142421 1.20 0.884052 14 142618 1.66 0.951116 15 142130 0.52 0.696928 16 142002 0.22 0.585708 17 141506 -0.94 0.173004 18 142078 0.39 0.653242 19 142117 0.49 0.686236 20 142011 0.24 0.593884 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-01-24_17:31 Bits used No. missing words z-score p-value 23 to 32 141894 -0.0529 0.478921 22 to 31 142430 1.7954 0.963706 21 to 30 142274 1.2575 0.895711 20 to 29 141852 -0.1977 0.421644 19 to 28 142064 0.5333 0.703103 18 to 27 141365 -1.8770 0.030259 17 to 26 141821 -0.3046 0.380341 16 to 25 141992 0.2851 0.612204 15 to 24 141794 -0.3977 0.345430 14 to 23 142106 0.6782 0.751169 13 to 22 142037 0.4402 0.670119 12 to 21 141612 -1.0253 0.152617 11 to 20 141661 -0.8563 0.195913 10 to 19 141867 -0.1460 0.441974 9 to 18 142104 0.6713 0.748978 8 to 17 141432 -1.6460 0.049885 7 to 16 142193 0.9782 0.836006 6 to 15 142005 0.3299 0.629261 5 to 14 141724 -0.6391 0.261389 4 to 13 142063 0.5299 0.701908 3 to 12 141868 -0.1425 0.443336 2 to 11 142198 0.9954 0.840233 1 to 10 142005 0.3299 0.629261 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-01-24_17:31 Bits used No. missing words z-score p-value 28 to 32 141147 -2.5842 0.004881 27 to 31 142070 0.5446 0.707001 26 to 30 142017 0.3650 0.642438 25 to 29 141767 -0.4825 0.314734 24 to 28 142673 2.5887 0.995183 23 to 27 141957 0.1616 0.564187 22 to 26 142231 1.0904 0.862233 21 to 25 141973 0.2158 0.585440 20 to 24 142312 1.3650 0.913871 19 to 23 141449 -1.5604 0.059328 18 to 22 142003 0.3175 0.624578 17 to 21 141550 -1.2181 0.111599 16 to 20 141450 -1.5571 0.059729 15 to 19 141958 0.1650 0.565521 14 to 18 142832 3.1277 0.999119 13 to 17 141565 -1.1672 0.121561 12 to 16 142129 0.7446 0.771757 11 to 15 142112 0.6870 0.753964 10 to 14 142196 0.9718 0.834416 9 to 13 141981 0.2429 0.595978 8 to 12 141851 -0.1977 0.421629 7 to 11 141966 0.1921 0.576169 6 to 10 141897 -0.0418 0.483330 5 to 9 142064 0.5243 0.699967 4 to 8 141658 -0.8520 0.197116 3 to 7 141507 -1.3638 0.086310 2 to 6 141867 -0.1435 0.442951 1 to 5 141752 -0.5333 0.296905 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-01-24_17:31 Bits used No. missing words z-score p-value 31 to 32 141888 -0.0629 0.474915 30 to 31 142124 0.6332 0.736713 29 to 30 141492 -1.2311 0.109150 28 to 29 141281 -1.8535 0.031907 27 to 28 142019 0.3235 0.626846 26 to 27 142290 1.1229 0.869264 25 to 26 142062 0.4504 0.673772 24 to 25 141848 -0.1809 0.428217 23 to 24 141701 -0.6145 0.269428 22 to 23 141884 -0.0747 0.470219 21 to 22 141706 -0.5998 0.274322 20 to 21 141649 -0.7679 0.221263 19 to 20 142250 1.0049 0.842534 18 to 19 141988 0.2321 0.591756 17 to 18 142070 0.4740 0.682233 16 to 17 142285 1.1082 0.866106 15 to 16 142149 0.7070 0.760214 14 to 15 141677 -0.6853 0.246565 13 to 14 142265 1.0492 0.852951 12 to 13 141830 -0.2340 0.407488 11 to 12 142298 1.1465 0.874210 10 to 11 141333 -1.7001 0.044557 9 to 10 142040 0.3855 0.650051 8 to 9 141855 -0.1603 0.436336 7 to 8 141806 -0.3048 0.380256 6 to 7 141743 -0.4906 0.311837 5 to 6 141964 0.1613 0.564059 4 to 5 142111 0.5949 0.724044 3 to 4 142005 0.2822 0.611110 2 to 3 141547 -1.0688 0.142575 1 to 2 141378 -1.5673 0.058517 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-01-24_17:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2396.40 -1.465 0.071439 Test results for specific bytes for dh-ranFile-2016-01-24_17:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2396.11 -1.469 0.070878 2 to 9 2521.66 0.306 0.620331 3 to 10 2463.86 -0.511 0.304624 4 to 11 2625.80 1.779 0.962381 5 to 12 2482.37 -0.249 0.401542 6 to 13 2402.11 -1.384 0.083120 7 to 14 2593.14 1.317 0.906121 8 to 15 2556.99 0.806 0.789863 9 to 16 2536.80 0.520 0.698637 10 to 17 2586.71 1.226 0.889957 11 to 18 2460.53 -0.558 0.288362 12 to 19 2516.11 0.228 0.590105 13 to 20 2569.85 0.988 0.838367 14 to 21 2525.42 0.359 0.640382 15 to 22 2383.69 -1.645 0.049994 16 to 23 2444.50 -0.785 0.216277 17 to 24 2519.06 0.270 0.606263 18 to 25 2450.04 -0.707 0.239923 19 to 26 2399.81 -1.417 0.078254 20 to 27 2605.12 1.487 0.931451 21 to 28 2440.69 -0.839 0.200815 22 to 29 2401.05 -1.399 0.080850 23 to 30 2404.92 -1.345 0.089375 24 to 31 2591.38 1.292 0.901882 25 to 32 2461.72 -0.541 0.294122 CDPARK for dh-ranFile-2016-01-24_17:31: 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 3489 -1.5525 0.060270 3531 0.3653 0.642555 3516 -0.3196 0.374623 3508 -0.6849 0.246694 3511 -0.5479 0.291865 3490 -1.5068 0.065925 3525 0.0913 0.536383 3521 -0.0913 0.463617 3524 0.0457 0.518210 3543 0.9132 0.819442 Square side=100, avg. no. parked=3515.80 sample std.=16.18 p-value of the KSTEST for those 10 p-values: 0.435155 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-01-24_17:31 0.0678,0.7856,0.2535,0.6708,0.5233,0.9620,0.2173,0.7814,0.1643,0.1891, The KS test for those 10 p-values: 0.829319 The 3DSPHERES test for dh-ranFile-2016-01-24_17:31 sample no r^3 equiv. uni. 1 24.311 0.555306 2 1.869 0.060397 3 28.772 0.616746 4 5.615 0.170685 5 47.759 0.796472 6 41.495 0.749221 7 23.642 0.545275 8 35.989 0.698700 9 35.902 0.697820 10 16.015 0.413649 11 24.038 0.551238 12 19.265 0.473847 13 21.254 0.507596 14 16.487 0.422809 15 55.172 0.841034 16 47.561 0.795131 17 21.039 0.504061 18 49.183 0.805910 19 68.036 0.896468 20 104.100 0.968883 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.108765 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-01-24_17:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.1 0.6 -0.1 1.2 -0.8 0.1 -0.3 -1.0 -0.0 0.8 -0.7 -1.6 0.3 2.3 -0.5 0.4 -1.8 -1.5 1.7 0.8 1.0 -0.8 0.3 -1.2 -0.2 -0.0 0.9 1.4 1.6 -1.8 -0.6 1.7 -1.1 -0.2 -0.1 -0.5 1.1 1.3 -0.7 0.1 -1.0 -0.1 Chi-square with 42 degrees of freedom:42.725269 z-score=0.079133, p-value=0.560170 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-01-24_17:31 Test no p-value 1 0.275715 2 0.035598 3 0.063581 4 0.008056 5 0.080024 6 0.689890 7 0.055913 8 0.273309 9 0.988460 10 0.984236 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.009076 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-01-24_17:31: (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 66602 0.06 66782 0.20 3 25000.00 25198 1.57 25016 0.01 4 6666.67 6556 1.84 6571 1.37 5 1388.89 1381 0.04 1377 0.10 6 238.10 227 0.52 221 1.23 7 34.72 31 0.40 27 1.72 8 4.96 4 0.19 5 0.00 p=0.40586 p=0.40777 Number of rngs required: 687120, p-value: 0.067 RESULTS OF CRAPS TEST for dh-ranFile-2016-01-24_17:31 No. of wins: Observed Expected 98670 98585.9 z-score= 0.376, pvalue=0.64666 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66871 66666.7 0.626 0.626 2 37821 37654.3 0.738 1.364 3 26959 26954.7 0.001 1.365 4 19303 19313.5 0.006 1.370 5 13725 13851.4 1.154 2.524 6 9885 9943.5 0.345 2.869 7 7130 7145.0 0.032 2.901 8 5119 5139.1 0.078 2.979 9 3662 3699.9 0.388 3.366 10 2596 2666.3 1.853 5.220 11 1885 1923.3 0.764 5.984 12 1397 1388.7 0.049 6.033 13 1022 1003.7 0.333 6.366 14 757 726.1 1.311 7.677 15 525 525.8 0.001 7.679 16 362 381.2 0.962 8.641 17 268 276.5 0.264 8.905 18 206 200.8 0.133 9.038 19 124 146.0 3.311 12.348 20 90 106.2 2.475 14.824 21 293 287.1 0.121 14.945 Chisq= 14.94 for 20 degrees of freedom, p= 0.22043 SUMMARY of craptest p-value for no. of wins: 0.646664 p-value for throws/game: 0.220429 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-01-24_17:31 No. of wins: Observed Expected 98368 98585.9 z-score=-0.974, pvalue=0.16493 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66578 66666.7 0.118 0.118 2 37753 37654.3 0.259 0.377 3 27002 26954.7 0.083 0.459 4 19283 19313.5 0.048 0.507 5 13884 13851.4 0.077 0.584 6 9950 9943.5 0.004 0.588 7 7178 7145.0 0.152 0.740 8 5145 5139.1 0.007 0.747 9 3597 3699.9 2.860 3.607 10 2627 2666.3 0.579 4.186 11 1893 1923.3 0.478 4.665 12 1441 1388.7 1.967 6.631 13 1013 1003.7 0.086 6.717 14 752 726.1 0.921 7.638 15 503 525.8 0.992 8.630 16 399 381.2 0.836 9.466 17 274 276.5 0.023 9.489 18 204 200.8 0.050 9.539 19 139 146.0 0.334 9.873 20 98 106.2 0.635 10.509 21 287 287.1 0.000 10.509 Chisq= 10.51 for 20 degrees of freedom, p= 0.04201 SUMMARY of craptest p-value for no. of wins: 0.164931 p-value for throws/game: 0.042015 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0049,0.0066,0.0081,0.0089,0.0091,0.0109,0.0256,0.0303,0.0319,0.0356, 0.0420,0.0446,0.0451,0.0472,0.0499,0.0500,0.0559,0.0585,0.0593,0.0597, 0.0603,0.0604,0.0636,0.0659,0.0670,0.0678,0.0709,0.0714,0.0783,0.0800, 0.0807,0.0808,0.0831,0.0863,0.0894,0.0917,0.0943,0.1088,0.1091,0.1116, 0.1200,0.1216,0.1426,0.1526,0.1536,0.1643,0.1649,0.1707,0.1708,0.1730, 0.1777,0.1785,0.1891,0.1898,0.1899,0.1955,0.1959,0.1971,0.2008,0.2124, 0.2141,0.2163,0.2173,0.2204,0.2213,0.2259,0.2328,0.2399,0.2466,0.2467, 0.2535,0.2614,0.2623,0.2684,0.2694,0.2733,0.2743,0.2757,0.2760,0.2884, 0.2919,0.2941,0.2944,0.2969,0.3046,0.3079,0.3118,0.3147,0.3171,0.3454, 0.3461,0.3475,0.3605,0.3625,0.3652,0.3697,0.3722,0.3746,0.3803,0.3803, 0.3866,0.3980,0.4015,0.4059,0.4075,0.4078,0.4136,0.4185,0.4210,0.4216, 0.4216,0.4228,0.4282,0.4352,0.4363,0.4393,0.4420,0.4430,0.4433,0.4565, 0.4636,0.4688,0.4702,0.4738,0.4749,0.4767,0.4789,0.4833,0.5041,0.5076, 0.5182,0.5233,0.5273,0.5323,0.5364,0.5397,0.5406,0.5453,0.5512,0.5541, 0.5553,0.5582,0.5602,0.5641,0.5642,0.5655,0.5733,0.5762,0.5807,0.5854, 0.5857,0.5901,0.5918,0.5939,0.5960,0.5973,0.6063,0.6111,0.6122,0.6167, 0.6203,0.6246,0.6268,0.6293,0.6293,0.6323,0.6353,0.6404,0.6424,0.6426, 0.6428,0.6456,0.6467,0.6501,0.6532,0.6541,0.6647,0.6684,0.6691,0.6701, 0.6708,0.6718,0.6738,0.6818,0.6822,0.6862,0.6899,0.6915,0.6933,0.6966, 0.6969,0.6978,0.6986,0.6987,0.7000,0.7019,0.7031,0.7070,0.7113,0.7240, 0.7264,0.7367,0.7490,0.7492,0.7512,0.7540,0.7586,0.7602,0.7718,0.7750, 0.7773,0.7807,0.7814,0.7823,0.7856,0.7899,0.7930,0.7951,0.7965,0.8029, 0.8058,0.8059,0.8194,0.8199,0.8209,0.8240,0.8293,0.8308,0.8344,0.8360, 0.8384,0.8402,0.8410,0.8425,0.8478,0.8495,0.8530,0.8554,0.8622,0.8635, 0.8661,0.8693,0.8742,0.8830,0.8841,0.8900,0.8911,0.8957,0.8965,0.9019, 0.9061,0.9139,0.9315,0.9362,0.9388,0.9437,0.9511,0.9615,0.9620,0.9624, 0.9637,0.9689,0.9736,0.9748,0.9842,0.9864,0.9885,0.9952,0.9991, Overall p-value after applying KStest on 269 p-values = 0.586961 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.