RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-08-23_07:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.56 34.8995 0.993587 2 to 25 15.71 14.1933 0.346625 3 to 26 15.88 19.2525 0.685766 4 to 27 15.73 26.1896 0.928924 5 to 28 15.62 24.5308 0.894285 6 to 29 15.77 16.4252 0.506086 7 to 30 15.86 13.2343 0.279634 8 to 31 15.95 14.9801 0.403084 9 to 32 15.99 15.3067 0.426599 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.286812 Tough bday spacings test for dh-ranFile-2015-08-23_07:31: 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 11 37 77 77 91 86 59 38 14 8 2 (O-E)^2/E 0.4 0.0 0.2 4.4 0.5 0.8 0.9 2.3 0.1 0.3 1.0 Birthday Spacings: Sum(O-E)^2/E= 10.773, p= 0.624 RESULTS OF GCD FOR dh-ranFile-2015-08-23_07:31 Euclid's algorithm: p-value, steps to gcd: 0.269810 p-value, dist. of gcd's: 0.127326 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-08-23_07:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.012 0.612 0.949 0.312 0.692 0.017 0.297 0.638 Bits 8 to 15---> 0.500 0.083 0.229 0.934 0.777 0.459 0.365 0.342 Bits 16 to 23---> 0.577 0.762 0.846 0.262 0.956 0.932 0.179 0.390 Bits 24 to 31---> 0.115 0.829 0.672 0.363 0.037 0.196 0.184 0.629 KS test for the above 32 p values: 0.101 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-08-23_07:31, p-values for 5 runs: 0.1404, 0.2809, 0.2541, 0.9241, 0.1376 Rank test for binary matrices (31x31) for dh-ranFile-2015-08-23_07:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 201 211.4 0.513 0.513 r= 29 5120 5134.0 0.038 0.552 r= 30 23153 23103.0 0.108 0.660 r= 31 11526 11551.5 0.056 0.716 chi-square = 0.716 with df = 3; p-value = 0.131 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-08-23_07:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 208 211.4 0.055 0.055 r= 30 5126 5134.0 0.012 0.068 r= 31 23201 23103.0 0.415 0.483 r= 32 11465 11551.5 0.648 1.131 chi-square = 1.131 with df = 3; p-value = 0.230 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-08-23_07:31 b-rank test for bits 1 to 8, p=0.03066 b-rank test for bits 2 to 9, p=0.93677 b-rank test for bits 3 to 10, p=0.60545 b-rank test for bits 4 to 11, p=0.55926 b-rank test for bits 5 to 12, p=0.95488 b-rank test for bits 6 to 13, p=0.47458 b-rank test for bits 7 to 14, p=0.14170 b-rank test for bits 8 to 15, p=0.74504 b-rank test for bits 9 to 16, p=0.39000 b-rank test for bits 10 to 17, p=0.27262 b-rank test for bits 11 to 18, p=0.83814 b-rank test for bits 12 to 19, p=0.50957 b-rank test for bits 13 to 20, p=0.11763 b-rank test for bits 14 to 21, p=0.88022 b-rank test for bits 15 to 22, p=0.88677 b-rank test for bits 16 to 23, p=0.71164 b-rank test for bits 17 to 24, p=0.54384 b-rank test for bits 18 to 25, p=0.79400 b-rank test for bits 19 to 26, p=0.54161 b-rank test for bits 20 to 27, p=0.27899 b-rank test for bits 21 to 28, p=0.01742 b-rank test for bits 22 to 29, p=0.43829 b-rank test for bits 23 to 30, p=0.94380 b-rank test for bits 24 to 31, p=0.82405 b-rank test for bits 25 to 32, p=0.81287 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 = 0.350869 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-08-23_07:31 (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 141602 -0.72 0.236360 2 142526 1.44 0.925182 3 142218 0.72 0.764604 4 141973 0.15 0.559129 5 141738 -0.40 0.344466 6 142246 0.79 0.784246 7 141526 -0.90 0.185225 8 142143 0.55 0.707453 9 141565 -0.80 0.210551 10 140878 -2.41 0.007984 11 141799 -0.26 0.398288 12 141284 -1.46 0.072001 13 142168 0.60 0.727201 14 142075 0.39 0.650651 15 142806 2.10 0.981916 16 142038 0.30 0.618152 17 141375 -1.25 0.105936 18 141673 -0.55 0.290415 19 142040 0.31 0.619933 20 142030 0.28 0.611005 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-08-23_07:31 Bits used No. missing words z-score p-value 23 to 32 141880 -0.1011 0.459721 22 to 31 141445 -1.6011 0.054673 21 to 30 141999 0.3092 0.621418 20 to 29 141043 -2.9873 0.001407 19 to 28 142036 0.4368 0.668869 18 to 27 142419 1.7575 0.960582 17 to 26 142261 1.2127 0.887369 16 to 25 142056 0.5058 0.693487 15 to 24 142100 0.6575 0.744565 14 to 23 142138 0.7885 0.784803 13 to 22 141573 -1.1598 0.123074 12 to 21 141935 0.0885 0.535267 11 to 20 141446 -1.5977 0.055056 10 to 19 142174 0.9127 0.819288 9 to 18 142134 0.7747 0.780749 8 to 17 141971 0.2127 0.584202 7 to 16 142164 0.8782 0.810075 6 to 15 142185 0.9506 0.829093 5 to 14 141400 -1.7563 0.039518 4 to 13 142243 1.1506 0.875049 3 to 12 141921 0.0402 0.516050 2 to 11 141827 -0.2839 0.388245 1 to 10 141548 -1.2460 0.106389 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-08-23_07:31 Bits used No. missing words z-score p-value 28 to 32 141641 -0.9096 0.181519 27 to 31 142038 0.4362 0.668643 26 to 30 142498 1.9955 0.977005 25 to 29 141708 -0.6825 0.247470 24 to 28 141940 0.1040 0.541402 23 to 27 141336 -1.9435 0.025978 22 to 26 141931 0.0735 0.529279 21 to 25 141509 -1.3571 0.087383 20 to 24 142022 0.3819 0.648744 19 to 23 142145 0.7989 0.787820 18 to 22 142349 1.4904 0.931941 17 to 21 141940 0.1040 0.541402 16 to 20 142122 0.7209 0.764519 15 to 19 142041 0.4463 0.672324 14 to 18 141970 0.2057 0.581472 13 to 17 141892 -0.0587 0.476577 12 to 16 141974 0.2192 0.586761 11 to 15 142136 0.7684 0.778867 10 to 14 142495 1.9853 0.976446 9 to 13 141485 -1.4384 0.075159 8 to 12 142186 0.9379 0.825843 7 to 11 141829 -0.2723 0.392694 6 to 10 141828 -0.2757 0.391391 5 to 9 142385 1.6124 0.946567 4 to 8 142077 0.5684 0.715109 3 to 7 142365 1.5446 0.938784 2 to 6 142065 0.5277 0.701145 1 to 5 142127 0.7379 0.769702 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-08-23_07:31 Bits used No. missing words z-score p-value 31 to 32 141241 -1.9715 0.024335 30 to 31 142680 2.2734 0.988498 29 to 30 142320 1.2114 0.887132 28 to 29 142410 1.4769 0.930149 27 to 28 142249 1.0020 0.841823 26 to 27 142038 0.3796 0.647863 25 to 26 142293 1.1318 0.871134 24 to 25 142313 1.1908 0.883127 23 to 24 142426 1.5241 0.936258 22 to 23 141932 0.0669 0.526659 21 to 22 142081 0.5064 0.693713 20 to 21 142356 1.3176 0.906183 19 to 20 141874 -0.1042 0.458498 18 to 19 141771 -0.4081 0.341617 17 to 18 141843 -0.1957 0.422437 16 to 17 141940 0.0905 0.536044 15 to 16 140983 -2.7325 0.003142 14 to 15 142003 0.2763 0.608846 13 to 14 141990 0.2380 0.594046 12 to 13 142470 1.6539 0.950925 11 to 12 141660 -0.7355 0.231022 10 to 11 141747 -0.4788 0.316023 9 to 10 141642 -0.7886 0.215178 8 to 9 142053 0.4238 0.664146 7 to 8 141826 -0.2458 0.402914 6 to 7 142229 0.9430 0.827154 5 to 6 141496 -1.2193 0.111372 4 to 5 142117 0.6126 0.729928 3 to 4 142150 0.7099 0.761130 2 to 3 142051 0.4179 0.661992 1 to 2 141653 -0.7561 0.224784 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-08-23_07:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2589.23 1.262 0.896507 Test results for specific bytes for dh-ranFile-2015-08-23_07:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2537.77 0.534 0.703378 2 to 9 2535.82 0.507 0.693793 3 to 10 2441.86 -0.822 0.205481 4 to 11 2476.89 -0.327 0.371892 5 to 12 2418.30 -1.155 0.123974 6 to 13 2534.20 0.484 0.685674 7 to 14 2416.93 -1.175 0.120048 8 to 15 2401.00 -1.400 0.080747 9 to 16 2460.37 -0.560 0.287596 10 to 17 2484.63 -0.217 0.413972 11 to 18 2465.32 -0.491 0.311884 12 to 19 2529.42 0.416 0.661305 13 to 20 2551.86 0.733 0.768361 14 to 21 2485.38 -0.207 0.418114 15 to 22 2505.63 0.080 0.531723 16 to 23 2522.40 0.317 0.624316 17 to 24 2457.83 -0.596 0.275453 18 to 25 2532.59 0.461 0.677574 19 to 26 2507.71 0.109 0.543415 20 to 27 2538.84 0.549 0.708572 21 to 28 2537.33 0.528 0.701217 22 to 29 2536.57 0.517 0.697499 23 to 30 2482.69 -0.245 0.403287 24 to 31 2451.26 -0.689 0.245311 25 to 32 2480.30 -0.279 0.390297 CDPARK for dh-ranFile-2015-08-23_07:31: 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 3524 0.0457 0.518210 3562 1.7808 0.962529 3482 -1.8721 0.030593 3533 0.4566 0.676028 3519 -0.1826 0.427537 3528 0.2283 0.590298 3518 -0.2283 0.409702 3500 -1.0502 0.146807 3545 1.0046 0.842447 3521 -0.0913 0.463617 Square side=100, avg. no. parked=3523.20 sample std.=20.94 p-value of the KSTEST for those 10 p-values: 0.955696 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-08-23_07:31 0.8060,0.4650,0.5500,0.8078,0.4637,0.8967,0.3370,0.3719,0.2471,0.3495, The KS test for those 10 p-values: 0.537997 The 3DSPHERES test for dh-ranFile-2015-08-23_07:31 sample no r^3 equiv. uni. 1 7.101 0.210784 2 209.321 0.999067 3 7.999 0.234037 4 4.795 0.147715 5 24.060 0.551566 6 36.619 0.704959 7 11.338 0.314731 8 6.527 0.195537 9 9.405 0.269114 10 47.161 0.792374 11 78.235 0.926305 12 21.329 0.508833 13 5.467 0.166605 14 33.402 0.671558 15 0.753 0.024777 16 25.459 0.572003 17 23.576 0.544279 18 11.864 0.326625 19 17.586 0.443558 20 7.454 0.220001 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.414970 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-08-23_07:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -0.3 0.1 0.2 0.2 1.8 1.7 -0.7 -1.6 0.7 -0.7 0.3 0.7 1.0 0.8 -0.5 0.7 -0.7 0.0 1.2 -1.4 -0.3 -0.3 -1.1 -0.0 -0.6 -2.1 1.6 1.0 -0.6 0.0 -0.1 1.0 -1.0 0.3 0.2 0.5 0.5 0.1 1.0 0.9 0.0 -1.1 Chi-square with 42 degrees of freedom:33.367122 z-score=-0.941924, p-value=0.173259 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-08-23_07:31 Test no p-value 1 0.129592 2 0.001033 3 0.000489 4 0.653001 5 0.274171 6 0.022129 7 0.414806 8 0.214975 9 0.550174 10 0.386368 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.002645 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-08-23_07:31: (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 67099 2.80 66591 0.09 3 25000.00 24753 2.44 25094 0.35 4 6666.67 6505 3.92 6652 0.03 5 1388.89 1368 0.31 1398 0.06 6 238.10 236 0.02 219 1.53 7 34.72 36 0.05 42 1.53 8 4.96 2 1.77 3 0.77 p=0.92077 p=0.37242 Number of rngs required: 687359, p-value: 0.112 RESULTS OF CRAPS TEST for dh-ranFile-2015-08-23_07:31 No. of wins: Observed Expected 98714 98585.9 z-score= 0.573, pvalue=0.71672 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66354 66666.7 1.466 1.466 2 37997 37654.3 3.119 4.585 3 26935 26954.7 0.014 4.599 4 19048 19313.5 3.649 8.248 5 13972 13851.4 1.050 9.298 6 10086 9943.5 2.041 11.339 7 7183 7145.0 0.202 11.541 8 5041 5139.1 1.872 13.412 9 3670 3699.9 0.241 13.653 10 2725 2666.3 1.292 14.946 11 1895 1923.3 0.417 15.363 12 1437 1388.7 1.677 17.040 13 977 1003.7 0.711 17.751 14 742 726.1 0.346 18.097 15 541 525.8 0.437 18.535 16 398 381.2 0.745 19.280 17 265 276.5 0.482 19.761 18 182 200.8 1.765 21.527 19 147 146.0 0.007 21.534 20 99 106.2 0.490 22.024 21 306 287.1 1.242 23.266 Chisq= 23.27 for 20 degrees of freedom, p= 0.72408 SUMMARY of craptest p-value for no. of wins: 0.716719 p-value for throws/game: 0.724084 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-08-23_07:31 No. of wins: Observed Expected 98357 98585.9 z-score=-1.024, pvalue=0.15301 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66603 66666.7 0.061 0.061 2 37564 37654.3 0.217 0.277 3 27089 26954.7 0.669 0.946 4 19241 19313.5 0.272 1.218 5 13974 13851.4 1.085 2.303 6 9976 9943.5 0.106 2.409 7 7154 7145.0 0.011 2.420 8 5070 5139.1 0.928 3.349 9 3723 3699.9 0.145 3.493 10 2652 2666.3 0.077 3.570 11 1911 1923.3 0.079 3.649 12 1407 1388.7 0.240 3.889 13 990 1003.7 0.187 4.076 14 720 726.1 0.052 4.128 15 526 525.8 0.000 4.128 16 389 381.2 0.162 4.290 17 312 276.5 4.547 8.837 18 191 200.8 0.481 9.318 19 131 146.0 1.538 10.856 20 95 106.2 1.184 12.040 21 282 287.1 0.091 12.132 Chisq= 12.13 for 20 degrees of freedom, p= 0.08853 SUMMARY of craptest p-value for no. of wins: 0.153015 p-value for throws/game: 0.088527 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0005,0.0010,0.0014,0.0026,0.0031,0.0080,0.0125,0.0173,0.0174,0.0221, 0.0243,0.0248,0.0260,0.0306,0.0307,0.0370,0.0395,0.0547,0.0551,0.0720, 0.0752,0.0807,0.0830,0.0874,0.0885,0.1012,0.1059,0.1064,0.1114,0.1125, 0.1153,0.1176,0.1200,0.1231,0.1240,0.1273,0.1296,0.1306,0.1376,0.1404, 0.1417,0.1468,0.1477,0.1530,0.1666,0.1733,0.1794,0.1815,0.1844,0.1852, 0.1955,0.1956,0.2055,0.2106,0.2108,0.2150,0.2152,0.2200,0.2248,0.2294, 0.2304,0.2310,0.2340,0.2364,0.2453,0.2471,0.2475,0.2541,0.2624,0.2691, 0.2698,0.2726,0.2742,0.2755,0.2790,0.2796,0.2809,0.2868,0.2876,0.2904, 0.2970,0.3117,0.3119,0.3147,0.3160,0.3266,0.3370,0.3416,0.3417,0.3445, 0.3466,0.3495,0.3509,0.3628,0.3648,0.3719,0.3719,0.3724,0.3864,0.3882, 0.3898,0.3900,0.3903,0.3914,0.3927,0.3983,0.4029,0.4031,0.4033,0.4097, 0.4140,0.4148,0.4150,0.4181,0.4224,0.4266,0.4275,0.4383,0.4436,0.4585, 0.4585,0.4597,0.4636,0.4637,0.4650,0.4746,0.4766,0.4995,0.5061,0.5088, 0.5096,0.5160,0.5182,0.5267,0.5293,0.5317,0.5353,0.5360,0.5380,0.5414, 0.5414,0.5416,0.5434,0.5438,0.5443,0.5500,0.5502,0.5516,0.5591,0.5593, 0.5720,0.5770,0.5815,0.5842,0.5868,0.5903,0.5940,0.6055,0.6088,0.6110, 0.6116,0.6182,0.6199,0.6214,0.6243,0.6245,0.6287,0.6377,0.6479,0.6487, 0.6507,0.6530,0.6613,0.6620,0.6641,0.6686,0.6689,0.6716,0.6718,0.6723, 0.6760,0.6776,0.6857,0.6858,0.6922,0.6935,0.6937,0.6938,0.6975,0.7011, 0.7012,0.7034,0.7050,0.7075,0.7086,0.7116,0.7151,0.7167,0.7241,0.7272, 0.7299,0.7446,0.7450,0.7611,0.7624,0.7645,0.7646,0.7684,0.7697,0.7774, 0.7789,0.7807,0.7842,0.7848,0.7878,0.7924,0.7940,0.8060,0.8078,0.8101, 0.8129,0.8193,0.8241,0.8258,0.8272,0.8290,0.8291,0.8381,0.8418,0.8424, 0.8462,0.8711,0.8750,0.8802,0.8831,0.8868,0.8871,0.8874,0.8943,0.8965, 0.8967,0.9062,0.9208,0.9241,0.9252,0.9263,0.9289,0.9301,0.9319,0.9323, 0.9335,0.9363,0.9368,0.9388,0.9438,0.9466,0.9493,0.9509,0.9549,0.9557, 0.9561,0.9606,0.9625,0.9764,0.9770,0.9819,0.9885,0.9936,0.9991, Overall p-value after applying KStest on 269 p-values = 0.858297 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.