RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-02-12_19:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.52 25.2253 0.910222 2 to 25 15.61 19.3223 0.689652 3 to 26 15.67 28.5781 0.961379 4 to 27 15.88 19.3306 0.690111 5 to 28 15.62 14.8147 0.391171 6 to 29 15.65 35.4505 0.994574 7 to 30 15.87 9.0180 0.060306 8 to 31 15.85 12.4443 0.227480 9 to 32 15.80 15.6315 0.449908 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.325035 Tough bday spacings test for dh-ranFile-2016-02-12_19:31: 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 6 32 71 86 99 82 61 35 14 8 6 (O-E)^2/E 1.1 0.6 0.1 1.4 0.0 0.2 1.5 0.9 0.1 0.3 0.9 Birthday Spacings: Sum(O-E)^2/E= 7.051, p= 0.279 RESULTS OF GCD FOR dh-ranFile-2016-02-12_19:31 Euclid's algorithm: p-value, steps to gcd: 0.597654 p-value, dist. of gcd's: 0.452386 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-02-12_19:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.363 0.542 0.152 0.204 0.139 0.912 0.404 0.165 Bits 8 to 15---> 0.976 0.845 0.387 0.394 0.911 0.086 0.678 0.200 Bits 16 to 23---> 0.935 0.850 0.736 0.371 0.085 0.002 0.409 0.555 Bits 24 to 31---> 0.202 0.499 0.360 0.185 0.965 0.316 0.158 0.647 KS test for the above 32 p values: 0.578 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-02-12_19:31, p-values for 5 runs: 0.7217, 0.3865, 0.0674, 0.2641, 0.3958 Rank test for binary matrices (31x31) for dh-ranFile-2016-02-12_19:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 197 211.4 0.983 0.983 r= 29 5168 5134.0 0.225 1.208 r= 30 23066 23103.0 0.059 1.268 r= 31 11569 11551.5 0.026 1.294 chi-square = 1.294 with df = 3; p-value = 0.269 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-02-12_19:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 207 211.4 0.092 0.092 r= 30 5159 5134.0 0.122 0.214 r= 31 23095 23103.0 0.003 0.217 r= 32 11539 11551.5 0.014 0.230 chi-square = 0.230 with df = 3; p-value = 0.027 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-02-12_19:31 b-rank test for bits 1 to 8, p=0.60071 b-rank test for bits 2 to 9, p=0.20166 b-rank test for bits 3 to 10, p=0.50279 b-rank test for bits 4 to 11, p=0.84913 b-rank test for bits 5 to 12, p=0.59961 b-rank test for bits 6 to 13, p=0.61869 b-rank test for bits 7 to 14, p=0.47104 b-rank test for bits 8 to 15, p=0.09245 b-rank test for bits 9 to 16, p=0.69099 b-rank test for bits 10 to 17, p=0.02536 b-rank test for bits 11 to 18, p=0.79839 b-rank test for bits 12 to 19, p=0.43743 b-rank test for bits 13 to 20, p=0.36733 b-rank test for bits 14 to 21, p=0.61760 b-rank test for bits 15 to 22, p=0.13476 b-rank test for bits 16 to 23, p=0.23069 b-rank test for bits 17 to 24, p=0.58332 b-rank test for bits 18 to 25, p=0.00582 b-rank test for bits 19 to 26, p=0.92307 b-rank test for bits 20 to 27, p=0.09061 b-rank test for bits 21 to 28, p=0.88872 b-rank test for bits 22 to 29, p=0.87794 b-rank test for bits 23 to 30, p=0.04101 b-rank test for bits 24 to 31, p=0.78802 b-rank test for bits 25 to 32, p=0.95600 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 = 0.757251 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-02-12_19:31 (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 141957 0.11 0.544342 2 141768 -0.33 0.370621 3 141751 -0.37 0.355717 4 142353 1.04 0.850042 5 141705 -0.48 0.316536 6 142177 0.63 0.734145 7 142277 0.86 0.804841 8 141600 -0.72 0.234922 9 142161 0.59 0.721739 10 141907 -0.01 0.497828 11 141912 0.01 0.502489 12 141336 -1.34 0.090195 13 140500 -3.29 0.000496 14 142160 0.59 0.720954 15 141680 -0.54 0.296042 16 142064 0.36 0.641092 17 142148 0.56 0.711455 18 142081 0.40 0.655826 19 141716 -0.45 0.325741 20 142336 1.00 0.840592 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-02-12_19:31 Bits used No. missing words z-score p-value 23 to 32 142111 0.6954 0.756602 22 to 31 142057 0.5092 0.694696 21 to 30 142026 0.4023 0.656272 20 to 29 141953 0.1506 0.559849 19 to 28 142108 0.6851 0.753350 18 to 27 141978 0.2368 0.593591 17 to 26 142165 0.8816 0.811009 16 to 25 142005 0.3299 0.629261 15 to 24 142104 0.6713 0.748978 14 to 23 141973 0.2196 0.586890 13 to 22 141508 -1.3839 0.083195 12 to 21 141509 -1.3804 0.083724 11 to 20 142161 0.8678 0.807256 10 to 19 142070 0.5540 0.710222 9 to 18 142203 1.0127 0.844388 8 to 17 141357 -1.9046 0.028417 7 to 16 141907 -0.0080 0.496795 6 to 15 141825 -0.2908 0.385605 5 to 14 142206 1.0230 0.846846 4 to 13 142006 0.3333 0.630563 3 to 12 141811 -0.3391 0.367279 2 to 11 141724 -0.6391 0.261389 1 to 10 141570 -1.1701 0.120980 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-02-12_19:31 Bits used No. missing words z-score p-value 28 to 32 141736 -0.5876 0.278414 27 to 31 141450 -1.5571 0.059729 26 to 30 142279 1.2531 0.894919 25 to 29 141784 -0.4248 0.335474 24 to 28 142219 1.0497 0.853079 23 to 27 141899 -0.0350 0.486033 22 to 26 141754 -0.5265 0.299256 21 to 25 141777 -0.4486 0.326869 20 to 24 141929 0.0667 0.526581 19 to 23 141717 -0.6520 0.257212 18 to 22 141769 -0.4757 0.317146 17 to 21 142027 0.3989 0.655010 16 to 20 141944 0.1175 0.546778 15 to 19 142066 0.5311 0.702320 14 to 18 142233 1.0972 0.863720 13 to 17 141841 -0.2316 0.408414 12 to 16 141895 -0.0486 0.480629 11 to 15 141848 -0.2079 0.417654 10 to 14 141529 -1.2893 0.098655 9 to 13 141540 -1.2520 0.105291 8 to 12 141628 -0.9537 0.170128 7 to 11 142033 0.4192 0.662473 6 to 10 141794 -0.3909 0.347917 5 to 9 141805 -0.3537 0.361797 4 to 8 141577 -1.1265 0.129968 3 to 7 141611 -1.0113 0.155939 2 to 6 141809 -0.3401 0.366890 1 to 5 142152 0.8226 0.794635 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-02-12_19:31 Bits used No. missing words z-score p-value 31 to 32 142176 0.7866 0.784253 30 to 31 142451 1.5978 0.944961 29 to 30 142850 2.7748 0.997239 28 to 29 141563 -1.0216 0.153480 27 to 28 141414 -1.4612 0.071987 26 to 27 142228 0.9400 0.826399 25 to 26 142120 0.6214 0.732847 24 to 25 142178 0.7925 0.785976 23 to 24 141743 -0.4906 0.311837 22 to 23 141533 -1.1101 0.133474 21 to 22 141255 -1.9302 0.026792 20 to 21 141312 -1.7620 0.039032 19 to 20 141772 -0.4051 0.342701 18 to 19 141849 -0.1780 0.429375 17 to 18 142447 1.5860 0.943636 16 to 17 141893 -0.0482 0.480790 15 to 16 141798 -0.3284 0.371302 14 to 15 141437 -1.3933 0.081764 13 to 14 142260 1.0344 0.849531 12 to 13 141452 -1.3491 0.088660 11 to 12 142570 1.9489 0.974345 10 to 11 141910 0.0020 0.500789 9 to 10 141691 -0.6440 0.259774 8 to 9 141904 -0.0157 0.493728 7 to 8 141880 -0.0865 0.465527 6 to 7 142035 0.3707 0.644573 5 to 6 141669 -0.7089 0.239182 4 to 5 141842 -0.1986 0.421283 3 to 4 141346 -1.6617 0.048282 2 to 3 141463 -1.3166 0.093985 1 to 2 141660 -0.7355 0.231022 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-02-12_19:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2446.82 -0.752 0.226018 Test results for specific bytes for dh-ranFile-2016-02-12_19:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2435.62 -0.910 0.181290 2 to 9 2437.00 -0.891 0.186478 3 to 10 2404.04 -1.357 0.087385 4 to 11 2554.46 0.770 0.779397 5 to 12 2651.75 2.146 0.984066 6 to 13 2485.36 -0.207 0.417964 7 to 14 2398.82 -1.431 0.076220 8 to 15 2475.27 -0.350 0.363286 9 to 16 2457.02 -0.608 0.271639 10 to 17 2491.97 -0.113 0.454818 11 to 18 2577.31 1.093 0.862867 12 to 19 2457.85 -0.596 0.275545 13 to 20 2359.42 -1.988 0.023402 14 to 21 2481.49 -0.262 0.396755 15 to 22 2543.26 0.612 0.729683 16 to 23 2404.48 -1.351 0.088365 17 to 24 2514.45 0.204 0.580941 18 to 25 2569.56 0.984 0.837370 19 to 26 2441.64 -0.825 0.204571 20 to 27 2586.97 1.230 0.890646 21 to 28 2634.42 1.901 0.971347 22 to 29 2572.19 1.021 0.846347 23 to 30 2501.03 0.015 0.505792 24 to 31 2549.72 0.703 0.759017 25 to 32 2565.86 0.931 0.824161 CDPARK for dh-ranFile-2016-02-12_19:31: 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 3503 -0.9132 0.180558 3523 0.0000 0.500000 3517 -0.2740 0.392053 3507 -0.7306 0.232514 3496 -1.2329 0.108811 3500 -1.0502 0.146807 3538 0.6849 0.753306 3562 1.7808 0.962529 3519 -0.1826 0.427537 3552 1.3242 0.907282 Square side=100, avg. no. parked=3521.70 sample std.=21.30 p-value of the KSTEST for those 10 p-values: 0.824935 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-02-12_19:31 0.7091,0.7905,0.2671,0.8256,0.0968,0.1418,0.8660,0.9263,0.2012,0.7294, The KS test for those 10 p-values: 0.522295 The 3DSPHERES test for dh-ranFile-2016-02-12_19:31 sample no r^3 equiv. uni. 1 15.583 0.405142 2 6.116 0.184416 3 28.652 0.615215 4 7.981 0.233574 5 61.588 0.871640 6 57.443 0.852625 7 25.099 0.566826 8 19.836 0.483770 9 2.659 0.084827 10 39.928 0.735767 11 15.748 0.408410 12 26.592 0.587867 13 25.086 0.566643 14 45.200 0.778352 15 85.727 0.942591 16 129.457 0.986637 17 34.649 0.684934 18 65.502 0.887343 19 44.835 0.775642 20 23.308 0.540191 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.150898 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-02-12_19:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 1.8 -0.1 0.2 -0.7 -1.6 0.0 0.5 -1.4 0.9 0.3 0.2 -1.4 1.0 0.0 -0.1 -0.2 0.7 -0.6 -0.5 1.2 -0.1 -0.6 1.2 0.9 -0.9 0.3 0.2 -0.7 -1.3 -1.5 0.6 -1.2 -0.4 0.5 -0.1 0.0 -0.1 -0.8 -0.7 0.1 -1.0 -0.1 Chi-square with 42 degrees of freedom:27.290163 z-score=-1.604975, p-value=0.038513 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-02-12_19:31 Test no p-value 1 0.536060 2 0.396016 3 0.182873 4 0.705280 5 0.005212 6 0.203202 7 0.199276 8 0.255669 9 0.643998 10 0.033133 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.059059 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-02-12_19:31: (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 66437 0.79 66710 0.03 3 25000.00 25319 4.07 24910 0.32 4 6666.67 6553 1.94 6651 0.04 5 1388.89 1404 0.16 1440 1.88 6 238.10 250 0.60 243 0.10 7 34.72 31 0.40 40 0.80 8 4.96 5 0.00 5 0.00 p=0.75883 p=0.21330 Number of rngs required: 688890, p-value: 0.713 RESULTS OF CRAPS TEST for dh-ranFile-2016-02-12_19:31 No. of wins: Observed Expected 98965 98585.9 z-score= 1.696, pvalue=0.95503 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67002 66666.7 1.687 1.687 2 37483 37654.3 0.779 2.466 3 26728 26954.7 1.907 4.373 4 19277 19313.5 0.069 4.442 5 13804 13851.4 0.162 4.605 6 10013 9943.5 0.485 5.090 7 7084 7145.0 0.521 5.611 8 5106 5139.1 0.213 5.824 9 3732 3699.9 0.279 6.103 10 2728 2666.3 1.428 7.531 11 1947 1923.3 0.291 7.822 12 1435 1388.7 1.541 9.363 13 1023 1003.7 0.371 9.734 14 705 726.1 0.615 10.349 15 538 525.8 0.281 10.630 16 377 381.2 0.045 10.676 17 265 276.5 0.482 11.157 18 216 200.8 1.146 12.303 19 150 146.0 0.110 12.414 20 103 106.2 0.097 12.511 21 284 287.1 0.034 12.545 Chisq= 12.54 for 20 degrees of freedom, p= 0.10394 SUMMARY of craptest p-value for no. of wins: 0.955033 p-value for throws/game: 0.103944 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-02-12_19:31 No. of wins: Observed Expected 98476 98585.9 z-score=-0.491, pvalue=0.31159 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66671 66666.7 0.000 0.000 2 37847 37654.3 0.986 0.986 3 26955 26954.7 0.000 0.986 4 19187 19313.5 0.828 1.814 5 13754 13851.4 0.685 2.499 6 9827 9943.5 1.366 3.865 7 7232 7145.0 1.059 4.924 8 5109 5139.1 0.176 5.100 9 3794 3699.9 2.395 7.495 10 2593 2666.3 2.015 9.510 11 1921 1923.3 0.003 9.513 12 1423 1388.7 0.845 10.358 13 988 1003.7 0.246 10.604 14 750 726.1 0.784 11.388 15 537 525.8 0.237 11.625 16 391 381.2 0.255 11.880 17 266 276.5 0.402 12.281 18 206 200.8 0.133 12.414 19 167 146.0 3.025 15.440 20 102 106.2 0.167 15.607 21 280 287.1 0.176 15.783 Chisq= 15.78 for 20 degrees of freedom, p= 0.27003 SUMMARY of craptest p-value for no. of wins: 0.311589 p-value for throws/game: 0.270031 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0005,0.0017,0.0052,0.0058,0.0234,0.0254,0.0268,0.0275,0.0284,0.0331, 0.0385,0.0390,0.0410,0.0483,0.0591,0.0597,0.0603,0.0674,0.0720,0.0762, 0.0818,0.0832,0.0837,0.0848,0.0852,0.0860,0.0874,0.0884,0.0887,0.0902, 0.0906,0.0924,0.0940,0.0968,0.0987,0.1039,0.1053,0.1088,0.1210,0.1300, 0.1335,0.1348,0.1389,0.1418,0.1468,0.1509,0.1517,0.1535,0.1559,0.1581, 0.1654,0.1701,0.1806,0.1813,0.1829,0.1844,0.1846,0.1865,0.1993,0.1997, 0.2012,0.2017,0.2017,0.2032,0.2044,0.2046,0.2133,0.2260,0.2275,0.2307, 0.2310,0.2325,0.2336,0.2349,0.2392,0.2557,0.2572,0.2598,0.2614,0.2641, 0.2671,0.2695,0.2700,0.2716,0.2755,0.2784,0.2794,0.2960,0.2993,0.3116, 0.3118,0.3162,0.3165,0.3171,0.3250,0.3257,0.3269,0.3355,0.3427,0.3479, 0.3557,0.3597,0.3618,0.3633,0.3635,0.3669,0.3673,0.3673,0.3706,0.3713, 0.3713,0.3856,0.3865,0.3870,0.3912,0.3921,0.3938,0.3958,0.3960,0.3968, 0.4037,0.4051,0.4084,0.4084,0.4087,0.4177,0.4180,0.4213,0.4275,0.4294, 0.4374,0.4499,0.4524,0.4548,0.4655,0.4710,0.4806,0.4808,0.4838,0.4860, 0.4937,0.4968,0.4978,0.4991,0.5000,0.5008,0.5025,0.5028,0.5058,0.5223, 0.5266,0.5361,0.5402,0.5421,0.5443,0.5468,0.5548,0.5598,0.5666,0.5668, 0.5783,0.5809,0.5833,0.5869,0.5879,0.5936,0.5977,0.5996,0.6007,0.6152, 0.6176,0.6187,0.6293,0.6306,0.6411,0.6440,0.6446,0.6472,0.6550,0.6558, 0.6563,0.6625,0.6781,0.6849,0.6897,0.6901,0.6910,0.6947,0.7023,0.7053, 0.7091,0.7102,0.7115,0.7128,0.7210,0.7217,0.7217,0.7294,0.7297,0.7328, 0.7341,0.7358,0.7362,0.7490,0.7533,0.7533,0.7566,0.7573,0.7588,0.7590, 0.7756,0.7784,0.7794,0.7843,0.7860,0.7880,0.7905,0.7946,0.7984,0.8048, 0.8073,0.8110,0.8242,0.8249,0.8256,0.8264,0.8374,0.8406,0.8444,0.8455, 0.8463,0.8468,0.8491,0.8495,0.8496,0.8500,0.8526,0.8531,0.8629,0.8637, 0.8660,0.8716,0.8779,0.8873,0.8887,0.8906,0.8949,0.9073,0.9102,0.9106, 0.9122,0.9231,0.9263,0.9352,0.9426,0.9436,0.9450,0.9550,0.9560,0.9614, 0.9625,0.9653,0.9713,0.9743,0.9760,0.9841,0.9866,0.9946,0.9972, Overall p-value after applying KStest on 269 p-values = 0.434393 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.