RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-08_15:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 16.03 14.2486 0.350569 2 to 25 15.89 13.7075 0.312309 3 to 26 15.79 15.1849 0.417837 4 to 27 15.36 33.5410 0.990382 5 to 28 15.95 27.6016 0.950186 6 to 29 15.64 18.6768 0.652605 7 to 30 15.65 14.7645 0.387557 8 to 31 15.62 18.9731 0.669922 9 to 32 15.39 26.1287 0.927852 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.175420 Tough bday spacings test for dh-ranFile-2018-07-08_15:31: 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 12 34 66 97 89 71 68 31 18 6 8 (O-E)^2/E 0.9 0.2 0.7 0.0 0.8 0.7 4.9 0.1 0.7 0.1 3.8 Birthday Spacings: Sum(O-E)^2/E= 12.641, p= 0.756 RESULTS OF GCD FOR dh-ranFile-2018-07-08_15:31 Euclid's algorithm: p-value, steps to gcd: 0.733177 p-value, dist. of gcd's: 0.404830 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-08_15:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.380 0.238 0.491 0.023 0.372 0.449 0.368 0.231 Bits 8 to 15---> 0.643 0.917 0.815 0.919 0.169 0.561 0.900 0.347 Bits 16 to 23---> 0.629 0.613 0.007 0.624 0.494 0.169 0.352 0.122 Bits 24 to 31---> 0.854 0.342 0.059 0.412 0.784 0.258 0.512 0.568 KS test for the above 32 p values: 0.481 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-08_15:31, p-values for 5 runs: 0.6881, 0.8503, 0.4503, 0.6437, 0.0501 Rank test for binary matrices (31x31) for dh-ranFile-2018-07-08_15:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 218 211.4 0.205 0.205 r= 29 5062 5134.0 1.010 1.215 r= 30 23103 23103.0 0.000 1.215 r= 31 11617 11551.5 0.371 1.586 chi-square = 1.586 with df = 3; p-value = 0.337 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-07-08_15:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 224 211.4 0.749 0.749 r= 30 5069 5134.0 0.823 1.572 r= 31 23291 23103.0 1.529 3.101 r= 32 11416 11551.5 1.590 4.691 chi-square = 4.691 with df = 3; p-value = 0.804 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-07-08_15:31 b-rank test for bits 1 to 8, p=0.44405 b-rank test for bits 2 to 9, p=0.20326 b-rank test for bits 3 to 10, p=0.90670 b-rank test for bits 4 to 11, p=0.17670 b-rank test for bits 5 to 12, p=0.17202 b-rank test for bits 6 to 13, p=0.86443 b-rank test for bits 7 to 14, p=0.36492 b-rank test for bits 8 to 15, p=0.35898 b-rank test for bits 9 to 16, p=0.74685 b-rank test for bits 10 to 17, p=0.27253 b-rank test for bits 11 to 18, p=0.26083 b-rank test for bits 12 to 19, p=0.40376 b-rank test for bits 13 to 20, p=0.12973 b-rank test for bits 14 to 21, p=0.80419 b-rank test for bits 15 to 22, p=0.62050 b-rank test for bits 16 to 23, p=0.97712 b-rank test for bits 17 to 24, p=0.66312 b-rank test for bits 18 to 25, p=0.12396 b-rank test for bits 19 to 26, p=0.62100 b-rank test for bits 20 to 27, p=0.77373 b-rank test for bits 21 to 28, p=0.50095 b-rank test for bits 22 to 29, p=0.19756 b-rank test for bits 23 to 30, p=0.47734 b-rank test for bits 24 to 31, p=0.49589 b-rank test for bits 25 to 32, p=0.29214 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 = 0.670572 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-08_15:31 (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 141654 -0.60 0.275399 2 141746 -0.38 0.351375 3 141702 -0.48 0.314045 4 142506 1.39 0.918355 5 141571 -0.79 0.214621 6 142227 0.74 0.771023 7 141906 -0.01 0.496896 8 141596 -0.73 0.232060 9 141996 0.20 0.580237 10 142231 0.75 0.773844 11 141759 -0.35 0.362705 12 141922 0.03 0.511808 13 141559 -0.82 0.206528 14 141808 -0.24 0.406425 15 142254 0.81 0.789678 16 142197 0.67 0.749248 17 142688 1.82 0.965569 18 142841 2.18 0.985252 19 142326 0.97 0.834855 20 141776 -0.31 0.377703 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-07-08_15:31 Bits used No. missing words z-score p-value 23 to 32 141848 -0.2115 0.416255 22 to 31 142333 1.4609 0.927983 21 to 30 142293 1.3230 0.907082 20 to 29 141643 -0.9184 0.179210 19 to 28 142131 0.7644 0.777679 18 to 27 142048 0.4782 0.683736 17 to 26 141623 -0.9873 0.161737 16 to 25 141810 -0.3425 0.365981 15 to 24 141560 -1.2046 0.114182 14 to 23 142110 0.6920 0.755521 13 to 22 141986 0.2644 0.604256 12 to 21 141935 0.0885 0.535267 11 to 20 142443 1.8402 0.967134 10 to 19 141715 -0.6701 0.251396 9 to 18 141669 -0.8287 0.203630 8 to 17 142310 1.3816 0.916456 7 to 16 142194 0.9816 0.836857 6 to 15 142046 0.4713 0.681278 5 to 14 141301 -2.0977 0.017966 4 to 13 142078 0.5816 0.719589 3 to 12 141799 -0.3804 0.351806 2 to 11 142130 0.7609 0.776651 1 to 10 141558 -1.2115 0.112855 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-07-08_15:31 Bits used No. missing words z-score p-value 28 to 32 141681 -0.7740 0.219465 27 to 31 142190 0.9514 0.829305 26 to 30 141468 -1.4960 0.067322 25 to 29 141572 -1.1435 0.126417 24 to 28 141508 -1.3604 0.086845 23 to 27 142117 0.7040 0.759273 22 to 26 142151 0.8192 0.793670 21 to 25 141878 -0.1062 0.457711 20 to 24 141539 -1.2554 0.104675 19 to 23 141711 -0.6723 0.250695 18 to 22 141854 -0.1876 0.425611 17 to 21 141653 -0.8689 0.192447 16 to 20 141603 -1.0384 0.149540 15 to 19 142061 0.5141 0.696421 14 to 18 142032 0.4158 0.661233 13 to 17 141546 -1.2316 0.109044 12 to 16 141849 -0.2045 0.418978 11 to 15 141892 -0.0587 0.476577 10 to 14 141761 -0.5028 0.307548 9 to 13 141585 -1.0994 0.135792 8 to 12 142233 1.0972 0.863720 7 to 11 141906 -0.0113 0.495497 6 to 10 142295 1.3074 0.904454 5 to 9 141567 -1.1604 0.122935 4 to 8 141535 -1.2689 0.102236 3 to 7 141998 0.3006 0.618131 2 to 6 141618 -0.9876 0.161684 1 to 5 141745 -0.5571 0.288746 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-07-08_15:31 Bits used No. missing words z-score p-value 31 to 32 142199 0.8545 0.803582 30 to 31 141818 -0.2694 0.393807 29 to 30 141840 -0.2045 0.418976 28 to 29 141987 0.2291 0.590610 27 to 28 141801 -0.3196 0.374652 26 to 27 142498 1.7365 0.958761 25 to 26 141846 -0.1868 0.425903 24 to 25 141577 -0.9803 0.163463 23 to 24 141161 -2.2075 0.013641 22 to 23 141616 -0.8653 0.193443 21 to 22 142013 0.3058 0.620126 20 to 21 141942 0.0964 0.538387 19 to 20 142199 0.8545 0.803582 18 to 19 142191 0.8309 0.796981 17 to 18 141594 -0.9302 0.176140 16 to 17 141845 -0.1898 0.424747 15 to 16 142002 0.2734 0.607713 14 to 15 141723 -0.5496 0.291281 13 to 14 141699 -0.6204 0.267483 12 to 13 141978 0.2026 0.580263 11 to 12 141679 -0.6794 0.248430 10 to 11 141759 -0.4435 0.328720 9 to 10 141602 -0.9066 0.182315 8 to 9 141971 0.1819 0.572176 7 to 8 142134 0.6627 0.746253 6 to 7 142159 0.7365 0.769284 5 to 6 141302 -1.7915 0.036604 4 to 5 141868 -0.1219 0.451482 3 to 4 142146 0.6981 0.757456 2 to 3 142123 0.6303 0.735749 1 to 2 142441 1.5683 0.941600 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-08_15:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2545.69 0.646 0.740916 Test results for specific bytes for dh-ranFile-2018-07-08_15:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2570.56 0.998 0.840837 2 to 9 2466.65 -0.472 0.318582 3 to 10 2470.50 -0.417 0.338245 4 to 11 2407.52 -1.308 0.095470 5 to 12 2486.66 -0.189 0.425197 6 to 13 2553.73 0.760 0.776350 7 to 14 2504.53 0.064 0.525532 8 to 15 2504.54 0.064 0.525596 9 to 16 2530.31 0.429 0.665893 10 to 17 2425.60 -1.052 0.146370 11 to 18 2514.36 0.203 0.580446 12 to 19 2435.17 -0.917 0.179613 13 to 20 2442.28 -0.816 0.207151 14 to 21 2486.51 -0.191 0.424367 15 to 22 2479.95 -0.284 0.388384 16 to 23 2493.27 -0.095 0.462065 17 to 24 2526.04 0.368 0.643682 18 to 25 2589.53 1.266 0.897282 19 to 26 2541.00 0.580 0.718974 20 to 27 2502.23 0.032 0.512579 21 to 28 2398.70 -1.433 0.075989 22 to 29 2478.13 -0.309 0.378569 23 to 30 2461.07 -0.551 0.290979 24 to 31 2486.54 -0.190 0.424540 25 to 32 2546.63 0.660 0.745214 CDPARK for dh-ranFile-2018-07-08_15:31: 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 3562 1.7808 0.962529 3557 1.5525 0.939730 3501 -1.0046 0.157553 3496 -1.2329 0.108811 3505 -0.8219 0.205562 3518 -0.2283 0.409702 3506 -0.7763 0.218799 3511 -0.5479 0.291865 3513 -0.4566 0.323972 3535 0.5479 0.708135 Square side=100, avg. no. parked=3520.40 sample std.=22.02 p-value of the KSTEST for those 10 p-values: 0.414562 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-08_15:31 0.3530,0.2755,0.4048,0.2361,0.0250,0.3263,0.6107,0.2882,0.0343,0.1686, The KS test for those 10 p-values: 0.016424 The 3DSPHERES test for dh-ranFile-2018-07-08_15:31 sample no r^3 equiv. uni. 1 7.685 0.225992 2 15.217 0.397849 3 40.705 0.742524 4 61.245 0.870166 5 22.802 0.532372 6 4.543 0.140522 7 20.136 0.488913 8 44.317 0.771732 9 21.676 0.514481 10 1.558 0.050615 11 9.872 0.280394 12 12.874 0.348934 13 2.108 0.067860 14 9.695 0.276154 15 6.811 0.203095 16 11.555 0.319662 17 59.267 0.861319 18 9.436 0.269858 19 47.081 0.791823 20 2.648 0.084492 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.264359 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-08_15:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 2.0 0.9 1.3 -0.4 0.1 -1.0 -1.9 -0.4 0.5 0.6 0.2 0.5 -0.9 0.5 1.6 1.6 -0.1 -0.8 0.7 -1.1 -0.7 0.4 0.1 -0.6 0.3 -1.2 0.2 -0.7 -0.9 0.2 -0.6 -2.3 -0.0 -1.1 0.3 0.4 0.5 -0.4 1.7 -0.1 -0.6 -1.0 -0.1 Chi-square with 42 degrees of freedom:36.552279 z-score=-0.594395, p-value=0.291641 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-07-08_15:31 Test no p-value 1 0.199277 2 0.160138 3 0.241130 4 0.504145 5 0.007952 6 0.211301 7 0.630077 8 0.154136 9 0.254437 10 0.167806 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.006786 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-08_15:31: (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 66709 0.03 66823 0.37 3 25000.00 24988 0.01 24998 0.00 4 6666.67 6623 0.29 6526 2.97 5 1388.89 1409 0.29 1364 0.45 6 238.10 230 0.28 246 0.26 7 34.72 35 0.00 38 0.31 8 4.96 5 0.00 4 0.19 p=0.01049 p=0.39587 Number of rngs required: 689419, p-value: 0.881 RESULTS OF CRAPS TEST for dh-ranFile-2018-07-08_15:31 No. of wins: Observed Expected 98921 98585.9 z-score= 1.499, pvalue=0.93306 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66637 66666.7 0.013 0.013 2 37587 37654.3 0.120 0.134 3 26887 26954.7 0.170 0.304 4 19284 19313.5 0.045 0.349 5 13947 13851.4 0.660 1.008 6 9980 9943.5 0.134 1.142 7 7159 7145.0 0.027 1.169 8 5069 5139.1 0.955 2.125 9 3749 3699.9 0.653 2.777 10 2709 2666.3 0.684 3.461 11 1883 1923.3 0.846 4.307 12 1399 1388.7 0.076 4.383 13 1024 1003.7 0.410 4.793 14 745 726.1 0.490 5.282 15 511 525.8 0.419 5.701 16 399 381.2 0.836 6.537 17 261 276.5 0.873 7.410 18 213 200.8 0.737 8.147 19 156 146.0 0.687 8.835 20 110 106.2 0.135 8.970 21 291 287.1 0.053 9.022 Chisq= 9.02 for 20 degrees of freedom, p= 0.01735 SUMMARY of craptest p-value for no. of wins: 0.933056 p-value for throws/game: 0.017350 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-08_15:31 No. of wins: Observed Expected 98396 98585.9 z-score=-0.849, pvalue=0.19790 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66796 66666.7 0.251 0.251 2 37679 37654.3 0.016 0.267 3 26701 26954.7 2.388 2.656 4 19369 19313.5 0.160 2.815 5 13703 13851.4 1.590 4.406 6 10063 9943.5 1.435 5.841 7 7135 7145.0 0.014 5.855 8 5108 5139.1 0.188 6.043 9 3787 3699.9 2.052 8.095 10 2685 2666.3 0.131 8.226 11 1971 1923.3 1.182 9.407 12 1366 1388.7 0.372 9.780 13 1018 1003.7 0.203 9.983 14 715 726.1 0.171 10.154 15 520 525.8 0.065 10.219 16 383 381.2 0.009 10.228 17 293 276.5 0.980 11.208 18 188 200.8 0.820 12.027 19 143 146.0 0.061 12.088 20 112 106.2 0.315 12.403 21 265 287.1 1.703 14.107 Chisq= 14.11 for 20 degrees of freedom, p= 0.17495 SUMMARY of craptest p-value for no. of wins: 0.197897 p-value for throws/game: 0.174947 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0068,0.0075,0.0080,0.0105,0.0136,0.0164,0.0174,0.0180,0.0226,0.0250, 0.0343,0.0366,0.0501,0.0506,0.0589,0.0673,0.0679,0.0760,0.0845,0.0868, 0.0955,0.1022,0.1047,0.1088,0.1090,0.1129,0.1142,0.1221,0.1229,0.1240, 0.1264,0.1297,0.1358,0.1405,0.1464,0.1495,0.1541,0.1576,0.1601,0.1617, 0.1617,0.1635,0.1678,0.1686,0.1692,0.1694,0.1720,0.1749,0.1754,0.1761, 0.1767,0.1792,0.1796,0.1823,0.1924,0.1934,0.1976,0.1979,0.1993,0.2031, 0.2033,0.2036,0.2056,0.2065,0.2072,0.2113,0.2146,0.2188,0.2195,0.2260, 0.2310,0.2321,0.2361,0.2382,0.2411,0.2484,0.2507,0.2514,0.2544,0.2581, 0.2608,0.2644,0.2675,0.2699,0.2725,0.2754,0.2755,0.2762,0.2804,0.2882, 0.2887,0.2910,0.2913,0.2916,0.2919,0.2921,0.3075,0.3123,0.3140,0.3186, 0.3197,0.3240,0.3263,0.3287,0.3374,0.3382,0.3418,0.3474,0.3489,0.3506, 0.3514,0.3518,0.3523,0.3530,0.3590,0.3627,0.3649,0.3660,0.3681,0.3717, 0.3747,0.3777,0.3786,0.3804,0.3876,0.3884,0.3938,0.3959,0.3978,0.4038, 0.4048,0.4048,0.4064,0.4097,0.4118,0.4146,0.4163,0.4178,0.4190,0.4190, 0.4244,0.4245,0.4247,0.4252,0.4256,0.4259,0.4441,0.4487,0.4503,0.4515, 0.4577,0.4621,0.4766,0.4773,0.4813,0.4889,0.4905,0.4937,0.4955,0.4959, 0.4969,0.5009,0.5041,0.5118,0.5120,0.5126,0.5145,0.5255,0.5256,0.5324, 0.5353,0.5384,0.5607,0.5684,0.5722,0.5802,0.5803,0.5804,0.5906,0.6043, 0.6077,0.6107,0.6126,0.6181,0.6201,0.6205,0.6210,0.6239,0.6289,0.6301, 0.6431,0.6437,0.6437,0.6526,0.6612,0.6631,0.6659,0.6699,0.6706,0.6813, 0.6837,0.6881,0.6964,0.7081,0.7190,0.7196,0.7332,0.7357,0.7409,0.7425, 0.7452,0.7463,0.7468,0.7492,0.7555,0.7556,0.7575,0.7593,0.7693,0.7710, 0.7717,0.7737,0.7738,0.7764,0.7767,0.7777,0.7843,0.7897,0.7918,0.7937, 0.7970,0.8036,0.8036,0.8041,0.8042,0.8145,0.8293,0.8349,0.8369,0.8408, 0.8503,0.8545,0.8613,0.8637,0.8644,0.8702,0.8811,0.8973,0.8995,0.9045, 0.9067,0.9071,0.9165,0.9174,0.9184,0.9190,0.9279,0.9280,0.9331,0.9397, 0.9416,0.9502,0.9588,0.9625,0.9656,0.9671,0.9771,0.9853,0.9904, Overall p-value after applying KStest on 269 p-values = 0.006847 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.