RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-03-16_23:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.84 15.8079 0.462509 2 to 25 15.74 15.5549 0.444422 3 to 26 15.50 30.6874 0.978207 4 to 27 15.59 24.7456 0.899450 5 to 28 15.76 11.2829 0.158517 6 to 29 15.59 17.6535 0.588988 7 to 30 15.94 9.5182 0.077411 8 to 31 15.50 36.9300 0.996561 9 to 32 15.68 18.9703 0.669763 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.289577 Tough bday spacings test for dh-ranFile-2018-03-16_23:31: 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 38 66 103 99 83 49 31 15 6 4 (O-E)^2/E 1.1 0.1 0.7 0.3 0.0 0.3 0.2 0.1 0.0 0.1 0.0 Birthday Spacings: Sum(O-E)^2/E= 2.763, p= 0.014 RESULTS OF GCD FOR dh-ranFile-2018-03-16_23:31 Euclid's algorithm: p-value, steps to gcd: 0.227560 p-value, dist. of gcd's: 0.004407 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-03-16_23:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.869 0.011 0.900 0.972 0.086 0.035 0.469 0.137 Bits 8 to 15---> 0.074 0.794 0.796 0.557 0.742 0.291 0.260 0.704 Bits 16 to 23---> 0.867 0.350 0.309 0.567 0.394 0.780 0.072 0.742 Bits 24 to 31---> 0.836 0.282 0.237 0.758 0.087 0.700 0.465 0.970 KS test for the above 32 p values: 0.223 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-03-16_23:31, p-values for 5 runs: 0.6041, 0.4885, 0.2004, 0.8683, 0.4735 Rank test for binary matrices (31x31) for dh-ranFile-2018-03-16_23:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 194 211.4 1.435 1.435 r= 29 5158 5134.0 0.112 1.547 r= 30 23084 23103.0 0.016 1.563 r= 31 11564 11551.5 0.013 1.576 chi-square = 1.576 with df = 3; p-value = 0.335 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-03-16_23:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 234 211.4 2.412 2.412 r= 30 5093 5134.0 0.328 2.740 r= 31 23103 23103.0 0.000 2.740 r= 32 11570 11551.5 0.030 2.769 chi-square = 2.769 with df = 3; p-value = 0.571 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-03-16_23:31 b-rank test for bits 1 to 8, p=0.75617 b-rank test for bits 2 to 9, p=0.10488 b-rank test for bits 3 to 10, p=0.41246 b-rank test for bits 4 to 11, p=0.43332 b-rank test for bits 5 to 12, p=0.19888 b-rank test for bits 6 to 13, p=0.08708 b-rank test for bits 7 to 14, p=0.67665 b-rank test for bits 8 to 15, p=0.00919 b-rank test for bits 9 to 16, p=0.96206 b-rank test for bits 10 to 17, p=0.43723 b-rank test for bits 11 to 18, p=0.22082 b-rank test for bits 12 to 19, p=0.74344 b-rank test for bits 13 to 20, p=0.90540 b-rank test for bits 14 to 21, p=0.10475 b-rank test for bits 15 to 22, p=0.07726 b-rank test for bits 16 to 23, p=0.49446 b-rank test for bits 17 to 24, p=0.44766 b-rank test for bits 18 to 25, p=0.47896 b-rank test for bits 19 to 26, p=0.55283 b-rank test for bits 20 to 27, p=0.67214 b-rank test for bits 21 to 28, p=0.33986 b-rank test for bits 22 to 29, p=0.58460 b-rank test for bits 23 to 30, p=0.21810 b-rank test for bits 24 to 31, p=0.94968 b-rank test for bits 25 to 32, p=0.55654 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 = 0.715934 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-03-16_23:31 (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 141237 -1.57 0.058107 2 142723 1.90 0.971355 3 141380 -1.24 0.108090 4 142313 0.94 0.827199 5 141969 0.14 0.555439 6 141511 -0.93 0.176010 7 141785 -0.29 0.385720 8 142109 0.47 0.679578 9 141082 -1.93 0.026617 10 142826 2.14 0.983893 11 142237 0.77 0.778038 12 142122 0.50 0.690368 13 141428 -1.12 0.130379 14 143025 2.61 0.995429 15 140943 -2.26 0.011980 16 142273 0.85 0.802253 17 141707 -0.47 0.318202 18 141600 -0.72 0.234922 19 141627 -0.66 0.254739 20 142281 0.87 0.807409 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-03-16_23:31 Bits used No. missing words z-score p-value 23 to 32 142220 1.0713 0.857977 22 to 31 142097 0.6471 0.741229 21 to 30 142488 1.9954 0.977001 20 to 29 142296 1.3333 0.908791 19 to 28 141740 -0.5839 0.279645 18 to 27 142048 0.4782 0.683736 17 to 26 142280 1.2782 0.899406 16 to 25 141845 -0.2218 0.412224 15 to 24 142323 1.4264 0.923131 14 to 23 142135 0.7782 0.781766 13 to 22 141970 0.2092 0.582857 12 to 21 142145 0.8127 0.791792 11 to 20 141955 0.1575 0.562568 10 to 19 142186 0.9540 0.829967 9 to 18 142309 1.3782 0.915925 8 to 17 141586 -1.1149 0.132440 7 to 16 141223 -2.3667 0.008975 6 to 15 141222 -2.3701 0.008892 5 to 14 141711 -0.6839 0.247020 4 to 13 141635 -0.9460 0.172083 3 to 12 141745 -0.5667 0.285474 2 to 11 142057 0.5092 0.694696 1 to 10 142216 1.0575 0.854854 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-03-16_23:31 Bits used No. missing words z-score p-value 28 to 32 142009 0.3379 0.632267 27 to 31 141959 0.1684 0.566855 26 to 30 141962 0.1785 0.570852 25 to 29 141827 -0.2791 0.390090 24 to 28 141499 -1.3909 0.082120 23 to 27 141801 -0.3672 0.356727 22 to 26 141528 -1.2926 0.098067 21 to 25 141918 0.0294 0.511723 20 to 24 141911 0.0057 0.502258 19 to 23 141905 -0.0147 0.494145 18 to 22 141867 -0.1435 0.442951 17 to 21 141941 0.1074 0.542747 16 to 20 141801 -0.3672 0.356727 15 to 19 141935 0.0870 0.534671 14 to 18 142424 1.7446 0.959477 13 to 17 141734 -0.5943 0.276143 12 to 16 141913 0.0124 0.504963 11 to 15 141897 -0.0418 0.483330 10 to 14 142007 0.3311 0.629710 9 to 13 142370 1.5616 0.940808 8 to 12 141309 -2.0350 0.020925 7 to 11 142121 0.7175 0.763475 6 to 10 141936 0.0904 0.536018 5 to 9 141935 0.0870 0.534671 4 to 8 141848 -0.2079 0.417654 3 to 7 141452 -1.5503 0.060538 2 to 6 141634 -0.9333 0.175327 1 to 5 141943 0.1141 0.545435 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-03-16_23:31 Bits used No. missing words z-score p-value 31 to 32 142066 0.4622 0.678014 30 to 31 141060 -2.5054 0.006116 29 to 30 141553 -1.0511 0.146602 28 to 29 142131 0.6539 0.743410 27 to 28 141553 -1.0511 0.146602 26 to 27 141877 -0.0954 0.462011 25 to 26 141807 -0.3019 0.381380 24 to 25 141507 -1.1868 0.117650 23 to 24 142215 0.9017 0.816387 22 to 23 141368 -1.5968 0.055150 21 to 22 142067 0.4651 0.679071 20 to 21 142186 0.8161 0.792789 19 to 20 141947 0.1111 0.544240 18 to 19 141876 -0.0983 0.460840 17 to 18 141501 -1.2045 0.114196 16 to 17 142068 0.4681 0.680127 15 to 16 142038 0.3796 0.647863 14 to 15 142389 1.4150 0.921459 13 to 14 142643 2.1642 0.984776 12 to 13 141983 0.2173 0.586019 11 to 12 142252 1.0108 0.843950 10 to 11 141977 0.1996 0.579110 9 to 10 141625 -0.8387 0.200810 8 to 9 142234 0.9577 0.830900 7 to 8 141404 -1.4906 0.068027 6 to 7 141704 -0.6057 0.272359 5 to 6 141773 -0.4022 0.343786 4 to 5 142361 1.3324 0.908629 3 to 4 141664 -0.7237 0.234629 2 to 3 142725 2.4061 0.991938 1 to 2 141340 -1.6794 0.046533 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-03-16_23:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2495.49 -0.064 0.474594 Test results for specific bytes for dh-ranFile-2018-03-16_23:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2515.77 0.223 0.588248 2 to 9 2520.65 0.292 0.614856 3 to 10 2443.90 -0.793 0.213761 4 to 11 2515.66 0.221 0.587611 5 to 12 2524.10 0.341 0.633377 6 to 13 2550.79 0.718 0.763710 7 to 14 2588.69 1.254 0.895132 8 to 15 2625.36 1.773 0.961868 9 to 16 2537.15 0.525 0.700354 10 to 17 2430.82 -0.978 0.163933 11 to 18 2596.19 1.360 0.913132 12 to 19 2502.87 0.041 0.516185 13 to 20 2498.34 -0.023 0.490659 14 to 21 2644.61 2.045 0.979578 15 to 22 2447.73 -0.739 0.229887 16 to 23 2387.00 -1.598 0.055008 17 to 24 2501.55 0.022 0.508732 18 to 25 2487.47 -0.177 0.429696 19 to 26 2448.08 -0.734 0.231374 20 to 27 2516.64 0.235 0.593036 21 to 28 2562.55 0.885 0.811826 22 to 29 2560.96 0.862 0.805675 23 to 30 2475.86 -0.341 0.366393 24 to 31 2415.10 -1.201 0.114951 25 to 32 2426.84 -1.035 0.150424 CDPARK for dh-ranFile-2018-03-16_23:31: 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 3502 -0.9589 0.168804 3511 -0.5479 0.291865 3524 0.0457 0.518210 3488 -1.5982 0.055002 3535 0.5479 0.708135 3511 -0.5479 0.291865 3494 -1.3242 0.092718 3545 1.0046 0.842447 3535 0.5479 0.708135 3541 0.8219 0.794438 Square side=100, avg. no. parked=3518.60 sample std.=19.23 p-value of the KSTEST for those 10 p-values: 0.805593 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-03-16_23:31 0.1809,0.3238,0.9742,0.8327,0.9561,0.6417,0.8009,0.7013,0.6106,0.2411, The KS test for those 10 p-values: 0.271066 The 3DSPHERES test for dh-ranFile-2018-03-16_23:31 sample no r^3 equiv. uni. 1 6.027 0.181995 2 15.767 0.408782 3 0.740 0.024354 4 24.505 0.558167 5 27.612 0.601641 6 63.559 0.879804 7 12.789 0.347080 8 10.611 0.297919 9 18.305 0.456739 10 53.304 0.830822 11 18.176 0.454401 12 18.094 0.452898 13 4.729 0.145844 14 53.518 0.832023 15 38.886 0.726432 16 16.049 0.414308 17 40.525 0.740973 18 5.435 0.165708 19 0.132 0.004394 20 41.950 0.752989 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.692534 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-03-16_23:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 -0.3 -0.4 -0.7 2.3 1.0 -1.1 -1.1 1.6 0.2 0.5 -1.8 -1.1 1.0 -1.3 -1.1 2.1 0.8 -0.7 -0.2 -0.2 1.3 1.3 -0.6 -0.2 -1.6 0.0 0.2 -0.1 -1.6 1.1 1.4 -0.5 0.0 1.6 0.1 -0.5 1.8 -0.8 -0.7 0.9 3.0 -0.1 Chi-square with 42 degrees of freedom:56.098589 z-score=1.538282, p-value=0.928479 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-03-16_23:31 Test no p-value 1 0.211641 2 0.358831 3 0.046476 4 0.500653 5 0.220128 6 0.200787 7 0.199843 8 0.248109 9 0.014010 10 0.007439 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000888 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-03-16_23:31: (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 66439 0.78 66583 0.11 3 25000.00 25172 1.18 25114 0.52 4 6666.67 6700 0.17 6601 0.65 5 1388.89 1402 0.12 1421 0.74 6 238.10 247 0.33 238 0.00 7 34.72 35 0.00 35 0.00 8 4.96 4 0.19 7 0.84 p=0.16317 p=0.17324 Number of rngs required: 688007, p-value: 0.324 RESULTS OF CRAPS TEST for dh-ranFile-2018-03-16_23:31 No. of wins: Observed Expected 98374 98585.9 z-score=-0.948, pvalue=0.17168 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66367 66666.7 1.347 1.347 2 37799 37654.3 0.556 1.903 3 26902 26954.7 0.103 2.006 4 19367 19313.5 0.148 2.154 5 13947 13851.4 0.660 2.814 6 9863 9943.5 0.652 3.466 7 7170 7145.0 0.087 3.554 8 5168 5139.1 0.163 3.717 9 3752 3699.9 0.735 4.451 10 2626 2666.3 0.609 5.060 11 1925 1923.3 0.001 5.062 12 1444 1388.7 2.199 7.261 13 1056 1003.7 2.724 9.984 14 692 726.1 1.605 11.589 15 554 525.8 1.508 13.098 16 363 381.2 0.864 13.962 17 280 276.5 0.043 14.005 18 205 200.8 0.087 14.092 19 142 146.0 0.109 14.201 20 98 106.2 0.635 14.836 21 280 287.1 0.176 15.012 Chisq= 15.01 for 20 degrees of freedom, p= 0.22430 SUMMARY of craptest p-value for no. of wins: 0.171678 p-value for throws/game: 0.224304 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-03-16_23:31 No. of wins: Observed Expected 98622 98585.9 z-score= 0.162, pvalue=0.56421 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66428 66666.7 0.854 0.854 2 37856 37654.3 1.080 1.935 3 27153 26954.7 1.458 3.393 4 19384 19313.5 0.258 3.651 5 13663 13851.4 2.563 6.214 6 9968 9943.5 0.060 6.274 7 7152 7145.0 0.007 6.281 8 5111 5139.1 0.153 6.434 9 3713 3699.9 0.047 6.481 10 2636 2666.3 0.344 6.825 11 1884 1923.3 0.804 7.629 12 1363 1388.7 0.477 8.106 13 1039 1003.7 1.240 9.347 14 741 726.1 0.304 9.651 15 538 525.8 0.281 9.932 16 413 381.2 2.661 12.593 17 254 276.5 1.837 14.431 18 172 200.8 4.139 18.569 19 138 146.0 0.437 19.006 20 103 106.2 0.097 19.103 21 291 287.1 0.053 19.156 Chisq= 19.16 for 20 degrees of freedom, p= 0.48828 SUMMARY of craptest p-value for no. of wins: 0.564207 p-value for throws/game: 0.488281 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0009,0.0044,0.0044,0.0061,0.0074,0.0089,0.0090,0.0092,0.0113,0.0120, 0.0135,0.0140,0.0209,0.0244,0.0266,0.0347,0.0465,0.0465,0.0550,0.0550, 0.0552,0.0581,0.0605,0.0680,0.0719,0.0737,0.0773,0.0774,0.0821,0.0862, 0.0871,0.0871,0.0927,0.0981,0.1048,0.1049,0.1081,0.1142,0.1150,0.1177, 0.1304,0.1324,0.1368,0.1458,0.1466,0.1466,0.1504,0.1585,0.1632,0.1639, 0.1657,0.1688,0.1717,0.1721,0.1732,0.1753,0.1760,0.1809,0.1820,0.1989, 0.1998,0.2004,0.2008,0.2008,0.2116,0.2138,0.2181,0.2201,0.2208,0.2232, 0.2243,0.2276,0.2299,0.2314,0.2346,0.2349,0.2368,0.2411,0.2470,0.2481, 0.2547,0.2600,0.2711,0.2724,0.2761,0.2796,0.2817,0.2855,0.2896,0.2910, 0.2919,0.2919,0.2979,0.3087,0.3182,0.3238,0.3241,0.3352,0.3399,0.3438, 0.3471,0.3500,0.3567,0.3567,0.3588,0.3664,0.3814,0.3857,0.3901,0.3945, 0.4088,0.4122,0.4125,0.4143,0.4177,0.4297,0.4333,0.4372,0.4430,0.4444, 0.4477,0.4529,0.4544,0.4567,0.4608,0.4620,0.4625,0.4650,0.4694,0.4735, 0.4746,0.4790,0.4833,0.4883,0.4885,0.4907,0.4941,0.4945,0.5007,0.5023, 0.5050,0.5087,0.5117,0.5162,0.5182,0.5347,0.5347,0.5360,0.5427,0.5442, 0.5454,0.5528,0.5554,0.5565,0.5566,0.5582,0.5626,0.5642,0.5666,0.5669, 0.5709,0.5714,0.5791,0.5829,0.5846,0.5860,0.5876,0.5882,0.5890,0.5930, 0.6016,0.6041,0.6106,0.6149,0.6297,0.6323,0.6334,0.6417,0.6479,0.6698, 0.6721,0.6767,0.6780,0.6791,0.6796,0.6801,0.6837,0.6904,0.6925,0.6947, 0.6999,0.7004,0.7013,0.7038,0.7081,0.7081,0.7159,0.7264,0.7410,0.7412, 0.7418,0.7421,0.7434,0.7434,0.7530,0.7562,0.7584,0.7635,0.7637,0.7780, 0.7804,0.7818,0.7918,0.7928,0.7944,0.7944,0.7961,0.8009,0.8023,0.8056, 0.8057,0.8074,0.8118,0.8164,0.8272,0.8300,0.8308,0.8309,0.8320,0.8327, 0.8364,0.8424,0.8440,0.8549,0.8580,0.8666,0.8683,0.8688,0.8798,0.8951, 0.8994,0.8994,0.8996,0.9054,0.9086,0.9088,0.9131,0.9159,0.9215,0.9231, 0.9285,0.9408,0.9497,0.9561,0.9595,0.9619,0.9621,0.9700,0.9714,0.9722, 0.9742,0.9770,0.9782,0.9796,0.9839,0.9848,0.9919,0.9954,0.9966, Overall p-value after applying KStest on 269 p-values = 0.345599 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.