RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-10-03_11:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.64 13.5071 0.298370 2 to 25 15.81 10.7495 0.130713 3 to 26 15.94 16.3101 0.498034 4 to 27 15.83 21.8222 0.808346 5 to 28 15.67 13.4190 0.292284 6 to 29 15.66 25.3942 0.913772 7 to 30 15.70 16.1566 0.487235 8 to 31 15.65 14.5706 0.373617 9 to 32 15.63 38.4052 0.997839 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.600673 Tough bday spacings test for dh-ranFile-2016-10-03_11:31: 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 37 81 79 101 69 69 27 13 8 5 (O-E)^2/E 0.4 0.0 0.8 3.6 0.1 1.1 5.5 0.3 0.2 0.3 0.2 Birthday Spacings: Sum(O-E)^2/E= 12.432, p= 0.743 RESULTS OF GCD FOR dh-ranFile-2016-10-03_11:31 Euclid's algorithm: p-value, steps to gcd: 0.290640 p-value, dist. of gcd's: 0.051699 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-10-03_11:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.154 0.177 0.307 0.597 0.549 0.736 0.960 0.147 Bits 8 to 15---> 0.022 0.851 0.012 0.613 0.064 0.002 0.081 0.384 Bits 16 to 23---> 0.797 0.628 0.376 0.172 0.540 0.353 0.554 0.280 Bits 24 to 31---> 0.399 0.144 0.127 0.432 0.198 0.103 0.172 0.474 KS test for the above 32 p values: 0.993 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-10-03_11:31, p-values for 5 runs: 0.4322, 0.6160, 0.6699, 0.2508, 0.4359 Rank test for binary matrices (31x31) for dh-ranFile-2016-10-03_11:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 216 211.4 0.099 0.099 r= 29 5150 5134.0 0.050 0.149 r= 30 23026 23103.0 0.257 0.406 r= 31 11608 11551.5 0.276 0.682 chi-square = 0.682 with df = 3; p-value = 0.123 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-10-03_11:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 200 211.4 0.617 0.617 r= 30 5012 5134.0 2.900 3.516 r= 31 23111 23103.0 0.003 3.519 r= 32 11677 11551.5 1.363 4.882 chi-square = 4.882 with df = 3; p-value = 0.819 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-10-03_11:31 b-rank test for bits 1 to 8, p=0.27564 b-rank test for bits 2 to 9, p=0.39840 b-rank test for bits 3 to 10, p=0.35934 b-rank test for bits 4 to 11, p=0.69716 b-rank test for bits 5 to 12, p=0.33446 b-rank test for bits 6 to 13, p=0.74120 b-rank test for bits 7 to 14, p=0.69604 b-rank test for bits 8 to 15, p=0.48880 b-rank test for bits 9 to 16, p=0.88280 b-rank test for bits 10 to 17, p=0.76816 b-rank test for bits 11 to 18, p=0.37221 b-rank test for bits 12 to 19, p=0.39488 b-rank test for bits 13 to 20, p=0.80223 b-rank test for bits 14 to 21, p=0.55150 b-rank test for bits 15 to 22, p=0.83796 b-rank test for bits 16 to 23, p=0.70936 b-rank test for bits 17 to 24, p=0.55576 b-rank test for bits 18 to 25, p=0.03783 b-rank test for bits 19 to 26, p=0.02671 b-rank test for bits 20 to 27, p=0.90790 b-rank test for bits 21 to 28, p=0.13986 b-rank test for bits 22 to 29, p=0.00742 b-rank test for bits 23 to 30, p=0.70587 b-rank test for bits 24 to 31, p=0.48836 b-rank test for bits 25 to 32, p=0.27252 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 = 0.727332 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-10-03_11:31 (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 142135 0.53 0.700996 2 141622 -0.67 0.251005 3 142140 0.54 0.705039 4 142475 1.32 0.906859 5 142071 0.38 0.647186 6 141720 -0.44 0.329114 7 142265 0.83 0.797015 8 142581 1.57 0.941714 9 142482 1.34 0.909554 10 142298 0.91 0.818089 11 142188 0.65 0.742508 12 142088 0.42 0.661827 13 141737 -0.40 0.343607 14 142135 0.53 0.700996 15 141756 -0.36 0.360079 16 141995 0.20 0.579324 17 142724 1.90 0.971508 18 141806 -0.24 0.404613 19 142250 0.80 0.786972 20 141925 0.04 0.514603 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-10-03_11:31 Bits used No. missing words z-score p-value 23 to 32 142078 0.5816 0.719589 22 to 31 142323 1.4264 0.923131 21 to 30 141759 -0.5184 0.302097 20 to 29 141626 -0.9770 0.164285 19 to 28 141673 -0.8149 0.207556 18 to 27 141877 -0.1115 0.455617 17 to 26 141817 -0.3184 0.375099 16 to 25 142411 1.7299 0.958176 15 to 24 142060 0.5196 0.698312 14 to 23 142144 0.8092 0.790802 13 to 22 142153 0.8402 0.799614 12 to 21 142091 0.6264 0.734490 11 to 20 141618 -1.0046 0.157548 10 to 19 141995 0.2954 0.616161 9 to 18 141761 -0.5115 0.304507 8 to 17 142227 1.0954 0.863332 7 to 16 142342 1.4920 0.932146 6 to 15 141715 -0.6701 0.251396 5 to 14 141537 -1.2839 0.099589 4 to 13 141522 -1.3356 0.090837 3 to 12 142000 0.3127 0.622729 2 to 11 142097 0.6471 0.741229 1 to 10 142189 0.9644 0.832572 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-10-03_11:31 Bits used No. missing words z-score p-value 28 to 32 141725 -0.6248 0.266036 27 to 31 141486 -1.4350 0.075641 26 to 30 142003 0.3175 0.624578 25 to 29 141942 0.1107 0.544091 24 to 28 142563 2.2158 0.986648 23 to 27 142388 1.6226 0.947664 22 to 26 141582 -1.1096 0.133587 21 to 25 142032 0.4158 0.661233 20 to 24 142142 0.7887 0.784860 19 to 23 142113 0.6904 0.755031 18 to 22 141766 -0.4859 0.313532 17 to 21 142011 0.3446 0.634819 16 to 20 141976 0.2260 0.589399 15 to 19 141539 -1.2554 0.104675 14 to 18 142084 0.5921 0.723109 13 to 17 142352 1.5006 0.933267 12 to 16 141382 -1.7876 0.036924 11 to 15 141561 -1.1808 0.118845 10 to 14 141377 -1.8045 0.035576 9 to 13 141774 -0.4587 0.323208 8 to 12 142546 2.1582 0.984544 7 to 11 142765 2.9006 0.998138 6 to 10 142167 0.8735 0.808793 5 to 9 142010 0.3413 0.633544 4 to 8 142064 0.5243 0.699967 3 to 7 141470 -1.4893 0.068210 2 to 6 141468 -1.4960 0.067322 1 to 5 141875 -0.1164 0.453679 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-10-03_11:31 Bits used No. missing words z-score p-value 31 to 32 141655 -0.7502 0.226556 30 to 31 141944 0.1023 0.540729 29 to 30 141870 -0.1160 0.453819 28 to 29 141658 -0.7414 0.229230 27 to 28 141588 -0.9479 0.171596 26 to 27 142508 1.7660 0.961301 25 to 26 141882 -0.0806 0.467872 24 to 25 142023 0.3353 0.631304 23 to 24 141419 -1.4464 0.074032 22 to 23 142609 2.0639 0.980488 21 to 22 141929 0.0580 0.523135 20 to 21 141692 -0.6411 0.260732 19 to 20 142023 0.3353 0.631304 18 to 19 141802 -0.3166 0.375771 17 to 18 142280 1.0934 0.862896 16 to 17 141710 -0.5880 0.278268 15 to 16 142146 0.6981 0.757456 14 to 15 141991 0.2409 0.595189 13 to 14 142022 0.3324 0.630191 12 to 13 141562 -1.0246 0.152783 11 to 12 142041 0.3884 0.651143 10 to 11 141599 -0.9154 0.179984 9 to 10 142013 0.3058 0.620126 8 to 9 141052 -2.5290 0.005719 7 to 8 141867 -0.1249 0.450314 6 to 7 141874 -0.1042 0.458498 5 to 6 142271 1.0669 0.856985 4 to 5 141993 0.2468 0.597474 3 to 4 142213 0.8958 0.814815 2 to 3 142084 0.5153 0.696811 1 to 2 142077 0.4946 0.689559 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-10-03_11:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2449.38 -0.716 0.237043 Test results for specific bytes for dh-ranFile-2016-10-03_11:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2416.95 -1.175 0.120086 2 to 9 2494.95 -0.071 0.471549 3 to 10 2511.79 0.167 0.566203 4 to 11 2504.38 0.062 0.524718 5 to 12 2466.60 -0.472 0.318343 6 to 13 2538.05 0.538 0.704770 7 to 14 2480.10 -0.281 0.389200 8 to 15 2484.44 -0.220 0.412902 9 to 16 2507.58 0.107 0.542670 10 to 17 2560.92 0.862 0.805538 11 to 18 2497.27 -0.039 0.484585 12 to 19 2540.14 0.568 0.714881 13 to 20 2440.64 -0.839 0.200613 14 to 21 2478.85 -0.299 0.382455 15 to 22 2447.73 -0.739 0.229911 16 to 23 2589.23 1.262 0.896510 17 to 24 2578.61 1.112 0.866865 18 to 25 2431.48 -0.969 0.166258 19 to 26 2431.88 -0.963 0.167695 20 to 27 2488.98 -0.156 0.438062 21 to 28 2372.12 -1.809 0.035260 22 to 29 2398.84 -1.431 0.076263 23 to 30 2604.73 1.481 0.930709 24 to 31 2675.96 2.488 0.993585 25 to 32 2547.32 0.669 0.748309 CDPARK for dh-ranFile-2016-10-03_11:31: 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 3536 0.5936 0.723613 3550 1.2329 0.891189 3531 0.3653 0.642555 3545 1.0046 0.842447 3523 0.0000 0.500000 3516 -0.3196 0.374623 3500 -1.0502 0.146807 3512 -0.5023 0.307734 3559 1.6438 0.949895 3499 -1.0959 0.136563 Square side=100, avg. no. parked=3527.10 sample std.=19.62 p-value of the KSTEST for those 10 p-values: 0.921628 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-10-03_11:31 0.9665,0.6432,0.5905,0.0845,0.5370,0.8248,0.2235,0.0958,0.3516,0.6401, The KS test for those 10 p-values: 0.980055 The 3DSPHERES test for dh-ranFile-2016-10-03_11:31 sample no r^3 equiv. uni. 1 21.634 0.513803 2 89.396 0.949200 3 11.313 0.314149 4 18.311 0.456845 5 56.339 0.847098 6 3.890 0.121613 7 16.837 0.429492 8 57.509 0.852949 9 18.680 0.463483 10 11.683 0.322564 11 6.452 0.193522 12 15.202 0.397531 13 61.115 0.869604 14 8.702 0.251792 15 18.483 0.459961 16 71.091 0.906493 17 7.496 0.221098 18 23.220 0.538840 19 68.030 0.896446 20 16.547 0.423952 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.456962 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-10-03_11:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 1.3 1.3 -0.5 1.2 -0.4 0.0 0.0 1.1 0.5 0.2 -1.7 0.9 0.6 -0.4 0.1 1.6 -0.3 -0.6 -0.3 -0.4 0.7 0.2 -1.9 -0.8 0.9 -0.1 -1.3 0.8 -0.9 -1.1 1.8 0.8 1.0 -1.2 -0.3 0.5 0.2 1.3 -0.1 0.9 0.0 -1.1 Chi-square with 42 degrees of freedom:34.723408 z-score=-0.793941, p-value=0.220311 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-10-03_11:31 Test no p-value 1 0.041260 2 0.014569 3 0.607048 4 0.182023 5 0.296298 6 0.458785 7 0.206373 8 0.006867 9 0.292741 10 0.217709 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.003285 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-10-03_11:31: (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 66929 1.03 66683 0.00 3 25000.00 24875 0.62 25029 0.03 4 6666.67 6560 1.71 6596 0.75 5 1388.89 1330 2.50 1406 0.21 6 238.10 271 4.55 242 0.06 7 34.72 32 0.21 37 0.15 8 4.96 2 1.77 6 0.22 p=0.94615 p=0.03595 Number of rngs required: 688609, p-value: 0.594 RESULTS OF CRAPS TEST for dh-ranFile-2016-10-03_11:31 No. of wins: Observed Expected 98575 98585.9 z-score=-0.049, pvalue=0.48063 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66657 66666.7 0.001 0.001 2 37699 37654.3 0.053 0.054 3 26903 26954.7 0.099 0.154 4 19316 19313.5 0.000 0.154 5 13662 13851.4 2.590 2.744 6 10082 9943.5 1.928 4.672 7 7227 7145.0 0.940 5.613 8 5190 5139.1 0.505 6.117 9 3696 3699.9 0.004 6.122 10 2610 2666.3 1.189 7.310 11 1925 1923.3 0.001 7.312 12 1453 1388.7 2.973 10.285 13 1001 1003.7 0.007 10.292 14 729 726.1 0.011 10.304 15 519 525.8 0.089 10.393 16 357 381.2 1.530 11.923 17 274 276.5 0.023 11.946 18 194 200.8 0.232 12.178 19 148 146.0 0.028 12.206 20 110 106.2 0.135 12.341 21 248 287.1 5.329 17.670 Chisq= 17.67 for 20 degrees of freedom, p= 0.39084 SUMMARY of craptest p-value for no. of wins: 0.480633 p-value for throws/game: 0.390839 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-10-03_11:31 No. of wins: Observed Expected 98621 98585.9 z-score= 0.157, pvalue=0.56245 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66296 66666.7 2.061 2.061 2 37894 37654.3 1.526 3.587 3 26916 26954.7 0.056 3.642 4 19494 19313.5 1.688 5.330 5 14058 13851.4 3.081 8.411 6 9987 9943.5 0.190 8.601 7 7257 7145.0 1.755 10.355 8 5084 5139.1 0.590 10.946 9 3661 3699.9 0.408 11.354 10 2621 2666.3 0.770 12.123 11 1884 1923.3 0.804 12.928 12 1342 1388.7 1.573 14.501 13 977 1003.7 0.711 15.212 14 681 726.1 2.806 18.018 15 505 525.8 0.826 18.844 16 380 381.2 0.003 18.847 17 259 276.5 1.112 19.960 18 188 200.8 0.820 20.779 19 141 146.0 0.170 20.949 20 110 106.2 0.135 21.084 21 265 287.1 1.703 22.787 Chisq= 22.79 for 20 degrees of freedom, p= 0.70065 SUMMARY of craptest p-value for no. of wins: 0.562446 p-value for throws/game: 0.700650 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0022,0.0033,0.0057,0.0069,0.0074,0.0123,0.0146,0.0223,0.0267,0.0353, 0.0356,0.0360,0.0369,0.0378,0.0413,0.0517,0.0639,0.0673,0.0682,0.0740, 0.0756,0.0763,0.0812,0.0845,0.0908,0.0958,0.0996,0.1035,0.1047,0.1188, 0.1201,0.1216,0.1226,0.1271,0.1307,0.1336,0.1366,0.1399,0.1439,0.1466, 0.1468,0.1528,0.1543,0.1575,0.1643,0.1663,0.1677,0.1716,0.1718,0.1719, 0.1767,0.1800,0.1820,0.1935,0.1985,0.2006,0.2064,0.2076,0.2177,0.2203, 0.2211,0.2235,0.2266,0.2292,0.2299,0.2370,0.2508,0.2510,0.2514,0.2518, 0.2607,0.2660,0.2725,0.2756,0.2783,0.2796,0.2906,0.2923,0.2927,0.2963, 0.2984,0.3021,0.3045,0.3067,0.3077,0.3135,0.3141,0.3183,0.3226,0.3232, 0.3291,0.3345,0.3436,0.3516,0.3526,0.3593,0.3601,0.3722,0.3736,0.3746, 0.3751,0.3755,0.3758,0.3825,0.3845,0.3892,0.3908,0.3949,0.3975,0.3984, 0.3994,0.4046,0.4129,0.4240,0.4295,0.4316,0.4322,0.4359,0.4381,0.4503, 0.4537,0.4538,0.4556,0.4568,0.4570,0.4585,0.4588,0.4600,0.4635,0.4679, 0.4715,0.4738,0.4806,0.4846,0.4872,0.4884,0.4888,0.4980,0.5000,0.5138, 0.5146,0.5231,0.5247,0.5370,0.5388,0.5402,0.5407,0.5427,0.5441,0.5494, 0.5515,0.5539,0.5558,0.5624,0.5662,0.5793,0.5894,0.5905,0.5937,0.5952, 0.5970,0.5975,0.6007,0.6070,0.6126,0.6160,0.6162,0.6201,0.6227,0.6246, 0.6277,0.6302,0.6313,0.6313,0.6335,0.6348,0.6401,0.6426,0.6432,0.6472, 0.6511,0.6612,0.6618,0.6699,0.6896,0.6960,0.6968,0.6972,0.6983,0.7000, 0.7007,0.7010,0.7010,0.7048,0.7050,0.7059,0.7094,0.7149,0.7196,0.7231, 0.7236,0.7273,0.7345,0.7356,0.7412,0.7412,0.7425,0.7428,0.7483,0.7550, 0.7575,0.7682,0.7849,0.7870,0.7908,0.7970,0.7970,0.7996,0.8022,0.8055, 0.8083,0.8088,0.8148,0.8181,0.8194,0.8248,0.8326,0.8380,0.8424,0.8471, 0.8515,0.8529,0.8570,0.8629,0.8633,0.8669,0.8696,0.8828,0.8912,0.8964, 0.8965,0.9065,0.9069,0.9079,0.9096,0.9138,0.9216,0.9231,0.9307,0.9321, 0.9333,0.9417,0.9461,0.9477,0.9492,0.9499,0.9582,0.9597,0.9613,0.9665, 0.9715,0.9801,0.9805,0.9845,0.9866,0.9928,0.9936,0.9978,0.9981, Overall p-value after applying KStest on 269 p-values = 0.995632 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.