RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-06-15_20:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.77 11.3263 0.160891 2 to 25 15.78 10.7990 0.133182 3 to 26 15.55 31.3842 0.982074 4 to 27 15.56 16.8035 0.532246 5 to 28 15.79 16.0744 0.481436 6 to 29 15.97 20.0993 0.730818 7 to 30 15.98 12.8804 0.255845 8 to 31 15.94 19.7579 0.713200 9 to 32 15.92 12.1079 0.206441 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.848797 Tough bday spacings test for dh-ranFile-2015-06-15_20:31: 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 31 59 101 113 78 50 37 11 4 2 (O-E)^2/E 2.6 0.9 2.8 0.1 2.4 0.0 0.1 1.8 1.0 1.0 1.0 Birthday Spacings: Sum(O-E)^2/E= 13.655, p= 0.811 RESULTS OF GCD FOR dh-ranFile-2015-06-15_20:31 Euclid's algorithm: p-value, steps to gcd: 0.395832 p-value, dist. of gcd's: 0.463836 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-06-15_20:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.348 0.800 0.105 0.978 0.909 0.711 0.033 0.769 Bits 8 to 15---> 0.564 0.663 0.710 0.431 0.928 0.304 0.255 0.583 Bits 16 to 23---> 0.508 0.450 0.639 0.594 0.808 0.584 0.460 0.481 Bits 24 to 31---> 0.286 0.166 0.498 0.877 0.304 0.820 0.457 0.233 KS test for the above 32 p values: 0.505 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-06-15_20:31, p-values for 5 runs: 0.6714, 0.9838, 0.8229, 0.3797, 0.8267 Rank test for binary matrices (31x31) for dh-ranFile-2015-06-15_20:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 209 211.4 0.028 0.028 r= 29 5139 5134.0 0.005 0.033 r= 30 23039 23103.0 0.178 0.210 r= 31 11613 11551.5 0.327 0.537 chi-square = 0.537 with df = 3; p-value = 0.089 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-06-15_20:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 208 211.4 0.055 0.055 r= 30 5080 5134.0 0.568 0.623 r= 31 23151 23103.0 0.100 0.723 r= 32 11561 11551.5 0.008 0.731 chi-square = 0.731 with df = 3; p-value = 0.134 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-06-15_20:31 b-rank test for bits 1 to 8, p=0.78889 b-rank test for bits 2 to 9, p=0.43193 b-rank test for bits 3 to 10, p=0.16204 b-rank test for bits 4 to 11, p=0.29974 b-rank test for bits 5 to 12, p=0.55356 b-rank test for bits 6 to 13, p=0.15985 b-rank test for bits 7 to 14, p=0.30043 b-rank test for bits 8 to 15, p=0.94519 b-rank test for bits 9 to 16, p=0.57611 b-rank test for bits 10 to 17, p=0.43516 b-rank test for bits 11 to 18, p=0.33351 b-rank test for bits 12 to 19, p=0.15716 b-rank test for bits 13 to 20, p=0.96136 b-rank test for bits 14 to 21, p=0.47678 b-rank test for bits 15 to 22, p=0.10235 b-rank test for bits 16 to 23, p=0.55951 b-rank test for bits 17 to 24, p=0.37398 b-rank test for bits 18 to 25, p=0.19336 b-rank test for bits 19 to 26, p=0.38912 b-rank test for bits 20 to 27, p=0.78591 b-rank test for bits 21 to 28, p=0.09119 b-rank test for bits 22 to 29, p=0.31385 b-rank test for bits 23 to 30, p=0.00244 b-rank test for bits 24 to 31, p=0.31395 b-rank test for bits 25 to 32, p=0.86080 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 = 0.232359 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-06-15_20:31 (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 141710 -0.47 0.320706 2 142150 0.56 0.713049 3 141936 0.06 0.524843 4 142380 1.10 0.864268 5 142113 0.48 0.682915 6 142385 1.11 0.866797 7 142501 1.38 0.916577 8 141852 -0.13 0.446722 9 142779 2.03 0.978920 10 141646 -0.62 0.269193 11 141452 -1.07 0.142641 12 142517 1.42 0.922166 13 141369 -1.26 0.103393 14 141913 0.01 0.503421 15 142284 0.88 0.809321 16 141657 -0.59 0.277744 17 141863 -0.11 0.456900 18 142084 0.41 0.658403 19 141819 -0.21 0.416424 20 142069 0.37 0.645448 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-06-15_20:31 Bits used No. missing words z-score p-value 23 to 32 141906 -0.0115 0.495419 22 to 31 141497 -1.4218 0.077538 21 to 30 141980 0.2437 0.596264 20 to 29 141572 -1.1632 0.122373 19 to 28 142149 0.8264 0.795725 18 to 27 141569 -1.1736 0.120287 17 to 26 141540 -1.2736 0.101411 16 to 25 142076 0.5747 0.717261 15 to 24 142114 0.7058 0.759831 14 to 23 142114 0.7058 0.759831 13 to 22 141922 0.0437 0.517424 12 to 21 141431 -1.6494 0.049531 11 to 20 141968 0.2023 0.580163 10 to 19 141891 -0.0632 0.474801 9 to 18 142336 1.4713 0.929392 8 to 17 141881 -0.0977 0.461089 7 to 16 141599 -1.0701 0.142286 6 to 15 141548 -1.2460 0.106389 5 to 14 142087 0.6127 0.729948 4 to 13 142041 0.4540 0.675098 3 to 12 142160 0.8644 0.806310 2 to 11 142159 0.8609 0.805362 1 to 10 141846 -0.2184 0.413567 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-06-15_20:31 Bits used No. missing words z-score p-value 28 to 32 142517 2.0599 0.980296 27 to 31 142182 0.9243 0.822336 26 to 30 141297 -2.0757 0.018961 25 to 29 141826 -0.2825 0.388790 24 to 28 141667 -0.8215 0.205693 23 to 27 141923 0.0463 0.518480 22 to 26 141522 -1.3130 0.094594 21 to 25 142093 0.6226 0.733230 20 to 24 142172 0.8904 0.813376 19 to 23 141396 -1.7401 0.040921 18 to 22 141962 0.1785 0.570852 17 to 21 141915 0.0192 0.507667 16 to 20 142057 0.5006 0.691665 15 to 19 141606 -1.0282 0.151919 14 to 18 142384 1.6091 0.946197 13 to 17 141755 -0.5232 0.300434 12 to 16 142123 0.7243 0.765561 11 to 15 141825 -0.2859 0.387491 10 to 14 142029 0.4057 0.657504 9 to 13 141131 -2.6384 0.004165 8 to 12 142092 0.6192 0.732114 7 to 11 141961 0.1752 0.569520 6 to 10 141910 0.0023 0.500906 5 to 9 141793 -0.3943 0.346665 4 to 8 142316 1.3785 0.915982 3 to 7 141722 -0.6350 0.262709 2 to 6 142155 0.8328 0.797516 1 to 5 142524 2.0836 0.981403 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-06-15_20:31 Bits used No. missing words z-score p-value 31 to 32 141999 0.2645 0.604308 30 to 31 142061 0.4474 0.672708 29 to 30 141455 -1.3402 0.090089 28 to 29 142274 1.0757 0.858974 27 to 28 141846 -0.1868 0.425903 26 to 27 141678 -0.6824 0.247496 25 to 26 142411 1.4799 0.930544 24 to 25 142131 0.6539 0.743410 23 to 24 142139 0.6775 0.750953 22 to 23 141754 -0.4582 0.323404 21 to 22 141440 -1.3845 0.083110 20 to 21 141844 -0.1927 0.423592 19 to 20 141678 -0.6824 0.247496 18 to 19 142016 0.3147 0.623490 17 to 18 142635 2.1406 0.983848 16 to 17 141986 0.2262 0.589464 15 to 16 141985 0.2232 0.588316 14 to 15 141507 -1.1868 0.117650 13 to 14 142301 1.1554 0.876030 12 to 13 141935 0.0757 0.530180 11 to 12 141990 0.2380 0.594046 10 to 11 141767 -0.4199 0.337297 9 to 10 142369 1.3560 0.912444 8 to 9 142108 0.5860 0.721078 7 to 8 142163 0.7483 0.772857 6 to 7 141272 -1.8800 0.030052 5 to 6 141567 -1.0098 0.156290 4 to 5 141420 -1.4435 0.074447 3 to 4 142137 0.6716 0.749079 2 to 3 141765 -0.4258 0.335144 1 to 2 142667 2.2350 0.987292 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-06-15_20:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2628.04 1.811 0.964909 Test results for specific bytes for dh-ranFile-2015-06-15_20:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2433.29 -0.943 0.172737 2 to 9 2460.79 -0.555 0.289601 3 to 10 2572.49 1.025 0.847363 4 to 11 2517.70 0.250 0.598829 5 to 12 2575.71 1.071 0.857848 6 to 13 2452.78 -0.668 0.252136 7 to 14 2483.52 -0.233 0.407831 8 to 15 2514.33 0.203 0.580304 9 to 16 2462.44 -0.531 0.297657 10 to 17 2446.06 -0.763 0.222788 11 to 18 2609.92 1.554 0.939961 12 to 19 2499.60 -0.006 0.497729 13 to 20 2515.32 0.217 0.585783 14 to 21 2666.74 2.358 0.990813 15 to 22 2444.55 -0.784 0.216456 16 to 23 2495.98 -0.057 0.477360 17 to 24 2476.89 -0.327 0.371905 18 to 25 2550.84 0.719 0.763905 19 to 26 2419.74 -1.135 0.128172 20 to 27 2494.66 -0.076 0.469882 21 to 28 2518.66 0.264 0.604081 22 to 29 2461.39 -0.546 0.292512 23 to 30 2380.12 -1.695 0.045005 24 to 31 2598.34 1.391 0.917838 25 to 32 2519.51 0.276 0.608676 CDPARK for dh-ranFile-2015-06-15_20:31: 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 3534 0.5023 0.692266 3537 0.6393 0.738676 3504 -0.8676 0.192812 3514 -0.4110 0.340551 3519 -0.1826 0.427537 3519 -0.1826 0.427537 3545 1.0046 0.842447 3530 0.3196 0.625377 3544 0.9589 0.831196 3530 0.3196 0.625377 Square side=100, avg. no. parked=3527.60 sample std.=12.66 p-value of the KSTEST for those 10 p-values: 0.430837 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-06-15_20:31 0.0503,0.5085,0.7926,0.9811,0.2777,0.0587,0.1352,0.4516,0.4760,0.0498, The KS test for those 10 p-values: 0.178200 The 3DSPHERES test for dh-ranFile-2015-06-15_20:31 sample no r^3 equiv. uni. 1 24.002 0.550706 2 30.194 0.634494 3 20.938 0.502381 4 7.655 0.225224 5 17.195 0.436258 6 36.826 0.706986 7 0.955 0.031348 8 1.261 0.041174 9 8.844 0.255324 10 12.775 0.346781 11 0.446 0.014742 12 16.236 0.417960 13 5.911 0.178841 14 58.070 0.855674 15 26.673 0.588980 16 6.191 0.186478 17 69.537 0.901518 18 8.312 0.242000 19 45.314 0.779193 20 19.732 0.481968 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.352720 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-06-15_20:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -1.2 0.1 -0.7 -2.2 0.1 0.0 2.7 0.4 -0.7 0.6 0.0 -0.1 0.4 -0.9 0.2 -0.2 -0.0 -0.9 0.3 -1.2 2.1 -1.7 -0.5 0.0 0.1 0.7 1.5 0.9 1.1 0.8 -0.6 -0.2 -0.4 2.0 0.6 -2.1 0.8 0.5 -0.1 0.1 -1.0 -0.1 Chi-square with 42 degrees of freedom:43.442979 z-score=0.157442, p-value=0.590290 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-06-15_20:31 Test no p-value 1 0.288644 2 0.013323 3 0.261226 4 0.726117 5 0.322163 6 0.633119 7 0.690693 8 0.346679 9 0.009456 10 0.984238 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.331199 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-06-15_20:31: (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 66667 0.00 66758 0.13 3 25000.00 24895 0.44 24921 0.25 4 6666.67 6770 1.60 6655 0.02 5 1388.89 1397 0.05 1397 0.05 6 238.10 234 0.07 233 0.11 7 34.72 29 0.94 27 1.72 8 4.96 7 0.84 8 1.86 p=0.31544 p=0.34109 Number of rngs required: 687382, p-value: 0.118 RESULTS OF CRAPS TEST for dh-ranFile-2015-06-15_20:31 No. of wins: Observed Expected 98759 98585.9 z-score= 0.774, pvalue=0.78065 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66447 66666.7 0.724 0.724 2 37613 37654.3 0.045 0.769 3 27146 26954.7 1.357 2.126 4 19389 19313.5 0.295 2.422 5 13891 13851.4 0.113 2.535 6 9932 9943.5 0.013 2.548 7 7169 7145.0 0.080 2.629 8 5209 5139.1 0.952 3.580 9 3662 3699.9 0.388 3.968 10 2708 2666.3 0.652 4.620 11 1886 1923.3 0.725 5.345 12 1361 1388.7 0.554 5.899 13 968 1003.7 1.271 7.169 14 718 726.1 0.091 7.261 15 543 525.8 0.560 7.821 16 351 381.2 2.385 10.206 17 270 276.5 0.155 10.361 18 182 200.8 1.765 12.126 19 143 146.0 0.061 12.187 20 115 106.2 0.727 12.914 21 297 287.1 0.340 13.254 Chisq= 13.25 for 20 degrees of freedom, p= 0.13379 SUMMARY of craptest p-value for no. of wins: 0.780650 p-value for throws/game: 0.133786 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-06-15_20:31 No. of wins: Observed Expected 98578 98585.9 z-score=-0.035, pvalue=0.48598 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66715 66666.7 0.035 0.035 2 37468 37654.3 0.922 0.957 3 26983 26954.7 0.030 0.987 4 19291 19313.5 0.026 1.013 5 14013 13851.4 1.885 2.898 6 9996 9943.5 0.277 3.174 7 7243 7145.0 1.343 4.518 8 5173 5139.1 0.224 4.742 9 3642 3699.9 0.905 5.647 10 2654 2666.3 0.057 5.704 11 1877 1923.3 1.116 6.819 12 1332 1388.7 2.318 9.138 13 1021 1003.7 0.298 9.435 14 671 726.1 4.187 13.623 15 535 525.8 0.160 13.782 16 379 381.2 0.012 13.794 17 258 276.5 1.243 15.037 18 213 200.8 0.737 15.775 19 146 146.0 0.000 15.775 20 115 106.2 0.727 16.501 21 275 287.1 0.511 17.013 Chisq= 17.01 for 20 degrees of freedom, p= 0.34784 SUMMARY of craptest p-value for no. of wins: 0.485981 p-value for throws/game: 0.347840 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0024,0.0042,0.0095,0.0133,0.0147,0.0190,0.0301,0.0313,0.0325,0.0409, 0.0412,0.0450,0.0495,0.0498,0.0503,0.0587,0.0744,0.0775,0.0831,0.0894, 0.0901,0.0912,0.0946,0.1014,0.1023,0.1034,0.1050,0.1064,0.1177,0.1178, 0.1203,0.1224,0.1282,0.1332,0.1338,0.1341,0.1352,0.1423,0.1426,0.1519, 0.1563,0.1572,0.1598,0.1609,0.1620,0.1664,0.1727,0.1782,0.1788,0.1865, 0.1928,0.1934,0.2057,0.2064,0.2165,0.2228,0.2252,0.2324,0.2329,0.2420, 0.2475,0.2475,0.2521,0.2553,0.2553,0.2558,0.2612,0.2627,0.2692,0.2777, 0.2777,0.2857,0.2886,0.2896,0.2925,0.2977,0.2997,0.3004,0.3004,0.3039, 0.3042,0.3138,0.3139,0.3154,0.3207,0.3222,0.3234,0.3312,0.3335,0.3351, 0.3373,0.3406,0.3411,0.3467,0.3467,0.3468,0.3475,0.3478,0.3527,0.3719, 0.3740,0.3797,0.3875,0.3888,0.3891,0.3958,0.4078,0.4136,0.4164,0.4180, 0.4236,0.4259,0.4275,0.4275,0.4305,0.4308,0.4319,0.4352,0.4363,0.4467, 0.4503,0.4516,0.4569,0.4571,0.4604,0.4611,0.4638,0.4699,0.4748,0.4760, 0.4768,0.4774,0.4814,0.4814,0.4820,0.4860,0.4954,0.4977,0.4979,0.5009, 0.5024,0.5034,0.5054,0.5077,0.5077,0.5085,0.5174,0.5185,0.5248,0.5302, 0.5322,0.5507,0.5536,0.5595,0.5635,0.5695,0.5709,0.5761,0.5802,0.5803, 0.5826,0.5842,0.5858,0.5883,0.5890,0.5895,0.5903,0.5939,0.5940,0.5963, 0.5988,0.6041,0.6043,0.6087,0.6235,0.6254,0.6254,0.6331,0.6345,0.6394, 0.6454,0.6575,0.6584,0.6632,0.6714,0.6727,0.6751,0.6829,0.6907,0.6917, 0.6923,0.7070,0.7099,0.7113,0.7130,0.7132,0.7173,0.7211,0.7261,0.7299, 0.7308,0.7321,0.7332,0.7387,0.7434,0.7491,0.7510,0.7598,0.7598,0.7639, 0.7656,0.7694,0.7729,0.7792,0.7806,0.7859,0.7889,0.7926,0.7957,0.7975, 0.8003,0.8054,0.8063,0.8077,0.8093,0.8107,0.8134,0.8199,0.8223,0.8229, 0.8267,0.8312,0.8424,0.8474,0.8488,0.8557,0.8578,0.8590,0.8608,0.8643, 0.8668,0.8760,0.8774,0.9015,0.9086,0.9124,0.9160,0.9166,0.9178,0.9222, 0.9281,0.9294,0.9305,0.9400,0.9452,0.9462,0.9614,0.9649,0.9785,0.9789, 0.9803,0.9811,0.9814,0.9821,0.9838,0.9838,0.9842,0.9873,0.9908, Overall p-value after applying KStest on 269 p-values = 0.838262 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.