RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-04-06_03:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.92 9.8363 0.089664 2 to 25 15.82 13.1656 0.274966 3 to 26 15.68 9.2861 0.069145 4 to 27 15.55 32.6870 0.987654 5 to 28 15.53 26.0160 0.925830 6 to 29 15.60 18.9511 0.668653 7 to 30 15.55 21.0822 0.777363 8 to 31 15.64 20.1060 0.731157 9 to 32 15.53 19.8885 0.720028 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.385055 Tough bday spacings test for dh-ranFile-2018-04-06_03:31: 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 13 36 72 89 79 78 53 45 18 9 8 (O-E)^2/E 1.6 0.0 0.0 0.8 3.6 0.0 0.0 7.8 0.7 0.9 3.8 Birthday Spacings: Sum(O-E)^2/E= 19.114, p= 0.961 RESULTS OF GCD FOR dh-ranFile-2018-04-06_03:31 Euclid's algorithm: p-value, steps to gcd: 0.410617 p-value, dist. of gcd's: 0.394652 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-04-06_03:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.859 0.896 0.223 0.642 0.982 0.391 0.243 0.934 Bits 8 to 15---> 0.490 0.179 0.969 0.230 0.306 0.534 0.919 0.276 Bits 16 to 23---> 0.145 0.651 0.603 0.172 0.258 0.630 0.513 0.634 Bits 24 to 31---> 0.433 0.780 0.303 0.309 0.222 0.973 0.444 0.948 KS test for the above 32 p values: 0.693 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-04-06_03:31, p-values for 5 runs: 0.1501, 0.6423, 0.3143, 0.2922, 0.4383 Rank test for binary matrices (31x31) for dh-ranFile-2018-04-06_03:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 229 211.4 1.462 1.462 r= 29 5075 5134.0 0.678 2.140 r= 30 23331 23103.0 2.249 4.390 r= 31 11365 11551.5 3.012 7.401 chi-square = 7.401 with df = 3; p-value = 0.940 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-04-06_03:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 207 211.4 0.092 0.092 r= 30 5180 5134.0 0.412 0.504 r= 31 23021 23103.0 0.291 0.796 r= 32 11592 11551.5 0.142 0.937 chi-square = 0.937 with df = 3; p-value = 0.184 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-04-06_03:31 b-rank test for bits 1 to 8, p=0.90208 b-rank test for bits 2 to 9, p=0.50637 b-rank test for bits 3 to 10, p=0.41847 b-rank test for bits 4 to 11, p=0.24004 b-rank test for bits 5 to 12, p=0.53782 b-rank test for bits 6 to 13, p=0.59643 b-rank test for bits 7 to 14, p=0.49692 b-rank test for bits 8 to 15, p=0.66656 b-rank test for bits 9 to 16, p=0.67677 b-rank test for bits 10 to 17, p=0.79386 b-rank test for bits 11 to 18, p=0.35010 b-rank test for bits 12 to 19, p=0.74442 b-rank test for bits 13 to 20, p=0.53458 b-rank test for bits 14 to 21, p=0.64419 b-rank test for bits 15 to 22, p=0.72590 b-rank test for bits 16 to 23, p=0.36087 b-rank test for bits 17 to 24, p=0.50675 b-rank test for bits 18 to 25, p=0.85082 b-rank test for bits 19 to 26, p=0.62721 b-rank test for bits 20 to 27, p=0.56962 b-rank test for bits 21 to 28, p=0.90627 b-rank test for bits 22 to 29, p=0.64854 b-rank test for bits 23 to 30, p=0.97627 b-rank test for bits 24 to 31, p=0.81388 b-rank test for bits 25 to 32, p=0.57842 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 = 0.014514 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-04-06_03:31 (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 141825 -0.20 0.421901 2 141720 -0.44 0.329114 3 141834 -0.18 0.430145 4 142411 1.17 0.879427 5 141482 -1.00 0.159034 6 141780 -0.30 0.381260 7 141944 0.08 0.532281 8 141632 -0.65 0.258503 9 142413 1.18 0.880362 10 141505 -0.94 0.172407 11 143114 2.81 0.997558 12 142335 0.99 0.840024 13 142136 0.53 0.701806 14 142179 0.63 0.735676 15 142090 0.42 0.663534 16 141962 0.12 0.548971 17 142283 0.87 0.808685 18 142312 0.94 0.826601 19 141946 0.09 0.534139 20 141844 -0.15 0.439341 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-04-06_03:31 Bits used No. missing words z-score p-value 23 to 32 142199 0.9989 0.841069 22 to 31 141478 -1.4873 0.068462 21 to 30 141791 -0.4080 0.341624 20 to 29 142154 0.8437 0.800579 19 to 28 141884 -0.0873 0.465199 18 to 27 141648 -0.9011 0.183758 17 to 26 142059 0.5161 0.697109 16 to 25 142344 1.4989 0.933045 15 to 24 142160 0.8644 0.806310 14 to 23 141843 -0.2287 0.409542 13 to 22 142333 1.4609 0.927983 12 to 21 141792 -0.4046 0.342891 11 to 20 141962 0.1816 0.572060 10 to 19 141940 0.1058 0.542113 9 to 18 141523 -1.3322 0.091402 8 to 17 141927 0.0609 0.524293 7 to 16 141642 -0.9218 0.178309 6 to 15 142228 1.0989 0.864086 5 to 14 142081 0.5920 0.723063 4 to 13 141708 -0.6942 0.243765 3 to 12 141443 -1.6080 0.053914 2 to 11 142225 1.0885 0.861817 1 to 10 141909 -0.0011 0.499546 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-04-06_03:31 Bits used No. missing words z-score p-value 28 to 32 142360 1.5277 0.936706 27 to 31 142006 0.3277 0.628429 26 to 30 142294 1.3040 0.903877 25 to 29 141931 0.0735 0.529279 24 to 28 142018 0.3684 0.643702 23 to 27 142295 1.3074 0.904454 22 to 26 142185 0.9345 0.824970 21 to 25 142033 0.4192 0.662473 20 to 24 141528 -1.2926 0.098067 19 to 23 141713 -0.6655 0.252857 18 to 22 141557 -1.1943 0.116173 17 to 21 141838 -0.2418 0.404469 16 to 20 141715 -0.6587 0.255030 15 to 19 141933 0.0802 0.531976 14 to 18 142206 1.0057 0.842711 13 to 17 141423 -1.6486 0.049617 12 to 16 142126 0.7345 0.768670 11 to 15 141462 -1.5164 0.064713 10 to 14 142034 0.4226 0.663710 9 to 13 141699 -0.7130 0.237928 8 to 12 142247 1.1446 0.873822 7 to 11 141892 -0.0587 0.476577 6 to 10 141710 -0.6757 0.249617 5 to 9 142389 1.6260 0.948025 4 to 8 142070 0.5446 0.707001 3 to 7 142230 1.0870 0.861485 2 to 6 142389 1.6260 0.948025 1 to 5 141725 -0.6248 0.266036 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-04-06_03:31 Bits used No. missing words z-score p-value 31 to 32 142624 2.1082 0.982492 30 to 31 141673 -0.6971 0.242858 29 to 30 141537 -1.0983 0.136033 28 to 29 141996 0.2557 0.600895 27 to 28 142192 0.8338 0.797813 26 to 27 142873 2.8427 0.997763 25 to 26 142112 0.5978 0.725029 24 to 25 141941 0.0934 0.537216 23 to 24 142351 1.3029 0.903689 22 to 23 142264 1.0462 0.852271 21 to 22 142586 1.9961 0.977037 20 to 21 142005 0.2822 0.611110 19 to 20 142272 1.0698 0.857651 18 to 19 142316 1.1996 0.884856 17 to 18 141101 -2.3845 0.008552 16 to 17 141910 0.0020 0.500789 15 to 16 142094 0.5447 0.707037 14 to 15 142599 2.0344 0.979046 13 to 14 142186 0.8161 0.792789 12 to 13 141740 -0.4995 0.308714 11 to 12 141360 -1.6204 0.052569 10 to 11 141848 -0.1809 0.428217 9 to 10 141966 0.1672 0.566381 8 to 9 141956 0.1377 0.554749 7 to 8 141947 0.1111 0.544240 6 to 7 142050 0.4150 0.660913 5 to 6 141330 -1.7089 0.043731 4 to 5 142642 2.1613 0.984663 3 to 4 141655 -0.7502 0.226556 2 to 3 141578 -0.9774 0.164192 1 to 2 141797 -0.3314 0.370187 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-04-06_03:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2507.95 0.112 0.544760 Test results for specific bytes for dh-ranFile-2018-04-06_03:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2446.85 -0.752 0.226148 2 to 9 2439.14 -0.861 0.194694 3 to 10 2562.22 0.880 0.810541 4 to 11 2561.20 0.866 0.806636 5 to 12 2546.89 0.663 0.746360 6 to 13 2544.78 0.633 0.736717 7 to 14 2480.92 -0.270 0.393629 8 to 15 2523.64 0.334 0.630916 9 to 16 2464.14 -0.507 0.306008 10 to 17 2534.86 0.493 0.688980 11 to 18 2372.17 -1.808 0.035320 12 to 19 2471.21 -0.407 0.341930 13 to 20 2646.20 2.068 0.980657 14 to 21 2448.76 -0.725 0.234322 15 to 22 2526.73 0.378 0.647270 16 to 23 2465.01 -0.495 0.310338 17 to 24 2422.95 -1.090 0.137933 18 to 25 2478.66 -0.302 0.381407 19 to 26 2478.68 -0.302 0.381514 20 to 27 2455.70 -0.627 0.265478 21 to 28 2615.52 1.634 0.948845 22 to 29 2477.06 -0.324 0.372831 23 to 30 2412.81 -1.233 0.108773 24 to 31 2465.91 -0.482 0.314855 25 to 32 2520.66 0.292 0.614933 CDPARK for dh-ranFile-2018-04-06_03:31: 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 3529 0.2740 0.607947 3514 -0.4110 0.340551 3514 -0.4110 0.340551 3522 -0.0457 0.481790 3543 0.9132 0.819442 3503 -0.9132 0.180558 3504 -0.8676 0.192812 3529 0.2740 0.607947 3518 -0.2283 0.409702 3516 -0.3196 0.374623 Square side=100, avg. no. parked=3519.20 sample std.=11.51 p-value of the KSTEST for those 10 p-values: 0.345607 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-04-06_03:31 0.7520,0.2045,0.2172,0.9420,0.3761,0.3522,0.9680,0.6428,0.7607,0.7501, The KS test for those 10 p-values: 0.435138 The 3DSPHERES test for dh-ranFile-2018-04-06_03:31 sample no r^3 equiv. uni. 1 55.847 0.844570 2 20.741 0.499117 3 46.805 0.789900 4 50.963 0.817090 5 27.383 0.598585 6 26.835 0.591192 7 15.847 0.410354 8 66.849 0.892290 9 70.411 0.904347 10 30.293 0.635697 11 69.805 0.902397 12 11.499 0.318386 13 52.855 0.828273 14 9.694 0.276117 15 54.787 0.838979 16 22.401 0.526067 17 6.066 0.183058 18 2.877 0.091451 19 39.980 0.736228 20 36.939 0.708087 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.080131 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-04-06_03:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 2.0 -0.3 1.3 -1.3 1.3 0.4 -0.2 0.1 0.6 2.3 -0.2 1.3 -1.4 0.0 0.5 0.5 -0.3 -0.5 -0.1 0.7 -2.8 -0.9 0.2 -0.2 -1.0 1.1 -0.2 1.4 -0.4 2.0 1.0 1.3 0.7 -0.6 -0.9 1.0 -1.9 -0.1 0.1 -0.1 -0.6 -1.0 -1.1 Chi-square with 42 degrees of freedom:48.427962 z-score=0.701348, p-value=0.770470 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-04-06_03:31 Test no p-value 1 0.607691 2 0.640388 3 0.834062 4 0.631492 5 0.398422 6 0.182741 7 0.381544 8 0.012364 9 0.649925 10 0.976768 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.808739 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-04-06_03:31: (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 66702 0.02 66744 0.09 3 25000.00 24877 0.61 24835 1.09 4 6666.67 6689 0.07 6658 0.01 5 1388.89 1400 0.09 1467 4.39 6 238.10 274 5.41 247 0.33 7 34.72 49 5.87 43 1.97 8 4.96 8 1.86 5 0.00 p=0.96967 p=0.75379 Number of rngs required: 689228, p-value: 0.830 RESULTS OF CRAPS TEST for dh-ranFile-2018-04-06_03:31 No. of wins: Observed Expected 98666 98585.9 z-score= 0.358, pvalue=0.63999 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66879 66666.7 0.676 0.676 2 37703 37654.3 0.063 0.739 3 26754 26954.7 1.495 2.234 4 19219 19313.5 0.462 2.696 5 13972 13851.4 1.050 3.746 6 9892 9943.5 0.267 4.013 7 7181 7145.0 0.181 4.194 8 5069 5139.1 0.955 5.150 9 3678 3699.9 0.129 5.279 10 2702 2666.3 0.478 5.757 11 1895 1923.3 0.417 6.174 12 1376 1388.7 0.117 6.291 13 1033 1003.7 0.854 7.145 14 706 726.1 0.559 7.704 15 530 525.8 0.033 7.737 16 371 381.2 0.270 8.007 17 252 276.5 2.178 10.185 18 214 200.8 0.864 11.049 19 150 146.0 0.110 11.159 20 112 106.2 0.315 11.474 21 312 287.1 2.157 13.631 Chisq= 13.63 for 20 degrees of freedom, p= 0.15130 SUMMARY of craptest p-value for no. of wins: 0.639993 p-value for throws/game: 0.151303 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-04-06_03:31 No. of wins: Observed Expected 98505 98585.9 z-score=-0.362, pvalue=0.35881 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66738 66666.7 0.076 0.076 2 37531 37654.3 0.404 0.480 3 26801 26954.7 0.877 1.357 4 19406 19313.5 0.443 1.800 5 13829 13851.4 0.036 1.837 6 9989 9943.5 0.208 2.044 7 7023 7145.0 2.084 4.128 8 5226 5139.1 1.470 5.599 9 3672 3699.9 0.210 5.809 10 2783 2666.3 5.108 10.917 11 1949 1923.3 0.343 11.259 12 1407 1388.7 0.240 11.499 13 1006 1003.7 0.005 11.505 14 727 726.1 0.001 11.506 15 533 525.8 0.098 11.603 16 373 381.2 0.174 11.778 17 246 276.5 3.373 15.150 18 204 200.8 0.050 15.200 19 156 146.0 0.687 15.887 20 108 106.2 0.030 15.917 21 293 287.1 0.121 16.038 Chisq= 16.04 for 20 degrees of freedom, p= 0.28574 SUMMARY of craptest p-value for no. of wins: 0.358808 p-value for throws/game: 0.285739 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0086,0.0124,0.0145,0.0353,0.0437,0.0496,0.0526,0.0539,0.0647,0.0685, 0.0691,0.0801,0.0897,0.0914,0.0915,0.0981,0.1088,0.1162,0.1360,0.1379, 0.1446,0.1501,0.1513,0.1590,0.1642,0.1719,0.1724,0.1783,0.1791,0.1806, 0.1827,0.1831,0.1836,0.1838,0.1928,0.1947,0.2045,0.2172,0.2220,0.2227, 0.2261,0.2266,0.2296,0.2343,0.2379,0.2400,0.2429,0.2433,0.2438,0.2496, 0.2529,0.2550,0.2576,0.2585,0.2655,0.2660,0.2750,0.2761,0.2764,0.2857, 0.2922,0.3027,0.3060,0.3060,0.3085,0.3087,0.3103,0.3143,0.3149,0.3184, 0.3291,0.3406,0.3406,0.3416,0.3419,0.3429,0.3456,0.3501,0.3522,0.3588, 0.3609,0.3702,0.3728,0.3746,0.3761,0.3813,0.3814,0.3815,0.3815,0.3851, 0.3909,0.3936,0.3947,0.3984,0.4045,0.4095,0.4097,0.4104,0.4106,0.4185, 0.4219,0.4282,0.4301,0.4330,0.4351,0.4383,0.4393,0.4445,0.4652,0.4766, 0.4818,0.4900,0.4969,0.4991,0.4995,0.5008,0.5064,0.5068,0.5133,0.5243, 0.5261,0.5293,0.5320,0.5323,0.5338,0.5341,0.5346,0.5372,0.5378,0.5421, 0.5442,0.5448,0.5490,0.5547,0.5664,0.5696,0.5721,0.5784,0.5912,0.5964, 0.5986,0.6009,0.6028,0.6077,0.6079,0.6079,0.6111,0.6149,0.6272,0.6284, 0.6299,0.6309,0.6315,0.6340,0.6357,0.6400,0.6404,0.6421,0.6423,0.6428, 0.6437,0.6442,0.6473,0.6485,0.6499,0.6513,0.6609,0.6625,0.6635,0.6637, 0.6666,0.6687,0.6768,0.6890,0.6933,0.6971,0.7018,0.7070,0.7070,0.7081, 0.7200,0.7231,0.7250,0.7259,0.7312,0.7357,0.7362,0.7367,0.7444,0.7464, 0.7501,0.7520,0.7538,0.7607,0.7687,0.7705,0.7774,0.7799,0.7899,0.7928, 0.7939,0.7978,0.8006,0.8063,0.8066,0.8087,0.8087,0.8105,0.8139,0.8171, 0.8194,0.8250,0.8266,0.8283,0.8303,0.8341,0.8390,0.8400,0.8411,0.8427, 0.8446,0.8508,0.8523,0.8577,0.8590,0.8615,0.8618,0.8641,0.8738,0.8794, 0.8804,0.8849,0.8923,0.8965,0.9021,0.9024,0.9037,0.9039,0.9043,0.9045, 0.9063,0.9186,0.9258,0.9280,0.9330,0.9337,0.9367,0.9399,0.9420,0.9478, 0.9480,0.9480,0.9488,0.9612,0.9680,0.9688,0.9697,0.9729,0.9763,0.9768, 0.9770,0.9790,0.9807,0.9816,0.9825,0.9847,0.9877,0.9976,0.9978, Overall p-value after applying KStest on 269 p-values = 0.006393 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.