RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-09-01_16:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.74 12.8719 0.255282 2 to 25 15.99 15.3082 0.426707 3 to 26 15.81 13.4042 0.291265 4 to 27 16.00 7.6855 0.027183 5 to 28 16.06 12.6487 0.240634 6 to 29 16.04 11.2941 0.159127 7 to 30 15.67 34.8231 0.993438 8 to 31 15.52 15.9251 0.470850 9 to 32 15.83 20.0190 0.726740 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.360494 Tough bday spacings test for dh-ranFile-2015-09-01_16:31: 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 9 34 70 106 97 73 64 24 12 9 2 (O-E)^2/E 0.0 0.2 0.1 0.7 0.0 0.3 2.7 1.1 0.6 0.9 1.0 Birthday Spacings: Sum(O-E)^2/E= 7.695, p= 0.341 RESULTS OF GCD FOR dh-ranFile-2015-09-01_16:31 Euclid's algorithm: p-value, steps to gcd: 0.672584 p-value, dist. of gcd's: 0.414112 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-09-01_16:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.462 0.293 0.330 0.629 0.321 0.601 0.938 0.313 Bits 8 to 15---> 0.169 0.942 0.155 0.809 0.208 0.118 0.030 0.767 Bits 16 to 23---> 0.560 0.458 0.701 0.613 0.460 0.785 0.762 0.022 Bits 24 to 31---> 0.453 0.413 0.504 0.857 0.257 0.026 0.522 0.542 KS test for the above 32 p values: 0.290 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-09-01_16:31, p-values for 5 runs: 0.9901, 0.0951, 0.1631, 0.6671, 0.8488 Rank test for binary matrices (31x31) for dh-ranFile-2015-09-01_16:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 210 211.4 0.010 0.010 r= 29 5070 5134.0 0.798 0.808 r= 30 23064 23103.0 0.066 0.874 r= 31 11656 11551.5 0.945 1.819 chi-square = 1.819 with df = 3; p-value = 0.389 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-09-01_16:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 236 211.4 2.858 2.858 r= 30 5144 5134.0 0.019 2.878 r= 31 23086 23103.0 0.013 2.890 r= 32 11534 11551.5 0.027 2.917 chi-square = 2.917 with df = 3; p-value = 0.595 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-09-01_16:31 b-rank test for bits 1 to 8, p=0.02114 b-rank test for bits 2 to 9, p=0.12792 b-rank test for bits 3 to 10, p=0.06034 b-rank test for bits 4 to 11, p=0.64179 b-rank test for bits 5 to 12, p=0.85592 b-rank test for bits 6 to 13, p=0.45557 b-rank test for bits 7 to 14, p=0.91831 b-rank test for bits 8 to 15, p=0.93151 b-rank test for bits 9 to 16, p=0.04831 b-rank test for bits 10 to 17, p=0.27655 b-rank test for bits 11 to 18, p=0.19930 b-rank test for bits 12 to 19, p=0.44152 b-rank test for bits 13 to 20, p=0.78329 b-rank test for bits 14 to 21, p=0.97334 b-rank test for bits 15 to 22, p=0.76665 b-rank test for bits 16 to 23, p=0.91588 b-rank test for bits 17 to 24, p=0.32318 b-rank test for bits 18 to 25, p=0.74822 b-rank test for bits 19 to 26, p=0.94227 b-rank test for bits 20 to 27, p=0.07393 b-rank test for bits 21 to 28, p=0.04463 b-rank test for bits 22 to 29, p=0.68885 b-rank test for bits 23 to 30, p=0.49276 b-rank test for bits 24 to 31, p=0.89921 b-rank test for bits 25 to 32, p=0.60378 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 = 0.317258 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-09-01_16:31 (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 141890 -0.05 0.481989 2 141310 -1.40 0.080711 3 141736 -0.40 0.342747 4 141776 -0.31 0.377703 5 142147 0.56 0.710657 6 141692 -0.51 0.305804 7 141867 -0.10 0.460608 8 141972 0.15 0.558207 9 142013 0.24 0.595695 10 142774 2.02 0.978322 11 141687 -0.52 0.301719 12 142441 1.24 0.892922 13 142470 1.31 0.904898 14 141663 -0.58 0.282464 15 141512 -0.93 0.176615 16 142098 0.44 0.670328 17 141994 0.20 0.578410 18 142170 0.61 0.728752 19 141985 0.18 0.570167 20 142014 0.24 0.596600 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-09-01_16:31 Bits used No. missing words z-score p-value 23 to 32 141979 0.2402 0.594928 22 to 31 141496 -1.4253 0.077039 21 to 30 141897 -0.0425 0.483043 20 to 29 141595 -1.0839 0.139205 19 to 28 142006 0.3333 0.630563 18 to 27 141950 0.1402 0.555765 17 to 26 142260 1.2092 0.886708 16 to 25 141697 -0.7322 0.232032 15 to 24 141852 -0.1977 0.421644 14 to 23 142116 0.7127 0.761970 13 to 22 141666 -0.8391 0.200715 12 to 21 141909 -0.0011 0.499546 11 to 20 141703 -0.7115 0.238393 10 to 19 141723 -0.6425 0.260269 9 to 18 142157 0.8540 0.803457 8 to 17 141969 0.2058 0.581510 7 to 16 142105 0.6747 0.750075 6 to 15 142084 0.6023 0.726516 5 to 14 141694 -0.7425 0.228887 4 to 13 141237 -2.3184 0.010214 3 to 12 142015 0.3644 0.642213 2 to 11 142799 3.0678 0.998922 1 to 10 142543 2.1851 0.985558 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-09-01_16:31 Bits used No. missing words z-score p-value 28 to 32 142334 1.4396 0.925004 27 to 31 142210 1.0192 0.845951 26 to 30 142234 1.1006 0.864459 25 to 29 141666 -0.8248 0.204729 24 to 28 141342 -1.9232 0.027230 23 to 27 141609 -1.0181 0.154323 22 to 26 141654 -0.8655 0.193375 21 to 25 142145 0.7989 0.787820 20 to 24 141726 -0.6215 0.267149 19 to 23 141586 -1.0960 0.136532 18 to 22 141974 0.2192 0.586761 17 to 21 141438 -1.5977 0.055052 16 to 20 142125 0.7311 0.767636 15 to 19 142079 0.5752 0.717406 14 to 18 141598 -1.0554 0.145631 13 to 17 141421 -1.6554 0.048926 12 to 16 142000 0.3074 0.620714 11 to 15 141440 -1.5909 0.055811 10 to 14 142039 0.4396 0.669872 9 to 13 141767 -0.4825 0.314734 8 to 12 141532 -1.2791 0.100434 7 to 11 142122 0.7209 0.764519 6 to 10 141716 -0.6554 0.256119 5 to 9 141206 -2.3842 0.008559 4 to 8 141546 -1.2316 0.109044 3 to 7 142046 0.4633 0.678421 2 to 6 142172 0.8904 0.813376 1 to 5 141669 -0.8147 0.207628 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-09-01_16:31 Bits used No. missing words z-score p-value 31 to 32 141363 -1.6116 0.053525 30 to 31 141337 -1.6883 0.045678 29 to 30 141619 -0.8564 0.195880 28 to 29 142356 1.3176 0.906183 27 to 28 142025 0.3412 0.633527 26 to 27 141448 -1.3609 0.086780 25 to 26 142059 0.4415 0.670576 24 to 25 142325 1.2262 0.889932 23 to 24 142301 1.1554 0.876030 22 to 23 141984 0.2203 0.587168 21 to 22 141577 -0.9803 0.163463 20 to 21 141739 -0.5024 0.307676 19 to 20 142499 1.7394 0.959021 18 to 19 142311 1.1849 0.881965 17 to 18 141660 -0.7355 0.231022 16 to 17 141802 -0.3166 0.375771 15 to 16 141972 0.1849 0.573333 14 to 15 141798 -0.3284 0.371302 13 to 14 141978 0.2026 0.580263 12 to 13 141565 -1.0157 0.154881 11 to 12 141931 0.0639 0.525484 10 to 11 141820 -0.2635 0.396079 9 to 10 141540 -1.0895 0.137974 8 to 9 141918 0.0256 0.510202 7 to 8 141597 -0.9213 0.178440 6 to 7 142022 0.3324 0.630191 5 to 6 142180 0.7984 0.787691 4 to 5 141339 -1.6824 0.046247 3 to 4 141829 -0.2370 0.406343 2 to 3 141786 -0.3638 0.358002 1 to 2 141753 -0.4612 0.322345 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-09-01_16:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2667.39 2.367 0.991039 Test results for specific bytes for dh-ranFile-2015-09-01_16:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2347.86 -2.152 0.015715 2 to 9 2523.17 0.328 0.628396 3 to 10 2625.80 1.779 0.962388 4 to 11 2499.63 -0.005 0.497933 5 to 12 2499.16 -0.012 0.495280 6 to 13 2466.34 -0.476 0.317027 7 to 14 2418.47 -1.153 0.124463 8 to 15 2402.62 -1.377 0.084234 9 to 16 2568.42 0.968 0.833378 10 to 17 2554.68 0.773 0.780312 11 to 18 2433.91 -0.935 0.174969 12 to 19 2495.56 -0.063 0.474948 13 to 20 2500.53 0.007 0.502984 14 to 21 2463.94 -0.510 0.305021 15 to 22 2345.62 -2.183 0.014506 16 to 23 2411.68 -1.249 0.105819 17 to 24 2401.34 -1.395 0.081467 18 to 25 2488.63 -0.161 0.436105 19 to 26 2415.55 -1.194 0.116184 20 to 27 2472.08 -0.395 0.346479 21 to 28 2513.19 0.187 0.574010 22 to 29 2492.90 -0.100 0.460020 23 to 30 2610.36 1.561 0.940704 24 to 31 2565.54 0.927 0.823021 25 to 32 2571.41 1.010 0.843715 CDPARK for dh-ranFile-2015-09-01_16:31: 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 3502 -0.9589 0.168804 3526 0.1370 0.554479 3499 -1.0959 0.136563 3459 -2.9224 0.001737 3537 0.6393 0.738676 3511 -0.5479 0.291865 3520 -0.1370 0.445521 3498 -1.1416 0.126820 3527 0.1826 0.572463 3523 0.0000 0.500000 Square side=100, avg. no. parked=3510.20 sample std.=21.15 p-value of the KSTEST for those 10 p-values: 0.137453 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-09-01_16:31 0.6231,0.8565,0.0160,0.0246,0.7779,0.4219,0.9481,0.5654,0.2611,0.5892, The KS test for those 10 p-values: 0.723929 The 3DSPHERES test for dh-ranFile-2015-09-01_16:31 sample no r^3 equiv. uni. 1 33.554 0.673223 2 31.033 0.644570 3 14.174 0.376531 4 8.555 0.248116 5 121.955 0.982840 6 12.234 0.334887 7 3.259 0.102953 8 6.685 0.199757 9 29.200 0.622181 10 76.323 0.921457 11 9.392 0.268802 12 8.857 0.255634 13 0.001 0.000021 14 11.358 0.315185 15 9.082 0.261196 16 120.750 0.982137 17 46.733 0.789394 18 9.415 0.269371 19 9.447 0.270130 20 49.551 0.808277 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.270897 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-09-01_16:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -1.2 -1.6 -0.4 1.5 -0.7 -0.0 -1.1 -1.5 0.3 1.1 -0.3 0.8 -0.4 0.4 0.5 1.2 -0.4 -1.0 0.5 0.2 -0.0 -0.4 0.3 -2.8 0.5 -0.0 0.1 0.0 0.8 -1.3 1.0 1.6 0.8 -0.5 -0.3 1.2 -0.7 0.1 0.4 0.9 0.0 0.8 Chi-square with 42 degrees of freedom:34.906928 z-score=-0.773918, p-value=0.227092 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-09-01_16:31 Test no p-value 1 0.124605 2 0.134454 3 0.133935 4 0.866756 5 0.034649 6 0.263067 7 0.361373 8 0.506470 9 0.415652 10 0.364843 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.072963 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-09-01_16:31: (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 66713 0.03 66635 0.02 3 25000.00 24873 0.65 25061 0.15 4 6666.67 6741 0.83 6623 0.29 5 1388.89 1379 0.07 1388 0.00 6 238.10 253 0.93 252 0.81 7 34.72 37 0.15 34 0.01 8 4.96 3 0.77 6 0.22 p=0.24725 p=0.04021 Number of rngs required: 688895, p-value: 0.715 RESULTS OF CRAPS TEST for dh-ranFile-2015-09-01_16:31 No. of wins: Observed Expected 98737 98585.9 z-score= 0.676, pvalue=0.75048 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66695 66666.7 0.012 0.012 2 37757 37654.3 0.280 0.292 3 27032 26954.7 0.221 0.514 4 19247 19313.5 0.229 0.742 5 13785 13851.4 0.318 1.061 6 9945 9943.5 0.000 1.061 7 7113 7145.0 0.144 1.204 8 5148 5139.1 0.016 1.220 9 3682 3699.9 0.086 1.306 10 2647 2666.3 0.140 1.446 11 1903 1923.3 0.215 1.661 12 1423 1388.7 0.845 2.506 13 997 1003.7 0.045 2.551 14 734 726.1 0.085 2.636 15 505 525.8 0.826 3.462 16 403 381.2 1.253 4.714 17 269 276.5 0.206 4.920 18 182 200.8 1.765 6.685 19 147 146.0 0.007 6.692 20 116 106.2 0.901 7.594 21 270 287.1 1.020 8.614 Chisq= 8.61 for 20 degrees of freedom, p= 0.01304 SUMMARY of craptest p-value for no. of wins: 0.750477 p-value for throws/game: 0.013035 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-09-01_16:31 No. of wins: Observed Expected 98793 98585.9 z-score= 0.926, pvalue=0.82290 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66826 66666.7 0.381 0.381 2 37679 37654.3 0.016 0.397 3 26906 26954.7 0.088 0.485 4 19424 19313.5 0.633 1.118 5 13965 13851.4 0.931 2.049 6 9837 9943.5 1.142 3.191 7 7003 7145.0 2.823 6.014 8 5109 5139.1 0.176 6.190 9 3599 3699.9 2.750 8.940 10 2694 2666.3 0.288 9.227 11 1863 1923.3 1.892 11.120 12 1350 1388.7 1.081 12.200 13 1022 1003.7 0.333 12.533 14 765 726.1 2.080 14.613 15 584 525.8 6.434 21.047 16 389 381.2 0.162 21.208 17 287 276.5 0.396 21.604 18 194 200.8 0.232 21.836 19 135 146.0 0.827 22.663 20 111 106.2 0.216 22.878 21 258 287.1 2.952 25.831 Chisq= 25.83 for 20 degrees of freedom, p= 0.82852 SUMMARY of craptest p-value for no. of wins: 0.822896 p-value for throws/game: 0.828521 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0000,0.0017,0.0086,0.0102,0.0130,0.0145,0.0157,0.0160,0.0211,0.0223, 0.0246,0.0262,0.0272,0.0272,0.0295,0.0346,0.0402,0.0446,0.0457,0.0462, 0.0483,0.0489,0.0535,0.0551,0.0558,0.0603,0.0730,0.0739,0.0770,0.0807, 0.0815,0.0842,0.0868,0.0951,0.1004,0.1030,0.1058,0.1090,0.1162,0.1181, 0.1245,0.1246,0.1268,0.1279,0.1339,0.1345,0.1365,0.1366,0.1375,0.1380, 0.1392,0.1456,0.1543,0.1547,0.1549,0.1591,0.1631,0.1635,0.1686,0.1688, 0.1750,0.1766,0.1784,0.1934,0.1959,0.1993,0.1998,0.2007,0.2047,0.2076, 0.2077,0.2271,0.2289,0.2310,0.2320,0.2384,0.2406,0.2472,0.2481,0.2553, 0.2556,0.2561,0.2570,0.2603,0.2611,0.2612,0.2631,0.2671,0.2688,0.2694, 0.2701,0.2709,0.2765,0.2825,0.2904,0.2913,0.2919,0.2929,0.3017,0.3050, 0.3058,0.3077,0.3133,0.3147,0.3152,0.3170,0.3173,0.3214,0.3223,0.3232, 0.3296,0.3349,0.3414,0.3427,0.3465,0.3580,0.3605,0.3614,0.3648,0.3713, 0.3758,0.3765,0.3777,0.3891,0.3961,0.4063,0.4127,0.4141,0.4157,0.4216, 0.4219,0.4267,0.4361,0.4415,0.4455,0.4530,0.4556,0.4581,0.4596,0.4600, 0.4606,0.4622,0.4709,0.4749,0.4820,0.4830,0.4928,0.4953,0.4979,0.4995, 0.5000,0.5030,0.5038,0.5065,0.5102,0.5225,0.5255,0.5417,0.5545,0.5558, 0.5582,0.5601,0.5654,0.5702,0.5725,0.5733,0.5740,0.5784,0.5803,0.5815, 0.5868,0.5872,0.5892,0.5949,0.5954,0.5957,0.5966,0.6007,0.6038,0.6126, 0.6207,0.6222,0.6231,0.6284,0.6289,0.6302,0.6306,0.6335,0.6418,0.6422, 0.6446,0.6671,0.6699,0.6703,0.6706,0.6726,0.6732,0.6784,0.6889,0.7008, 0.7107,0.7147,0.7174,0.7239,0.7265,0.7267,0.7288,0.7387,0.7482,0.7501, 0.7505,0.7620,0.7624,0.7645,0.7666,0.7667,0.7676,0.7779,0.7803,0.7833, 0.7850,0.7877,0.7878,0.7894,0.8035,0.8083,0.8089,0.8134,0.8229,0.8230, 0.8285,0.8334,0.8437,0.8460,0.8488,0.8559,0.8565,0.8574,0.8645,0.8668, 0.8760,0.8820,0.8867,0.8899,0.8929,0.8992,0.9049,0.9062,0.9159,0.9183, 0.9215,0.9250,0.9315,0.9376,0.9407,0.9423,0.9424,0.9481,0.9590,0.9624, 0.9733,0.9783,0.9821,0.9828,0.9856,0.9901,0.9910,0.9934,0.9989, Overall p-value after applying KStest on 269 p-values = 0.025345 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.