RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-09-19_12:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.69 21.7843 0.806842 2 to 25 16.12 20.7760 0.763530 3 to 26 16.18 13.8197 0.320179 4 to 27 15.92 12.6685 0.241922 5 to 28 16.03 19.3093 0.688929 6 to 29 15.59 14.6833 0.381717 7 to 30 15.47 29.6918 0.971345 8 to 31 15.90 17.7431 0.594781 9 to 32 15.84 12.4183 0.225825 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.805131 Tough bday spacings test for dh-ranFile-2015-09-19_12:31: 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 14 30 69 118 84 74 49 34 15 6 7 (O-E)^2/E 2.6 1.2 0.2 4.2 1.9 0.2 0.2 0.6 0.0 0.1 2.1 Birthday Spacings: Sum(O-E)^2/E= 13.331, p= 0.794 RESULTS OF GCD FOR dh-ranFile-2015-09-19_12:31 Euclid's algorithm: p-value, steps to gcd: 0.294383 p-value, dist. of gcd's: 0.270707 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-09-19_12:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.083 0.943 0.459 0.718 0.921 0.911 0.904 0.079 Bits 8 to 15---> 0.934 0.950 0.810 0.956 0.024 0.531 0.660 0.884 Bits 16 to 23---> 0.890 0.019 0.406 0.748 0.244 0.152 0.920 0.740 Bits 24 to 31---> 0.771 0.990 0.697 0.893 0.736 0.001 0.554 0.896 KS test for the above 32 p values: 0.999 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-09-19_12:31, p-values for 5 runs: 0.0041, 0.4786, 0.4450, 0.0500, 0.3903 Rank test for binary matrices (31x31) for dh-ranFile-2015-09-19_12:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 239 211.4 3.598 3.598 r= 29 5252 5134.0 2.712 6.310 r= 30 22975 23103.0 0.710 7.020 r= 31 11534 11551.5 0.027 7.046 chi-square = 7.046 with df = 3; p-value = 0.930 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-09-19_12:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 240 211.4 3.864 3.864 r= 30 5143 5134.0 0.016 3.880 r= 31 23189 23103.0 0.320 4.200 r= 32 11428 11551.5 1.321 5.520 chi-square = 5.520 with df = 3; p-value = 0.863 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-09-19_12:31 b-rank test for bits 1 to 8, p=0.66814 b-rank test for bits 2 to 9, p=0.97055 b-rank test for bits 3 to 10, p=0.30625 b-rank test for bits 4 to 11, p=0.13601 b-rank test for bits 5 to 12, p=0.87619 b-rank test for bits 6 to 13, p=0.07180 b-rank test for bits 7 to 14, p=0.55134 b-rank test for bits 8 to 15, p=0.91297 b-rank test for bits 9 to 16, p=0.43358 b-rank test for bits 10 to 17, p=0.51127 b-rank test for bits 11 to 18, p=0.11091 b-rank test for bits 12 to 19, p=0.36270 b-rank test for bits 13 to 20, p=0.44767 b-rank test for bits 14 to 21, p=0.93538 b-rank test for bits 15 to 22, p=0.20268 b-rank test for bits 16 to 23, p=0.22006 b-rank test for bits 17 to 24, p=0.77712 b-rank test for bits 18 to 25, p=0.87806 b-rank test for bits 19 to 26, p=0.92777 b-rank test for bits 20 to 27, p=0.86569 b-rank test for bits 21 to 28, p=0.99128 b-rank test for bits 22 to 29, p=0.11344 b-rank test for bits 23 to 30, p=0.86703 b-rank test for bits 24 to 31, p=0.19843 b-rank test for bits 25 to 32, p=0.19866 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 = 0.260408 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-09-19_12:31 (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 141319 -1.38 0.083905 2 142333 0.99 0.838884 3 141579 -0.77 0.220117 4 141572 -0.79 0.215303 5 141867 -0.10 0.460608 6 142127 0.51 0.694475 7 141277 -1.48 0.069783 8 142034 0.29 0.614583 9 142041 0.31 0.620822 10 141390 -1.21 0.112491 11 142357 1.05 0.852210 12 141122 -1.84 0.032917 13 141718 -0.45 0.327426 14 141967 0.13 0.553593 15 141328 -1.36 0.087193 16 141534 -0.88 0.190260 17 141792 -0.27 0.391990 18 142218 0.72 0.764604 19 141992 0.19 0.576581 20 142263 0.83 0.795692 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-09-19_12:31 Bits used No. missing words z-score p-value 23 to 32 142198 0.9954 0.840233 22 to 31 142079 0.5851 0.720749 21 to 30 141984 0.2575 0.601597 20 to 29 141709 -0.6908 0.244848 19 to 28 141953 0.1506 0.559849 18 to 27 142082 0.5954 0.724217 17 to 26 141481 -1.4770 0.069838 16 to 25 141756 -0.5287 0.298498 15 to 24 141649 -0.8977 0.184676 14 to 23 142014 0.3609 0.640925 13 to 22 141829 -0.2770 0.390890 12 to 21 142081 0.5920 0.723063 11 to 20 142113 0.7023 0.758757 10 to 19 142087 0.6127 0.729948 9 to 18 141287 -2.1460 0.015938 8 to 17 141878 -0.1080 0.456984 7 to 16 142011 0.3506 0.637051 6 to 15 141893 -0.0563 0.477547 5 to 14 142257 1.1989 0.884709 4 to 13 141866 -0.1494 0.440614 3 to 12 141691 -0.7529 0.225766 2 to 11 142197 0.9920 0.839393 1 to 10 142595 2.3644 0.990970 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-09-19_12:31 Bits used No. missing words z-score p-value 28 to 32 141677 -0.7876 0.215477 27 to 31 142678 2.6057 0.995415 26 to 30 141915 0.0192 0.507667 25 to 29 141819 -0.3062 0.379725 24 to 28 141451 -1.5537 0.060133 23 to 27 141742 -0.5672 0.285282 22 to 26 141488 -1.4282 0.076612 21 to 25 141804 -0.3571 0.360527 20 to 24 141717 -0.6520 0.257212 19 to 23 141747 -0.5503 0.291067 18 to 22 142004 0.3209 0.625863 17 to 21 142187 0.9413 0.826713 16 to 20 141570 -1.1503 0.125016 15 to 19 142063 0.5209 0.698787 14 to 18 141860 -0.1672 0.433598 13 to 17 141698 -0.7164 0.236881 12 to 16 142092 0.6192 0.732114 11 to 15 142206 1.0057 0.842711 10 to 14 142035 0.4260 0.664946 9 to 13 141081 -2.8079 0.002493 8 to 12 141578 -1.1232 0.130686 7 to 11 141577 -1.1265 0.129968 6 to 10 141706 -0.6893 0.245332 5 to 9 141691 -0.7401 0.229619 4 to 8 141980 0.2396 0.594664 3 to 7 142073 0.5548 0.710489 2 to 6 142415 1.7141 0.956748 1 to 5 142434 1.7785 0.962343 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-09-19_12:31 Bits used No. missing words z-score p-value 31 to 32 142192 0.8338 0.797813 30 to 31 141903 -0.0187 0.492551 29 to 30 142698 2.3265 0.990003 28 to 29 141832 -0.2281 0.409780 27 to 28 142074 0.4858 0.686429 26 to 27 142217 0.9076 0.817950 25 to 26 142065 0.4592 0.676956 24 to 25 141640 -0.7945 0.213457 23 to 24 141766 -0.4228 0.336220 22 to 23 141823 -0.2547 0.399493 21 to 22 142127 0.6421 0.739594 20 to 21 142309 1.1790 0.880794 19 to 20 141949 0.1170 0.546578 18 to 19 141272 -1.8800 0.030052 17 to 18 141523 -1.1396 0.127223 16 to 17 142721 2.3943 0.991674 15 to 16 141644 -0.7827 0.216906 14 to 15 141261 -1.9125 0.027907 13 to 14 141636 -0.8063 0.210040 12 to 13 142113 0.6008 0.726012 11 to 12 142174 0.7807 0.782522 10 to 11 142006 0.2852 0.612240 9 to 10 142551 1.8928 0.970810 8 to 9 142072 0.4799 0.684334 7 to 8 141889 -0.0600 0.476090 6 to 7 142129 0.6480 0.741506 5 to 6 142475 1.6686 0.952406 4 to 5 141724 -0.5467 0.292294 3 to 4 142264 1.0462 0.852271 2 to 3 142063 0.4533 0.674835 1 to 2 142313 1.1908 0.883127 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-09-19_12:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2525.59 0.362 0.641262 Test results for specific bytes for dh-ranFile-2015-09-19_12:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2433.73 -0.937 0.174317 2 to 9 2418.60 -1.151 0.124835 3 to 10 2487.53 -0.176 0.429998 4 to 11 2632.23 1.870 0.969259 5 to 12 2496.10 -0.055 0.477980 6 to 13 2558.91 0.833 0.797617 7 to 14 2479.09 -0.296 0.383733 8 to 15 2573.18 1.035 0.849637 9 to 16 2602.81 1.454 0.927030 10 to 17 2515.11 0.214 0.584590 11 to 18 2407.62 -1.306 0.095691 12 to 19 2463.84 -0.511 0.304552 13 to 20 2625.03 1.768 0.961491 14 to 21 2563.32 0.895 0.814734 15 to 22 2558.15 0.822 0.794553 16 to 23 2443.08 -0.805 0.210426 17 to 24 2589.89 1.271 0.898180 18 to 25 2545.22 0.639 0.738742 19 to 26 2511.16 0.158 0.562703 20 to 27 2448.11 -0.734 0.231519 21 to 28 2525.64 0.363 0.641528 22 to 29 2496.98 -0.043 0.482941 23 to 30 2401.90 -1.387 0.082660 24 to 31 2522.77 0.322 0.626260 25 to 32 2592.90 1.314 0.905536 CDPARK for dh-ranFile-2015-09-19_12:31: 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 3521 -0.0913 0.463617 3542 0.8676 0.807188 3500 -1.0502 0.146807 3516 -0.3196 0.374623 3535 0.5479 0.708135 3567 2.0091 0.977738 3562 1.7808 0.962529 3563 1.8265 0.966111 3545 1.0046 0.842447 3544 0.9589 0.831196 Square side=100, avg. no. parked=3539.50 sample std.=20.85 p-value of the KSTEST for those 10 p-values: 0.020039 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-09-19_12:31 0.3614,0.5389,0.8872,0.4916,0.7350,0.3556,0.2515,0.0992,0.8311,0.8647, The KS test for those 10 p-values: 0.889998 The 3DSPHERES test for dh-ranFile-2015-09-19_12:31 sample no r^3 equiv. uni. 1 46.052 0.784559 2 183.204 0.997772 3 38.897 0.726529 4 39.336 0.730506 5 0.682 0.022473 6 55.834 0.844506 7 9.721 0.276772 8 11.405 0.316251 9 39.608 0.732939 10 52.453 0.825951 11 25.810 0.576984 12 93.000 0.954951 13 132.167 0.987791 14 52.583 0.826705 15 66.054 0.889397 16 52.300 0.825062 17 9.037 0.260092 18 77.058 0.923358 19 32.712 0.663919 20 0.527 0.017429 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.007867 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-09-19_12:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 -0.7 -1.3 1.2 1.4 1.2 -0.3 0.4 0.7 1.1 -0.1 -0.9 0.7 -0.1 -0.3 -1.1 -0.3 -0.1 -0.3 1.3 -0.4 -0.4 2.3 0.5 -2.2 0.7 -0.8 -0.2 -0.6 0.4 0.6 -0.8 0.2 -1.4 1.7 -1.2 -0.7 0.5 -0.4 0.4 -1.3 0.0 0.8 Chi-square with 42 degrees of freedom:37.124473 z-score=-0.531964, p-value=0.315430 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-09-19_12:31 Test no p-value 1 0.058474 2 0.682888 3 0.010993 4 0.028978 5 0.957839 6 0.958466 7 0.224405 8 0.415801 9 0.614205 10 0.723523 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.310932 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-09-19_12:31: (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 66875 0.65 66675 0.00 3 25000.00 24872 0.66 25089 0.32 4 6666.67 6602 0.63 6601 0.65 5 1388.89 1363 0.48 1371 0.23 6 238.10 247 0.33 218 1.70 7 34.72 33 0.09 38 0.31 8 4.96 7 0.84 7 0.84 p=0.27925 p=0.32875 Number of rngs required: 688009, p-value: 0.325 RESULTS OF CRAPS TEST for dh-ranFile-2015-09-19_12:31 No. of wins: Observed Expected 98426 98585.9 z-score=-0.715, pvalue=0.23731 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66476 66666.7 0.545 0.545 2 37951 37654.3 2.338 2.883 3 26806 26954.7 0.821 3.704 4 19231 19313.5 0.352 4.056 5 13964 13851.4 0.915 4.971 6 9911 9943.5 0.107 5.077 7 7226 7145.0 0.918 5.995 8 5159 5139.1 0.077 6.072 9 3676 3699.9 0.154 6.226 10 2685 2666.3 0.131 6.357 11 1874 1923.3 1.265 7.622 12 1338 1388.7 1.854 9.476 13 1037 1003.7 1.104 10.580 14 718 726.1 0.091 10.671 15 530 525.8 0.033 10.704 16 380 381.2 0.003 10.708 17 284 276.5 0.201 10.909 18 214 200.8 0.864 11.773 19 155 146.0 0.557 12.330 20 111 106.2 0.216 12.545 21 274 287.1 0.599 13.144 Chisq= 13.14 for 20 degrees of freedom, p= 0.12888 SUMMARY of craptest p-value for no. of wins: 0.237310 p-value for throws/game: 0.128882 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-09-19_12:31 No. of wins: Observed Expected 98215 98585.9 z-score=-1.659, pvalue=0.04859 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66695 66666.7 0.012 0.012 2 37596 37654.3 0.090 0.102 3 26997 26954.7 0.066 0.169 4 19204 19313.5 0.620 0.789 5 13892 13851.4 0.119 0.908 6 9919 9943.5 0.061 0.969 7 7092 7145.0 0.394 1.362 8 5311 5139.1 5.752 7.114 9 3654 3699.9 0.569 7.682 10 2576 2666.3 3.058 10.740 11 1953 1923.3 0.458 11.198 12 1392 1388.7 0.008 11.206 13 1077 1003.7 5.351 16.557 14 732 726.1 0.047 16.604 15 513 525.8 0.313 16.917 16 395 381.2 0.503 17.420 17 302 276.5 2.344 19.765 18 161 200.8 7.899 27.664 19 148 146.0 0.028 27.692 20 106 106.2 0.000 27.692 21 285 287.1 0.016 27.708 Chisq= 27.71 for 20 degrees of freedom, p= 0.88350 SUMMARY of craptest p-value for no. of wins: 0.048589 p-value for throws/game: 0.883500 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0008,0.0025,0.0041,0.0079,0.0110,0.0159,0.0174,0.0186,0.0200,0.0225, 0.0236,0.0279,0.0290,0.0301,0.0329,0.0486,0.0500,0.0585,0.0601,0.0698, 0.0698,0.0718,0.0766,0.0786,0.0827,0.0834,0.0839,0.0872,0.0957,0.0992, 0.1109,0.1125,0.1134,0.1248,0.1250,0.1272,0.1289,0.1300,0.1307,0.1360, 0.1468,0.1522,0.1743,0.1847,0.1903,0.1984,0.1987,0.2027,0.2100,0.2104, 0.2135,0.2153,0.2155,0.2169,0.2201,0.2201,0.2244,0.2258,0.2258,0.2296, 0.2315,0.2369,0.2373,0.2419,0.2441,0.2448,0.2453,0.2515,0.2572,0.2601, 0.2604,0.2707,0.2768,0.2793,0.2853,0.2911,0.2923,0.2944,0.2985,0.3046, 0.3062,0.3109,0.3154,0.3163,0.3202,0.3249,0.3274,0.3288,0.3362,0.3556, 0.3605,0.3614,0.3627,0.3746,0.3797,0.3817,0.3837,0.3903,0.3909,0.3920, 0.3995,0.4056,0.4098,0.4158,0.4300,0.4336,0.4336,0.4406,0.4450,0.4477, 0.4570,0.4590,0.4606,0.4636,0.4761,0.4775,0.4780,0.4786,0.4829,0.4916, 0.4926,0.5077,0.5113,0.5306,0.5389,0.5466,0.5513,0.5535,0.5536,0.5598, 0.5627,0.5766,0.5770,0.5846,0.5947,0.5948,0.6016,0.6122,0.6142,0.6146, 0.6208,0.6259,0.6263,0.6371,0.6409,0.6413,0.6415,0.6597,0.6639,0.6649, 0.6681,0.6748,0.6770,0.6829,0.6843,0.6864,0.6889,0.6945,0.6967,0.6988, 0.7081,0.7105,0.7176,0.7207,0.7231,0.7235,0.7242,0.7260,0.7265,0.7299, 0.7305,0.7321,0.7329,0.7350,0.7363,0.7387,0.7396,0.7399,0.7415,0.7482, 0.7588,0.7635,0.7646,0.7714,0.7771,0.7825,0.7846,0.7943,0.7946,0.7957, 0.7976,0.7978,0.8051,0.8068,0.8072,0.8104,0.8147,0.8180,0.8251,0.8260, 0.8267,0.8267,0.8311,0.8312,0.8389,0.8394,0.8402,0.8424,0.8427,0.8445, 0.8496,0.8522,0.8523,0.8626,0.8647,0.8657,0.8670,0.8762,0.8781,0.8808, 0.8831,0.8835,0.8839,0.8847,0.8872,0.8894,0.8897,0.8900,0.8931,0.8955, 0.8982,0.9042,0.9055,0.9105,0.9130,0.9201,0.9208,0.9234,0.9270,0.9278, 0.9296,0.9338,0.9354,0.9427,0.9496,0.9524,0.9550,0.9558,0.9567,0.9578, 0.9585,0.9615,0.9623,0.9625,0.9661,0.9693,0.9706,0.9708,0.9713,0.9777, 0.9878,0.9900,0.9900,0.9910,0.9913,0.9917,0.9954,0.9978,0.9989, Overall p-value after applying KStest on 269 p-values = 0.002355 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.