RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-08-14_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 15.76 15.0012 0.404606 2 to 25 15.83 22.3039 0.826689 3 to 26 15.76 17.7106 0.592688 4 to 27 15.76 21.0928 0.777833 5 to 28 15.84 9.0947 0.062758 6 to 29 15.63 16.4614 0.508604 7 to 30 15.69 32.1614 0.985632 8 to 31 15.77 18.2316 0.625625 9 to 32 15.85 20.7639 0.762972 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.355605 Tough bday spacings test for dh-ranFile-2016-08-14_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 11 34 72 100 105 70 45 28 15 12 8 (O-E)^2/E 0.4 0.2 0.0 0.1 0.5 0.8 1.0 0.1 0.0 4.4 3.8 Birthday Spacings: Sum(O-E)^2/E= 11.295, p= 0.665 RESULTS OF GCD FOR dh-ranFile-2016-08-14_21:31 Euclid's algorithm: p-value, steps to gcd: 0.901911 p-value, dist. of gcd's: 0.847030 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-08-14_21:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.625 0.154 0.669 0.903 0.429 0.426 0.322 0.774 Bits 8 to 15---> 0.120 0.637 0.006 0.513 0.266 0.564 0.424 0.978 Bits 16 to 23---> 0.304 0.878 0.776 0.301 0.320 0.359 0.389 0.453 Bits 24 to 31---> 0.408 0.903 0.396 0.815 0.098 0.592 0.155 0.889 KS test for the above 32 p values: 0.232 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-08-14_21:31, p-values for 5 runs: 0.5827, 0.9455, 0.3721, 0.0779, 0.2885 Rank test for binary matrices (31x31) for dh-ranFile-2016-08-14_21:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 230 211.4 1.633 1.633 r= 29 5198 5134.0 0.798 2.431 r= 30 23077 23103.0 0.029 2.460 r= 31 11495 11551.5 0.277 2.737 chi-square = 2.737 with df = 3; p-value = 0.566 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-08-14_21:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 229 211.4 1.462 1.462 r= 30 5079 5134.0 0.589 2.052 r= 31 23102 23103.0 0.000 2.052 r= 32 11590 11551.5 0.128 2.180 chi-square = 2.180 with df = 3; p-value = 0.464 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-08-14_21:31 b-rank test for bits 1 to 8, p=0.19821 b-rank test for bits 2 to 9, p=0.24718 b-rank test for bits 3 to 10, p=0.32498 b-rank test for bits 4 to 11, p=0.81988 b-rank test for bits 5 to 12, p=0.33749 b-rank test for bits 6 to 13, p=0.48723 b-rank test for bits 7 to 14, p=0.07112 b-rank test for bits 8 to 15, p=0.04934 b-rank test for bits 9 to 16, p=0.35828 b-rank test for bits 10 to 17, p=0.24179 b-rank test for bits 11 to 18, p=0.57864 b-rank test for bits 12 to 19, p=0.61325 b-rank test for bits 13 to 20, p=0.77722 b-rank test for bits 14 to 21, p=0.25052 b-rank test for bits 15 to 22, p=0.58792 b-rank test for bits 16 to 23, p=0.68240 b-rank test for bits 17 to 24, p=0.43549 b-rank test for bits 18 to 25, p=0.87907 b-rank test for bits 19 to 26, p=0.90485 b-rank test for bits 20 to 27, p=0.98086 b-rank test for bits 21 to 28, p=0.57410 b-rank test for bits 22 to 29, p=0.73579 b-rank test for bits 23 to 30, p=0.33651 b-rank test for bits 24 to 31, p=0.33510 b-rank test for bits 25 to 32, p=0.66963 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 = 0.874618 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-08-14_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 141722 -0.44 0.330807 2 142021 0.26 0.602920 3 141449 -1.08 0.141067 4 142263 0.83 0.795692 5 141633 -0.65 0.259259 6 141428 -1.12 0.130379 7 141483 -1.00 0.159601 8 141278 -1.48 0.070097 9 142428 1.21 0.887214 10 141563 -0.81 0.209205 11 141992 0.19 0.576581 12 140931 -2.29 0.011132 13 142135 0.53 0.700996 14 141938 0.07 0.526704 15 142325 0.97 0.834274 16 141636 -0.64 0.261535 17 142050 0.33 0.628797 18 141629 -0.65 0.256241 19 141949 0.09 0.536924 20 142211 0.70 0.759544 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-08-14_21:31 Bits used No. missing words z-score p-value 23 to 32 141567 -1.1804 0.118911 22 to 31 141844 -0.2253 0.410882 21 to 30 142413 1.7368 0.958788 20 to 29 141815 -0.3253 0.372486 19 to 28 141578 -1.1425 0.126620 18 to 27 142159 0.8609 0.805362 17 to 26 142000 0.3127 0.622729 16 to 25 142133 0.7713 0.779728 15 to 24 141709 -0.6908 0.244848 14 to 23 142132 0.7678 0.778705 13 to 22 142267 1.2333 0.891276 12 to 21 141909 -0.0011 0.499546 11 to 20 141829 -0.2770 0.390890 10 to 19 141948 0.1333 0.553040 9 to 18 141929 0.0678 0.527039 8 to 17 142010 0.3471 0.635756 7 to 16 141663 -0.8494 0.197826 6 to 15 142130 0.7609 0.776651 5 to 14 141860 -0.1701 0.432464 4 to 13 141880 -0.1011 0.459721 3 to 12 141978 0.2368 0.593591 2 to 11 142029 0.4127 0.660070 1 to 10 142288 1.3058 0.904183 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-08-14_21:31 Bits used No. missing words z-score p-value 28 to 32 141705 -0.6926 0.244267 27 to 31 141575 -1.1333 0.128540 26 to 30 141746 -0.5537 0.289905 25 to 29 141997 0.2972 0.616838 24 to 28 142028 0.4023 0.656258 23 to 27 142055 0.4938 0.689275 22 to 26 141615 -0.9977 0.159205 21 to 25 141791 -0.4011 0.344166 20 to 24 141511 -1.3503 0.088465 19 to 23 141485 -1.4384 0.075159 18 to 22 142276 1.2429 0.893057 17 to 21 142063 0.5209 0.698787 16 to 20 141408 -1.6994 0.044620 15 to 19 141866 -0.1469 0.441613 14 to 18 142122 0.7209 0.764519 13 to 17 142315 1.3752 0.915458 12 to 16 141655 -0.8621 0.194306 11 to 15 141721 -0.6384 0.261605 10 to 14 141919 0.0328 0.513075 9 to 13 142039 0.4396 0.669872 8 to 12 142016 0.3616 0.641172 7 to 11 142238 1.1141 0.867390 6 to 10 142302 1.3311 0.908419 5 to 9 141418 -1.6655 0.047904 4 to 8 142034 0.4226 0.663710 3 to 7 141711 -0.6723 0.250695 2 to 6 141594 -1.0689 0.142554 1 to 5 142110 0.6802 0.751823 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-08-14_21:31 Bits used No. missing words z-score p-value 31 to 32 141720 -0.5585 0.288253 30 to 31 142068 0.4681 0.680127 29 to 30 142666 2.2321 0.987195 28 to 29 141723 -0.5496 0.291281 27 to 28 142274 1.0757 0.858974 26 to 27 142469 1.6509 0.950625 25 to 26 142177 0.7896 0.785116 24 to 25 141367 -1.5998 0.054822 23 to 24 142360 1.3294 0.908144 22 to 23 142019 0.3235 0.626846 21 to 22 141866 -0.1278 0.449147 20 to 21 141661 -0.7325 0.231921 19 to 20 142178 0.7925 0.785976 18 to 19 141717 -0.5673 0.285240 17 to 18 141940 0.0905 0.536044 16 to 17 141806 -0.3048 0.380256 15 to 16 141490 -1.2370 0.108051 14 to 15 141803 -0.3137 0.376891 13 to 14 142014 0.3088 0.621248 12 to 13 142192 0.8338 0.797813 11 to 12 141492 -1.2311 0.109150 10 to 11 141105 -2.3727 0.008830 9 to 10 141775 -0.3963 0.345959 8 to 9 141746 -0.4818 0.314974 7 to 8 142247 0.9961 0.840394 6 to 7 141842 -0.1986 0.421283 5 to 6 142193 0.8368 0.798643 4 to 5 141941 0.0934 0.537216 3 to 4 141788 -0.3579 0.360207 2 to 3 141130 -2.2989 0.010755 1 to 2 141777 -0.3904 0.348137 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-08-14_21:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2494.28 -0.081 0.467758 Test results for specific bytes for dh-ranFile-2016-08-14_21:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2517.22 0.243 0.596182 2 to 9 2577.37 1.094 0.863069 3 to 10 2457.69 -0.598 0.274807 4 to 11 2432.72 -0.951 0.170682 5 to 12 2475.55 -0.346 0.364731 6 to 13 2537.50 0.530 0.702056 7 to 14 2535.20 0.498 0.690690 8 to 15 2538.32 0.542 0.706073 9 to 16 2546.74 0.661 0.745715 10 to 17 2422.43 -1.097 0.136306 11 to 18 2480.42 -0.277 0.390923 12 to 19 2540.34 0.570 0.715805 13 to 20 2400.39 -1.409 0.079454 14 to 21 2449.87 -0.709 0.239184 15 to 22 2513.88 0.196 0.577812 16 to 23 2620.72 1.707 0.956114 17 to 24 2403.03 -1.371 0.085129 18 to 25 2447.06 -0.749 0.227037 19 to 26 2587.35 1.235 0.891653 20 to 27 2506.39 0.090 0.536002 21 to 28 2461.25 -0.548 0.291842 22 to 29 2591.66 1.296 0.902570 23 to 30 2575.20 1.064 0.856226 24 to 31 2519.45 0.275 0.608350 25 to 32 2561.38 0.868 0.807316 CDPARK for dh-ranFile-2016-08-14_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 3540 0.7763 0.781201 3464 -2.6941 0.003529 3562 1.7808 0.962529 3487 -1.6438 0.050105 3537 0.6393 0.738676 3515 -0.3653 0.357445 3532 0.4110 0.659449 3527 0.1826 0.572463 3540 0.7763 0.781201 3506 -0.7763 0.218799 Square side=100, avg. no. parked=3521.00 sample std.=27.35 p-value of the KSTEST for those 10 p-values: 0.660964 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-08-14_21:31 0.6424,0.1636,0.4030,0.3316,0.3728,0.2751,0.6349,0.8234,0.7523,0.1507, The KS test for those 10 p-values: 0.691678 The 3DSPHERES test for dh-ranFile-2016-08-14_21:31 sample no r^3 equiv. uni. 1 28.711 0.615965 2 72.845 0.911801 3 42.870 0.760455 4 37.841 0.716730 5 47.957 0.797813 6 13.029 0.352275 7 11.610 0.320910 8 47.994 0.798064 9 30.204 0.634611 10 0.592 0.019537 11 6.548 0.196076 12 67.373 0.894153 13 71.805 0.908692 14 14.953 0.392523 15 27.569 0.601063 16 4.490 0.138995 17 2.306 0.073975 18 114.244 0.977811 19 8.541 0.247771 20 31.274 0.647415 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.730936 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-08-14_21:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -0.7 0.6 -0.5 -0.3 -1.5 0.4 -0.1 2.3 -0.2 0.3 0.6 -0.3 3.1 -0.9 -0.0 -1.0 0.3 -1.7 -0.7 0.4 1.3 -0.9 -1.6 -0.9 1.4 -0.9 1.2 -0.0 -0.2 0.1 0.0 1.9 0.3 0.3 0.1 0.7 0.5 -0.4 1.0 0.1 0.0 -0.1 Chi-square with 42 degrees of freedom:40.964117 z-score=-0.113024, p-value=0.483649 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-08-14_21:31 Test no p-value 1 0.316401 2 0.952736 3 0.719913 4 0.962131 5 0.006733 6 0.557906 7 0.113633 8 0.686344 9 0.241016 10 0.802605 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.712422 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-08-14_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 66148 4.04 66859 0.55 3 25000.00 25511 10.44 24800 1.60 4 6666.67 6636 0.14 6577 1.21 5 1388.89 1419 0.65 1493 7.80 6 238.10 241 0.04 240 0.02 7 34.72 40 0.80 25 2.72 8 4.96 4 0.19 5 0.00 p=0.98776 p=0.96925 Number of rngs required: 689308, p-value: 0.853 RESULTS OF CRAPS TEST for dh-ranFile-2016-08-14_21:31 No. of wins: Observed Expected 98583 98585.9 z-score=-0.013, pvalue=0.49490 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66950 66666.7 1.204 1.204 2 37604 37654.3 0.067 1.271 3 26984 26954.7 0.032 1.303 4 19168 19313.5 1.096 2.399 5 13881 13851.4 0.063 2.462 6 9880 9943.5 0.406 2.868 7 7092 7145.0 0.394 3.262 8 5084 5139.1 0.590 3.852 9 3660 3699.9 0.430 4.281 10 2696 2666.3 0.331 4.612 11 1959 1923.3 0.662 5.274 12 1353 1388.7 0.920 6.193 13 1035 1003.7 0.975 7.169 14 695 726.1 1.335 8.504 15 531 525.8 0.051 8.555 16 399 381.2 0.836 9.391 17 296 276.5 1.369 10.760 18 178 200.8 2.595 13.355 19 155 146.0 0.557 13.912 20 111 106.2 0.216 14.128 21 289 287.1 0.012 14.140 Chisq= 14.14 for 20 degrees of freedom, p= 0.17668 SUMMARY of craptest p-value for no. of wins: 0.494900 p-value for throws/game: 0.176679 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-08-14_21:31 No. of wins: Observed Expected 98663 98585.9 z-score= 0.345, pvalue=0.63496 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66679 66666.7 0.002 0.002 2 37782 37654.3 0.433 0.435 3 26862 26954.7 0.319 0.754 4 19059 19313.5 3.353 4.107 5 13864 13851.4 0.011 4.118 6 9996 9943.5 0.277 4.395 7 7244 7145.0 1.371 5.766 8 5019 5139.1 2.805 8.571 9 3730 3699.9 0.245 8.817 10 2703 2666.3 0.505 9.322 11 1910 1923.3 0.092 9.415 12 1347 1388.7 1.255 10.669 13 1037 1003.7 1.104 11.773 14 707 726.1 0.505 12.277 15 598 525.8 9.904 22.181 16 389 381.2 0.162 22.343 17 304 276.5 2.727 25.069 18 193 200.8 0.305 25.375 19 143 146.0 0.061 25.436 20 129 106.2 4.888 30.323 21 305 287.1 1.114 31.438 Chisq= 31.44 for 20 degrees of freedom, p= 0.95033 SUMMARY of craptest p-value for no. of wins: 0.634961 p-value for throws/game: 0.950329 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0035,0.0061,0.0067,0.0088,0.0108,0.0111,0.0195,0.0446,0.0479,0.0493, 0.0501,0.0548,0.0628,0.0701,0.0711,0.0740,0.0752,0.0779,0.0795,0.0851, 0.0885,0.0979,0.1081,0.1091,0.1136,0.1189,0.1201,0.1266,0.1285,0.1304, 0.1363,0.1390,0.1411,0.1426,0.1507,0.1542,0.1550,0.1592,0.1596,0.1636, 0.1707,0.1767,0.1943,0.1961,0.1978,0.1982,0.2092,0.2188,0.2270,0.2319, 0.2322,0.2392,0.2410,0.2418,0.2443,0.2448,0.2472,0.2478,0.2505,0.2507, 0.2562,0.2593,0.2615,0.2616,0.2662,0.2748,0.2751,0.2852,0.2883,0.2885, 0.2899,0.2913,0.2918,0.3009,0.3041,0.3150,0.3164,0.3197,0.3209,0.3216, 0.3250,0.3308,0.3316,0.3351,0.3365,0.3375,0.3442,0.3460,0.3481,0.3523, 0.3556,0.3574,0.3583,0.3592,0.3602,0.3647,0.3721,0.3725,0.3728,0.3769, 0.3803,0.3891,0.3909,0.3909,0.3925,0.3955,0.4030,0.4046,0.4078,0.4109, 0.4213,0.4245,0.4264,0.4286,0.4325,0.4355,0.4416,0.4491,0.4528,0.4597, 0.4641,0.4678,0.4836,0.4872,0.4949,0.4995,0.5086,0.5129,0.5131,0.5267, 0.5270,0.5360,0.5360,0.5369,0.5372,0.5530,0.5579,0.5642,0.5660,0.5725, 0.5741,0.5766,0.5778,0.5786,0.5827,0.5879,0.5922,0.5927,0.5936,0.5962, 0.6011,0.6029,0.6084,0.6133,0.6160,0.6168,0.6212,0.6227,0.6246,0.6256, 0.6268,0.6288,0.6346,0.6349,0.6350,0.6358,0.6373,0.6412,0.6424,0.6474, 0.6563,0.6594,0.6601,0.6610,0.6637,0.6650,0.6691,0.6696,0.6699,0.6801, 0.6824,0.6863,0.6893,0.6907,0.6917,0.6988,0.7010,0.7021,0.7061,0.7124, 0.7158,0.7167,0.7199,0.7309,0.7358,0.7387,0.7457,0.7518,0.7523,0.7595, 0.7605,0.7630,0.7645,0.7739,0.7757,0.7767,0.7772,0.7778,0.7787,0.7797, 0.7812,0.7812,0.7851,0.7860,0.7957,0.7978,0.7978,0.7981,0.7986,0.8026, 0.8054,0.8073,0.8152,0.8199,0.8234,0.8267,0.8343,0.8404,0.8470,0.8530, 0.8562,0.8590,0.8631,0.8674,0.8746,0.8782,0.8791,0.8872,0.8892,0.8913, 0.8917,0.8931,0.8942,0.9019,0.9026,0.9026,0.9028,0.9042,0.9049,0.9081, 0.9084,0.9087,0.9118,0.9155,0.9455,0.9503,0.9506,0.9527,0.9561,0.9588, 0.9621,0.9625,0.9692,0.9778,0.9781,0.9809,0.9856,0.9872,0.9878, Overall p-value after applying KStest on 269 p-values = 0.423497 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.