RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-11-04_14:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.54 28.9423 0.964938 2 to 25 15.62 17.9968 0.610957 3 to 26 15.75 28.7075 0.962680 4 to 27 15.53 28.6642 0.962249 5 to 28 15.66 26.9767 0.941589 6 to 29 15.56 21.4121 0.791603 7 to 30 15.65 15.2012 0.419007 8 to 31 15.78 25.6865 0.919636 9 to 32 15.91 19.2335 0.684706 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.000780 Tough bday spacings test for dh-ranFile-2015-11-04_14:31: 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 14 26 63 100 100 82 59 27 15 9 5 (O-E)^2/E 2.6 3.1 1.4 0.1 0.1 0.2 0.9 0.3 0.0 0.9 0.2 Birthday Spacings: Sum(O-E)^2/E= 9.630, p= 0.526 RESULTS OF GCD FOR dh-ranFile-2015-11-04_14:31 Euclid's algorithm: p-value, steps to gcd: 0.392548 p-value, dist. of gcd's: 0.698876 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-11-04_14:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.380 0.034 0.773 0.144 0.346 0.688 0.077 0.375 Bits 8 to 15---> 0.768 0.347 0.939 0.827 0.361 0.429 0.488 0.220 Bits 16 to 23---> 0.307 0.277 0.565 0.538 0.275 0.165 0.468 0.898 Bits 24 to 31---> 0.907 0.553 0.250 0.136 0.702 0.529 0.249 0.640 KS test for the above 32 p values: 0.542 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-11-04_14:31, p-values for 5 runs: 0.0427, 0.7237, 0.9570, 0.5052, 0.9848 Rank test for binary matrices (31x31) for dh-ranFile-2015-11-04_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 225 211.4 0.873 0.873 r= 29 5172 5134.0 0.281 1.154 r= 30 23019 23103.0 0.306 1.459 r= 31 11584 11551.5 0.091 1.551 chi-square = 1.551 with df = 3; p-value = 0.329 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-11-04_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 215 211.4 0.061 0.061 r= 30 5090 5134.0 0.377 0.438 r= 31 23160 23103.0 0.140 0.578 r= 32 11535 11551.5 0.024 0.602 chi-square = 0.602 with df = 3; p-value = 0.104 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-11-04_14:31 b-rank test for bits 1 to 8, p=0.58442 b-rank test for bits 2 to 9, p=0.20236 b-rank test for bits 3 to 10, p=0.34858 b-rank test for bits 4 to 11, p=0.44836 b-rank test for bits 5 to 12, p=0.66347 b-rank test for bits 6 to 13, p=0.06802 b-rank test for bits 7 to 14, p=0.78880 b-rank test for bits 8 to 15, p=0.99849 b-rank test for bits 9 to 16, p=0.99800 b-rank test for bits 10 to 17, p=0.60918 b-rank test for bits 11 to 18, p=0.05942 b-rank test for bits 12 to 19, p=0.44774 b-rank test for bits 13 to 20, p=0.40645 b-rank test for bits 14 to 21, p=0.28251 b-rank test for bits 15 to 22, p=0.93511 b-rank test for bits 16 to 23, p=0.09348 b-rank test for bits 17 to 24, p=0.52980 b-rank test for bits 18 to 25, p=0.44791 b-rank test for bits 19 to 26, p=0.06092 b-rank test for bits 20 to 27, p=0.53143 b-rank test for bits 21 to 28, p=0.97025 b-rank test for bits 22 to 29, p=0.64218 b-rank test for bits 23 to 30, p=0.10085 b-rank test for bits 24 to 31, p=0.24595 b-rank test for bits 25 to 32, p=0.18577 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 = 0.339932 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-11-04_14:31 (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 141785 -0.29 0.385720 2 141482 -1.00 0.159034 3 141854 -0.13 0.448570 4 141951 0.10 0.538780 5 141383 -1.23 0.109397 6 141642 -0.62 0.266116 7 141642 -0.62 0.266116 8 141961 0.12 0.548045 9 141936 0.06 0.524843 10 142658 1.75 0.959874 11 142059 0.35 0.636717 12 141613 -0.69 0.244356 13 141303 -1.42 0.078291 14 141893 -0.04 0.484782 15 142629 1.68 0.953664 16 141680 -0.54 0.296042 17 141880 -0.07 0.472683 18 141220 -1.61 0.053635 19 141906 -0.01 0.496896 20 141950 0.10 0.537852 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-11-04_14:31 Bits used No. missing words z-score p-value 23 to 32 142319 1.4127 0.921121 22 to 31 142180 0.9333 0.824679 21 to 30 141549 -1.2425 0.107023 20 to 29 142049 0.4816 0.684962 19 to 28 141680 -0.7908 0.214532 18 to 27 142042 0.4575 0.676338 17 to 26 141873 -0.1253 0.450153 16 to 25 141753 -0.5391 0.294920 15 to 24 141770 -0.4804 0.315454 14 to 23 141769 -0.4839 0.314230 13 to 22 141806 -0.3563 0.360804 12 to 21 141687 -0.7667 0.221643 11 to 20 141653 -0.8839 0.188376 10 to 19 142080 0.5885 0.721907 9 to 18 142276 1.2644 0.896953 8 to 17 142094 0.6368 0.737870 7 to 16 141596 -1.0804 0.139971 6 to 15 142169 0.8954 0.814717 5 to 14 141528 -1.3149 0.094267 4 to 13 141933 0.0816 0.532526 3 to 12 141969 0.2058 0.581510 2 to 11 141621 -0.9942 0.160053 1 to 10 142443 1.8402 0.967134 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-11-04_14:31 Bits used No. missing words z-score p-value 28 to 32 141796 -0.3842 0.350426 27 to 31 141924 0.0497 0.519831 26 to 30 142530 2.1040 0.982309 25 to 29 141999 0.3040 0.619423 24 to 28 142159 0.8463 0.801318 23 to 27 141712 -0.6689 0.251775 22 to 26 141774 -0.4587 0.323208 21 to 25 141612 -1.0079 0.156752 20 to 24 141676 -0.7909 0.214487 19 to 23 142350 1.4938 0.932386 18 to 22 142304 1.3379 0.909530 17 to 21 142099 0.6429 0.739872 16 to 20 141679 -0.7808 0.217466 15 to 19 142337 1.4497 0.926433 14 to 18 141813 -0.3265 0.372007 13 to 17 142241 1.1243 0.869558 12 to 16 141485 -1.4384 0.075159 11 to 15 141334 -1.9503 0.025572 10 to 14 141943 0.1141 0.545435 9 to 13 141692 -0.7367 0.230649 8 to 12 142368 1.5548 0.940005 7 to 11 141691 -0.7401 0.229619 6 to 10 141761 -0.5028 0.307548 5 to 9 141606 -1.0282 0.151919 4 to 8 141238 -2.2757 0.011432 3 to 7 141869 -0.1367 0.445629 2 to 6 141996 0.2938 0.615543 1 to 5 142107 0.6701 0.748593 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-11-04_14:31 Bits used No. missing words z-score p-value 31 to 32 141959 0.1465 0.558244 30 to 31 141771 -0.4081 0.341617 29 to 30 142079 0.5005 0.691639 28 to 29 142032 0.3619 0.641271 27 to 28 142829 2.7129 0.996665 26 to 27 142140 0.6804 0.751888 25 to 26 141970 0.1790 0.571018 24 to 25 142029 0.3530 0.637959 23 to 24 141970 0.1790 0.571018 22 to 23 141869 -0.1190 0.452651 21 to 22 141720 -0.5585 0.288253 20 to 21 141252 -1.9390 0.026249 19 to 20 142112 0.5978 0.725029 18 to 19 142040 0.3855 0.650051 17 to 18 141438 -1.3904 0.082211 16 to 17 142318 1.2055 0.885998 15 to 16 142395 1.4327 0.924022 14 to 15 141707 -0.5968 0.275306 13 to 14 141636 -0.8063 0.210040 12 to 13 141575 -0.9862 0.162012 11 to 12 141804 -0.3107 0.378011 10 to 11 141624 -0.8417 0.199983 9 to 10 141267 -1.8948 0.029061 8 to 9 141546 -1.0718 0.141912 7 to 8 141827 -0.2429 0.404056 6 to 7 142321 1.2144 0.887696 5 to 6 142236 0.9636 0.832384 4 to 5 142141 0.6834 0.752821 3 to 4 141984 0.2203 0.587168 2 to 3 141642 -0.7886 0.215178 1 to 2 142164 0.7512 0.773746 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-11-04_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2526.27 0.371 0.644856 Test results for specific bytes for dh-ranFile-2015-11-04_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2406.28 -1.325 0.092509 2 to 9 2494.09 -0.084 0.466691 3 to 10 2498.28 -0.024 0.490292 4 to 11 2461.92 -0.538 0.295126 5 to 12 2627.68 1.806 0.964514 6 to 13 2563.13 0.893 0.814026 7 to 14 2621.10 1.713 0.956613 8 to 15 2531.31 0.443 0.671023 9 to 16 2515.93 0.225 0.589143 10 to 17 2467.26 -0.463 0.321692 11 to 18 2497.23 -0.039 0.484361 12 to 19 2547.81 0.676 0.750507 13 to 20 2525.35 0.358 0.640002 14 to 21 2505.88 0.083 0.533116 15 to 22 2639.19 1.968 0.975488 16 to 23 2516.72 0.236 0.593469 17 to 24 2451.61 -0.684 0.246866 18 to 25 2691.28 2.705 0.996586 19 to 26 2443.62 -0.797 0.212640 20 to 27 2475.98 -0.340 0.367023 21 to 28 2500.29 0.004 0.501634 22 to 29 2578.79 1.114 0.867409 23 to 30 2532.96 0.466 0.679428 24 to 31 2592.23 1.304 0.903931 25 to 32 2533.99 0.481 0.684617 CDPARK for dh-ranFile-2015-11-04_14:31: 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 3574 2.3288 0.990064 3521 -0.0913 0.463617 3505 -0.8219 0.205562 3515 -0.3653 0.357445 3510 -0.5936 0.276387 3530 0.3196 0.625377 3508 -0.6849 0.246694 3523 0.0000 0.500000 3522 -0.0457 0.481790 3544 0.9589 0.831196 Square side=100, avg. no. parked=3525.20 sample std.=19.57 p-value of the KSTEST for those 10 p-values: 0.646379 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-11-04_14:31 0.2740,0.4506,0.0999,0.8692,0.2805,0.4140,0.2739,0.4347,0.2681,0.0441, The KS test for those 10 p-values: 0.092868 The 3DSPHERES test for dh-ranFile-2015-11-04_14:31 sample no r^3 equiv. uni. 1 23.003 0.535485 2 67.909 0.896029 3 7.692 0.226170 4 20.057 0.487553 5 5.495 0.167365 6 85.169 0.941515 7 1.578 0.051236 8 29.746 0.628998 9 47.745 0.796378 10 7.508 0.221406 11 78.564 0.927111 12 19.105 0.471043 13 2.866 0.091106 14 79.255 0.928770 15 58.459 0.857531 16 21.596 0.513175 17 59.111 0.860594 18 53.395 0.831335 19 8.881 0.256246 20 30.209 0.634679 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.404606 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-11-04_14:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 0.5 0.3 -0.5 0.6 -0.9 0.4 -0.1 -0.9 1.0 -0.8 0.1 -0.9 -0.3 1.3 -1.2 0.7 0.4 0.3 0.1 -0.5 0.8 1.5 -1.0 -2.4 1.1 -0.2 -1.7 1.1 -0.5 -0.2 0.1 1.0 -0.1 0.9 0.2 0.3 3.6 -0.4 -1.3 3.1 1.0 -1.1 Chi-square with 42 degrees of freedom:54.394857 z-score=1.352390, p-value=0.904833 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-11-04_14:31 Test no p-value 1 0.986188 2 0.155226 3 0.969157 4 0.014461 5 0.641400 6 0.343998 7 0.944429 8 0.332611 9 0.149161 10 0.608276 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.373601 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-11-04_14:31: (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 66617 0.04 66749 0.10 3 25000.00 24979 0.02 24933 0.18 4 6666.67 6720 0.43 6646 0.06 5 1388.89 1411 0.35 1375 0.14 6 238.10 229 0.35 256 1.35 7 34.72 35 0.00 34 0.01 8 4.96 8 1.86 6 0.22 p=0.19697 p=0.08625 Number of rngs required: 688478, p-value: 0.534 RESULTS OF CRAPS TEST for dh-ranFile-2015-11-04_14:31 No. of wins: Observed Expected 98515 98585.9 z-score=-0.317, pvalue=0.37565 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66699 66666.7 0.016 0.016 2 37417 37654.3 1.496 1.511 3 26920 26954.7 0.045 1.556 4 19212 19313.5 0.533 2.089 5 13816 13851.4 0.091 2.180 6 10259 9943.5 10.008 12.188 7 7155 7145.0 0.014 12.202 8 5149 5139.1 0.019 12.221 9 3666 3699.9 0.310 12.531 10 2686 2666.3 0.146 12.676 11 1937 1923.3 0.097 12.773 12 1444 1388.7 2.199 14.972 13 979 1003.7 0.609 15.581 14 726 726.1 0.000 15.581 15 475 525.8 4.915 20.496 16 395 381.2 0.503 20.999 17 283 276.5 0.151 21.150 18 229 200.8 3.951 25.101 19 157 146.0 0.831 25.932 20 96 106.2 0.982 26.915 21 300 287.1 0.578 27.493 Chisq= 27.49 for 20 degrees of freedom, p= 0.87805 SUMMARY of craptest p-value for no. of wins: 0.375652 p-value for throws/game: 0.878046 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-11-04_14:31 No. of wins: Observed Expected 98645 98585.9 z-score= 0.265, pvalue=0.60431 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66932 66666.7 1.056 1.056 2 37860 37654.3 1.123 2.180 3 26531 26954.7 6.661 8.841 4 19101 19313.5 2.337 11.178 5 13980 13851.4 1.194 12.371 6 9938 9943.5 0.003 12.375 7 7087 7145.0 0.471 12.846 8 5192 5139.1 0.545 13.391 9 3717 3699.9 0.079 13.470 10 2674 2666.3 0.022 13.493 11 1926 1923.3 0.004 13.496 12 1425 1388.7 0.947 14.443 13 1027 1003.7 0.540 14.983 14 737 726.1 0.162 15.146 15 486 525.8 3.018 18.163 16 379 381.2 0.012 18.176 17 273 276.5 0.045 18.221 18 213 200.8 0.737 18.958 19 145 146.0 0.007 18.965 20 93 106.2 1.644 20.609 21 284 287.1 0.034 20.643 Chisq= 20.64 for 20 degrees of freedom, p= 0.58159 SUMMARY of craptest p-value for no. of wins: 0.604308 p-value for throws/game: 0.581591 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0008,0.0114,0.0145,0.0256,0.0262,0.0291,0.0338,0.0427,0.0441,0.0512, 0.0536,0.0594,0.0609,0.0680,0.0752,0.0773,0.0783,0.0822,0.0862,0.0911, 0.0925,0.0929,0.0935,0.0943,0.0999,0.1008,0.1040,0.1070,0.1094,0.1356, 0.1400,0.1419,0.1436,0.1492,0.1519,0.1552,0.1568,0.1590,0.1601,0.1620, 0.1653,0.1674,0.1858,0.1884,0.1970,0.2000,0.2024,0.2056,0.2100,0.2126, 0.2145,0.2145,0.2152,0.2175,0.2197,0.2214,0.2216,0.2262,0.2296,0.2306, 0.2444,0.2459,0.2467,0.2469,0.2486,0.2501,0.2518,0.2562,0.2661,0.2661, 0.2681,0.2739,0.2740,0.2745,0.2753,0.2764,0.2768,0.2805,0.2825,0.2883, 0.2949,0.2951,0.2960,0.3065,0.3075,0.3142,0.3155,0.3217,0.3232,0.3294, 0.3326,0.3399,0.3416,0.3440,0.3456,0.3470,0.3486,0.3504,0.3574,0.3608, 0.3608,0.3670,0.3720,0.3736,0.3753,0.3757,0.3780,0.3803,0.3857,0.3925, 0.4041,0.4046,0.4064,0.4140,0.4190,0.4288,0.4347,0.4456,0.4477,0.4479, 0.4484,0.4486,0.4502,0.4506,0.4527,0.4636,0.4667,0.4684,0.4710,0.4727, 0.4818,0.4844,0.4848,0.4876,0.4883,0.4903,0.4969,0.5000,0.5016,0.5052, 0.5132,0.5198,0.5248,0.5265,0.5292,0.5298,0.5314,0.5325,0.5331,0.5344, 0.5355,0.5379,0.5384,0.5388,0.5425,0.5454,0.5480,0.5531,0.5582,0.5647, 0.5710,0.5710,0.5815,0.5816,0.5844,0.5872,0.5891,0.5935,0.6043,0.6083, 0.6092,0.6110,0.6155,0.6194,0.6254,0.6290,0.6347,0.6367,0.6380,0.6399, 0.6400,0.6413,0.6414,0.6422,0.6449,0.6464,0.6501,0.6635,0.6710,0.6763, 0.6794,0.6846,0.6847,0.6850,0.6884,0.6916,0.6989,0.7024,0.7219,0.7237, 0.7250,0.7379,0.7399,0.7486,0.7505,0.7519,0.7528,0.7677,0.7727,0.7737, 0.7888,0.7916,0.7964,0.8013,0.8140,0.8147,0.8247,0.8273,0.8312,0.8313, 0.8324,0.8575,0.8606,0.8674,0.8692,0.8696,0.8780,0.8860,0.8877,0.8960, 0.8970,0.8977,0.9039,0.9048,0.9073,0.9095,0.9196,0.9211,0.9240,0.9264, 0.9271,0.9288,0.9324,0.9351,0.9390,0.9400,0.9415,0.9416,0.9444,0.9537, 0.9566,0.9570,0.9599,0.9622,0.9627,0.9645,0.9649,0.9671,0.9692,0.9703, 0.9755,0.9823,0.9848,0.9862,0.9901,0.9966,0.9967,0.9980,0.9985, Overall p-value after applying KStest on 269 p-values = 0.380690 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.