RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-03-01_10:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.88 8.1232 0.036159 2 to 25 15.83 27.6403 0.950679 3 to 26 16.07 10.3765 0.112916 4 to 27 15.95 12.3990 0.224600 5 to 28 15.51 16.9334 0.541111 6 to 29 15.89 23.4350 0.864381 7 to 30 15.49 15.7197 0.456211 8 to 31 15.96 13.7916 0.318208 9 to 32 16.01 8.3198 0.040778 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.331331 Tough bday spacings test for dh-ranFile-2016-03-01_10:31: 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 10 39 66 103 88 76 71 26 15 4 2 (O-E)^2/E 0.1 0.2 0.7 0.3 1.0 0.1 6.9 0.5 0.0 1.0 1.0 Birthday Spacings: Sum(O-E)^2/E= 11.679, p= 0.693 RESULTS OF GCD FOR dh-ranFile-2016-03-01_10:31 Euclid's algorithm: p-value, steps to gcd: 0.950813 p-value, dist. of gcd's: 0.741676 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-03-01_10:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.508 0.093 0.855 0.499 0.682 0.086 0.174 0.844 Bits 8 to 15---> 0.643 0.460 0.552 0.588 0.904 0.870 0.084 0.052 Bits 16 to 23---> 0.138 0.138 0.260 0.599 0.431 0.219 0.754 0.321 Bits 24 to 31---> 0.214 0.864 0.355 0.663 0.879 0.480 0.687 0.164 KS test for the above 32 p values: 0.269 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-03-01_10:31, p-values for 5 runs: 0.9011, 0.5806, 0.0995, 0.1250, 0.7548 Rank test for binary matrices (31x31) for dh-ranFile-2016-03-01_10:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 228 211.4 1.301 1.301 r= 29 5166 5134.0 0.199 1.500 r= 30 23041 23103.0 0.167 1.667 r= 31 11565 11551.5 0.016 1.682 chi-square = 1.682 with df = 3; p-value = 0.359 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-03-01_10:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 183 211.4 3.820 3.820 r= 30 5165 5134.0 0.187 4.007 r= 31 23043 23103.0 0.156 4.163 r= 32 11609 11551.5 0.286 4.449 chi-square = 4.449 with df = 3; p-value = 0.783 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-03-01_10:31 b-rank test for bits 1 to 8, p=0.16943 b-rank test for bits 2 to 9, p=0.24079 b-rank test for bits 3 to 10, p=0.40106 b-rank test for bits 4 to 11, p=0.15916 b-rank test for bits 5 to 12, p=0.65227 b-rank test for bits 6 to 13, p=0.13290 b-rank test for bits 7 to 14, p=0.81839 b-rank test for bits 8 to 15, p=0.23881 b-rank test for bits 9 to 16, p=0.15947 b-rank test for bits 10 to 17, p=0.72418 b-rank test for bits 11 to 18, p=0.54348 b-rank test for bits 12 to 19, p=0.00394 b-rank test for bits 13 to 20, p=0.49181 b-rank test for bits 14 to 21, p=0.12673 b-rank test for bits 15 to 22, p=0.14505 b-rank test for bits 16 to 23, p=0.29344 b-rank test for bits 17 to 24, p=0.06170 b-rank test for bits 18 to 25, p=0.57652 b-rank test for bits 19 to 26, p=0.77386 b-rank test for bits 20 to 27, p=0.36510 b-rank test for bits 21 to 28, p=0.58229 b-rank test for bits 22 to 29, p=0.72544 b-rank test for bits 23 to 30, p=0.82004 b-rank test for bits 24 to 31, p=0.62439 b-rank test for bits 25 to 32, p=0.25799 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 = 0.124437 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-03-01_10:31 (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 142217 0.72 0.763885 2 142022 0.26 0.603820 3 141672 -0.55 0.289615 4 142617 1.65 0.950879 5 142230 0.75 0.773140 6 141289 -1.45 0.073617 7 141915 0.01 0.505285 8 141701 -0.49 0.313217 9 142023 0.27 0.604720 10 142320 0.96 0.831349 11 143010 2.57 0.994939 12 141759 -0.35 0.362705 13 141845 -0.15 0.440263 14 141828 -0.19 0.424645 15 142196 0.67 0.748504 16 141395 -1.20 0.114739 17 141212 -1.63 0.051627 18 141577 -0.78 0.218735 19 141751 -0.37 0.355717 20 141434 -1.11 0.133374 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-03-01_10:31 Bits used No. missing words z-score p-value 23 to 32 141792 -0.4046 0.342891 22 to 31 141900 -0.0322 0.487167 21 to 30 141670 -0.8253 0.204608 20 to 29 141673 -0.8149 0.207556 19 to 28 142117 0.7161 0.763036 18 to 27 142425 1.7782 0.962312 17 to 26 141721 -0.6494 0.258036 16 to 25 141836 -0.2529 0.400187 15 to 24 142156 0.8506 0.802500 14 to 23 141646 -0.9080 0.181930 13 to 22 142157 0.8540 0.803457 12 to 21 141519 -1.3460 0.089157 11 to 20 142754 2.9127 0.998208 10 to 19 142469 1.9299 0.973190 9 to 18 141813 -0.3322 0.369880 8 to 17 141834 -0.2598 0.397525 7 to 16 141642 -0.9218 0.178309 6 to 15 141826 -0.2873 0.386924 5 to 14 142393 1.6678 0.952325 4 to 13 141544 -1.2598 0.103878 3 to 12 142197 0.9920 0.839393 2 to 11 142512 2.0782 0.981153 1 to 10 142233 1.1161 0.867811 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-03-01_10:31 Bits used No. missing words z-score p-value 28 to 32 142016 0.3616 0.641172 27 to 31 141785 -0.4215 0.336711 26 to 30 141764 -0.4926 0.311132 25 to 29 142432 1.7718 0.961783 24 to 28 142239 1.1175 0.868115 23 to 27 141595 -1.0655 0.143319 22 to 26 142412 1.7040 0.955806 21 to 25 142652 2.5175 0.994091 20 to 24 141888 -0.0723 0.471180 19 to 23 141528 -1.2926 0.098067 18 to 22 141953 0.1480 0.558842 17 to 21 141731 -0.6045 0.272753 16 to 20 141502 -1.3808 0.083673 15 to 19 142141 0.7853 0.783868 14 to 18 141790 -0.4045 0.342919 13 to 17 141827 -0.2791 0.390090 12 to 16 141468 -1.4960 0.067322 11 to 15 142133 0.7582 0.775835 10 to 14 141641 -0.9096 0.181519 9 to 13 142131 0.7514 0.773801 8 to 12 141826 -0.2825 0.388790 7 to 11 141433 -1.6147 0.053190 6 to 10 142039 0.4396 0.669872 5 to 9 142126 0.7345 0.768670 4 to 8 141400 -1.7265 0.042125 3 to 7 141966 0.1921 0.576169 2 to 6 141720 -0.6418 0.260503 1 to 5 141883 -0.0893 0.464440 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-03-01_10:31 Bits used No. missing words z-score p-value 31 to 32 141646 -0.7768 0.218643 30 to 31 141678 -0.6824 0.247496 29 to 30 141598 -0.9184 0.179211 28 to 29 142153 0.7188 0.763865 27 to 28 141983 0.2173 0.586019 26 to 27 141956 0.1377 0.554749 25 to 26 141618 -0.8594 0.195065 24 to 25 142340 1.2704 0.898031 23 to 24 142038 0.3796 0.647863 22 to 23 142083 0.5123 0.695780 21 to 22 141605 -0.8977 0.184665 20 to 21 141945 0.1052 0.541900 19 to 20 141953 0.1288 0.551250 18 to 19 142202 0.8633 0.806023 17 to 18 141781 -0.3786 0.352509 16 to 17 141661 -0.7325 0.231921 15 to 16 142259 1.0315 0.848841 14 to 15 141909 -0.0010 0.499612 13 to 14 142306 1.1701 0.879023 12 to 13 142109 0.5890 0.722068 11 to 12 142158 0.7335 0.768385 10 to 11 141253 -1.9361 0.026429 9 to 10 141852 -0.1691 0.432853 8 to 9 142121 0.6244 0.733816 7 to 8 142157 0.7306 0.767485 6 to 7 141911 0.0049 0.501965 5 to 6 141861 -0.1426 0.443316 4 to 5 141979 0.2055 0.581416 3 to 4 141418 -1.4494 0.073620 2 to 3 141880 -0.0865 0.465527 1 to 2 142106 0.5801 0.719092 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-03-01_10:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2598.97 1.400 0.919199 Test results for specific bytes for dh-ranFile-2016-03-01_10:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2347.30 -2.159 0.015407 2 to 9 2568.57 0.970 0.833923 3 to 10 2599.43 1.406 0.920163 4 to 11 2554.64 0.773 0.780162 5 to 12 2469.48 -0.432 0.333003 6 to 13 2546.41 0.656 0.744218 7 to 14 2483.19 -0.238 0.406072 8 to 15 2432.07 -0.961 0.168365 9 to 16 2564.10 0.907 0.817671 10 to 17 2534.23 0.484 0.685814 11 to 18 2569.27 0.980 0.836355 12 to 19 2486.67 -0.189 0.425214 13 to 20 2568.24 0.965 0.832738 14 to 21 2534.66 0.490 0.687987 15 to 22 2409.68 -1.277 0.100750 16 to 23 2522.04 0.312 0.622339 17 to 24 2545.76 0.647 0.741251 18 to 25 2532.82 0.464 0.678728 19 to 26 2502.52 0.036 0.514200 20 to 27 2510.28 0.145 0.557769 21 to 28 2472.08 -0.395 0.346492 22 to 29 2557.69 0.816 0.792694 23 to 30 2566.45 0.940 0.826334 24 to 31 2521.27 0.301 0.618233 25 to 32 2562.82 0.888 0.812845 CDPARK for dh-ranFile-2016-03-01_10:31: 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 3525 0.0913 0.536383 3566 1.9635 0.975204 3508 -0.6849 0.246694 3534 0.5023 0.692266 3557 1.5525 0.939730 3561 1.7352 0.958644 3521 -0.0913 0.463617 3538 0.6849 0.753306 3527 0.1826 0.572463 3535 0.5479 0.708135 Square side=100, avg. no. parked=3537.20 sample std.=17.81 p-value of the KSTEST for those 10 p-values: 0.060690 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-03-01_10:31 0.8611,0.3160,0.0454,0.8764,0.1019,0.1581,0.3929,0.5164,0.7789,0.1063, The KS test for those 10 p-values: 0.477914 The 3DSPHERES test for dh-ranFile-2016-03-01_10:31 sample no r^3 equiv. uni. 1 11.886 0.327132 2 47.963 0.797851 3 78.045 0.925837 4 8.597 0.249170 5 43.018 0.761631 6 45.475 0.780377 7 20.760 0.499434 8 46.628 0.788655 9 26.180 0.582160 10 66.839 0.892253 11 19.385 0.475958 12 65.474 0.887237 13 0.581 0.019167 14 10.229 0.288922 15 46.717 0.789281 16 19.982 0.486275 17 34.488 0.683233 18 81.325 0.933518 19 27.168 0.595695 20 14.217 0.377437 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.135847 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-03-01_10:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 2.0 -0.7 1.1 2.1 0.4 0.3 0.2 -1.5 0.8 0.2 1.6 -0.7 0.9 -0.3 0.2 -0.3 1.2 -1.7 -1.8 0.7 -0.4 0.3 0.0 0.4 0.2 -0.8 0.3 0.1 1.5 -0.3 0.1 -0.1 -0.2 -0.3 -0.8 1.1 0.5 0.5 -0.8 -0.1 0.1 -1.0 1.8 Chi-square with 42 degrees of freedom:36.384898 z-score=-0.612658, p-value=0.284798 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-03-01_10:31 Test no p-value 1 0.042043 2 0.619258 3 0.462324 4 0.021402 5 0.520768 6 0.618846 7 0.059720 8 0.307962 9 0.076181 10 0.435427 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.041575 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-03-01_10:31: (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 66854 0.53 66759 0.13 3 25000.00 24710 3.36 25006 0.00 4 6666.67 6827 3.86 6600 0.67 5 1388.89 1338 1.86 1372 0.21 6 238.10 234 0.07 234 0.07 7 34.72 32 0.21 21 5.42 8 4.96 4 0.19 7 0.84 p=0.87869 p=0.70881 Number of rngs required: 687679, p-value: 0.201 RESULTS OF CRAPS TEST for dh-ranFile-2016-03-01_10:31 No. of wins: Observed Expected 98102 98585.9 z-score=-2.164, pvalue=0.01523 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66809 66666.7 0.304 0.304 2 37556 37654.3 0.257 0.561 3 26960 26954.7 0.001 0.562 4 19240 19313.5 0.279 0.841 5 13732 13851.4 1.030 1.871 6 9903 9943.5 0.165 2.036 7 7266 7145.0 2.048 4.084 8 5173 5139.1 0.224 4.308 9 3612 3699.9 2.087 6.395 10 2673 2666.3 0.017 6.412 11 1951 1923.3 0.398 6.810 12 1396 1388.7 0.038 6.848 13 1032 1003.7 0.797 7.645 14 732 726.1 0.047 7.692 15 560 525.8 2.220 9.912 16 381 381.2 0.000 9.912 17 276 276.5 0.001 9.913 18 185 200.8 1.248 11.161 19 145 146.0 0.007 11.167 20 112 106.2 0.315 11.482 21 306 287.1 1.242 12.725 Chisq= 12.72 for 20 degrees of freedom, p= 0.11112 SUMMARY of craptest p-value for no. of wins: 0.015228 p-value for throws/game: 0.111115 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-03-01_10:31 No. of wins: Observed Expected 98367 98585.9 z-score=-0.979, pvalue=0.16382 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66606 66666.7 0.055 0.055 2 37554 37654.3 0.267 0.322 3 26954 26954.7 0.000 0.323 4 19462 19313.5 1.142 1.465 5 13816 13851.4 0.091 1.555 6 9997 9943.5 0.287 1.843 7 7088 7145.0 0.455 2.298 8 5170 5139.1 0.186 2.484 9 3763 3699.9 1.077 3.561 10 2587 2666.3 2.358 5.920 11 1903 1923.3 0.215 6.135 12 1378 1388.7 0.083 6.218 13 1028 1003.7 0.588 6.805 14 742 726.1 0.346 7.152 15 559 525.8 2.092 9.243 16 372 381.2 0.220 9.463 17 267 276.5 0.329 9.792 18 211 200.8 0.515 10.307 19 151 146.0 0.172 10.479 20 115 106.2 0.727 11.206 21 277 287.1 0.356 11.562 Chisq= 11.56 for 20 degrees of freedom, p= 0.06968 SUMMARY of craptest p-value for no. of wins: 0.163824 p-value for throws/game: 0.069682 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0039,0.0152,0.0154,0.0192,0.0214,0.0264,0.0362,0.0408,0.0416,0.0420, 0.0421,0.0454,0.0516,0.0519,0.0532,0.0597,0.0607,0.0617,0.0673,0.0697, 0.0736,0.0736,0.0762,0.0837,0.0840,0.0857,0.0892,0.0932,0.0981,0.0995, 0.1008,0.1019,0.1039,0.1063,0.1111,0.1129,0.1147,0.1244,0.1250,0.1267, 0.1329,0.1334,0.1358,0.1382,0.1384,0.1433,0.1451,0.1581,0.1592,0.1595, 0.1638,0.1639,0.1684,0.1694,0.1738,0.1783,0.1792,0.1815,0.1819,0.1847, 0.1951,0.2013,0.2046,0.2076,0.2144,0.2186,0.2187,0.2188,0.2246,0.2319, 0.2388,0.2408,0.2467,0.2475,0.2492,0.2580,0.2580,0.2599,0.2605,0.2692, 0.2728,0.2848,0.2889,0.2896,0.2934,0.3080,0.3111,0.3132,0.3160,0.3182, 0.3206,0.3271,0.3313,0.3330,0.3367,0.3429,0.3429,0.3465,0.3525,0.3545, 0.3557,0.3591,0.3627,0.3651,0.3699,0.3774,0.3869,0.3888,0.3901,0.3929, 0.3975,0.4002,0.4011,0.4061,0.4246,0.4252,0.4306,0.4329,0.4354,0.4403, 0.4433,0.4562,0.4597,0.4623,0.4636,0.4644,0.4655,0.4712,0.4760,0.4779, 0.4795,0.4863,0.4872,0.4918,0.4994,0.4994,0.4996,0.5020,0.5053,0.5077, 0.5142,0.5164,0.5208,0.5364,0.5411,0.5419,0.5435,0.5513,0.5517,0.5547, 0.5578,0.5588,0.5725,0.5762,0.5765,0.5806,0.5814,0.5822,0.5823,0.5860, 0.5881,0.5957,0.5990,0.6038,0.6047,0.6182,0.6188,0.6193,0.6223,0.6244, 0.6412,0.6432,0.6479,0.6523,0.6627,0.6699,0.6787,0.6822,0.6832,0.6858, 0.6870,0.6880,0.6923,0.6929,0.6958,0.7081,0.7088,0.7191,0.7221,0.7242, 0.7254,0.7338,0.7413,0.7417,0.7442,0.7485,0.7533,0.7537,0.7548,0.7616, 0.7630,0.7639,0.7639,0.7675,0.7684,0.7687,0.7731,0.7738,0.7739,0.7758, 0.7789,0.7802,0.7804,0.7831,0.7839,0.7887,0.7893,0.7927,0.7979,0.8025, 0.8035,0.8060,0.8128,0.8177,0.8184,0.8200,0.8263,0.8313,0.8327,0.8339, 0.8364,0.8394,0.8437,0.8488,0.8552,0.8611,0.8641,0.8644,0.8678,0.8681, 0.8695,0.8764,0.8787,0.8787,0.8790,0.8872,0.8923,0.8980,0.9011,0.9042, 0.9192,0.9202,0.9258,0.9335,0.9397,0.9507,0.9508,0.9509,0.9523,0.9558, 0.9586,0.9618,0.9623,0.9732,0.9752,0.9812,0.9941,0.9949,0.9982, Overall p-value after applying KStest on 269 p-values = 0.739086 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.