RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-01-26_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 15.72 9.1726 0.065308 2 to 25 15.76 22.6704 0.839708 3 to 26 16.06 7.8542 0.030434 4 to 27 15.59 18.7030 0.654156 5 to 28 15.70 18.9023 0.665834 6 to 29 15.71 12.8009 0.250593 7 to 30 15.60 19.4907 0.698898 8 to 31 15.84 20.6947 0.759755 9 to 32 15.77 18.9925 0.671040 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.489672 Tough bday spacings test for dh-ranFile-2016-01-26_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 5 42 70 96 90 86 55 22 19 9 6 (O-E)^2/E 1.9 0.8 0.1 0.0 0.6 0.8 0.2 2.0 1.1 0.9 0.9 Birthday Spacings: Sum(O-E)^2/E= 9.349, p= 0.501 RESULTS OF GCD FOR dh-ranFile-2016-01-26_13:31 Euclid's algorithm: p-value, steps to gcd: 0.587568 p-value, dist. of gcd's: 0.715447 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-01-26_13:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.332 0.804 0.322 0.615 0.911 0.896 0.201 0.643 Bits 8 to 15---> 0.946 0.299 0.728 0.748 0.786 0.271 0.719 0.649 Bits 16 to 23---> 0.734 0.442 0.124 0.712 0.215 0.607 0.245 0.125 Bits 24 to 31---> 0.069 0.730 0.804 0.613 0.834 0.362 0.192 0.209 KS test for the above 32 p values: 0.495 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-01-26_13:31, p-values for 5 runs: 0.5034, 0.4954, 0.5776, 0.4064, 0.8688 Rank test for binary matrices (31x31) for dh-ranFile-2016-01-26_13:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 216 211.4 0.099 0.099 r= 29 5106 5134.0 0.153 0.252 r= 30 23085 23103.0 0.014 0.266 r= 31 11593 11551.5 0.149 0.415 chi-square = 0.415 with df = 3; p-value = 0.063 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-01-26_13:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 199 211.4 0.729 0.729 r= 30 5212 5134.0 1.185 1.914 r= 31 23136 23103.0 0.047 1.961 r= 32 11453 11551.5 0.840 2.801 chi-square = 2.801 with df = 3; p-value = 0.577 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-01-26_13:31 b-rank test for bits 1 to 8, p=0.27595 b-rank test for bits 2 to 9, p=0.41613 b-rank test for bits 3 to 10, p=0.72801 b-rank test for bits 4 to 11, p=0.95277 b-rank test for bits 5 to 12, p=0.41748 b-rank test for bits 6 to 13, p=0.53100 b-rank test for bits 7 to 14, p=0.93974 b-rank test for bits 8 to 15, p=0.18078 b-rank test for bits 9 to 16, p=0.15850 b-rank test for bits 10 to 17, p=0.96476 b-rank test for bits 11 to 18, p=0.07793 b-rank test for bits 12 to 19, p=0.14275 b-rank test for bits 13 to 20, p=0.66370 b-rank test for bits 14 to 21, p=0.18425 b-rank test for bits 15 to 22, p=0.00159 b-rank test for bits 16 to 23, p=0.61010 b-rank test for bits 17 to 24, p=0.83294 b-rank test for bits 18 to 25, p=0.40788 b-rank test for bits 19 to 26, p=0.38811 b-rank test for bits 20 to 27, p=0.48859 b-rank test for bits 21 to 28, p=0.65178 b-rank test for bits 22 to 29, p=0.11984 b-rank test for bits 23 to 30, p=0.01077 b-rank test for bits 24 to 31, p=0.10390 b-rank test for bits 25 to 32, p=0.34288 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 = 0.247697 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-01-26_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 142488 1.35 0.911818 2 141515 -0.92 0.178439 3 142229 0.75 0.772436 4 141935 0.06 0.523913 5 141606 -0.71 0.239251 6 143087 2.75 0.997034 7 141612 -0.69 0.243623 8 141900 -0.02 0.491304 9 142861 2.22 0.986910 10 141586 -0.76 0.224991 11 141432 -1.12 0.132370 12 141677 -0.54 0.293624 13 141927 0.04 0.516466 14 142247 0.79 0.784929 15 142445 1.25 0.894636 16 141551 -0.84 0.201235 17 141951 0.10 0.538780 18 142040 0.31 0.619933 19 142389 1.12 0.868797 20 142050 0.33 0.628797 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-01-26_13:31 Bits used No. missing words z-score p-value 23 to 32 141682 -0.7839 0.216550 22 to 31 141917 0.0264 0.510550 21 to 30 142434 1.8092 0.964791 20 to 29 142320 1.4161 0.921627 19 to 28 141758 -0.5218 0.300895 18 to 27 141435 -1.6356 0.050960 17 to 26 141628 -0.9701 0.165998 16 to 25 142314 1.3954 0.918554 15 to 24 141735 -0.6011 0.273874 14 to 23 142240 1.1402 0.872907 13 to 22 141814 -0.3287 0.371182 12 to 21 141535 -1.2908 0.098388 11 to 20 142208 1.0299 0.848471 10 to 19 142125 0.7437 0.771468 9 to 18 142114 0.7058 0.759831 8 to 17 141678 -0.7977 0.212525 7 to 16 141339 -1.9667 0.024611 6 to 15 141500 -1.4115 0.079051 5 to 14 142245 1.1575 0.876462 4 to 13 142808 3.0989 0.999029 3 to 12 141915 0.0196 0.507800 2 to 11 142205 1.0196 0.846029 1 to 10 142073 0.5644 0.713752 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-01-26_13:31 Bits used No. missing words z-score p-value 28 to 32 141807 -0.3469 0.364340 27 to 31 141684 -0.7638 0.222484 26 to 30 141451 -1.5537 0.060133 25 to 29 142456 1.8531 0.968067 24 to 28 142258 1.1819 0.881384 23 to 27 141970 0.2057 0.581472 22 to 26 142165 0.8667 0.806941 21 to 25 141901 -0.0282 0.488737 20 to 24 141938 0.0972 0.538711 19 to 23 141282 -2.1265 0.016729 18 to 22 142201 0.9887 0.838598 17 to 21 141978 0.2328 0.592034 16 to 20 141861 -0.1638 0.434932 15 to 19 142301 1.3277 0.907861 14 to 18 142305 1.3413 0.910081 13 to 17 141937 0.0938 0.537365 12 to 16 141573 -1.1401 0.127122 11 to 15 141549 -1.2215 0.110956 10 to 14 142034 0.4226 0.663710 9 to 13 142056 0.4972 0.690471 8 to 12 141993 0.2836 0.611652 7 to 11 141537 -1.2621 0.103450 6 to 10 141839 -0.2384 0.405783 5 to 9 141639 -0.9164 0.179736 4 to 8 141971 0.2091 0.582796 3 to 7 141838 -0.2418 0.404469 2 to 6 142353 1.5040 0.933705 1 to 5 141476 -1.4689 0.070928 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-01-26_13:31 Bits used No. missing words z-score p-value 31 to 32 142195 0.8427 0.800298 30 to 31 141968 0.1731 0.568701 29 to 30 141957 0.1406 0.555915 28 to 29 141679 -0.6794 0.248430 27 to 28 142281 1.0964 0.863542 26 to 27 141484 -1.2547 0.104801 25 to 26 141820 -0.2635 0.396079 24 to 25 142119 0.6185 0.731876 23 to 24 142144 0.6922 0.755607 22 to 23 141585 -0.9567 0.169353 21 to 22 141754 -0.4582 0.323404 20 to 21 142094 0.5447 0.707037 19 to 20 142807 2.6480 0.995951 18 to 19 141899 -0.0305 0.487845 17 to 18 141597 -0.9213 0.178440 16 to 17 141926 0.0492 0.519610 15 to 16 141979 0.2055 0.581416 14 to 15 141507 -1.1868 0.117650 13 to 14 142393 1.4268 0.923175 12 to 13 141725 -0.5437 0.293308 11 to 12 141773 -0.4022 0.343786 10 to 11 141700 -0.6175 0.268455 9 to 10 142296 1.1406 0.872986 8 to 9 142263 1.0433 0.851589 7 to 8 142090 0.5329 0.702966 6 to 7 141741 -0.4965 0.309754 5 to 6 142182 0.8043 0.789399 4 to 5 141403 -1.4936 0.067640 3 to 4 142372 1.3648 0.913843 2 to 3 141621 -0.8505 0.197515 1 to 2 141872 -0.1101 0.456158 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-01-26_13:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2512.35 0.175 0.569348 Test results for specific bytes for dh-ranFile-2016-01-26_13:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2482.19 -0.252 0.400553 2 to 9 2539.34 0.556 0.711004 3 to 10 2461.84 -0.540 0.294733 4 to 11 2585.52 1.209 0.886739 5 to 12 2475.81 -0.342 0.366114 6 to 13 2604.10 1.472 0.929509 7 to 14 2405.22 -1.340 0.090063 8 to 15 2438.34 -0.872 0.191618 9 to 16 2525.06 0.354 0.638457 10 to 17 2475.36 -0.349 0.363726 11 to 18 2497.88 -0.030 0.488067 12 to 19 2392.78 -1.516 0.064713 13 to 20 2457.95 -0.595 0.276025 14 to 21 2463.06 -0.522 0.300676 15 to 22 2481.96 -0.255 0.399294 16 to 23 2512.22 0.173 0.568601 17 to 24 2600.41 1.420 0.922198 18 to 25 2473.17 -0.379 0.352189 19 to 26 2521.40 0.303 0.618918 20 to 27 2548.83 0.690 0.755059 21 to 28 2448.18 -0.733 0.231826 22 to 29 2359.41 -1.988 0.023393 23 to 30 2553.04 0.750 0.773422 24 to 31 2497.18 -0.040 0.484078 25 to 32 2522.76 0.322 0.626216 CDPARK for dh-ranFile-2016-01-26_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 3513 -0.4566 0.323972 3469 -2.4658 0.006836 3505 -0.8219 0.205562 3527 0.1826 0.572463 3489 -1.5525 0.060270 3486 -1.6895 0.045562 3521 -0.0913 0.463617 3540 0.7763 0.781201 3517 -0.2740 0.392053 3531 0.3653 0.642555 Square side=100, avg. no. parked=3509.80 sample std.=21.29 p-value of the KSTEST for those 10 p-values: 0.130942 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-01-26_13:31 0.5168,0.3177,0.1117,0.1914,0.3250,0.5160,0.3748,0.8525,0.9276,0.3542, The KS test for those 10 p-values: 0.614790 The 3DSPHERES test for dh-ranFile-2016-01-26_13:31 sample no r^3 equiv. uni. 1 27.957 0.606193 2 48.035 0.798340 3 6.788 0.202501 4 33.161 0.668906 5 4.674 0.144263 6 32.793 0.664827 7 29.899 0.630874 8 2.460 0.078720 9 63.616 0.880031 10 66.654 0.891587 11 20.139 0.488950 12 59.255 0.861260 13 54.087 0.835182 14 15.368 0.400854 15 18.709 0.464006 16 3.722 0.116684 17 17.776 0.447075 18 81.958 0.934907 19 9.095 0.261530 20 12.023 0.330205 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.888939 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-01-26_13:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 2.0 -0.7 -0.1 -1.0 0.1 0.3 -0.1 -0.1 -0.4 -0.4 -1.4 0.1 -1.2 -1.1 0.9 0.0 0.5 -1.2 1.5 0.1 -1.7 2.0 -0.8 -0.5 1.1 0.9 -0.1 1.2 1.6 -0.3 0.3 0.9 1.6 -0.6 -0.4 0.4 -1.2 -0.1 -0.8 -0.7 0.9 0.0 -0.1 Chi-square with 42 degrees of freedom:36.283605 z-score=-0.623710, p-value=0.280684 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-01-26_13:31 Test no p-value 1 0.012283 2 0.154532 3 0.021637 4 0.389648 5 0.390042 6 0.092849 7 0.128512 8 0.099068 9 0.023927 10 0.364328 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000141 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-01-26_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 66825 0.38 66652 0.00 3 25000.00 24892 0.47 25110 0.48 4 6666.67 6593 0.81 6579 1.15 5 1388.89 1385 0.01 1368 0.31 6 238.10 262 2.40 250 0.60 7 34.72 35 0.00 38 0.31 8 4.96 7 0.84 2 1.77 p=0.44445 p=0.40739 Number of rngs required: 687412, p-value: 0.125 RESULTS OF CRAPS TEST for dh-ranFile-2016-01-26_13:31 No. of wins: Observed Expected 98957 98585.9 z-score= 1.660, pvalue=0.95154 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66617 66666.7 0.037 0.037 2 37845 37654.3 0.966 1.003 3 26991 26954.7 0.049 1.051 4 19317 19313.5 0.001 1.052 5 13756 13851.4 0.657 1.709 6 10023 9943.5 0.635 2.344 7 7110 7145.0 0.172 2.516 8 5113 5139.1 0.132 2.648 9 3711 3699.9 0.034 2.682 10 2631 2666.3 0.467 3.149 11 1882 1923.3 0.888 4.037 12 1390 1388.7 0.001 4.038 13 1033 1003.7 0.854 4.893 14 703 726.1 0.737 5.630 15 545 525.8 0.698 6.329 16 352 381.2 2.229 8.558 17 268 276.5 0.264 8.822 18 191 200.8 0.481 9.303 19 158 146.0 0.989 10.292 20 95 106.2 1.184 11.476 21 269 287.1 1.143 12.619 Chisq= 12.62 for 20 degrees of freedom, p= 0.10687 SUMMARY of craptest p-value for no. of wins: 0.951539 p-value for throws/game: 0.106869 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-01-26_13:31 No. of wins: Observed Expected 98328 98585.9 z-score=-1.153, pvalue=0.12439 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66880 66666.7 0.683 0.683 2 37455 37654.3 1.055 1.738 3 26782 26954.7 1.107 2.845 4 19226 19313.5 0.396 3.241 5 13770 13851.4 0.479 3.719 6 10125 9943.5 3.311 7.031 7 7268 7145.0 2.117 9.147 8 5160 5139.1 0.085 9.232 9 3735 3699.9 0.334 9.566 10 2626 2666.3 0.609 10.175 11 1889 1923.3 0.613 10.788 12 1440 1388.7 1.892 12.680 13 950 1003.7 2.875 15.555 14 721 726.1 0.036 15.591 15 555 525.8 1.618 17.208 16 408 381.2 1.891 19.100 17 291 276.5 0.756 19.856 18 189 200.8 0.697 20.553 19 161 146.0 1.544 22.097 20 107 106.2 0.006 22.103 21 262 287.1 2.197 24.300 Chisq= 24.30 for 20 degrees of freedom, p= 0.77046 SUMMARY of craptest p-value for no. of wins: 0.124395 p-value for throws/game: 0.770459 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0001,0.0016,0.0068,0.0108,0.0123,0.0167,0.0216,0.0234,0.0239,0.0246, 0.0304,0.0456,0.0510,0.0601,0.0603,0.0629,0.0647,0.0653,0.0676,0.0686, 0.0709,0.0779,0.0787,0.0791,0.0901,0.0928,0.0984,0.0991,0.1035,0.1039, 0.1048,0.1069,0.1110,0.1117,0.1167,0.1177,0.1198,0.1239,0.1244,0.1247, 0.1249,0.1271,0.1285,0.1309,0.1324,0.1428,0.1443,0.1545,0.1585,0.1660, 0.1694,0.1784,0.1784,0.1797,0.1808,0.1843,0.1914,0.1916,0.1921,0.1975, 0.2012,0.2012,0.2025,0.2056,0.2093,0.2125,0.2149,0.2166,0.2225,0.2250, 0.2318,0.2393,0.2436,0.2447,0.2477,0.2484,0.2506,0.2615,0.2685,0.2711, 0.2739,0.2760,0.2760,0.2807,0.2933,0.2936,0.2947,0.2991,0.3007,0.3009, 0.3098,0.3177,0.3216,0.3234,0.3240,0.3250,0.3302,0.3319,0.3429,0.3438, 0.3522,0.3542,0.3621,0.3637,0.3643,0.3643,0.3661,0.3712,0.3748,0.3881, 0.3896,0.3900,0.3921,0.3961,0.3993,0.4006,0.4009,0.4045,0.4058,0.4064, 0.4074,0.4079,0.4161,0.4175,0.4349,0.4419,0.4445,0.4471,0.4562,0.4636, 0.4640,0.4841,0.4878,0.4881,0.4886,0.4887,0.4889,0.4897,0.4913,0.4952, 0.4954,0.5007,0.5034,0.5078,0.5106,0.5160,0.5165,0.5168,0.5196,0.5239, 0.5310,0.5374,0.5387,0.5388,0.5559,0.5686,0.5687,0.5693,0.5725,0.5767, 0.5776,0.5814,0.5815,0.5828,0.5876,0.5920,0.6062,0.6065,0.6101,0.6117, 0.6125,0.6148,0.6149,0.6189,0.6199,0.6262,0.6288,0.6309,0.6385,0.6426, 0.6426,0.6488,0.6518,0.6542,0.6637,0.6637,0.6648,0.6658,0.6689,0.6710, 0.6905,0.6989,0.7030,0.7070,0.7110,0.7119,0.7138,0.7154,0.7189,0.7280, 0.7284,0.7304,0.7319,0.7339,0.7484,0.7551,0.7556,0.7598,0.7598,0.7705, 0.7715,0.7724,0.7734,0.7812,0.7849,0.7857,0.7894,0.7983,0.8003,0.8040, 0.8041,0.8069,0.8329,0.8340,0.8352,0.8386,0.8397,0.8460,0.8485,0.8516, 0.8525,0.8613,0.8635,0.8688,0.8688,0.8729,0.8730,0.8765,0.8800,0.8814, 0.8867,0.8889,0.8916,0.8946,0.8962,0.9079,0.9101,0.9106,0.9118,0.9138, 0.9186,0.9216,0.9222,0.9232,0.9276,0.9295,0.9337,0.9349,0.9397,0.9457, 0.9515,0.9528,0.9648,0.9648,0.9681,0.9869,0.9960,0.9970,0.9990, Overall p-value after applying KStest on 269 p-values = 0.552023 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.