RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-02-11_21:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.90 10.4995 0.118629 2 to 25 15.59 32.7310 0.987810 3 to 26 15.62 22.8479 0.845732 4 to 27 15.75 17.6071 0.585974 5 to 28 15.71 17.6087 0.586084 6 to 29 15.71 17.0718 0.550485 7 to 30 15.73 10.9926 0.143051 8 to 31 15.45 34.1012 0.991853 9 to 32 15.49 17.0696 0.550337 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.206701 Tough bday spacings test for dh-ranFile-2016-02-11_21:31: 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 4 36 66 107 111 81 41 29 13 7 5 (O-E)^2/E 2.9 0.0 0.7 0.9 1.8 0.1 2.4 0.0 0.2 0.0 0.2 Birthday Spacings: Sum(O-E)^2/E= 9.303, p= 0.496 RESULTS OF GCD FOR dh-ranFile-2016-02-11_21:31 Euclid's algorithm: p-value, steps to gcd: 0.110449 p-value, dist. of gcd's: 0.539354 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-02-11_21:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.212 0.718 0.127 0.827 0.442 0.613 0.356 0.969 Bits 8 to 15---> 0.543 0.866 0.555 0.819 0.879 0.427 0.145 0.259 Bits 16 to 23---> 0.440 0.213 0.362 0.221 0.714 0.203 0.105 0.813 Bits 24 to 31---> 0.420 0.090 0.256 0.985 0.337 0.398 0.632 0.765 KS test for the above 32 p values: 0.171 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-02-11_21:31, p-values for 5 runs: 0.3429, 0.5493, 0.4181, 0.0016, 0.6476 Rank test for binary matrices (31x31) for dh-ranFile-2016-02-11_21:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 219 211.4 0.272 0.272 r= 29 5095 5134.0 0.296 0.568 r= 30 23186 23103.0 0.298 0.866 r= 31 11500 11551.5 0.230 1.096 chi-square = 1.096 with df = 3; p-value = 0.222 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-02-11_21:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 229 211.4 1.462 1.462 r= 30 5110 5134.0 0.112 1.574 r= 31 23098 23103.0 0.001 1.576 r= 32 11563 11551.5 0.011 1.587 chi-square = 1.587 with df = 3; p-value = 0.338 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-02-11_21:31 b-rank test for bits 1 to 8, p=0.46820 b-rank test for bits 2 to 9, p=0.26225 b-rank test for bits 3 to 10, p=0.84744 b-rank test for bits 4 to 11, p=0.49600 b-rank test for bits 5 to 12, p=0.34776 b-rank test for bits 6 to 13, p=0.46684 b-rank test for bits 7 to 14, p=0.27758 b-rank test for bits 8 to 15, p=0.28312 b-rank test for bits 9 to 16, p=0.62050 b-rank test for bits 10 to 17, p=0.97132 b-rank test for bits 11 to 18, p=0.31185 b-rank test for bits 12 to 19, p=0.68148 b-rank test for bits 13 to 20, p=0.09125 b-rank test for bits 14 to 21, p=0.34220 b-rank test for bits 15 to 22, p=0.84226 b-rank test for bits 16 to 23, p=0.26917 b-rank test for bits 17 to 24, p=0.86609 b-rank test for bits 18 to 25, p=0.91101 b-rank test for bits 19 to 26, p=0.86335 b-rank test for bits 20 to 27, p=0.58111 b-rank test for bits 21 to 28, p=0.72983 b-rank test for bits 22 to 29, p=0.13112 b-rank test for bits 23 to 30, p=0.78563 b-rank test for bits 24 to 31, p=0.71975 b-rank test for bits 25 to 32, p=0.76499 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 = 0.453347 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-02-11_21:31 (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 141754 -0.36 0.358332 2 142053 0.34 0.631443 3 141900 -0.02 0.491304 4 141845 -0.15 0.440263 5 141670 -0.56 0.288019 6 142116 0.48 0.685407 7 141786 -0.29 0.386614 8 142103 0.45 0.674546 9 141775 -0.31 0.376816 10 142190 0.66 0.744014 11 141819 -0.21 0.416424 12 141384 -1.23 0.109835 13 141683 -0.53 0.298469 14 142285 0.88 0.809956 15 141541 -0.86 0.194734 16 141498 -0.96 0.168263 17 142296 0.90 0.816852 18 141532 -0.88 0.188993 19 141458 -1.05 0.145825 20 141724 -0.43 0.332502 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-02-11_21:31 Bits used No. missing words z-score p-value 23 to 32 142001 0.3161 0.624038 22 to 31 142236 1.1264 0.870012 21 to 30 142357 1.5437 0.938668 20 to 29 141972 0.2161 0.585547 19 to 28 141930 0.0713 0.528411 18 to 27 141676 -0.8046 0.210529 17 to 26 142140 0.7954 0.786814 16 to 25 141859 -0.1736 0.431109 15 to 24 141881 -0.0977 0.461089 14 to 23 141447 -1.5942 0.055441 13 to 22 142019 0.3782 0.647349 12 to 21 142210 1.0368 0.850084 11 to 20 141886 -0.0804 0.467940 10 to 19 142028 0.4092 0.658806 9 to 18 142063 0.5299 0.701908 8 to 17 142233 1.1161 0.867811 7 to 16 142140 0.7954 0.786814 6 to 15 142224 1.0851 0.861054 5 to 14 142181 0.9368 0.825568 4 to 13 141899 -0.0356 0.485792 3 to 12 142099 0.6540 0.743455 2 to 11 141759 -0.5184 0.302097 1 to 10 141767 -0.4908 0.311786 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-02-11_21:31 Bits used No. missing words z-score p-value 28 to 32 142125 0.7311 0.767636 27 to 31 141228 -2.3096 0.010455 26 to 30 142083 0.5887 0.721973 25 to 29 141983 0.2497 0.598602 24 to 28 141703 -0.6994 0.242144 23 to 27 141789 -0.4079 0.341674 22 to 26 141553 -1.2079 0.113543 21 to 25 142600 2.3413 0.990390 20 to 24 141708 -0.6825 0.247470 19 to 23 141817 -0.3130 0.377147 18 to 22 141812 -0.3299 0.370726 17 to 21 141479 -1.4587 0.072318 16 to 20 142255 1.1718 0.879354 15 to 19 141938 0.0972 0.538711 14 to 18 142339 1.4565 0.927374 13 to 17 141757 -0.5164 0.302797 12 to 16 141703 -0.6994 0.242144 11 to 15 141814 -0.3232 0.373290 10 to 14 142247 1.1446 0.873822 9 to 13 141540 -1.2520 0.105291 8 to 12 142038 0.4362 0.668643 7 to 11 142090 0.6124 0.729877 6 to 10 141792 -0.3977 0.345415 5 to 9 141523 -1.3096 0.095167 4 to 8 142089 0.6091 0.728755 3 to 7 141682 -0.7706 0.220469 2 to 6 142071 0.5480 0.708166 1 to 5 141845 -0.2181 0.413688 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-02-11_21:31 Bits used No. missing words z-score p-value 31 to 32 141921 0.0344 0.513731 30 to 31 141774 -0.3992 0.344872 29 to 30 141331 -1.7060 0.044005 28 to 29 141631 -0.8210 0.205814 27 to 28 142070 0.4740 0.682233 26 to 27 141981 0.2114 0.583719 25 to 26 141748 -0.4759 0.317073 24 to 25 141498 -1.2134 0.112496 23 to 24 141535 -1.1042 0.134749 22 to 23 141989 0.2350 0.592901 21 to 22 142239 0.9725 0.834594 20 to 21 142013 0.3058 0.620126 19 to 20 141983 0.2173 0.586019 18 to 19 141525 -1.1337 0.128457 17 to 18 142161 0.7424 0.771074 16 to 17 142140 0.6804 0.751888 15 to 16 142149 0.7070 0.760214 14 to 15 142045 0.4002 0.655498 13 to 14 142012 0.3029 0.619002 12 to 13 141982 0.2144 0.584869 11 to 12 141854 -0.1632 0.435174 10 to 11 142146 0.6981 0.757456 9 to 10 142141 0.6834 0.752821 8 to 9 142175 0.7837 0.783388 7 to 8 142358 1.3235 0.907167 6 to 7 141415 -1.4582 0.072393 5 to 6 141644 -0.7827 0.216906 4 to 5 142297 1.1436 0.873599 3 to 4 142385 1.4032 0.919715 2 to 3 141620 -0.8535 0.196696 1 to 2 141678 -0.6824 0.247496 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-02-11_21:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2516.63 0.235 0.592979 Test results for specific bytes for dh-ranFile-2016-02-11_21:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2599.23 1.403 0.919730 2 to 9 2624.46 1.760 0.960809 3 to 10 2526.83 0.379 0.647804 4 to 11 2429.61 -0.995 0.159749 5 to 12 2604.83 1.482 0.930892 6 to 13 2524.43 0.346 0.635149 7 to 14 2408.09 -1.300 0.096827 8 to 15 2480.76 -0.272 0.392785 9 to 16 2424.89 -1.062 0.144069 10 to 17 2335.22 -2.330 0.009895 11 to 18 2520.39 0.288 0.613488 12 to 19 2468.28 -0.449 0.326873 13 to 20 2496.37 -0.051 0.479519 14 to 21 2600.09 1.415 0.921533 15 to 22 2417.09 -1.173 0.120480 16 to 23 2539.74 0.562 0.712942 17 to 24 2493.46 -0.092 0.463153 18 to 25 2509.85 0.139 0.555387 19 to 26 2457.36 -0.603 0.273249 20 to 27 2576.60 1.083 0.860669 21 to 28 2503.39 0.048 0.519109 22 to 29 2523.93 0.338 0.632463 23 to 30 2464.71 -0.499 0.308865 24 to 31 2562.41 0.883 0.811272 25 to 32 2531.63 0.447 0.672693 CDPARK for dh-ranFile-2016-02-11_21:31: 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 3517 -0.2740 0.392053 3529 0.2740 0.607947 3530 0.3196 0.625377 3522 -0.0457 0.481790 3479 -2.0091 0.022262 3533 0.4566 0.676028 3520 -0.1370 0.445521 3509 -0.6393 0.261324 3520 -0.1370 0.445521 3479 -2.0091 0.022262 Square side=100, avg. no. parked=3513.80 sample std.=18.61 p-value of the KSTEST for those 10 p-values: 0.202018 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-02-11_21:31 0.5372,0.0667,0.2547,0.4494,0.0955,0.4688,0.7375,0.5938,0.5133,0.7104, The KS test for those 10 p-values: 0.524792 The 3DSPHERES test for dh-ranFile-2016-02-11_21:31 sample no r^3 equiv. uni. 1 103.452 0.968203 2 117.578 0.980144 3 92.275 0.953848 4 9.199 0.264073 5 8.312 0.241990 6 0.732 0.024098 7 2.554 0.081621 8 35.646 0.695235 9 28.896 0.618331 10 66.197 0.889921 11 15.055 0.394587 12 3.917 0.122415 13 88.253 0.947228 14 23.500 0.543124 15 45.030 0.777090 16 80.102 0.930753 17 7.810 0.229210 18 43.168 0.762823 19 4.463 0.138231 20 13.232 0.356652 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.290893 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-02-11_21:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 -2.4 -0.4 1.2 1.2 -1.3 -0.9 1.3 -3.0 2.1 -0.2 0.4 1.1 -2.0 -0.2 -0.0 0.0 1.4 -0.8 -0.7 -1.6 -0.7 0.7 0.3 2.1 -0.2 1.2 1.7 0.0 0.7 -0.6 0.6 0.1 -0.3 -1.5 -0.8 -0.7 -0.7 0.5 -0.7 0.1 0.0 -0.1 Chi-square with 42 degrees of freedom:54.684436 z-score=1.383985, p-value=0.909251 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-02-11_21:31 Test no p-value 1 0.894055 2 0.740886 3 0.932514 4 0.187231 5 0.025449 6 0.719188 7 0.382837 8 0.364697 9 0.637380 10 0.805652 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.719467 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-02-11_21:31: (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 66540 0.24 66893 0.77 3 25000.00 25024 0.02 24840 1.02 4 6666.67 6746 0.94 6623 0.29 5 1388.89 1412 0.38 1348 1.20 6 238.10 231 0.21 249 0.50 7 34.72 42 1.53 44 2.48 8 4.96 4 0.19 2 1.77 p=0.25815 p=0.76398 Number of rngs required: 689121, p-value: 0.797 RESULTS OF CRAPS TEST for dh-ranFile-2016-02-11_21:31 No. of wins: Observed Expected 98580 98585.9 z-score=-0.026, pvalue=0.48955 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66559 66666.7 0.174 0.174 2 37625 37654.3 0.023 0.197 3 27024 26954.7 0.178 0.375 4 19283 19313.5 0.048 0.423 5 13976 13851.4 1.120 1.543 6 9947 9943.5 0.001 1.544 7 7129 7145.0 0.036 1.580 8 5157 5139.1 0.063 1.643 9 3717 3699.9 0.079 1.722 10 2657 2666.3 0.032 1.755 11 1956 1923.3 0.555 2.310 12 1331 1388.7 2.401 4.710 13 1007 1003.7 0.011 4.721 14 716 726.1 0.142 4.863 15 520 525.8 0.065 4.928 16 347 381.2 3.060 7.987 17 272 276.5 0.075 8.062 18 219 200.8 1.644 9.706 19 143 146.0 0.061 9.767 20 105 106.2 0.014 9.781 21 310 287.1 1.824 11.605 Chisq= 11.60 for 20 degrees of freedom, p= 0.07100 SUMMARY of craptest p-value for no. of wins: 0.489548 p-value for throws/game: 0.070998 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-02-11_21:31 No. of wins: Observed Expected 98923 98585.9 z-score= 1.508, pvalue=0.93421 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66866 66666.7 0.596 0.596 2 37689 37654.3 0.032 0.628 3 26767 26954.7 1.308 1.935 4 19463 19313.5 1.158 3.093 5 13658 13851.4 2.701 5.794 6 9863 9943.5 0.652 6.447 7 6980 7145.0 3.812 10.258 8 5106 5139.1 0.213 10.471 9 3779 3699.9 1.693 12.164 10 2668 2666.3 0.001 12.165 11 1935 1923.3 0.071 12.235 12 1413 1388.7 0.424 12.659 13 1018 1003.7 0.203 12.863 14 777 726.1 3.562 16.425 15 540 525.8 0.382 16.806 16 396 381.2 0.579 17.385 17 294 276.5 1.102 18.487 18 233 200.8 5.153 23.640 19 142 146.0 0.109 23.749 20 107 106.2 0.006 23.755 21 306 287.1 1.242 24.997 Chisq= 25.00 for 20 degrees of freedom, p= 0.79847 SUMMARY of craptest p-value for no. of wins: 0.934209 p-value for throws/game: 0.798465 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0016,0.0099,0.0105,0.0223,0.0223,0.0241,0.0254,0.0440,0.0554,0.0667, 0.0710,0.0723,0.0724,0.0816,0.0905,0.0912,0.0952,0.0955,0.0968,0.1047, 0.1053,0.1098,0.1104,0.1125,0.1135,0.1186,0.1205,0.1224,0.1274,0.1285, 0.1311,0.1347,0.1382,0.1431,0.1441,0.1447,0.1458,0.1597,0.1683,0.1712, 0.1872,0.1890,0.1947,0.1967,0.2020,0.2033,0.2058,0.2067,0.2105,0.2121, 0.2126,0.2169,0.2205,0.2211,0.2220,0.2292,0.2420,0.2421,0.2421,0.2475, 0.2475,0.2547,0.2557,0.2582,0.2587,0.2613,0.2622,0.2641,0.2692,0.2732, 0.2776,0.2831,0.2880,0.2909,0.2985,0.3021,0.3028,0.3089,0.3118,0.3119, 0.3171,0.3269,0.3325,0.3374,0.3376,0.3417,0.3422,0.3429,0.3449,0.3454, 0.3478,0.3561,0.3567,0.3583,0.3619,0.3647,0.3707,0.3733,0.3768,0.3771, 0.3828,0.3866,0.3921,0.3928,0.3946,0.3981,0.4137,0.4164,0.4181,0.4202, 0.4266,0.4311,0.4352,0.4400,0.4403,0.4421,0.4455,0.4455,0.4494,0.4533, 0.4611,0.4632,0.4668,0.4679,0.4682,0.4688,0.4795,0.4818,0.4858,0.4895, 0.4913,0.4960,0.4964,0.5133,0.5137,0.5191,0.5248,0.5284,0.5372,0.5387, 0.5394,0.5428,0.5431,0.5493,0.5503,0.5505,0.5548,0.5554,0.5811,0.5837, 0.5849,0.5855,0.5860,0.5860,0.5861,0.5929,0.5930,0.5938,0.5986,0.6079, 0.6134,0.6135,0.6183,0.6190,0.6201,0.6205,0.6240,0.6254,0.6314,0.6316, 0.6325,0.6351,0.6374,0.6473,0.6476,0.6478,0.6555,0.6588,0.6686,0.6727, 0.6745,0.6760,0.6815,0.6822,0.6854,0.6952,0.7019,0.7082,0.7104,0.7129, 0.7143,0.7177,0.7192,0.7195,0.7197,0.7220,0.7288,0.7298,0.7299,0.7375, 0.7409,0.7435,0.7440,0.7519,0.7528,0.7575,0.7602,0.7628,0.7640,0.7650, 0.7651,0.7676,0.7711,0.7771,0.7834,0.7856,0.7868,0.7868,0.7968,0.7985, 0.8057,0.8100,0.8113,0.8131,0.8169,0.8191,0.8256,0.8274,0.8346,0.8423, 0.8457,0.8474,0.8501,0.8607,0.8611,0.8633,0.8655,0.8661,0.8678,0.8700, 0.8736,0.8738,0.8794,0.8794,0.8899,0.8941,0.9072,0.9093,0.9110,0.9197, 0.9197,0.9215,0.9274,0.9308,0.9309,0.9325,0.9342,0.9387,0.9472,0.9538, 0.9608,0.9682,0.9685,0.9713,0.9801,0.9850,0.9878,0.9904,0.9919, Overall p-value after applying KStest on 269 p-values = 0.587981 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.