RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-28_05:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.87 13.0061 0.264221 2 to 25 15.58 21.8194 0.808234 3 to 26 15.75 18.4425 0.638548 4 to 27 15.62 20.1499 0.733367 5 to 28 15.77 10.7651 0.131491 6 to 29 15.53 25.5832 0.917604 7 to 30 15.33 26.3997 0.932521 8 to 31 15.66 19.9838 0.724943 9 to 32 15.73 16.3472 0.500631 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.318575 Tough bday spacings test for dh-ranFile-2018-06-28_05:31: 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 8 34 67 98 114 74 51 27 17 6 4 (O-E)^2/E 0.1 0.2 0.5 0.0 2.7 0.2 0.0 0.3 0.3 0.1 0.0 Birthday Spacings: Sum(O-E)^2/E= 4.457, p= 0.076 RESULTS OF GCD FOR dh-ranFile-2018-06-28_05:31 Euclid's algorithm: p-value, steps to gcd: 0.029893 p-value, dist. of gcd's: 0.045908 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-28_05:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.447 0.933 0.089 0.181 0.248 0.281 0.640 0.192 Bits 8 to 15---> 0.878 0.003 0.062 0.099 0.599 0.061 0.908 0.202 Bits 16 to 23---> 0.749 0.063 0.806 0.152 0.910 0.621 0.850 0.480 Bits 24 to 31---> 0.634 0.497 0.464 0.397 0.927 0.046 0.583 0.790 KS test for the above 32 p values: 0.539 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-28_05:31, p-values for 5 runs: 0.7006, 0.8579, 0.0715, 0.6800, 0.1552 Rank test for binary matrices (31x31) for dh-ranFile-2018-06-28_05:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 219 211.4 0.272 0.272 r= 29 5103 5134.0 0.187 0.459 r= 30 23237 23103.0 0.777 1.236 r= 31 11441 11551.5 1.057 2.293 chi-square = 2.293 with df = 3; p-value = 0.486 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-06-28_05:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 222 211.4 0.530 0.530 r= 30 5094 5134.0 0.312 0.841 r= 31 23144 23103.0 0.073 0.914 r= 32 11540 11551.5 0.011 0.926 chi-square = 0.926 with df = 3; p-value = 0.181 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-06-28_05:31 b-rank test for bits 1 to 8, p=0.19231 b-rank test for bits 2 to 9, p=0.77842 b-rank test for bits 3 to 10, p=0.57521 b-rank test for bits 4 to 11, p=0.68802 b-rank test for bits 5 to 12, p=0.84552 b-rank test for bits 6 to 13, p=0.90151 b-rank test for bits 7 to 14, p=0.81879 b-rank test for bits 8 to 15, p=0.76726 b-rank test for bits 9 to 16, p=0.43065 b-rank test for bits 10 to 17, p=0.64004 b-rank test for bits 11 to 18, p=0.43485 b-rank test for bits 12 to 19, p=0.89756 b-rank test for bits 13 to 20, p=0.13812 b-rank test for bits 14 to 21, p=0.02746 b-rank test for bits 15 to 22, p=0.20284 b-rank test for bits 16 to 23, p=0.12710 b-rank test for bits 17 to 24, p=0.71577 b-rank test for bits 18 to 25, p=0.24076 b-rank test for bits 19 to 26, p=0.61574 b-rank test for bits 20 to 27, p=0.17323 b-rank test for bits 21 to 28, p=0.18029 b-rank test for bits 22 to 29, p=0.95873 b-rank test for bits 23 to 30, p=0.91195 b-rank test for bits 24 to 31, p=0.84722 b-rank test for bits 25 to 32, p=0.83628 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 = 0.329940 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-28_05:31 (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 143203 3.02 0.998747 2 141987 0.18 0.572001 3 142251 0.80 0.787650 4 142412 1.17 0.879895 5 142206 0.69 0.755894 6 141973 0.15 0.559129 7 142073 0.38 0.648920 8 141644 -0.62 0.267652 9 141826 -0.19 0.422815 10 141637 -0.64 0.262295 11 141773 -0.32 0.375042 12 141673 -0.55 0.290415 13 141831 -0.18 0.427394 14 141523 -0.90 0.183358 15 141407 -1.17 0.120264 16 142205 0.69 0.755160 17 142325 0.97 0.834274 18 142708 1.87 0.968983 19 142194 0.67 0.747012 20 142234 0.76 0.775947 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-06-28_05:31 Bits used No. missing words z-score p-value 23 to 32 141871 -0.1322 0.447424 22 to 31 142180 0.9333 0.824679 21 to 30 142078 0.5816 0.719589 20 to 29 141983 0.2540 0.600266 19 to 28 142221 1.0747 0.858751 18 to 27 141969 0.2058 0.581510 17 to 26 141444 -1.6046 0.054292 16 to 25 141865 -0.1529 0.439254 15 to 24 142134 0.7747 0.780749 14 to 23 141586 -1.1149 0.132440 13 to 22 141681 -0.7873 0.215540 12 to 21 142031 0.4196 0.662594 11 to 20 141858 -0.1770 0.429754 10 to 19 141635 -0.9460 0.172083 9 to 18 141769 -0.4839 0.314230 8 to 17 142327 1.4402 0.925100 7 to 16 141958 0.1678 0.566641 6 to 15 141967 0.1989 0.578815 5 to 14 141713 -0.6770 0.249203 4 to 13 141951 0.1437 0.557127 3 to 12 141766 -0.4942 0.310568 2 to 11 141783 -0.4356 0.331556 1 to 10 141895 -0.0494 0.480295 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-06-28_05:31 Bits used No. missing words z-score p-value 28 to 32 142107 0.6701 0.748593 27 to 31 141831 -0.2655 0.395302 26 to 30 141603 -1.0384 0.149540 25 to 29 141652 -0.8723 0.191521 24 to 28 142285 1.2735 0.898572 23 to 27 141776 -0.4520 0.325647 22 to 26 142057 0.5006 0.691665 21 to 25 141699 -0.7130 0.237928 20 to 24 142033 0.4192 0.662473 19 to 23 141734 -0.5943 0.276143 18 to 22 141467 -1.4994 0.066882 17 to 21 141967 0.1955 0.577496 16 to 20 142170 0.8836 0.811551 15 to 19 141850 -0.2011 0.420303 14 to 18 142151 0.8192 0.793670 13 to 17 142108 0.6735 0.749672 12 to 16 141466 -1.5028 0.066444 11 to 15 142342 1.4667 0.928768 10 to 14 141782 -0.4316 0.333006 9 to 13 141464 -1.5096 0.065574 8 to 12 141776 -0.4520 0.325647 7 to 11 141746 -0.5537 0.289905 6 to 10 142270 1.2226 0.889262 5 to 9 142015 0.3582 0.639905 4 to 8 141597 -1.0587 0.144858 3 to 7 142036 0.4294 0.666180 2 to 6 141730 -0.6079 0.271628 1 to 5 142199 0.9819 0.836933 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-06-28_05:31 Bits used No. missing words z-score p-value 31 to 32 141948 0.1141 0.545409 30 to 31 141834 -0.2222 0.412074 29 to 30 141743 -0.4906 0.311837 28 to 29 141678 -0.6824 0.247496 27 to 28 140632 -3.7679 0.000082 26 to 27 141916 0.0197 0.507849 25 to 26 141829 -0.2370 0.406343 24 to 25 141963 0.1583 0.562897 23 to 24 142570 1.9489 0.974345 22 to 23 142272 1.0698 0.857651 21 to 22 141768 -0.4169 0.338375 20 to 21 141789 -0.3550 0.361311 19 to 20 142916 2.9695 0.998509 18 to 19 142055 0.4297 0.666295 17 to 18 142138 0.6745 0.750017 16 to 17 141882 -0.0806 0.467872 15 to 16 142372 1.3648 0.913843 14 to 15 141583 -0.9626 0.167868 13 to 14 141622 -0.8476 0.198336 12 to 13 141463 -1.3166 0.093985 11 to 12 142126 0.6391 0.738636 10 to 11 141794 -0.3402 0.366851 9 to 10 141981 0.2114 0.583719 8 to 9 141409 -1.4759 0.069985 7 to 8 142263 1.0433 0.851589 6 to 7 141930 0.0610 0.524310 5 to 6 142404 1.4592 0.927745 4 to 5 142298 1.1465 0.874210 3 to 4 142333 1.2498 0.894307 2 to 3 142394 1.4297 0.923599 1 to 2 142076 0.4917 0.688517 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-28_05:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2496.21 -0.054 0.478628 Test results for specific bytes for dh-ranFile-2018-06-28_05:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2528.01 0.396 0.654008 2 to 9 2619.77 1.694 0.954852 3 to 10 2690.02 2.687 0.996398 4 to 11 2468.41 -0.447 0.327544 5 to 12 2397.03 -1.456 0.072674 6 to 13 2449.13 -0.719 0.235965 7 to 14 2486.49 -0.191 0.424232 8 to 15 2369.86 -1.840 0.032855 9 to 16 2363.69 -1.928 0.026948 10 to 17 2615.90 1.639 0.949400 11 to 18 2419.60 -1.137 0.127769 12 to 19 2467.81 -0.455 0.324487 13 to 20 2583.36 1.179 0.880787 14 to 21 2417.32 -1.169 0.121134 15 to 22 2494.24 -0.081 0.467542 16 to 23 2466.84 -0.469 0.319537 17 to 24 2564.36 0.910 0.818657 18 to 25 2415.70 -1.192 0.116603 19 to 26 2591.49 1.294 0.902153 20 to 27 2479.01 -0.297 0.383270 21 to 28 2351.31 -2.103 0.017743 22 to 29 2498.27 -0.025 0.490217 23 to 30 2403.19 -1.369 0.085489 24 to 31 2556.49 0.799 0.787829 25 to 32 2498.91 -0.015 0.493827 CDPARK for dh-ranFile-2018-06-28_05:31: 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 3528 0.2283 0.590298 3522 -0.0457 0.481790 3559 1.6438 0.949895 3561 1.7352 0.958644 3496 -1.2329 0.108811 3519 -0.1826 0.427537 3510 -0.5936 0.276387 3518 -0.2283 0.409702 3534 0.5023 0.692266 3537 0.6393 0.738676 Square side=100, avg. no. parked=3528.40 sample std.=19.31 p-value of the KSTEST for those 10 p-values: 0.737399 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-28_05:31 0.0571,0.2351,0.6080,0.1510,0.4080,0.8966,0.6656,0.2027,0.4874,0.3021, The KS test for those 10 p-values: 0.521761 The 3DSPHERES test for dh-ranFile-2018-06-28_05:31 sample no r^3 equiv. uni. 1 13.091 0.353621 2 64.996 0.885425 3 39.722 0.733946 4 13.608 0.364665 5 64.372 0.883017 6 28.295 0.610612 7 5.193 0.158959 8 6.116 0.184436 9 11.531 0.319109 10 9.738 0.277177 11 10.886 0.304321 12 7.181 0.212863 13 8.338 0.242640 14 38.485 0.722749 15 81.975 0.934943 16 26.712 0.589512 17 22.539 0.528255 18 40.490 0.740676 19 34.358 0.681865 20 37.646 0.714887 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.639152 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-28_05:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 -0.7 0.1 0.5 -0.4 -1.0 -2.2 -0.7 1.1 1.2 0.2 2.3 0.1 -0.9 -1.9 -0.5 -1.5 0.5 -0.2 0.5 0.9 -1.3 0.2 0.9 -0.0 0.7 -0.3 1.6 -0.2 0.8 0.9 -0.3 0.6 1.5 0.8 -0.1 -1.2 0.8 0.1 -0.7 0.1 1.0 -0.1 Chi-square with 42 degrees of freedom:40.001360 z-score=-0.218070, p-value=0.440968 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-06-28_05:31 Test no p-value 1 0.002624 2 0.148386 3 0.245983 4 0.166348 5 0.943020 6 0.120412 7 0.051597 8 0.657829 9 0.320778 10 0.163574 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.012400 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-28_05:31: (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 66440 0.77 66416 0.94 3 25000.00 25195 1.52 25144 0.83 4 6666.67 6716 0.37 6735 0.70 5 1388.89 1413 0.42 1420 0.70 6 238.10 204 4.88 240 0.02 7 34.72 29 0.94 36 0.05 8 4.96 2 1.77 8 1.86 p=0.90075 p=0.46829 Number of rngs required: 688847, p-value: 0.696 RESULTS OF CRAPS TEST for dh-ranFile-2018-06-28_05:31 No. of wins: Observed Expected 99015 98585.9 z-score= 1.919, pvalue=0.97253 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66904 66666.7 0.845 0.845 2 37374 37654.3 2.087 2.932 3 26829 26954.7 0.586 3.518 4 19351 19313.5 0.073 3.591 5 13827 13851.4 0.043 3.634 6 9839 9943.5 1.099 4.733 7 7186 7145.0 0.235 4.968 8 5201 5139.1 0.746 5.715 9 3642 3699.9 0.905 6.620 10 2710 2666.3 0.716 7.336 11 1992 1923.3 2.452 9.788 12 1441 1388.7 1.967 11.754 13 1027 1003.7 0.540 12.295 14 679 726.1 3.060 15.355 15 534 525.8 0.127 15.482 16 382 381.2 0.002 15.484 17 309 276.5 3.810 19.294 18 191 200.8 0.481 19.775 19 158 146.0 0.989 20.764 20 123 106.2 2.652 23.416 21 301 287.1 0.672 24.088 Chisq= 24.09 for 20 degrees of freedom, p= 0.76143 SUMMARY of craptest p-value for no. of wins: 0.972531 p-value for throws/game: 0.761428 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-28_05:31 No. of wins: Observed Expected 99017 98585.9 z-score= 1.928, pvalue=0.97309 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66636 66666.7 0.014 0.014 2 37462 37654.3 0.982 0.996 3 27149 26954.7 1.400 2.397 4 19211 19313.5 0.544 2.940 5 13740 13851.4 0.896 3.836 6 10115 9943.5 2.956 6.793 7 7158 7145.0 0.024 6.816 8 5122 5139.1 0.057 6.873 9 3717 3699.9 0.079 6.952 10 2655 2666.3 0.048 7.000 11 1885 1923.3 0.764 7.764 12 1407 1388.7 0.240 8.004 13 1005 1003.7 0.002 8.006 14 746 726.1 0.543 8.549 15 539 525.8 0.330 8.879 16 368 381.2 0.454 9.332 17 307 276.5 3.355 12.687 18 200 200.8 0.003 12.691 19 157 146.0 0.831 13.522 20 118 106.2 1.308 14.830 21 303 287.1 0.879 15.709 Chisq= 15.71 for 20 degrees of freedom, p= 0.26547 SUMMARY of craptest p-value for no. of wins: 0.973092 p-value for throws/game: 0.265473 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0001,0.0026,0.0033,0.0124,0.0177,0.0269,0.0275,0.0299,0.0329,0.0459, 0.0460,0.0516,0.0543,0.0571,0.0608,0.0618,0.0628,0.0656,0.0664,0.0669, 0.0700,0.0715,0.0727,0.0756,0.0855,0.0894,0.0940,0.0988,0.1088,0.1166, 0.1203,0.1204,0.1211,0.1271,0.1278,0.1315,0.1324,0.1381,0.1449,0.1484, 0.1495,0.1510,0.1521,0.1552,0.1590,0.1636,0.1663,0.1679,0.1721,0.1732, 0.1803,0.1807,0.1812,0.1834,0.1844,0.1915,0.1916,0.1923,0.1983,0.2023, 0.2027,0.2028,0.2129,0.2155,0.2351,0.2360,0.2379,0.2408,0.2426,0.2460, 0.2475,0.2475,0.2492,0.2623,0.2642,0.2655,0.2677,0.2716,0.2761,0.2764, 0.2772,0.2805,0.2899,0.2904,0.3021,0.3043,0.3106,0.3118,0.3142,0.3186, 0.3191,0.3195,0.3208,0.3245,0.3256,0.3256,0.3275,0.3299,0.3316,0.3330, 0.3384,0.3536,0.3613,0.3647,0.3669,0.3750,0.3833,0.3953,0.3966,0.4063, 0.4080,0.4097,0.4121,0.4203,0.4228,0.4242,0.4274,0.4275,0.4298,0.4306, 0.4348,0.4393,0.4410,0.4470,0.4474,0.4638,0.4675,0.4679,0.4683,0.4786, 0.4803,0.4804,0.4818,0.4862,0.4874,0.4902,0.4938,0.4970,0.5006,0.5078, 0.5218,0.5243,0.5283,0.5386,0.5454,0.5571,0.5591,0.5629,0.5666,0.5720, 0.5752,0.5775,0.5788,0.5815,0.5835,0.5837,0.5895,0.5903,0.5987,0.6003, 0.6080,0.6106,0.6157,0.6210,0.6338,0.6385,0.6392,0.6397,0.6399,0.6400, 0.6489,0.6540,0.6578,0.6625,0.6626,0.6656,0.6662,0.6663,0.6800,0.6819, 0.6880,0.6885,0.6917,0.6923,0.6956,0.7006,0.7149,0.7158,0.7196,0.7227, 0.7249,0.7334,0.7339,0.7374,0.7386,0.7387,0.7407,0.7470,0.7486,0.7487, 0.7497,0.7500,0.7552,0.7559,0.7614,0.7673,0.7759,0.7784,0.7807,0.7877, 0.7878,0.7902,0.7937,0.8059,0.8082,0.8116,0.8187,0.8188,0.8247,0.8343, 0.8363,0.8369,0.8455,0.8472,0.8495,0.8516,0.8577,0.8579,0.8588,0.8742, 0.8778,0.8799,0.8808,0.8830,0.8854,0.8893,0.8943,0.8966,0.8976,0.8986, 0.9008,0.9015,0.9022,0.9078,0.9102,0.9120,0.9138,0.9176,0.9236,0.9251, 0.9266,0.9277,0.9288,0.9325,0.9329,0.9349,0.9430,0.9494,0.9499,0.9549, 0.9586,0.9587,0.9690,0.9725,0.9731,0.9743,0.9964,0.9985,0.9987, Overall p-value after applying KStest on 269 p-values = 0.916514 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.