RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-01-06_16:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.98 16.0637 0.480673 2 to 25 15.67 15.4800 0.439048 3 to 26 15.67 15.4743 0.438640 4 to 27 15.48 28.4909 0.960481 5 to 28 16.15 26.7426 0.938047 6 to 29 15.53 16.4557 0.508212 7 to 30 15.79 12.2252 0.213690 8 to 31 15.58 15.7698 0.459789 9 to 32 15.76 18.1819 0.622548 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.371297 Tough bday spacings test for dh-ranFile-2016-01-06_16:31: 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 38 75 104 105 76 37 25 20 4 5 (O-E)^2/E 0.4 0.1 0.0 0.4 0.5 0.1 4.4 0.8 1.8 1.0 0.2 Birthday Spacings: Sum(O-E)^2/E= 9.624, p= 0.526 RESULTS OF GCD FOR dh-ranFile-2016-01-06_16:31 Euclid's algorithm: p-value, steps to gcd: 0.282435 p-value, dist. of gcd's: 0.201811 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-01-06_16:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.694 0.228 0.052 0.450 0.717 0.986 0.272 0.873 Bits 8 to 15---> 0.925 0.422 0.480 0.685 0.643 0.489 0.705 0.482 Bits 16 to 23---> 0.168 0.847 0.772 0.779 0.544 0.417 0.851 0.939 Bits 24 to 31---> 0.809 0.921 0.380 0.789 0.779 0.762 0.652 0.971 KS test for the above 32 p values: 0.991 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-01-06_16:31, p-values for 5 runs: 0.1227, 0.5995, 0.6568, 0.8583, 0.7647 Rank test for binary matrices (31x31) for dh-ranFile-2016-01-06_16:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 202 211.4 0.420 0.420 r= 29 5233 5134.0 1.909 2.328 r= 30 22973 23103.0 0.732 3.060 r= 31 11592 11551.5 0.142 3.202 chi-square = 3.202 with df = 3; p-value = 0.638 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-01-06_16:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 208 211.4 0.055 0.055 r= 30 5035 5134.0 1.909 1.965 r= 31 23147 23103.0 0.084 2.048 r= 32 11610 11551.5 0.296 2.344 chi-square = 2.344 with df = 3; p-value = 0.496 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-01-06_16:31 b-rank test for bits 1 to 8, p=0.09028 b-rank test for bits 2 to 9, p=0.86575 b-rank test for bits 3 to 10, p=0.46321 b-rank test for bits 4 to 11, p=0.15688 b-rank test for bits 5 to 12, p=0.01597 b-rank test for bits 6 to 13, p=0.24499 b-rank test for bits 7 to 14, p=0.28046 b-rank test for bits 8 to 15, p=0.87025 b-rank test for bits 9 to 16, p=0.71999 b-rank test for bits 10 to 17, p=0.26556 b-rank test for bits 11 to 18, p=0.12019 b-rank test for bits 12 to 19, p=0.12668 b-rank test for bits 13 to 20, p=0.56031 b-rank test for bits 14 to 21, p=0.95851 b-rank test for bits 15 to 22, p=0.93831 b-rank test for bits 16 to 23, p=0.29200 b-rank test for bits 17 to 24, p=0.83749 b-rank test for bits 18 to 25, p=0.15688 b-rank test for bits 19 to 26, p=0.37181 b-rank test for bits 20 to 27, p=0.40653 b-rank test for bits 21 to 28, p=0.15766 b-rank test for bits 22 to 29, p=0.01286 b-rank test for bits 23 to 30, p=0.30461 b-rank test for bits 24 to 31, p=0.79113 b-rank test for bits 25 to 32, p=0.65179 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 = 0.242385 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-01-06_16:31 (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 141369 -1.26 0.103393 2 141571 -0.79 0.214621 3 141424 -1.13 0.128408 4 141990 0.19 0.574750 5 141922 0.03 0.511808 6 141854 -0.13 0.448570 7 141971 0.14 0.557285 8 142096 0.44 0.668634 9 142158 0.58 0.719381 10 142297 0.91 0.817471 11 142136 0.53 0.701806 12 142092 0.43 0.665237 13 141331 -1.35 0.088310 14 142011 0.24 0.593884 15 142311 0.94 0.826001 16 141852 -0.13 0.446722 17 141393 -1.21 0.113836 18 142165 0.60 0.724866 19 142494 1.37 0.914039 20 142380 1.10 0.864268 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-01-06_16:31 Bits used No. missing words z-score p-value 23 to 32 141933 0.0816 0.532526 22 to 31 141956 0.1609 0.563926 21 to 30 141919 0.0333 0.513300 20 to 29 142612 2.4230 0.992304 19 to 28 141899 -0.0356 0.485792 18 to 27 141844 -0.2253 0.410882 17 to 26 141985 0.2609 0.602927 16 to 25 141964 0.1885 0.574764 15 to 24 141964 0.1885 0.574764 14 to 23 141558 -1.2115 0.112855 13 to 22 141763 -0.5046 0.306925 12 to 21 141542 -1.2667 0.102639 11 to 20 142277 1.2678 0.897570 10 to 19 141601 -1.0632 0.143844 9 to 18 141739 -0.5873 0.278486 8 to 17 141701 -0.7184 0.236262 7 to 16 142252 1.1816 0.881322 6 to 15 142080 0.5885 0.721907 5 to 14 142183 0.9437 0.827336 4 to 13 141849 -0.2080 0.417601 3 to 12 141035 -3.0149 0.001285 2 to 11 142131 0.7644 0.777679 1 to 10 142049 0.4816 0.684962 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-01-06_16:31 Bits used No. missing words z-score p-value 28 to 32 141586 -1.0960 0.136532 27 to 31 141813 -0.3265 0.372007 26 to 30 141890 -0.0655 0.473878 25 to 29 142078 0.5718 0.716259 24 to 28 142224 1.0667 0.856941 23 to 27 141738 -0.5808 0.280695 22 to 26 141995 0.2904 0.614248 21 to 25 141729 -0.6113 0.270504 20 to 24 142077 0.5684 0.715109 19 to 23 141594 -1.0689 0.142554 18 to 22 141593 -1.0723 0.141792 17 to 21 141610 -1.0147 0.155130 16 to 20 141748 -0.5469 0.292230 15 to 19 141805 -0.3537 0.361797 14 to 18 141987 0.2633 0.603836 13 to 17 142010 0.3413 0.633544 12 to 16 142131 0.7514 0.773801 11 to 15 142421 1.7345 0.958583 10 to 14 141839 -0.2384 0.405783 9 to 13 142142 0.7887 0.784860 8 to 12 141901 -0.0282 0.488737 7 to 11 142341 1.4633 0.928306 6 to 10 141648 -0.8859 0.187845 5 to 9 141733 -0.5977 0.275010 4 to 8 142028 0.4023 0.656258 3 to 7 141701 -0.7062 0.240031 2 to 6 142132 0.7548 0.774820 1 to 5 142295 1.3074 0.904454 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-01-06_16:31 Bits used No. missing words z-score p-value 31 to 32 141562 -1.0246 0.152783 30 to 31 142765 2.5241 0.994200 29 to 30 142693 2.3117 0.989603 28 to 29 142337 1.2616 0.896447 27 to 28 142272 1.0698 0.857651 26 to 27 142170 0.7689 0.779035 25 to 26 141783 -0.3727 0.354703 24 to 25 141507 -1.1868 0.117650 23 to 24 141622 -0.8476 0.198336 22 to 23 142139 0.6775 0.750953 21 to 22 141506 -1.1898 0.117070 20 to 21 141848 -0.1809 0.428217 19 to 20 141278 -1.8623 0.031278 18 to 19 141623 -0.8446 0.199158 17 to 18 141811 -0.2901 0.385886 16 to 17 142015 0.3117 0.622370 15 to 16 142156 0.7276 0.766583 14 to 15 141969 0.1760 0.569860 13 to 14 141500 -1.2075 0.113627 12 to 13 141270 -1.8859 0.029652 11 to 12 142543 1.8692 0.969205 10 to 11 142696 2.3206 0.989845 9 to 10 142486 1.7011 0.955537 8 to 9 142228 0.9400 0.826399 7 to 8 141406 -1.4847 0.068805 6 to 7 142062 0.4504 0.673772 5 to 6 141740 -0.4995 0.308714 4 to 5 141526 -1.1308 0.129077 3 to 4 141965 0.1642 0.565220 2 to 3 142275 1.0787 0.859633 1 to 2 142187 0.8191 0.793631 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-01-06_16:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2515.83 0.224 0.588577 Test results for specific bytes for dh-ranFile-2016-01-06_16:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2518.20 0.257 0.601559 2 to 9 2516.65 0.235 0.593065 3 to 10 2508.80 0.124 0.549536 4 to 11 2456.30 -0.618 0.268303 5 to 12 2382.28 -1.665 0.047981 6 to 13 2530.01 0.424 0.664357 7 to 14 2590.63 1.282 0.900035 8 to 15 2542.87 0.606 0.727814 9 to 16 2647.39 2.084 0.981438 10 to 17 2386.14 -1.610 0.053669 11 to 18 2528.68 0.406 0.657466 12 to 19 2596.87 1.370 0.914657 13 to 20 2466.05 -0.480 0.315594 14 to 21 2570.94 1.003 0.842115 15 to 22 2454.53 -0.643 0.260106 16 to 23 2452.77 -0.668 0.252092 17 to 24 2617.11 1.656 0.951157 18 to 25 2424.05 -1.074 0.141381 19 to 26 2332.27 -2.372 0.008846 20 to 27 2311.23 -2.670 0.003797 21 to 28 2547.64 0.674 0.749756 22 to 29 2497.28 -0.038 0.484672 23 to 30 2405.47 -1.337 0.090646 24 to 31 2452.75 -0.668 0.252016 25 to 32 2447.79 -0.738 0.230136 CDPARK for dh-ranFile-2016-01-06_16:31: 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 3543 0.9132 0.819442 3556 1.5068 0.934075 3522 -0.0457 0.481790 3521 -0.0913 0.463617 3530 0.3196 0.625377 3537 0.6393 0.738676 3541 0.8219 0.794438 3544 0.9589 0.831196 3506 -0.7763 0.218799 3546 1.0502 0.853193 Square side=100, avg. no. parked=3534.60 sample std.=14.06 p-value of the KSTEST for those 10 p-values: 0.074833 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-01-06_16:31 0.8984,0.2315,0.5657,0.2679,0.5538,0.1522,0.2654,0.9351,0.5278,0.8046, The KS test for those 10 p-values: 0.892091 The 3DSPHERES test for dh-ranFile-2016-01-06_16:31 sample no r^3 equiv. uni. 1 18.147 0.453877 2 18.357 0.457684 3 23.365 0.541063 4 5.718 0.173526 5 4.061 0.126617 6 23.234 0.539043 7 7.886 0.231144 8 40.790 0.743253 9 95.579 0.958661 10 35.696 0.695739 11 5.341 0.163085 12 5.320 0.162511 13 7.830 0.229713 14 5.734 0.173971 15 14.752 0.388437 16 1.443 0.046953 17 17.292 0.438077 18 65.288 0.886535 19 11.289 0.313602 20 23.850 0.548426 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.240657 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-01-06_16:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 1.3 2.2 1.8 0.9 -0.2 -1.8 0.7 -0.1 -0.7 -0.3 1.0 0.4 -0.1 -0.2 -1.1 -0.2 0.2 -0.8 1.9 -0.7 -1.6 0.6 -0.0 -0.8 1.2 0.8 -0.0 1.7 0.4 -0.5 0.3 0.6 1.0 -0.4 1.2 0.1 -0.2 -0.4 -1.6 -0.7 -1.3 0.0 -1.1 Chi-square with 42 degrees of freedom:40.109856 z-score=-0.206232, p-value=0.445787 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-01-06_16:31 Test no p-value 1 0.815108 2 0.096414 3 0.454100 4 0.564797 5 0.430684 6 0.014530 7 0.784162 8 0.006626 9 0.005075 10 0.006424 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.001925 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-01-06_16:31: (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 66546 0.22 66679 0.00 3 25000.00 25167 1.12 25010 0.00 4 6666.67 6572 1.34 6622 0.30 5 1388.89 1429 1.16 1395 0.03 6 238.10 254 1.06 252 0.81 7 34.72 27 1.72 39 0.53 8 4.96 4 0.19 2 1.77 p=0.66040 p=0.24788 Number of rngs required: 689012, p-value: 0.759 RESULTS OF CRAPS TEST for dh-ranFile-2016-01-06_16:31 No. of wins: Observed Expected 98195 98585.9 z-score=-1.748, pvalue=0.04022 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66516 66666.7 0.341 0.341 2 37750 37654.3 0.243 0.584 3 26952 26954.7 0.000 0.584 4 19697 19313.5 7.617 8.200 5 13742 13851.4 0.864 9.065 6 10023 9943.5 0.635 9.700 7 7050 7145.0 1.264 10.964 8 5091 5139.1 0.450 11.413 9 3618 3699.9 1.811 13.225 10 2659 2666.3 0.020 13.245 11 1930 1923.3 0.023 13.268 12 1369 1388.7 0.281 13.548 13 1023 1003.7 0.371 13.919 14 693 726.1 1.513 15.431 15 469 525.8 6.143 21.575 16 374 381.2 0.134 21.709 17 276 276.5 0.001 21.710 18 217 200.8 1.302 23.012 19 148 146.0 0.028 23.040 20 123 106.2 2.652 25.692 21 280 287.1 0.176 25.868 Chisq= 25.87 for 20 degrees of freedom, p= 0.82979 SUMMARY of craptest p-value for no. of wins: 0.040219 p-value for throws/game: 0.829792 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-01-06_16:31 No. of wins: Observed Expected 98579 98585.9 z-score=-0.031, pvalue=0.48776 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66626 66666.7 0.025 0.025 2 37738 37654.3 0.186 0.211 3 26779 26954.7 1.146 1.356 4 19485 19313.5 1.524 2.880 5 13925 13851.4 0.391 3.271 6 9870 9943.5 0.544 3.815 7 7166 7145.0 0.062 3.876 8 5079 5139.1 0.702 4.579 9 3730 3699.9 0.245 4.824 10 2666 2666.3 0.000 4.824 11 1918 1923.3 0.015 4.839 12 1394 1388.7 0.020 4.859 13 998 1003.7 0.033 4.891 14 701 726.1 0.870 5.762 15 569 525.8 3.543 9.305 16 386 381.2 0.062 9.367 17 277 276.5 0.001 9.367 18 184 200.8 1.410 10.778 19 139 146.0 0.334 11.112 20 99 106.2 0.490 11.602 21 271 287.1 0.904 12.506 Chisq= 12.51 for 20 degrees of freedom, p= 0.10246 SUMMARY of craptest p-value for no. of wins: 0.487764 p-value for throws/game: 0.102457 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0013,0.0019,0.0038,0.0051,0.0064,0.0066,0.0088,0.0129,0.0145,0.0160, 0.0297,0.0313,0.0402,0.0470,0.0480,0.0524,0.0537,0.0688,0.0748,0.0883, 0.0903,0.0906,0.0964,0.1025,0.1026,0.1034,0.1129,0.1136,0.1138,0.1171, 0.1177,0.1202,0.1227,0.1266,0.1267,0.1284,0.1291,0.1365,0.1414,0.1418, 0.1426,0.1438,0.1522,0.1528,0.1551,0.1569,0.1569,0.1577,0.1625,0.1631, 0.1678,0.1735,0.1740,0.1878,0.1983,0.1992,0.2018,0.2137,0.2146,0.2188, 0.2279,0.2297,0.2301,0.2311,0.2315,0.2363,0.2400,0.2407,0.2424,0.2450, 0.2479,0.2520,0.2521,0.2601,0.2654,0.2656,0.2679,0.2683,0.2705,0.2723, 0.2750,0.2785,0.2805,0.2807,0.2824,0.2920,0.2922,0.3046,0.3069,0.3087, 0.3136,0.3156,0.3547,0.3618,0.3713,0.3718,0.3720,0.3803,0.3859,0.3884, 0.4058,0.4065,0.4109,0.4173,0.4176,0.4220,0.4282,0.4307,0.4381,0.4386, 0.4390,0.4458,0.4467,0.4486,0.4495,0.4539,0.4541,0.4577,0.4598,0.4632, 0.4636,0.4739,0.4805,0.4807,0.4818,0.4824,0.4847,0.4858,0.4878,0.4887, 0.4887,0.4959,0.5082,0.5118,0.5133,0.5259,0.5278,0.5325,0.5390,0.5411, 0.5439,0.5484,0.5495,0.5538,0.5573,0.5603,0.5639,0.5648,0.5652,0.5657, 0.5699,0.5748,0.5748,0.5748,0.5886,0.5931,0.5939,0.5995,0.6016,0.6029, 0.6038,0.6142,0.6224,0.6225,0.6254,0.6335,0.6385,0.6434,0.6518,0.6522, 0.6563,0.6568,0.6575,0.6604,0.6644,0.6652,0.6686,0.6738,0.6849,0.6850, 0.6939,0.6957,0.7018,0.7047,0.7151,0.7163,0.7170,0.7194,0.7200,0.7219, 0.7249,0.7278,0.7387,0.7433,0.7498,0.7510,0.7590,0.7621,0.7647,0.7666, 0.7718,0.7738,0.7748,0.7777,0.7787,0.7790,0.7791,0.7842,0.7849,0.7890, 0.7911,0.7936,0.7944,0.8046,0.8087,0.8151,0.8175,0.8194,0.8260,0.8264, 0.8273,0.8298,0.8312,0.8375,0.8421,0.8472,0.8506,0.8532,0.8569,0.8577, 0.8583,0.8596,0.8643,0.8657,0.8702,0.8731,0.8813,0.8865,0.8921,0.8964, 0.8976,0.8984,0.9000,0.9045,0.9140,0.9147,0.9207,0.9246,0.9283,0.9341, 0.9351,0.9380,0.9383,0.9391,0.9512,0.9555,0.9585,0.9586,0.9587,0.9605, 0.9692,0.9705,0.9814,0.9856,0.9896,0.9898,0.9906,0.9923,0.9942, Overall p-value after applying KStest on 269 p-values = 0.767342 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.