RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-09-06_09:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.83 14.8362 0.392724 2 to 25 15.71 14.3283 0.356258 3 to 26 15.55 23.5307 0.867243 4 to 27 15.61 29.6991 0.971402 5 to 28 15.39 30.7934 0.978841 6 to 29 15.81 8.1776 0.037400 7 to 30 15.80 9.5775 0.079612 8 to 31 15.71 29.9442 0.973250 9 to 32 15.88 17.9542 0.608264 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.106554 Tough bday spacings test for dh-ranFile-2016-09-06_09:31: 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 28 56 108 113 83 50 25 15 6 2 (O-E)^2/E 2.6 2.0 4.1 1.1 2.4 0.3 0.1 0.8 0.0 0.1 1.0 Birthday Spacings: Sum(O-E)^2/E= 14.411, p= 0.845 RESULTS OF GCD FOR dh-ranFile-2016-09-06_09:31 Euclid's algorithm: p-value, steps to gcd: 0.519927 p-value, dist. of gcd's: 0.317693 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-09-06_09:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.959 0.869 0.883 0.644 0.536 0.280 0.629 0.137 Bits 8 to 15---> 0.698 0.240 0.595 0.549 0.032 0.415 0.249 0.979 Bits 16 to 23---> 0.540 0.813 0.099 0.703 0.489 0.190 0.815 0.182 Bits 24 to 31---> 0.023 0.541 0.661 0.735 0.480 0.954 0.228 0.328 KS test for the above 32 p values: 0.015 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-09-06_09:31, p-values for 5 runs: 0.6969, 0.9595, 0.8479, 0.0716, 0.2487 Rank test for binary matrices (31x31) for dh-ranFile-2016-09-06_09:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 183 211.4 3.820 3.820 r= 29 5074 5134.0 0.701 4.521 r= 30 23112 23103.0 0.003 4.525 r= 31 11631 11551.5 0.547 5.072 chi-square = 5.072 with df = 3; p-value = 0.833 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-09-06_09:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 223 211.4 0.634 0.634 r= 30 5038 5134.0 1.795 2.430 r= 31 22902 23103.0 1.750 4.180 r= 32 11837 11551.5 7.055 11.235 chi-square = 11.235 with df = 3; p-value = 0.989 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-09-06_09:31 b-rank test for bits 1 to 8, p=0.69108 b-rank test for bits 2 to 9, p=0.64547 b-rank test for bits 3 to 10, p=0.06134 b-rank test for bits 4 to 11, p=0.49050 b-rank test for bits 5 to 12, p=0.27052 b-rank test for bits 6 to 13, p=0.70475 b-rank test for bits 7 to 14, p=0.19860 b-rank test for bits 8 to 15, p=0.76709 b-rank test for bits 9 to 16, p=0.90515 b-rank test for bits 10 to 17, p=0.46539 b-rank test for bits 11 to 18, p=0.64879 b-rank test for bits 12 to 19, p=0.92221 b-rank test for bits 13 to 20, p=0.99850 b-rank test for bits 14 to 21, p=0.77319 b-rank test for bits 15 to 22, p=0.00664 b-rank test for bits 16 to 23, p=0.52532 b-rank test for bits 17 to 24, p=0.13650 b-rank test for bits 18 to 25, p=0.89735 b-rank test for bits 19 to 26, p=0.30740 b-rank test for bits 20 to 27, p=0.25760 b-rank test for bits 21 to 28, p=0.87383 b-rank test for bits 22 to 29, p=0.15657 b-rank test for bits 23 to 30, p=0.62532 b-rank test for bits 24 to 31, p=0.89002 b-rank test for bits 25 to 32, p=0.88045 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 = 0.356177 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-09-06_09:31 (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 142022 0.26 0.603820 2 142092 0.43 0.665237 3 141861 -0.11 0.455047 4 141907 -0.01 0.497828 5 141860 -0.12 0.454121 6 142393 1.13 0.870777 7 142479 1.33 0.908406 8 142948 2.43 0.992384 9 141862 -0.11 0.455973 10 141552 -0.83 0.201892 11 141526 -0.90 0.185225 12 141525 -0.90 0.184602 13 141692 -0.51 0.305804 14 141395 -1.20 0.114739 15 142814 2.11 0.982730 16 142580 1.57 0.941441 17 142222 0.73 0.767469 18 141337 -1.34 0.090575 19 142619 1.66 0.951352 20 142228 0.74 0.771730 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-09-06_09:31 Bits used No. missing words z-score p-value 23 to 32 142018 0.3747 0.646067 22 to 31 142022 0.3885 0.651183 21 to 30 142191 0.9713 0.834295 20 to 29 142008 0.3402 0.633163 19 to 28 141959 0.1713 0.567997 18 to 27 142144 0.8092 0.790802 17 to 26 142093 0.6333 0.736746 16 to 25 141512 -1.3701 0.085327 15 to 24 142133 0.7713 0.779728 14 to 23 142104 0.6713 0.748978 13 to 22 141878 -0.1080 0.456984 12 to 21 141991 0.2816 0.610883 11 to 20 142402 1.6989 0.955327 10 to 19 142245 1.1575 0.876462 9 to 18 142688 2.6851 0.996374 8 to 17 141950 0.1402 0.555765 7 to 16 142331 1.4540 0.927032 6 to 15 141926 0.0575 0.522920 5 to 14 142134 0.7747 0.780749 4 to 13 141788 -0.4184 0.337835 3 to 12 142233 1.1161 0.867811 2 to 11 142101 0.6609 0.745672 1 to 10 142197 0.9920 0.839393 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-09-06_09:31 Bits used No. missing words z-score p-value 28 to 32 142412 1.7040 0.955806 27 to 31 141884 -0.0859 0.465787 26 to 30 142384 1.6091 0.946197 25 to 29 141798 -0.3774 0.352942 24 to 28 142208 1.0124 0.844336 23 to 27 141552 -1.2113 0.112893 22 to 26 141678 -0.7842 0.216470 21 to 25 141765 -0.4893 0.312331 20 to 24 142160 0.8497 0.802262 19 to 23 141432 -1.6181 0.052824 18 to 22 142375 1.5785 0.942779 17 to 21 142032 0.4158 0.661233 16 to 20 141738 -0.5808 0.280695 15 to 19 142052 0.4836 0.685675 14 to 18 142026 0.3955 0.653760 13 to 17 141675 -0.7943 0.213499 12 to 16 142225 1.0701 0.857706 11 to 15 141507 -1.3638 0.086310 10 to 14 141401 -1.7232 0.042430 9 to 13 141841 -0.2316 0.408414 8 to 12 141277 -2.1435 0.016037 7 to 11 142025 0.3921 0.652509 6 to 10 141318 -2.0045 0.022508 5 to 9 141712 -0.6689 0.251775 4 to 8 141913 0.0124 0.504963 3 to 7 141913 0.0124 0.504963 2 to 6 141781 -0.4350 0.331775 1 to 5 142226 1.0735 0.858467 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-09-06_09:31 Bits used No. missing words z-score p-value 31 to 32 141719 -0.5614 0.287247 30 to 31 141563 -1.0216 0.153480 29 to 30 142382 1.3943 0.918388 28 to 29 142321 1.2144 0.887696 27 to 28 141777 -0.3904 0.348137 26 to 27 141231 -2.0010 0.022698 25 to 26 142408 1.4710 0.929355 24 to 25 141899 -0.0305 0.487845 23 to 24 141913 0.0108 0.504319 22 to 23 142216 0.9046 0.817170 21 to 22 142168 0.7630 0.777280 20 to 21 142290 1.1229 0.869264 19 to 20 141320 -1.7384 0.041067 18 to 19 141836 -0.2163 0.414372 17 to 18 141863 -0.1367 0.445647 16 to 17 141580 -0.9715 0.165656 15 to 16 142515 1.7866 0.963002 14 to 15 141874 -0.1042 0.458498 13 to 14 142237 0.9666 0.833123 12 to 13 141901 -0.0246 0.490198 11 to 12 141631 -0.8210 0.205814 10 to 11 142036 0.3737 0.645671 9 to 10 141616 -0.8653 0.193443 8 to 9 141592 -0.9361 0.174617 7 to 8 142398 1.4415 0.925279 6 to 7 141353 -1.6411 0.050389 5 to 6 141987 0.2291 0.590610 4 to 5 141749 -0.4729 0.318125 3 to 4 141534 -1.1072 0.134111 2 to 3 142143 0.6893 0.754680 1 to 2 141854 -0.1632 0.435174 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-09-06_09:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2482.03 -0.254 0.399689 Test results for specific bytes for dh-ranFile-2016-09-06_09:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2358.92 -1.995 0.023014 2 to 9 2465.16 -0.493 0.311127 3 to 10 2602.52 1.450 0.926441 4 to 11 2489.15 -0.153 0.439036 5 to 12 2551.77 0.732 0.767937 6 to 13 2449.41 -0.715 0.237153 7 to 14 2475.81 -0.342 0.366112 8 to 15 2646.25 2.068 0.980693 9 to 16 2542.01 0.594 0.723781 10 to 17 2512.10 0.171 0.567921 11 to 18 2495.90 -0.058 0.476899 12 to 19 2623.95 1.753 0.960192 13 to 20 2548.46 0.685 0.753436 14 to 21 2339.33 -2.272 0.011535 15 to 22 2411.58 -1.251 0.105556 16 to 23 2534.02 0.481 0.684785 17 to 24 2452.87 -0.666 0.252550 18 to 25 2534.15 0.483 0.685459 19 to 26 2465.79 -0.484 0.314240 20 to 27 2541.68 0.589 0.722220 21 to 28 2544.84 0.634 0.737026 22 to 29 2406.33 -1.325 0.092635 23 to 30 2542.64 0.603 0.726742 24 to 31 2415.18 -1.200 0.115151 25 to 32 2600.79 1.425 0.922969 CDPARK for dh-ranFile-2016-09-06_09:31: 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 3529 0.2740 0.607947 3508 -0.6849 0.246694 3517 -0.2740 0.392053 3535 0.5479 0.708135 3522 -0.0457 0.481790 3541 0.8219 0.794438 3519 -0.1826 0.427537 3529 0.2740 0.607947 3515 -0.3653 0.357445 3547 1.0959 0.863437 Square side=100, avg. no. parked=3526.20 sample std.=11.64 p-value of the KSTEST for those 10 p-values: 0.464243 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-09-06_09:31 0.3571,0.3632,0.2944,0.6607,0.7454,0.1848,0.7590,0.4694,0.4083,0.6790, The KS test for those 10 p-values: 0.484049 The 3DSPHERES test for dh-ranFile-2016-09-06_09:31 sample no r^3 equiv. uni. 1 15.571 0.404912 2 32.498 0.661507 3 4.688 0.144660 4 74.869 0.917556 5 24.472 0.557689 6 89.836 0.949940 7 3.849 0.120421 8 30.130 0.633713 9 16.058 0.414481 10 26.918 0.592314 11 1.293 0.042194 12 12.727 0.345739 13 32.940 0.666465 14 7.518 0.221661 15 3.341 0.105385 16 14.427 0.381764 17 22.367 0.525539 18 50.764 0.815874 19 12.265 0.335582 20 70.254 0.903845 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.983530 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-09-06_09:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 1.3 -1.6 -1.3 -1.1 -1.6 0.7 -0.6 0.4 -0.3 -0.4 0.2 -1.7 -0.2 1.2 -1.2 -0.2 -0.7 -0.0 -0.2 1.5 1.0 -0.2 0.1 1.8 0.9 -0.8 0.1 -1.5 1.4 -0.4 -1.2 -0.2 -0.6 0.1 1.3 -2.1 0.3 -1.0 0.1 0.4 0.1 3.0 0.8 Chi-square with 42 degrees of freedom:49.050731 z-score=0.769298, p-value=0.788690 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-09-06_09:31 Test no p-value 1 0.639345 2 0.000521 3 0.534100 4 0.317032 5 0.841462 6 0.098830 7 0.865196 8 0.084886 9 0.198169 10 0.492129 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.319437 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-09-06_09:31: (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 66567 0.15 66657 0.00 3 25000.00 25184 1.35 24888 0.50 4 6666.67 6638 0.12 6762 1.36 5 1388.89 1360 0.60 1419 0.65 6 238.10 213 2.65 226 0.61 7 34.72 30 0.64 44 2.48 8 4.96 7 0.84 3 0.77 p=0.61519 p=0.61889 Number of rngs required: 689704, p-value: 0.936 RESULTS OF CRAPS TEST for dh-ranFile-2016-09-06_09:31 No. of wins: Observed Expected 98517 98585.9 z-score=-0.308, pvalue=0.37905 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66531 66666.7 0.276 0.276 2 37577 37654.3 0.159 0.435 3 26885 26954.7 0.180 0.615 4 19575 19313.5 3.542 4.157 5 13661 13851.4 2.618 6.775 6 10068 9943.5 1.558 8.332 7 7266 7145.0 2.048 10.381 8 5139 5139.1 0.000 10.381 9 3683 3699.9 0.077 10.458 10 2681 2666.3 0.081 10.539 11 1943 1923.3 0.201 10.740 12 1343 1388.7 1.507 12.246 13 963 1003.7 1.652 13.898 14 761 726.1 1.673 15.571 15 507 525.8 0.675 16.246 16 393 381.2 0.368 16.615 17 280 276.5 0.043 16.658 18 180 200.8 2.160 18.818 19 164 146.0 2.223 21.042 20 105 106.2 0.014 21.055 21 295 287.1 0.217 21.272 Chisq= 21.27 for 20 degrees of freedom, p= 0.61872 SUMMARY of craptest p-value for no. of wins: 0.379050 p-value for throws/game: 0.618721 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-09-06_09:31 No. of wins: Observed Expected 98529 98585.9 z-score=-0.254, pvalue=0.39963 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66632 66666.7 0.018 0.018 2 37515 37654.3 0.515 0.534 3 26924 26954.7 0.035 0.569 4 19425 19313.5 0.644 1.213 5 13973 13851.4 1.067 2.280 6 9978 9943.5 0.119 2.399 7 7002 7145.0 2.863 5.262 8 5131 5139.1 0.013 5.275 9 3715 3699.9 0.062 5.337 10 2645 2666.3 0.170 5.507 11 2022 1923.3 5.062 10.569 12 1337 1388.7 1.928 12.497 13 1018 1003.7 0.203 12.700 14 702 726.1 0.803 13.503 15 530 525.8 0.033 13.536 16 404 381.2 1.370 14.905 17 278 276.5 0.008 14.913 18 213 200.8 0.737 15.651 19 165 146.0 2.477 18.127 20 99 106.2 0.490 18.618 21 292 287.1 0.083 18.701 Chisq= 18.70 for 20 degrees of freedom, p= 0.45865 SUMMARY of craptest p-value for no. of wins: 0.399630 p-value for throws/game: 0.458653 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0005,0.0066,0.0115,0.0154,0.0160,0.0225,0.0225,0.0227,0.0230,0.0317, 0.0374,0.0411,0.0422,0.0424,0.0504,0.0528,0.0613,0.0716,0.0796,0.0849, 0.0853,0.0863,0.0906,0.0926,0.0988,0.0994,0.1054,0.1056,0.1066,0.1129, 0.1147,0.1152,0.1204,0.1341,0.1365,0.1367,0.1447,0.1535,0.1566,0.1657, 0.1746,0.1821,0.1846,0.1848,0.1852,0.1904,0.1934,0.1982,0.1986,0.2019, 0.2058,0.2135,0.2165,0.2217,0.2280,0.2372,0.2403,0.2467,0.2487,0.2492, 0.2518,0.2525,0.2576,0.2705,0.2797,0.2807,0.2872,0.2944,0.3058,0.3074, 0.3111,0.3123,0.3142,0.3170,0.3177,0.3181,0.3194,0.3277,0.3318,0.3356, 0.3378,0.3457,0.3481,0.3529,0.3562,0.3563,0.3571,0.3574,0.3632,0.3661, 0.3791,0.3818,0.3921,0.3927,0.3996,0.3997,0.4049,0.4083,0.4084,0.4144, 0.4145,0.4151,0.4275,0.4352,0.4390,0.4456,0.4541,0.4550,0.4560,0.4570, 0.4585,0.4587,0.4642,0.4654,0.4658,0.4694,0.4769,0.4802,0.4818,0.4840, 0.4878,0.4886,0.4902,0.4905,0.4921,0.4978,0.5043,0.5050,0.5050,0.5199, 0.5229,0.5253,0.5255,0.5341,0.5363,0.5403,0.5405,0.5491,0.5558,0.5577, 0.5679,0.5680,0.5906,0.5923,0.5946,0.6038,0.6079,0.6079,0.6083,0.6109, 0.6152,0.6187,0.6189,0.6253,0.6292,0.6332,0.6337,0.6393,0.6435,0.6455, 0.6457,0.6461,0.6488,0.6512,0.6525,0.6538,0.6607,0.6610,0.6612,0.6615, 0.6652,0.6665,0.6790,0.6848,0.6855,0.6857,0.6911,0.6969,0.6978,0.7033, 0.7047,0.7081,0.7222,0.7238,0.7267,0.7345,0.7367,0.7370,0.7454,0.7457, 0.7490,0.7534,0.7547,0.7590,0.7671,0.7675,0.7679,0.7717,0.7732,0.7773, 0.7797,0.7807,0.7887,0.7908,0.7944,0.8023,0.8130,0.8146,0.8159,0.8172, 0.8331,0.8334,0.8343,0.8394,0.8415,0.8443,0.8449,0.8479,0.8577,0.8585, 0.8634,0.8652,0.8672,0.8678,0.8689,0.8693,0.8708,0.8738,0.8765,0.8805, 0.8825,0.8877,0.8900,0.8973,0.9038,0.9052,0.9084,0.9176,0.9184,0.9222, 0.9230,0.9253,0.9264,0.9270,0.9294,0.9358,0.9414,0.9428,0.9462,0.9499, 0.9514,0.9542,0.9553,0.9558,0.9594,0.9595,0.9602,0.9630,0.9714,0.9732, 0.9788,0.9793,0.9807,0.9827,0.9835,0.9895,0.9924,0.9964,0.9985, Overall p-value after applying KStest on 269 p-values = 0.118896 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.