RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-05-21_22:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.52 26.1132 0.927577 2 to 25 15.53 37.7366 0.997329 3 to 26 15.53 27.0676 0.942916 4 to 27 15.74 26.0329 0.926137 5 to 28 15.79 22.2312 0.824010 6 to 29 15.72 22.5377 0.835087 7 to 30 15.71 22.0789 0.818295 8 to 31 15.74 23.3007 0.860285 9 to 32 15.89 12.4885 0.230304 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.000313 Tough bday spacings test for dh-ranFile-2016-05-21_22:31: 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 6 37 71 104 91 80 50 42 12 6 1 (O-E)^2/E 1.1 0.0 0.1 0.4 0.5 0.0 0.1 5.0 0.6 0.1 2.3 Birthday Spacings: Sum(O-E)^2/E= 10.109, p= 0.569 RESULTS OF GCD FOR dh-ranFile-2016-05-21_22:31 Euclid's algorithm: p-value, steps to gcd: 0.119542 p-value, dist. of gcd's: 0.840315 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-05-21_22:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.887 0.631 0.745 0.271 0.977 0.849 0.049 0.095 Bits 8 to 15---> 0.523 0.311 0.557 0.647 0.181 0.821 0.666 0.312 Bits 16 to 23---> 0.223 0.865 0.591 0.243 0.573 0.247 0.753 0.293 Bits 24 to 31---> 0.439 0.526 0.179 0.997 0.748 0.763 0.228 0.863 KS test for the above 32 p values: 0.300 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-05-21_22:31, p-values for 5 runs: 0.3709, 0.9904, 0.7089, 0.8566, 0.9868 Rank test for binary matrices (31x31) for dh-ranFile-2016-05-21_22:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 208 211.4 0.055 0.055 r= 29 5181 5134.0 0.430 0.485 r= 30 23072 23103.0 0.042 0.527 r= 31 11539 11551.5 0.014 0.541 chi-square = 0.541 with df = 3; p-value = 0.090 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-05-21_22:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 219 211.4 0.272 0.272 r= 30 5164 5134.0 0.175 0.447 r= 31 23106 23103.0 0.000 0.447 r= 32 11511 11551.5 0.142 0.590 chi-square = 0.590 with df = 3; p-value = 0.101 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-05-21_22:31 b-rank test for bits 1 to 8, p=0.18244 b-rank test for bits 2 to 9, p=0.47581 b-rank test for bits 3 to 10, p=0.04784 b-rank test for bits 4 to 11, p=0.77390 b-rank test for bits 5 to 12, p=0.46707 b-rank test for bits 6 to 13, p=0.94449 b-rank test for bits 7 to 14, p=0.83488 b-rank test for bits 8 to 15, p=0.17732 b-rank test for bits 9 to 16, p=0.15296 b-rank test for bits 10 to 17, p=0.60641 b-rank test for bits 11 to 18, p=0.35842 b-rank test for bits 12 to 19, p=0.73123 b-rank test for bits 13 to 20, p=0.21957 b-rank test for bits 14 to 21, p=0.13292 b-rank test for bits 15 to 22, p=0.09816 b-rank test for bits 16 to 23, p=0.08664 b-rank test for bits 17 to 24, p=0.98043 b-rank test for bits 18 to 25, p=0.62804 b-rank test for bits 19 to 26, p=0.92451 b-rank test for bits 20 to 27, p=0.31203 b-rank test for bits 21 to 28, p=0.37896 b-rank test for bits 22 to 29, p=0.03968 b-rank test for bits 23 to 30, p=0.99999 b-rank test for bits 24 to 31, p=0.37675 b-rank test for bits 25 to 32, p=0.84393 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 = 0.383382 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-05-21_22:31 (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 141572 -0.79 0.215303 2 141608 -0.70 0.240703 3 141501 -0.95 0.170031 4 142289 0.89 0.812482 5 141634 -0.64 0.260017 6 141973 0.15 0.559129 7 142040 0.31 0.619933 8 141686 -0.52 0.300905 9 141940 0.07 0.528563 10 141783 -0.30 0.383935 11 142033 0.29 0.613690 12 142097 0.44 0.669481 13 141461 -1.05 0.147435 14 142037 0.30 0.617261 15 142110 0.47 0.680413 16 142304 0.92 0.821769 17 142735 1.93 0.973143 18 141585 -0.76 0.224291 19 141696 -0.50 0.309089 20 141299 -1.43 0.076934 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-05-21_22:31 Bits used No. missing words z-score p-value 23 to 32 142231 1.1092 0.866330 22 to 31 141915 0.0196 0.507800 21 to 30 141307 -2.0770 0.018901 20 to 29 141689 -0.7598 0.223699 19 to 28 141862 -0.1632 0.435178 18 to 27 142281 1.2816 0.900012 17 to 26 141899 -0.0356 0.485792 16 to 25 141750 -0.5494 0.291361 15 to 24 141698 -0.7287 0.233085 14 to 23 142220 1.0713 0.857977 13 to 22 142105 0.6747 0.750075 12 to 21 141851 -0.2011 0.420295 11 to 20 142122 0.7333 0.768326 10 to 19 141630 -0.9632 0.167722 9 to 18 141911 0.0058 0.502297 8 to 17 141906 -0.0115 0.495419 7 to 16 141878 -0.1080 0.456984 6 to 15 141881 -0.0977 0.461089 5 to 14 141933 0.0816 0.532526 4 to 13 142225 1.0885 0.861817 3 to 12 142164 0.8782 0.810075 2 to 11 141847 -0.2149 0.414911 1 to 10 141999 0.3092 0.621418 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-05-21_22:31 Bits used No. missing words z-score p-value 28 to 32 142113 0.6904 0.755031 27 to 31 142153 0.8260 0.795598 26 to 30 141486 -1.4350 0.075641 25 to 29 141711 -0.6723 0.250695 24 to 28 142142 0.7887 0.784860 23 to 27 141948 0.1311 0.552146 22 to 26 142356 1.5141 0.935004 21 to 25 141596 -1.0621 0.144087 20 to 24 141583 -1.1062 0.134319 19 to 23 142152 0.8226 0.794635 18 to 22 142130 0.7480 0.772780 17 to 21 141456 -1.5367 0.062182 16 to 20 142331 1.4294 0.923554 15 to 19 142031 0.4124 0.659992 14 to 18 142080 0.5785 0.718551 13 to 17 141869 -0.1367 0.445629 12 to 16 142002 0.3141 0.623291 11 to 15 142781 2.9548 0.998436 10 to 14 141904 -0.0181 0.492792 9 to 13 142360 1.5277 0.936706 8 to 12 141822 -0.2960 0.383602 7 to 11 141841 -0.2316 0.408414 6 to 10 142160 0.8497 0.802262 5 to 9 142165 0.8667 0.806941 4 to 8 142192 0.9582 0.831020 3 to 7 141564 -1.1706 0.120878 2 to 6 141895 -0.0486 0.480629 1 to 5 142346 1.4802 0.930595 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-05-21_22:31 Bits used No. missing words z-score p-value 31 to 32 141566 -1.0128 0.155584 30 to 31 141166 -2.1927 0.014164 29 to 30 141894 -0.0452 0.481966 28 to 29 141785 -0.3668 0.356901 27 to 28 141609 -0.8859 0.187828 26 to 27 142398 1.4415 0.925279 25 to 26 141622 -0.8476 0.198336 24 to 25 141785 -0.3668 0.356901 23 to 24 141893 -0.0482 0.480790 22 to 23 141934 0.0728 0.529007 21 to 22 141500 -1.2075 0.113627 20 to 21 142005 0.2822 0.611110 19 to 20 141993 0.2468 0.597474 18 to 19 142142 0.6863 0.753751 17 to 18 141759 -0.4435 0.328720 16 to 17 141613 -0.8741 0.191024 15 to 16 142120 0.6214 0.732847 14 to 15 141978 0.2026 0.580263 13 to 14 142229 0.9430 0.827154 12 to 13 141481 -1.2635 0.103203 11 to 12 141635 -0.8092 0.209191 10 to 11 141815 -0.2783 0.390407 9 to 10 141675 -0.6912 0.244708 8 to 9 141581 -0.9685 0.166391 7 to 8 142007 0.2881 0.613370 6 to 7 141727 -0.5378 0.295342 5 to 6 141903 -0.0187 0.492551 4 to 5 141238 -1.9803 0.023834 3 to 4 141598 -0.9184 0.179211 2 to 3 141766 -0.4228 0.336220 1 to 2 141893 -0.0482 0.480790 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-05-21_22:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2469.15 -0.436 0.331340 Test results for specific bytes for dh-ranFile-2016-05-21_22:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2519.53 0.276 0.608825 2 to 9 2410.20 -1.270 0.102055 3 to 10 2438.90 -0.864 0.193781 4 to 11 2566.34 0.938 0.825934 5 to 12 2492.17 -0.111 0.455899 6 to 13 2348.58 -2.141 0.016121 7 to 14 2539.23 0.555 0.710499 8 to 15 2576.87 1.087 0.861517 9 to 16 2513.38 0.189 0.575014 10 to 17 2534.97 0.495 0.689565 11 to 18 2435.93 -0.906 0.182452 12 to 19 2477.98 -0.311 0.377758 13 to 20 2596.03 1.358 0.912789 14 to 21 2473.73 -0.372 0.355129 15 to 22 2465.84 -0.483 0.314506 16 to 23 2527.00 0.382 0.648711 17 to 24 2601.32 1.433 0.924044 18 to 25 2498.89 -0.016 0.493728 19 to 26 2440.21 -0.846 0.198890 20 to 27 2458.53 -0.587 0.278756 21 to 28 2556.87 0.804 0.789368 22 to 29 2566.42 0.939 0.826225 23 to 30 2441.80 -0.823 0.205248 24 to 31 2421.34 -1.112 0.132966 25 to 32 2530.45 0.431 0.666626 CDPARK for dh-ranFile-2016-05-21_22:31: 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 3491 -1.4612 0.071982 3489 -1.5525 0.060270 3557 1.5525 0.939730 3486 -1.6895 0.045562 3517 -0.2740 0.392053 3520 -0.1370 0.445521 3502 -0.9589 0.168804 3512 -0.5023 0.307734 3529 0.2740 0.607947 3542 0.8676 0.807188 Square side=100, avg. no. parked=3514.50 sample std.=22.33 p-value of the KSTEST for those 10 p-values: 0.292318 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-05-21_22:31 0.9232,0.2879,0.9836,0.5156,0.7643,0.5908,0.9093,0.3102,0.8961,0.4785, The KS test for those 10 p-values: 0.094510 The 3DSPHERES test for dh-ranFile-2016-05-21_22:31 sample no r^3 equiv. uni. 1 6.773 0.202101 2 33.292 0.670349 3 63.487 0.879514 4 28.247 0.609984 5 61.122 0.869634 6 37.304 0.711618 7 17.402 0.440140 8 13.972 0.372317 9 25.089 0.566684 10 4.607 0.142366 11 40.896 0.744161 12 0.561 0.018535 13 24.057 0.551523 14 52.022 0.823434 15 2.762 0.087970 16 3.156 0.099846 17 4.240 0.131787 18 90.490 0.951020 19 4.127 0.128534 20 9.021 0.259704 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.780896 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-05-21_22:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -0.7 0.8 -0.5 0.7 0.1 0.1 0.2 -0.8 2.1 -0.6 -0.9 0.6 -1.0 0.8 -0.1 0.1 -0.6 -0.4 1.4 0.0 -0.3 -0.4 -0.3 1.1 -1.2 0.3 -0.6 0.0 -0.5 0.2 2.2 0.6 -0.5 0.3 0.2 -1.2 -1.0 -0.4 1.5 -0.6 1.0 -1.1 Chi-square with 42 degrees of freedom:29.857790 z-score=-1.324824, p-value=0.080033 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-05-21_22:31 Test no p-value 1 0.042013 2 0.754630 3 0.767459 4 0.709748 5 0.070946 6 0.395376 7 0.454054 8 0.999908 9 0.880602 10 0.745994 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.213637 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-05-21_22:31: (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 66389 1.16 66591 0.09 3 25000.00 25185 1.37 25060 0.14 4 6666.67 6793 2.39 6666 0.00 5 1388.89 1345 1.39 1404 0.16 6 238.10 246 0.26 230 0.28 7 34.72 34 0.01 39 0.53 8 4.96 7 0.84 9 3.29 p=0.71649 p=0.38904 Number of rngs required: 688906, p-value: 0.719 RESULTS OF CRAPS TEST for dh-ranFile-2016-05-21_22:31 No. of wins: Observed Expected 98847 98585.9 z-score= 1.168, pvalue=0.87859 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66773 66666.7 0.170 0.170 2 37725 37654.3 0.133 0.302 3 26896 26954.7 0.128 0.430 4 19208 19313.5 0.576 1.006 5 13874 13851.4 0.037 1.043 6 9997 9943.5 0.287 1.330 7 7190 7145.0 0.283 1.613 8 5037 5139.1 2.027 3.641 9 3660 3699.9 0.430 4.070 10 2657 2666.3 0.032 4.103 11 1983 1923.3 1.851 5.954 12 1334 1388.7 2.158 8.112 13 994 1003.7 0.094 8.206 14 730 726.1 0.021 8.226 15 539 525.8 0.330 8.556 16 380 381.2 0.003 8.559 17 274 276.5 0.023 8.583 18 208 200.8 0.256 8.839 19 147 146.0 0.007 8.846 20 92 106.2 1.902 10.748 21 302 287.1 0.772 11.520 Chisq= 11.52 for 20 degrees of freedom, p= 0.06839 SUMMARY of craptest p-value for no. of wins: 0.878592 p-value for throws/game: 0.068391 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-05-21_22:31 No. of wins: Observed Expected 98414 98585.9 z-score=-0.769, pvalue=0.22105 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66704 66666.7 0.021 0.021 2 37619 37654.3 0.033 0.054 3 26833 26954.7 0.550 0.604 4 19211 19313.5 0.544 1.147 5 13808 13851.4 0.136 1.283 6 10053 9943.5 1.205 2.488 7 7234 7145.0 1.108 3.596 8 5160 5139.1 0.085 3.682 9 3751 3699.9 0.707 4.388 10 2675 2666.3 0.028 4.417 11 1949 1923.3 0.343 4.759 12 1375 1388.7 0.136 4.895 13 952 1003.7 2.665 7.560 14 765 726.1 2.080 9.639 15 571 525.8 3.879 13.519 16 323 381.2 8.872 22.390 17 263 276.5 0.663 23.053 18 226 200.8 3.155 26.208 19 150 146.0 0.110 26.318 20 97 106.2 0.800 27.118 21 281 287.1 0.130 27.248 Chisq= 27.25 for 20 degrees of freedom, p= 0.87157 SUMMARY of craptest p-value for no. of wins: 0.221050 p-value for throws/game: 0.871570 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0003,0.0142,0.0161,0.0185,0.0189,0.0238,0.0397,0.0420,0.0456,0.0478, 0.0495,0.0603,0.0622,0.0684,0.0709,0.0720,0.0756,0.0769,0.0800,0.0866, 0.0880,0.0901,0.0945,0.0949,0.0982,0.0998,0.1012,0.1021,0.1032,0.1136, 0.1195,0.1209,0.1285,0.1318,0.1329,0.1330,0.1343,0.1424,0.1441,0.1474, 0.1530,0.1556,0.1664,0.1677,0.1688,0.1700,0.1773,0.1788,0.1792,0.1815, 0.1824,0.1825,0.1878,0.1910,0.1938,0.1983,0.1989,0.2021,0.2052,0.2092, 0.2136,0.2153,0.2196,0.2211,0.2229,0.2237,0.2243,0.2282,0.2303,0.2331, 0.2407,0.2426,0.2447,0.2470,0.2507,0.2597,0.2600,0.2714,0.2788,0.2879, 0.2914,0.2923,0.2926,0.2953,0.2996,0.3009,0.3077,0.3091,0.3102,0.3113, 0.3120,0.3124,0.3145,0.3287,0.3313,0.3362,0.3551,0.3569,0.3569,0.3584, 0.3709,0.3723,0.3767,0.3778,0.3790,0.3834,0.3836,0.3839,0.3890,0.3904, 0.3921,0.3954,0.4084,0.4149,0.4203,0.4352,0.4387,0.4401,0.4455,0.4456, 0.4541,0.4559,0.4570,0.4611,0.4671,0.4758,0.4785,0.4806,0.4808,0.4808, 0.4820,0.4858,0.4926,0.4928,0.4937,0.4954,0.5023,0.5078,0.5156,0.5228, 0.5265,0.5286,0.5290,0.5325,0.5515,0.5521,0.5566,0.5591,0.5667,0.5690, 0.5727,0.5750,0.5803,0.5908,0.5909,0.5975,0.6064,0.6079,0.6088,0.6100, 0.6111,0.6134,0.6137,0.6173,0.6199,0.6214,0.6233,0.6280,0.6308,0.6473, 0.6487,0.6600,0.6658,0.6666,0.6695,0.6703,0.6804,0.6896,0.7089,0.7097, 0.7105,0.7116,0.7165,0.7186,0.7191,0.7312,0.7328,0.7442,0.7447,0.7460, 0.7480,0.7501,0.7534,0.7538,0.7546,0.7550,0.7628,0.7643,0.7675,0.7683, 0.7728,0.7739,0.7809,0.7849,0.7894,0.7946,0.7956,0.8023,0.8069,0.8072, 0.8101,0.8125,0.8183,0.8209,0.8218,0.8234,0.8240,0.8259,0.8262,0.8272, 0.8310,0.8349,0.8351,0.8403,0.8439,0.8492,0.8566,0.8580,0.8603,0.8615, 0.8618,0.8633,0.8651,0.8663,0.8696,0.8716,0.8786,0.8795,0.8806,0.8867, 0.8961,0.9000,0.9093,0.9128,0.9232,0.9236,0.9240,0.9245,0.9253,0.9261, 0.9276,0.9306,0.9350,0.9367,0.9397,0.9429,0.9445,0.9510,0.9731,0.9766, 0.9804,0.9836,0.9868,0.9904,0.9965,0.9973,0.9984,0.9999,1.0000, Overall p-value after applying KStest on 269 p-values = 0.617907 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.