RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-11-07_13:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.96 17.8952 0.604521 2 to 25 16.38 24.4708 0.892803 3 to 26 15.98 11.8703 0.192076 4 to 27 15.76 10.6087 0.123831 5 to 28 15.86 15.0119 0.405377 6 to 29 15.82 27.0935 0.943289 7 to 30 15.98 13.4997 0.297858 8 to 31 16.02 29.4633 0.969515 9 to 32 15.73 18.3841 0.634994 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.664144 Tough bday spacings test for dh-ranFile-2015-11-07_13:31: 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 6 26 74 97 113 66 58 32 16 8 4 (O-E)^2/E 1.1 3.1 0.0 0.0 2.4 1.9 0.7 0.2 0.1 0.3 0.0 Birthday Spacings: Sum(O-E)^2/E= 9.686, p= 0.532 RESULTS OF GCD FOR dh-ranFile-2015-11-07_13:31 Euclid's algorithm: p-value, steps to gcd: 0.472905 p-value, dist. of gcd's: 0.943015 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-11-07_13:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.111 0.600 0.628 0.077 0.274 0.989 0.363 0.478 Bits 8 to 15---> 0.726 0.581 0.892 0.697 0.761 0.207 0.631 0.178 Bits 16 to 23---> 0.633 0.489 0.395 0.943 0.812 0.148 0.598 0.424 Bits 24 to 31---> 0.881 0.932 0.773 0.890 0.502 0.567 0.711 0.879 KS test for the above 32 p values: 0.857 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-11-07_13:31, p-values for 5 runs: 0.6483, 0.4825, 0.8268, 0.3390, 0.7098 Rank test for binary matrices (31x31) for dh-ranFile-2015-11-07_13:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 232 211.4 2.004 2.004 r= 29 5138 5134.0 0.003 2.007 r= 30 23074 23103.0 0.037 2.043 r= 31 11556 11551.5 0.002 2.045 chi-square = 2.045 with df = 3; p-value = 0.437 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-11-07_13:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 201 211.4 0.513 0.513 r= 30 5108 5134.0 0.132 0.645 r= 31 22984 23103.0 0.613 1.259 r= 32 11707 11551.5 2.093 3.351 chi-square = 3.351 with df = 3; p-value = 0.659 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-11-07_13:31 b-rank test for bits 1 to 8, p=0.10723 b-rank test for bits 2 to 9, p=0.82450 b-rank test for bits 3 to 10, p=0.79835 b-rank test for bits 4 to 11, p=0.39258 b-rank test for bits 5 to 12, p=0.60613 b-rank test for bits 6 to 13, p=0.44488 b-rank test for bits 7 to 14, p=0.94594 b-rank test for bits 8 to 15, p=0.60128 b-rank test for bits 9 to 16, p=0.98870 b-rank test for bits 10 to 17, p=0.10270 b-rank test for bits 11 to 18, p=0.32658 b-rank test for bits 12 to 19, p=0.88356 b-rank test for bits 13 to 20, p=0.47289 b-rank test for bits 14 to 21, p=0.32711 b-rank test for bits 15 to 22, p=0.52656 b-rank test for bits 16 to 23, p=0.80685 b-rank test for bits 17 to 24, p=0.98830 b-rank test for bits 18 to 25, p=0.96765 b-rank test for bits 19 to 26, p=0.42995 b-rank test for bits 20 to 27, p=0.04458 b-rank test for bits 21 to 28, p=0.00832 b-rank test for bits 22 to 29, p=0.32761 b-rank test for bits 23 to 30, p=0.00344 b-rank test for bits 24 to 31, p=0.14457 b-rank test for bits 25 to 32, p=0.13706 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 = 0.368573 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-11-07_13:31 (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 142339 1.00 0.842287 2 141954 0.10 0.541562 3 142507 1.40 0.918707 4 141550 -0.84 0.200579 5 142152 0.57 0.714638 6 142158 0.58 0.719381 7 141886 -0.05 0.478265 8 142256 0.81 0.791023 9 141423 -1.14 0.127919 10 142706 1.86 0.968655 11 142063 0.36 0.640218 12 141493 -0.97 0.165343 13 142090 0.42 0.663534 14 141402 -1.19 0.117939 15 141595 -0.73 0.231348 16 141830 -0.19 0.426477 17 141244 -1.55 0.060031 18 141756 -0.36 0.360079 19 142130 0.52 0.696928 20 141294 -1.44 0.075261 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-11-07_13:31 Bits used No. missing words z-score p-value 23 to 32 141054 -2.9494 0.001592 22 to 31 141579 -1.1391 0.127337 21 to 30 141424 -1.6736 0.047109 20 to 29 141792 -0.4046 0.342891 19 to 28 141778 -0.4529 0.325324 18 to 27 141575 -1.1529 0.124484 17 to 26 141698 -0.7287 0.233085 16 to 25 141865 -0.1529 0.439254 15 to 24 142065 0.5368 0.704295 14 to 23 142041 0.4540 0.675098 13 to 22 142208 1.0299 0.848471 12 to 21 142163 0.8747 0.809138 11 to 20 142163 0.8747 0.809138 10 to 19 142015 0.3644 0.642213 9 to 18 141564 -1.1908 0.116867 8 to 17 141150 -2.6184 0.004417 7 to 16 142271 1.2471 0.893827 6 to 15 141508 -1.3839 0.083195 5 to 14 141763 -0.5046 0.306925 4 to 13 142292 1.3196 0.906508 3 to 12 141731 -0.6149 0.269300 2 to 11 141603 -1.0563 0.145413 1 to 10 142121 0.7299 0.767273 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-11-07_13:31 Bits used No. missing words z-score p-value 28 to 32 141466 -1.5028 0.066444 27 to 31 141827 -0.2791 0.390090 26 to 30 141983 0.2497 0.598602 25 to 29 141588 -1.0893 0.138021 24 to 28 141696 -0.7232 0.234793 23 to 27 141790 -0.4045 0.342919 22 to 26 141833 -0.2587 0.397916 21 to 25 141742 -0.5672 0.285282 20 to 24 142343 1.4701 0.929228 19 to 23 141704 -0.6960 0.243204 18 to 22 142163 0.8599 0.805077 17 to 21 141944 0.1175 0.546778 16 to 20 141614 -1.0011 0.158385 15 to 19 141615 -0.9977 0.159205 14 to 18 142169 0.8802 0.810635 13 to 17 141707 -0.6859 0.246399 12 to 16 142015 0.3582 0.639905 11 to 15 141612 -1.0079 0.156752 10 to 14 141681 -0.7740 0.219465 9 to 13 141936 0.0904 0.536018 8 to 12 142181 0.9209 0.821453 7 to 11 142137 0.7718 0.779873 6 to 10 142210 1.0192 0.845951 5 to 9 142023 0.3853 0.650001 4 to 8 142216 1.0396 0.850728 3 to 7 142196 0.9718 0.834416 2 to 6 141832 -0.2621 0.396609 1 to 5 141515 -1.3367 0.090658 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-11-07_13:31 Bits used No. missing words z-score p-value 31 to 32 140672 -3.6499 0.000131 30 to 31 142303 1.1613 0.877234 29 to 30 141640 -0.7945 0.213457 28 to 29 141327 -1.7178 0.042918 27 to 28 142735 2.4356 0.992567 26 to 27 142087 0.5241 0.699896 25 to 26 141991 0.2409 0.595189 24 to 25 141760 -0.4405 0.329787 23 to 24 142138 0.6745 0.750017 22 to 23 142041 0.3884 0.651143 21 to 22 141524 -1.1367 0.127839 20 to 21 142378 1.3825 0.916592 19 to 20 142392 1.4238 0.922749 18 to 19 142012 0.3029 0.619002 17 to 18 142346 1.2881 0.901147 16 to 17 142066 0.4622 0.678014 15 to 16 141913 0.0108 0.504319 14 to 15 140978 -2.7473 0.003005 13 to 14 141691 -0.6440 0.259774 12 to 13 142090 0.5329 0.702966 11 to 12 141791 -0.3491 0.363524 10 to 11 142026 0.3442 0.634637 9 to 10 141942 0.0964 0.538387 8 to 9 142328 1.2350 0.891588 7 to 8 140952 -2.8240 0.002372 6 to 7 142389 1.4150 0.921459 5 to 6 142292 1.1288 0.870513 4 to 5 142051 0.4179 0.661992 3 to 4 141896 -0.0393 0.484317 2 to 3 142052 0.4209 0.663070 1 to 2 141979 0.2055 0.581416 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-11-07_13:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2577.79 1.100 0.864363 Test results for specific bytes for dh-ranFile-2015-11-07_13:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2509.15 0.129 0.551474 2 to 9 2511.43 0.162 0.564214 3 to 10 2518.78 0.266 0.604698 4 to 11 2574.69 1.056 0.854574 5 to 12 2467.41 -0.461 0.322424 6 to 13 2477.05 -0.325 0.372771 7 to 14 2514.52 0.205 0.581373 8 to 15 2635.03 1.910 0.971912 9 to 16 2465.52 -0.488 0.312904 10 to 17 2562.18 0.879 0.810379 11 to 18 2524.20 0.342 0.633920 12 to 19 2369.18 -1.850 0.032151 13 to 20 2326.54 -2.453 0.007080 14 to 21 2567.42 0.953 0.829814 15 to 22 2455.30 -0.632 0.263621 16 to 23 2457.51 -0.601 0.273973 17 to 24 2628.55 1.818 0.965462 18 to 25 2586.53 1.224 0.889458 19 to 26 2516.92 0.239 0.594571 20 to 27 2501.85 0.026 0.510447 21 to 28 2611.29 1.574 0.942243 22 to 29 2416.05 -1.187 0.117561 23 to 30 2358.80 -1.997 0.022921 24 to 31 2414.36 -1.211 0.112912 25 to 32 2596.49 1.365 0.913804 CDPARK for dh-ranFile-2015-11-07_13:31: 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 3557 1.5525 0.939730 3499 -1.0959 0.136563 3541 0.8219 0.794438 3517 -0.2740 0.392053 3519 -0.1826 0.427537 3562 1.7808 0.962529 3490 -1.5068 0.065925 3523 0.0000 0.500000 3506 -0.7763 0.218799 3551 1.2785 0.899470 Square side=100, avg. no. parked=3526.50 sample std.=23.81 p-value of the KSTEST for those 10 p-values: 0.737490 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-11-07_13:31 0.6937,0.3604,0.5737,0.4064,0.5289,0.8585,0.2786,0.9223,0.9042,0.6469, The KS test for those 10 p-values: 0.300286 The 3DSPHERES test for dh-ranFile-2015-11-07_13:31 sample no r^3 equiv. uni. 1 0.245 0.008122 2 28.863 0.617911 3 51.907 0.822756 4 29.751 0.629054 5 7.074 0.210051 6 1.707 0.055311 7 54.789 0.838994 8 53.353 0.831095 9 81.640 0.934212 10 65.689 0.888042 11 0.951 0.031217 12 5.154 0.157841 13 125.318 0.984660 14 4.325 0.134251 15 70.363 0.904193 16 45.241 0.778652 17 17.674 0.445198 18 64.152 0.882158 19 3.911 0.122235 20 13.935 0.371554 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.216996 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-11-07_13:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 1.3 0.5 -1.8 0.8 -1.1 -2.7 -0.6 0.6 0.7 -0.6 -1.0 -0.8 -1.1 -1.2 -0.1 -0.2 0.2 1.6 0.7 -0.9 1.0 1.7 0.1 -1.3 -0.8 0.9 -1.2 2.5 1.4 -0.3 0.3 -0.3 -1.2 -0.2 -0.1 -0.8 1.0 0.8 3.0 0.4 -1.3 -1.0 -0.1 Chi-square with 42 degrees of freedom:56.847119 z-score=1.619953, p-value=0.937199 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-11-07_13:31 Test no p-value 1 0.099185 2 0.057907 3 0.002088 4 0.113643 5 0.093091 6 0.087217 7 0.867124 8 0.938121 9 0.014267 10 0.436959 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.001164 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-11-07_13:31: (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 66573 0.13 66739 0.08 3 25000.00 25038 0.06 24889 0.49 4 6666.67 6667 0.00 6658 0.01 5 1388.89 1436 1.60 1435 1.53 6 238.10 250 0.60 232 0.16 7 34.72 33 0.09 41 1.14 8 4.96 2 1.77 5 0.00 p=0.35499 p=0.24352 Number of rngs required: 689454, p-value: 0.889 RESULTS OF CRAPS TEST for dh-ranFile-2015-11-07_13:31 No. of wins: Observed Expected 98424 98585.9 z-score=-0.724, pvalue=0.23456 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66595 66666.7 0.077 0.077 2 37650 37654.3 0.000 0.078 3 27114 26954.7 0.941 1.019 4 19215 19313.5 0.502 1.521 5 13846 13851.4 0.002 1.523 6 10002 9943.5 0.344 1.866 7 7206 7145.0 0.520 2.387 8 5166 5139.1 0.141 2.528 9 3673 3699.9 0.195 2.723 10 2584 2666.3 2.540 5.263 11 1866 1923.3 1.709 6.972 12 1371 1388.7 0.227 7.198 13 1014 1003.7 0.105 7.304 14 737 726.1 0.162 7.466 15 521 525.8 0.044 7.511 16 378 381.2 0.026 7.537 17 315 276.5 5.349 12.886 18 190 200.8 0.584 13.470 19 156 146.0 0.687 14.157 20 113 106.2 0.433 14.590 21 288 287.1 0.003 14.593 Chisq= 14.59 for 20 degrees of freedom, p= 0.20080 SUMMARY of craptest p-value for no. of wins: 0.234556 p-value for throws/game: 0.200801 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-11-07_13:31 No. of wins: Observed Expected 98750 98585.9 z-score= 0.734, pvalue=0.76857 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66197 66666.7 3.309 3.309 2 37706 37654.3 0.071 3.380 3 27112 26954.7 0.918 4.297 4 19430 19313.5 0.703 5.000 5 13949 13851.4 0.687 5.688 6 9827 9943.5 1.366 7.054 7 7254 7145.0 1.662 8.716 8 5109 5139.1 0.176 8.892 9 3732 3699.9 0.279 9.171 10 2639 2666.3 0.279 9.450 11 1941 1923.3 0.162 9.613 12 1397 1388.7 0.049 9.662 13 1056 1003.7 2.724 12.386 14 710 726.1 0.359 12.744 15 511 525.8 0.419 13.163 16 410 381.2 2.184 15.347 17 273 276.5 0.045 15.392 18 214 200.8 0.864 16.255 19 172 146.0 4.636 20.892 20 98 106.2 0.635 21.527 21 263 287.1 2.025 23.552 Chisq= 23.55 for 20 degrees of freedom, p= 0.73751 SUMMARY of craptest p-value for no. of wins: 0.768567 p-value for throws/game: 0.737508 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0001,0.0012,0.0016,0.0021,0.0024,0.0030,0.0034,0.0044,0.0071,0.0081, 0.0083,0.0143,0.0229,0.0312,0.0322,0.0429,0.0446,0.0471,0.0553,0.0579, 0.0600,0.0659,0.0664,0.0753,0.0767,0.0832,0.0872,0.0907,0.0931,0.0992, 0.1027,0.1072,0.1106,0.1129,0.1136,0.1169,0.1176,0.1179,0.1222,0.1238, 0.1245,0.1273,0.1278,0.1279,0.1343,0.1366,0.1371,0.1380,0.1446,0.1454, 0.1478,0.1568,0.1578,0.1584,0.1592,0.1653,0.1777,0.1921,0.2006,0.2008, 0.2072,0.2101,0.2135,0.2170,0.2188,0.2195,0.2313,0.2331,0.2346,0.2348, 0.2432,0.2435,0.2464,0.2598,0.2636,0.2693,0.2736,0.2740,0.2786,0.2853, 0.2979,0.3003,0.3069,0.3129,0.3224,0.3253,0.3266,0.3271,0.3276,0.3298, 0.3390,0.3429,0.3429,0.3550,0.3601,0.3604,0.3632,0.3635,0.3686,0.3716, 0.3728,0.3901,0.3921,0.3926,0.3950,0.3966,0.3979,0.4054,0.4064,0.4241, 0.4265,0.4275,0.4300,0.4369,0.4370,0.4393,0.4449,0.4452,0.4729,0.4729, 0.4778,0.4783,0.4825,0.4843,0.4888,0.5000,0.5016,0.5043,0.5104,0.5266, 0.5289,0.5316,0.5360,0.5384,0.5416,0.5468,0.5515,0.5642,0.5669,0.5737, 0.5813,0.5814,0.5814,0.5946,0.5952,0.5979,0.5986,0.5998,0.6013,0.6045, 0.6047,0.6061,0.6179,0.6190,0.6277,0.6291,0.6306,0.6332,0.6339,0.6346, 0.6350,0.6399,0.6402,0.6422,0.6469,0.6483,0.6500,0.6511,0.6594,0.6620, 0.6631,0.6635,0.6641,0.6751,0.6780,0.6937,0.6966,0.6969,0.6999,0.7030, 0.7043,0.7098,0.7108,0.7146,0.7194,0.7261,0.7375,0.7375,0.7500,0.7606, 0.7673,0.7686,0.7730,0.7787,0.7799,0.7910,0.7944,0.7983,0.8051,0.8069, 0.8091,0.8091,0.8104,0.8106,0.8115,0.8215,0.8228,0.8245,0.8268,0.8298, 0.8311,0.8344,0.8390,0.8423,0.8460,0.8485,0.8507,0.8546,0.8569,0.8585, 0.8644,0.8671,0.8705,0.8772,0.8787,0.8808,0.8822,0.8836,0.8880,0.8891, 0.8895,0.8903,0.8916,0.8920,0.8928,0.8938,0.8995,0.9011,0.9042,0.9042, 0.9065,0.9138,0.9166,0.9187,0.9215,0.9223,0.9227,0.9292,0.9315,0.9342, 0.9372,0.9381,0.9397,0.9422,0.9430,0.9431,0.9433,0.9459,0.9625,0.9655, 0.9677,0.9687,0.9695,0.9719,0.9847,0.9883,0.9887,0.9887,0.9926, Overall p-value after applying KStest on 269 p-values = 0.079767 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.