RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-08-14_09:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.92 22.9218 0.848186 2 to 25 15.91 20.6885 0.759464 3 to 26 15.64 14.2220 0.348667 4 to 27 16.00 12.9224 0.258634 5 to 28 15.54 12.3718 0.222879 6 to 29 15.65 15.1800 0.417485 7 to 30 15.81 9.3125 0.070056 8 to 31 15.92 18.0000 0.611162 9 to 32 15.71 17.2158 0.560162 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.912875 Tough bday spacings test for dh-ranFile-2015-08-14_09:31: 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 10 42 91 91 90 73 54 20 12 13 4 (O-E)^2/E 0.1 0.8 4.3 0.5 0.6 0.3 0.1 3.2 0.6 6.2 0.0 Birthday Spacings: Sum(O-E)^2/E= 16.557, p= 0.915 RESULTS OF GCD FOR dh-ranFile-2015-08-14_09:31 Euclid's algorithm: p-value, steps to gcd: 0.251039 p-value, dist. of gcd's: 0.312875 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-08-14_09:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.555 0.095 0.701 0.418 0.450 0.672 0.059 0.414 Bits 8 to 15---> 0.529 0.234 0.502 0.670 0.095 0.173 0.750 0.347 Bits 16 to 23---> 0.848 0.919 0.220 0.186 0.328 0.717 0.436 0.191 Bits 24 to 31---> 0.501 0.472 0.073 0.809 0.017 0.357 0.265 0.259 KS test for the above 32 p values: 0.865 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-08-14_09:31, p-values for 5 runs: 0.1127, 0.3858, 0.2705, 0.9792, 0.7298 Rank test for binary matrices (31x31) for dh-ranFile-2015-08-14_09:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 205 211.4 0.195 0.195 r= 29 5053 5134.0 1.278 1.473 r= 30 23199 23103.0 0.399 1.872 r= 31 11543 11551.5 0.006 1.878 chi-square = 1.878 with df = 3; p-value = 0.402 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-08-14_09:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 189 211.4 2.377 2.377 r= 30 5108 5134.0 0.132 2.509 r= 31 23190 23103.0 0.327 2.836 r= 32 11513 11551.5 0.128 2.965 chi-square = 2.965 with df = 3; p-value = 0.603 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-08-14_09:31 b-rank test for bits 1 to 8, p=0.13238 b-rank test for bits 2 to 9, p=0.55857 b-rank test for bits 3 to 10, p=0.90539 b-rank test for bits 4 to 11, p=0.83334 b-rank test for bits 5 to 12, p=0.61266 b-rank test for bits 6 to 13, p=0.32450 b-rank test for bits 7 to 14, p=0.36351 b-rank test for bits 8 to 15, p=0.46908 b-rank test for bits 9 to 16, p=0.79138 b-rank test for bits 10 to 17, p=0.90908 b-rank test for bits 11 to 18, p=0.89326 b-rank test for bits 12 to 19, p=0.98403 b-rank test for bits 13 to 20, p=0.42149 b-rank test for bits 14 to 21, p=0.38719 b-rank test for bits 15 to 22, p=0.30420 b-rank test for bits 16 to 23, p=0.00288 b-rank test for bits 17 to 24, p=0.62471 b-rank test for bits 18 to 25, p=0.54709 b-rank test for bits 19 to 26, p=0.66449 b-rank test for bits 20 to 27, p=0.67865 b-rank test for bits 21 to 28, p=0.57252 b-rank test for bits 22 to 29, p=0.89136 b-rank test for bits 23 to 30, p=0.37022 b-rank test for bits 24 to 31, p=0.87268 b-rank test for bits 25 to 32, p=0.89193 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 = 0.104426 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-08-14_09:31 (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 142373 1.08 0.860672 2 142299 0.91 0.818706 3 141519 -0.91 0.180888 4 141215 -1.62 0.052373 5 141712 -0.46 0.322381 6 143108 2.80 0.997450 7 142160 0.59 0.720954 8 141524 -0.90 0.183979 9 142345 1.02 0.845642 10 141525 -0.90 0.184602 11 141463 -1.04 0.148514 12 141795 -0.27 0.394686 13 141885 -0.06 0.477334 14 142182 0.64 0.737963 15 142383 1.11 0.865789 16 141749 -0.37 0.353978 17 141992 0.19 0.576581 18 142456 1.28 0.899246 19 142027 0.27 0.608315 20 141284 -1.46 0.072001 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-08-14_09:31 Bits used No. missing words z-score p-value 23 to 32 142135 0.7782 0.781766 22 to 31 142024 0.3954 0.653731 21 to 30 141923 0.0471 0.518798 20 to 29 142092 0.6299 0.735619 19 to 28 141676 -0.8046 0.210529 18 to 27 142194 0.9816 0.836857 17 to 26 141903 -0.0218 0.491293 16 to 25 141908 -0.0046 0.498170 15 to 24 141733 -0.6080 0.271582 14 to 23 141539 -1.2770 0.100801 13 to 22 142031 0.4196 0.662594 12 to 21 141732 -0.6115 0.270440 11 to 20 142650 2.5540 0.994676 10 to 19 142016 0.3678 0.643499 9 to 18 141834 -0.2598 0.397525 8 to 17 141826 -0.2873 0.386924 7 to 16 142208 1.0299 0.848471 6 to 15 142169 0.8954 0.814717 5 to 14 142166 0.8851 0.811940 4 to 13 141911 0.0058 0.502297 3 to 12 141662 -0.8529 0.196868 2 to 11 141866 -0.1494 0.440614 1 to 10 141568 -1.1770 0.119598 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-08-14_09:31 Bits used No. missing words z-score p-value 28 to 32 142243 1.1311 0.870990 27 to 31 142323 1.4023 0.919583 26 to 30 141831 -0.2655 0.395302 25 to 29 141663 -0.8350 0.201854 24 to 28 141269 -2.1706 0.014980 23 to 27 141710 -0.6757 0.249617 22 to 26 142075 0.5616 0.712803 21 to 25 142212 1.0260 0.847554 20 to 24 142306 1.3446 0.910630 19 to 23 142187 0.9413 0.826713 18 to 22 141798 -0.3774 0.352942 17 to 21 142201 0.9887 0.838598 16 to 20 142128 0.7413 0.770730 15 to 19 141995 0.2904 0.614248 14 to 18 141633 -0.9367 0.174453 13 to 17 141855 -0.1842 0.426940 12 to 16 142482 1.9413 0.973886 11 to 15 141688 -0.7503 0.226546 10 to 14 141516 -1.3333 0.091213 9 to 13 141995 0.2904 0.614248 8 to 12 141984 0.2531 0.599912 7 to 11 141591 -1.0791 0.140275 6 to 10 141876 -0.1130 0.455022 5 to 9 141612 -1.0079 0.156752 4 to 8 141735 -0.5909 0.277277 3 to 7 142091 0.6158 0.730997 2 to 6 141528 -1.2926 0.098067 1 to 5 141444 -1.5774 0.057353 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-08-14_09:31 Bits used No. missing words z-score p-value 31 to 32 141801 -0.3196 0.374652 30 to 31 142081 0.5064 0.693713 29 to 30 142169 0.7660 0.778158 28 to 29 141875 -0.1013 0.459669 27 to 28 141897 -0.0364 0.485493 26 to 27 141774 -0.3992 0.344872 25 to 26 142100 0.5624 0.713095 24 to 25 142236 0.9636 0.832384 23 to 24 141899 -0.0305 0.487845 22 to 23 141486 -1.2488 0.105876 21 to 22 142266 1.0521 0.853629 20 to 21 142571 1.9518 0.974521 19 to 20 142562 1.9253 0.972903 18 to 19 141500 -1.2075 0.113627 17 to 18 142341 1.2734 0.898555 16 to 17 142433 1.5447 0.938797 15 to 16 141891 -0.0541 0.478439 14 to 15 141868 -0.1219 0.451482 13 to 14 141416 -1.4553 0.072800 12 to 13 141793 -0.3432 0.365740 11 to 12 141865 -0.1308 0.447980 10 to 11 141892 -0.0511 0.479615 9 to 10 141999 0.2645 0.604308 8 to 9 141734 -0.5172 0.302509 7 to 8 142058 0.4386 0.669508 6 to 7 141821 -0.2606 0.397216 5 to 6 141717 -0.5673 0.285240 4 to 5 141786 -0.3638 0.358002 3 to 4 142116 0.6096 0.728952 2 to 3 141352 -1.6440 0.050084 1 to 2 141703 -0.6086 0.271381 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-08-14_09:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2473.70 -0.372 0.354981 Test results for specific bytes for dh-ranFile-2015-08-14_09:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2453.61 -0.656 0.255879 2 to 9 2453.72 -0.654 0.256412 3 to 10 2401.64 -1.391 0.082117 4 to 11 2563.43 0.897 0.815168 5 to 12 2541.85 0.592 0.723001 6 to 13 2467.55 -0.459 0.323172 7 to 14 2459.48 -0.573 0.283304 8 to 15 2540.23 0.569 0.715282 9 to 16 2426.83 -1.035 0.150400 10 to 17 2480.33 -0.278 0.390454 11 to 18 2524.86 0.352 0.637408 12 to 19 2434.12 -0.932 0.175760 13 to 20 2467.70 -0.457 0.323906 14 to 21 2399.31 -1.424 0.077222 15 to 22 2555.38 0.783 0.783222 16 to 23 2352.73 -2.083 0.018639 17 to 24 2576.89 1.087 0.861553 18 to 25 2530.30 0.428 0.665853 19 to 26 2339.09 -2.276 0.011434 20 to 27 2650.61 2.130 0.983410 21 to 28 2526.18 0.370 0.644390 22 to 29 2483.88 -0.228 0.409851 23 to 30 2306.94 -2.730 0.003163 24 to 31 2462.80 -0.526 0.299413 25 to 32 2473.32 -0.377 0.352972 CDPARK for dh-ranFile-2015-08-14_09:31: 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 3528 0.2283 0.590298 3528 0.2283 0.590298 3541 0.8219 0.794438 3467 -2.5571 0.005278 3525 0.0913 0.536383 3526 0.1370 0.554479 3540 0.7763 0.781201 3511 -0.5479 0.291865 3521 -0.0913 0.463617 3526 0.1370 0.554479 Square side=100, avg. no. parked=3521.30 sample std.=19.85 p-value of the KSTEST for those 10 p-values: 0.327663 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-08-14_09:31 0.7372,0.2378,0.0320,0.2579,0.8150,0.0770,0.8691,0.4774,0.2855,0.7645, The KS test for those 10 p-values: 0.797984 The 3DSPHERES test for dh-ranFile-2015-08-14_09:31 sample no r^3 equiv. uni. 1 12.653 0.344108 2 16.139 0.416069 3 2.625 0.083795 4 28.035 0.607216 5 34.758 0.686076 6 21.274 0.507926 7 42.793 0.759833 8 37.609 0.714534 9 28.621 0.614814 10 77.106 0.923480 11 21.253 0.507590 12 20.059 0.487583 13 13.563 0.363700 14 12.038 0.330526 15 14.104 0.375074 16 1.234 0.040283 17 1.594 0.051736 18 25.092 0.566737 19 4.240 0.131803 20 13.324 0.358628 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.360028 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-08-14_09:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 -0.3 -0.6 1.8 -0.3 2.5 0.6 0.1 -0.3 -1.0 -1.1 -1.4 0.4 0.9 -0.1 0.6 -1.3 0.5 -1.8 1.2 1.6 -0.1 -0.1 -1.1 -0.5 0.6 1.2 0.5 0.3 -0.7 2.0 1.0 -0.4 -1.1 -0.4 -1.0 0.7 0.2 -0.8 0.4 -0.6 -1.0 -1.1 Chi-square with 42 degrees of freedom:41.197924 z-score=-0.087514, p-value=0.493960 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-08-14_09:31 Test no p-value 1 0.076754 2 0.628230 3 0.004976 4 0.474389 5 0.009215 6 0.319889 7 0.371977 8 0.211142 9 0.257449 10 0.630819 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.026580 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-08-14_09:31: (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 66591 0.09 66613 0.04 3 25000.00 25103 0.42 25141 0.80 4 6666.67 6664 0.00 6596 0.75 5 1388.89 1377 0.10 1361 0.56 6 238.10 229 0.35 247 0.33 7 34.72 33 0.09 31 0.40 8 4.96 2 1.77 10 5.12 p=0.16798 p=0.76194 Number of rngs required: 687797, p-value: 0.242 RESULTS OF CRAPS TEST for dh-ranFile-2015-08-14_09:31 No. of wins: Observed Expected 98991 98585.9 z-score= 1.812, pvalue=0.96501 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66945 66666.7 1.162 1.162 2 37782 37654.3 0.433 1.595 3 26662 26954.7 3.179 4.774 4 19406 19313.5 0.443 5.217 5 13995 13851.4 1.488 6.706 6 9663 9943.5 7.915 14.621 7 7083 7145.0 0.538 15.159 8 5129 5139.1 0.020 15.179 9 3612 3699.9 2.087 17.266 10 2626 2666.3 0.609 17.875 11 1887 1923.3 0.686 18.561 12 1417 1388.7 0.575 19.136 13 1033 1003.7 0.854 19.990 14 769 726.1 2.530 22.520 15 558 525.8 1.967 24.488 16 379 381.2 0.012 24.500 17 274 276.5 0.023 24.523 18 203 200.8 0.023 24.546 19 175 146.0 5.767 30.314 20 96 106.2 0.982 31.296 21 306 287.1 1.242 32.538 Chisq= 32.54 for 20 degrees of freedom, p= 0.96211 SUMMARY of craptest p-value for no. of wins: 0.965009 p-value for throws/game: 0.962111 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-08-14_09:31 No. of wins: Observed Expected 98601 98585.9 z-score= 0.068, pvalue=0.52700 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66821 66666.7 0.357 0.357 2 37675 37654.3 0.011 0.369 3 26550 26954.7 6.077 6.446 4 19178 19313.5 0.950 7.396 5 14146 13851.4 6.265 13.661 6 10036 9943.5 0.860 14.520 7 7162 7145.0 0.040 14.561 8 5116 5139.1 0.104 14.664 9 3632 3699.9 1.245 15.909 10 2624 2666.3 0.671 16.580 11 1892 1923.3 0.510 17.091 12 1413 1388.7 0.424 17.514 13 1008 1003.7 0.018 17.533 14 726 726.1 0.000 17.533 15 585 525.8 6.657 24.189 16 404 381.2 1.370 25.559 17 311 276.5 4.294 29.853 18 198 200.8 0.040 29.893 19 141 146.0 0.170 30.064 20 88 106.2 3.124 33.187 21 294 287.1 0.165 33.352 Chisq= 33.35 for 20 degrees of freedom, p= 0.96915 SUMMARY of craptest p-value for no. of wins: 0.526996 p-value for throws/game: 0.969146 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0029,0.0032,0.0050,0.0053,0.0092,0.0114,0.0150,0.0172,0.0186,0.0266, 0.0320,0.0403,0.0501,0.0517,0.0524,0.0574,0.0592,0.0701,0.0720,0.0728, 0.0734,0.0768,0.0770,0.0772,0.0821,0.0838,0.0912,0.0949,0.0952,0.0981, 0.1008,0.1044,0.1059,0.1127,0.1136,0.1196,0.1318,0.1324,0.1403,0.1485, 0.1504,0.1568,0.1680,0.1730,0.1745,0.1758,0.1809,0.1840,0.1846,0.1858, 0.1914,0.1969,0.2019,0.2105,0.2111,0.2196,0.2229,0.2265,0.2343,0.2378, 0.2421,0.2496,0.2510,0.2559,0.2564,0.2574,0.2579,0.2586,0.2592,0.2645, 0.2704,0.2705,0.2714,0.2716,0.2773,0.2833,0.2852,0.2855,0.2919,0.2994, 0.3025,0.3042,0.3129,0.3199,0.3224,0.3232,0.3239,0.3245,0.3276,0.3277, 0.3305,0.3441,0.3449,0.3472,0.3487,0.3529,0.3530,0.3540,0.3550,0.3571, 0.3580,0.3586,0.3600,0.3635,0.3637,0.3657,0.3702,0.3720,0.3747,0.3751, 0.3858,0.3869,0.3872,0.3905,0.3947,0.3953,0.3972,0.3975,0.4019,0.4099, 0.4143,0.4161,0.4175,0.4183,0.4215,0.4269,0.4362,0.4406,0.4480,0.4503, 0.4515,0.4550,0.4597,0.4636,0.4691,0.4717,0.4744,0.4773,0.4774,0.4784, 0.4796,0.4855,0.4876,0.4878,0.4913,0.4940,0.4982,0.5011,0.5018,0.5023, 0.5076,0.5079,0.5188,0.5270,0.5290,0.5364,0.5471,0.5545,0.5545,0.5553, 0.5586,0.5602,0.5667,0.5725,0.5766,0.5903,0.5903,0.5999,0.6029,0.6043, 0.6072,0.6083,0.6112,0.6127,0.6142,0.6142,0.6148,0.6247,0.6282,0.6308, 0.6374,0.6435,0.6444,0.6537,0.6626,0.6645,0.6659,0.6695,0.6701,0.6720, 0.6786,0.6861,0.6937,0.7006,0.7128,0.7131,0.7145,0.7153,0.7166,0.7210, 0.7230,0.7290,0.7298,0.7310,0.7356,0.7372,0.7380,0.7503,0.7595,0.7598, 0.7619,0.7645,0.7707,0.7782,0.7812,0.7818,0.7832,0.7914,0.7944,0.7980, 0.8088,0.8119,0.8147,0.8150,0.8152,0.8187,0.8267,0.8324,0.8333,0.8369, 0.8386,0.8456,0.8476,0.8482,0.8484,0.8485,0.8536,0.8607,0.8616,0.8651, 0.8658,0.8691,0.8710,0.8727,0.8914,0.8919,0.8933,0.8986,0.8992,0.9054, 0.9091,0.9106,0.9129,0.9152,0.9191,0.9196,0.9235,0.9388,0.9621,0.9650, 0.9691,0.9729,0.9739,0.9745,0.9792,0.9834,0.9840,0.9947,0.9974, Overall p-value after applying KStest on 269 p-values = 0.450928 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.