RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-08-14_21:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.91 18.9994 0.671431 2 to 25 15.67 19.7930 0.715044 3 to 26 15.61 17.5554 0.582607 4 to 27 15.71 15.9611 0.473403 5 to 28 15.62 11.4956 0.170327 6 to 29 15.58 21.7837 0.806820 7 to 30 15.88 17.2670 0.563578 8 to 31 15.94 18.8695 0.663929 9 to 32 15.52 1653268998690766848.0000 1.000000 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.001293 Tough bday spacings test for dh-ranFile-2015-08-14_21:31: 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 35 81 97 98 77 57 20 16 4 7 (O-E)^2/E 0.1 0.1 0.8 0.0 0.0 0.0 0.5 3.2 0.1 1.0 2.1 Birthday Spacings: Sum(O-E)^2/E= 7.961, p= 0.367 RESULTS OF GCD FOR dh-ranFile-2015-08-14_21:31 Euclid's algorithm: p-value, steps to gcd: 0.244583 p-value, dist. of gcd's: 0.541082 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-08-14_21:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.264 0.048 0.441 0.293 0.202 0.850 0.290 0.417 Bits 8 to 15---> 0.657 0.188 0.137 0.213 0.610 0.527 0.586 0.191 Bits 16 to 23---> 0.016 0.839 0.614 0.193 0.196 0.668 0.593 0.959 Bits 24 to 31---> 0.104 0.406 0.811 0.619 0.685 0.252 0.392 0.838 KS test for the above 32 p values: 0.678 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-08-14_21:31, p-values for 5 runs: 0.3422, 0.4951, 0.7545, 0.3059, 0.2012 Rank test for binary matrices (31x31) for dh-ranFile-2015-08-14_21:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 207 211.4 0.092 0.092 r= 29 5141 5134.0 0.010 0.102 r= 30 22962 23103.0 0.861 0.963 r= 31 11690 11551.5 1.660 2.623 chi-square = 2.623 with df = 3; p-value = 0.547 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-08-14_21:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 202 211.4 0.420 0.420 r= 30 5054 5134.0 1.247 1.666 r= 31 23024 23103.0 0.270 1.937 r= 32 11720 11551.5 2.457 4.394 chi-square = 4.394 with df = 3; p-value = 0.778 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-08-14_21:31 b-rank test for bits 1 to 8, p=0.61575 b-rank test for bits 2 to 9, p=0.19684 b-rank test for bits 3 to 10, p=0.16068 b-rank test for bits 4 to 11, p=0.01972 b-rank test for bits 5 to 12, p=0.88815 b-rank test for bits 6 to 13, p=0.73444 b-rank test for bits 7 to 14, p=0.48297 b-rank test for bits 8 to 15, p=0.50276 b-rank test for bits 9 to 16, p=0.60959 b-rank test for bits 10 to 17, p=0.86648 b-rank test for bits 11 to 18, p=0.29798 b-rank test for bits 12 to 19, p=0.42826 b-rank test for bits 13 to 20, p=0.53544 b-rank test for bits 14 to 21, p=0.56852 b-rank test for bits 15 to 22, p=0.10217 b-rank test for bits 16 to 23, p=0.10357 b-rank test for bits 17 to 24, p=0.77517 b-rank test for bits 18 to 25, p=0.55249 b-rank test for bits 19 to 26, p=0.49964 b-rank test for bits 20 to 27, p=0.45512 b-rank test for bits 21 to 28, p=0.27081 b-rank test for bits 22 to 29, p=0.97958 b-rank test for bits 23 to 30, p=0.73705 b-rank test for bits 24 to 31, p=0.96699 b-rank test for bits 25 to 32, p=0.56623 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 = 0.861339 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-08-14_21:31 (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 141561 -0.81 0.207864 2 141635 -0.64 0.260775 3 142672 1.78 0.962620 4 141218 -1.62 0.053128 5 141682 -0.53 0.297659 6 142619 1.66 0.951352 7 142352 1.03 0.849496 8 142062 0.36 0.639344 9 142303 0.92 0.821159 10 141909 -0.00 0.499692 11 141742 -0.39 0.347914 12 142369 1.07 0.858588 13 141739 -0.40 0.345327 14 142394 1.13 0.871268 15 141815 -0.22 0.412781 16 141867 -0.10 0.460608 17 141679 -0.54 0.295235 18 141897 -0.03 0.488509 19 142440 1.24 0.892491 20 142143 0.55 0.707453 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-08-14_21:31 Bits used No. missing words z-score p-value 23 to 32 141487 -1.4563 0.072653 22 to 31 141319 -2.0356 0.020894 21 to 30 142002 0.3196 0.625346 20 to 29 141847 -0.2149 0.414911 19 to 28 142758 2.9264 0.998286 18 to 27 141676 -0.8046 0.210529 17 to 26 141526 -1.3218 0.093113 16 to 25 141659 -0.8632 0.194012 15 to 24 141640 -0.9287 0.176516 14 to 23 142138 0.7885 0.784803 13 to 22 142115 0.7092 0.760902 12 to 21 142087 0.6127 0.729948 11 to 20 141878 -0.1080 0.456984 10 to 19 141158 -2.5908 0.004788 9 to 18 141531 -1.3046 0.096017 8 to 17 141581 -1.1322 0.128781 7 to 16 142050 0.4851 0.686186 6 to 15 142460 1.8989 0.971209 5 to 14 141873 -0.1253 0.450153 4 to 13 142122 0.7333 0.768326 3 to 12 142117 0.7161 0.763036 2 to 11 141772 -0.4736 0.317910 1 to 10 142100 0.6575 0.744565 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-08-14_21:31 Bits used No. missing words z-score p-value 28 to 32 142379 1.5921 0.944319 27 to 31 142083 0.5887 0.721973 26 to 30 141697 -0.7198 0.235836 25 to 29 141780 -0.4384 0.330546 24 to 28 141512 -1.3469 0.089009 23 to 27 141825 -0.2859 0.387491 22 to 26 141840 -0.2350 0.407098 21 to 25 141629 -0.9503 0.170987 20 to 24 141716 -0.6554 0.256119 19 to 23 141911 0.0057 0.502258 18 to 22 141662 -0.8384 0.200901 17 to 21 142100 0.6463 0.740970 16 to 20 142385 1.6124 0.946567 15 to 19 142330 1.4260 0.923066 14 to 18 141820 -0.3028 0.381016 13 to 17 142009 0.3379 0.632267 12 to 16 141904 -0.0181 0.492792 11 to 15 141580 -1.1164 0.132131 10 to 14 141437 -1.6011 0.054675 9 to 13 142259 1.1853 0.882055 8 to 12 141678 -0.7842 0.216470 7 to 11 141738 -0.5808 0.280695 6 to 10 141483 -1.4452 0.074203 5 to 9 142374 1.5752 0.942389 4 to 8 142226 1.0735 0.858467 3 to 7 141658 -0.8520 0.197116 2 to 6 141792 -0.3977 0.345415 1 to 5 141206 -2.3842 0.008559 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-08-14_21:31 Bits used No. missing words z-score p-value 31 to 32 141807 -0.3019 0.381380 30 to 31 142064 0.4563 0.675896 29 to 30 142411 1.4799 0.930544 28 to 29 141887 -0.0659 0.473741 27 to 28 141842 -0.1986 0.421283 26 to 27 141992 0.2439 0.596332 25 to 26 142442 1.5713 0.941943 24 to 25 141450 -1.3550 0.087716 23 to 24 141900 -0.0275 0.489022 22 to 23 141833 -0.2252 0.410927 21 to 22 141545 -1.0747 0.141250 20 to 21 141886 -0.0688 0.472566 19 to 20 141808 -0.2989 0.382505 18 to 19 141943 0.0993 0.539559 17 to 18 141505 -1.1927 0.116491 16 to 17 141643 -0.7856 0.216041 15 to 16 141943 0.0993 0.539559 14 to 15 142358 1.3235 0.907167 13 to 14 141527 -1.1278 0.129699 12 to 13 142035 0.3707 0.644573 11 to 12 142268 1.0580 0.854978 10 to 11 141379 -1.5644 0.058862 9 to 10 141484 -1.2547 0.104801 8 to 9 142383 1.3973 0.918832 7 to 8 142109 0.5890 0.722068 6 to 7 141965 0.1642 0.565220 5 to 6 141386 -1.5437 0.061325 4 to 5 142458 1.6185 0.947222 3 to 4 141990 0.2380 0.594046 2 to 3 141799 -0.3255 0.372418 1 to 2 141636 -0.8063 0.210040 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-08-14_21:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2561.58 0.871 0.808100 Test results for specific bytes for dh-ranFile-2015-08-14_21:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2527.14 0.384 0.649441 2 to 9 2373.25 -1.793 0.036520 3 to 10 2498.96 -0.015 0.494156 4 to 11 2395.58 -1.477 0.069872 5 to 12 2534.63 0.490 0.687825 6 to 13 2556.68 0.802 0.788606 7 to 14 2498.29 -0.024 0.490333 8 to 15 2573.05 1.033 0.849233 9 to 16 2516.41 0.232 0.591754 10 to 17 2583.02 1.174 0.879811 11 to 18 2474.31 -0.363 0.358170 12 to 19 2424.25 -1.071 0.142013 13 to 20 2434.41 -0.928 0.176822 14 to 21 2380.15 -1.695 0.045044 15 to 22 2521.24 0.300 0.618058 16 to 23 2549.86 0.705 0.759624 17 to 24 2538.32 0.542 0.706058 18 to 25 2538.02 0.538 0.704608 19 to 26 2481.92 -0.256 0.399078 20 to 27 2495.18 -0.068 0.472802 21 to 28 2493.43 -0.093 0.463008 22 to 29 2376.29 -1.750 0.040097 23 to 30 2565.92 0.932 0.824396 24 to 31 2532.25 0.456 0.675837 25 to 32 2484.30 -0.222 0.412160 CDPARK for dh-ranFile-2015-08-14_21:31: 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 3486 -1.6895 0.045562 3562 1.7808 0.962529 3536 0.5936 0.723613 3515 -0.3653 0.357445 3514 -0.4110 0.340551 3522 -0.0457 0.481790 3527 0.1826 0.572463 3542 0.8676 0.807188 3529 0.2740 0.607947 3484 -1.7808 0.037471 Square side=100, avg. no. parked=3521.70 sample std.=22.63 p-value of the KSTEST for those 10 p-values: 0.927786 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-08-14_21:31 0.6956,0.1258,0.8719,0.1115,0.7420,0.7231,0.0200,0.6916,0.5851,0.4911, The KS test for those 10 p-values: 0.620547 The 3DSPHERES test for dh-ranFile-2015-08-14_21:31 sample no r^3 equiv. uni. 1 17.135 0.435135 2 20.875 0.501342 3 95.372 0.958375 4 44.193 0.770790 5 34.470 0.683052 6 14.836 0.390153 7 2.199 0.070683 8 79.257 0.928774 9 6.877 0.204845 10 23.901 0.549188 11 13.841 0.369587 12 24.235 0.554172 13 11.623 0.321212 14 35.849 0.697286 15 35.656 0.695335 16 10.268 0.289846 17 67.232 0.893655 18 8.039 0.235058 19 28.809 0.617222 20 62.838 0.876881 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.654725 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-08-14_21:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 0.1 -0.6 -1.0 -0.5 -1.2 1.3 0.1 0.1 -0.3 -0.3 0.2 -0.7 -0.8 0.7 -0.2 0.3 -0.6 0.9 0.3 -0.3 -0.5 1.9 -0.1 0.5 -0.5 -0.0 -0.7 0.2 -0.8 -0.5 1.6 -1.8 -1.1 -1.0 0.1 -0.5 0.2 1.3 -0.1 0.1 -1.0 1.8 Chi-square with 42 degrees of freedom:28.309024 z-score=-1.493808, p-value=0.052475 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-08-14_21:31 Test no p-value 1 0.787265 2 0.026669 3 0.692909 4 0.243748 5 0.000820 6 0.728265 7 0.830153 8 0.099389 9 0.249922 10 0.762408 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.204926 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-08-14_21:31: (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 66802 0.27 66595 0.08 3 25000.00 24789 1.78 25015 0.01 4 6666.67 6781 1.96 6740 0.81 5 1388.89 1383 0.02 1373 0.18 6 238.10 207 4.06 240 0.02 7 34.72 36 0.05 30 0.64 8 4.96 1 3.16 6 0.22 p=0.92077 p=0.07571 Number of rngs required: 687438, p-value: 0.131 RESULTS OF CRAPS TEST for dh-ranFile-2015-08-14_21:31 No. of wins: Observed Expected 98052 98585.9 z-score=-2.388, pvalue=0.00848 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66740 66666.7 0.081 0.081 2 37282 37654.3 3.681 3.762 3 27085 26954.7 0.630 4.392 4 19345 19313.5 0.051 4.443 5 13724 13851.4 1.172 5.615 6 9996 9943.5 0.277 5.892 7 7193 7145.0 0.322 6.214 8 5148 5139.1 0.016 6.230 9 3765 3699.9 1.147 7.376 10 2686 2666.3 0.146 7.522 11 1978 1923.3 1.554 9.076 12 1416 1388.7 0.535 9.611 13 997 1003.7 0.045 9.656 14 728 726.1 0.005 9.661 15 545 525.8 0.698 10.359 16 371 381.2 0.270 10.630 17 276 276.5 0.001 10.631 18 194 200.8 0.232 10.863 19 146 146.0 0.000 10.863 20 107 106.2 0.006 10.869 21 278 287.1 0.289 11.158 Chisq= 11.16 for 20 degrees of freedom, p= 0.05798 SUMMARY of craptest p-value for no. of wins: 0.008476 p-value for throws/game: 0.057977 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-08-14_21:31 No. of wins: Observed Expected 98528 98585.9 z-score=-0.259, pvalue=0.39790 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66761 66666.7 0.133 0.133 2 37490 37654.3 0.717 0.851 3 27104 26954.7 0.827 1.677 4 19363 19313.5 0.127 1.804 5 13681 13851.4 2.097 3.901 6 10029 9943.5 0.734 4.635 7 7105 7145.0 0.224 4.860 8 5082 5139.1 0.634 5.493 9 3687 3699.9 0.045 5.538 10 2669 2666.3 0.003 5.541 11 1903 1923.3 0.215 5.756 12 1400 1388.7 0.091 5.847 13 1015 1003.7 0.127 5.974 14 782 726.1 4.297 10.271 15 504 525.8 0.907 11.178 16 393 381.2 0.368 11.546 17 273 276.5 0.045 11.591 18 212 200.8 0.621 12.213 19 133 146.0 1.155 13.368 20 108 106.2 0.030 13.398 21 306 287.1 1.242 14.640 Chisq= 14.64 for 20 degrees of freedom, p= 0.20337 SUMMARY of craptest p-value for no. of wins: 0.397904 p-value for throws/game: 0.203372 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0008,0.0013,0.0048,0.0085,0.0086,0.0155,0.0197,0.0200,0.0209,0.0267, 0.0365,0.0375,0.0401,0.0450,0.0456,0.0483,0.0525,0.0531,0.0547,0.0580, 0.0589,0.0613,0.0699,0.0707,0.0727,0.0742,0.0757,0.0877,0.0890,0.0931, 0.0960,0.0994,0.1022,0.1036,0.1043,0.1048,0.1115,0.1165,0.1258,0.1288, 0.1297,0.1313,0.1321,0.1367,0.1413,0.1420,0.1607,0.1703,0.1710,0.1765, 0.1768,0.1882,0.1912,0.1927,0.1940,0.1962,0.1968,0.1971,0.2009,0.2012, 0.2019,0.2034,0.2048,0.2049,0.2079,0.2100,0.2105,0.2127,0.2160,0.2165, 0.2351,0.2358,0.2437,0.2446,0.2499,0.2523,0.2561,0.2608,0.2637,0.2708, 0.2807,0.2898,0.2905,0.2926,0.2952,0.2977,0.2980,0.3059,0.3179,0.3212, 0.3305,0.3406,0.3422,0.3453,0.3454,0.3479,0.3574,0.3582,0.3674,0.3696, 0.3724,0.3810,0.3814,0.3825,0.3875,0.3902,0.3918,0.3979,0.3991,0.4057, 0.4071,0.4109,0.4122,0.4128,0.4149,0.4172,0.4213,0.4283,0.4351,0.4412, 0.4502,0.4551,0.4570,0.4606,0.4630,0.4726,0.4728,0.4734,0.4737,0.4818, 0.4830,0.4885,0.4890,0.4903,0.4911,0.4928,0.4942,0.4951,0.4996,0.4997, 0.5013,0.5023,0.5028,0.5273,0.5354,0.5396,0.5396,0.5411,0.5465,0.5492, 0.5525,0.5542,0.5636,0.5652,0.5662,0.5685,0.5725,0.5826,0.5851,0.5863, 0.5918,0.5934,0.5940,0.5963,0.6079,0.6096,0.6103,0.6137,0.6158,0.6172, 0.6181,0.6193,0.6205,0.6253,0.6323,0.6393,0.6446,0.6494,0.6547,0.6572, 0.6639,0.6677,0.6714,0.6758,0.6759,0.6776,0.6831,0.6850,0.6862,0.6878, 0.6916,0.6929,0.6953,0.6956,0.6973,0.7046,0.7061,0.7075,0.7150,0.7220, 0.7221,0.7231,0.7236,0.7283,0.7299,0.7344,0.7370,0.7410,0.7420,0.7446, 0.7545,0.7596,0.7609,0.7624,0.7630,0.7683,0.7708,0.7752,0.7781,0.7848, 0.7873,0.7886,0.8068,0.8072,0.8081,0.8106,0.8212,0.8244,0.8302,0.8380, 0.8388,0.8492,0.8495,0.8505,0.8550,0.8585,0.8586,0.8613,0.8665,0.8713, 0.8719,0.8769,0.8798,0.8821,0.8881,0.8925,0.8937,0.9072,0.9188,0.9208, 0.9231,0.9278,0.9288,0.9305,0.9419,0.9424,0.9443,0.9466,0.9472,0.9514, 0.9584,0.9592,0.9625,0.9626,0.9670,0.9712,0.9796,0.9983,1.0000, Overall p-value after applying KStest on 269 p-values = 0.505629 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.