RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-08-17_15:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.63 22.8429 0.845566 2 to 25 15.56 21.6222 0.800313 3 to 26 15.49 24.9137 0.903343 4 to 27 15.46 32.0092 0.984992 5 to 28 15.70 16.3043 0.497625 6 to 29 15.54 27.2031 0.944845 7 to 30 15.99 13.2891 0.283369 8 to 31 16.02 22.5049 0.833925 9 to 32 16.16 15.8420 0.464935 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.021025 Tough bday spacings test for dh-ranFile-2016-08-17_15:31: 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 33 77 97 94 79 65 24 13 4 1 (O-E)^2/E 1.6 0.4 0.2 0.0 0.1 0.0 3.2 1.1 0.2 1.0 2.3 Birthday Spacings: Sum(O-E)^2/E= 10.214, p= 0.578 RESULTS OF GCD FOR dh-ranFile-2016-08-17_15:31 Euclid's algorithm: p-value, steps to gcd: 0.290614 p-value, dist. of gcd's: 0.973162 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-08-17_15:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.247 0.952 0.618 0.857 0.097 0.171 0.476 0.318 Bits 8 to 15---> 0.150 0.668 0.966 0.585 0.337 0.101 0.120 0.606 Bits 16 to 23---> 0.046 0.006 0.088 0.020 0.566 0.478 0.020 0.187 Bits 24 to 31---> 0.932 0.331 0.761 0.363 0.496 0.712 0.115 0.121 KS test for the above 32 p values: 0.966 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-08-17_15:31, p-values for 5 runs: 0.1932, 0.2882, 0.5744, 0.9409, 0.7581 Rank test for binary matrices (31x31) for dh-ranFile-2016-08-17_15:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 196 211.4 1.124 1.124 r= 29 5087 5134.0 0.430 1.555 r= 30 23019 23103.0 0.306 1.861 r= 31 11698 11551.5 1.857 3.718 chi-square = 3.718 with df = 3; p-value = 0.706 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-08-17_15:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 204 211.4 0.260 0.260 r= 30 5076 5134.0 0.655 0.916 r= 31 23191 23103.0 0.335 1.251 r= 32 11529 11551.5 0.044 1.295 chi-square = 1.295 with df = 3; p-value = 0.270 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-08-17_15:31 b-rank test for bits 1 to 8, p=0.73903 b-rank test for bits 2 to 9, p=0.87095 b-rank test for bits 3 to 10, p=0.47195 b-rank test for bits 4 to 11, p=0.52148 b-rank test for bits 5 to 12, p=0.19937 b-rank test for bits 6 to 13, p=0.12993 b-rank test for bits 7 to 14, p=0.37752 b-rank test for bits 8 to 15, p=0.90540 b-rank test for bits 9 to 16, p=0.41860 b-rank test for bits 10 to 17, p=0.94790 b-rank test for bits 11 to 18, p=0.73588 b-rank test for bits 12 to 19, p=0.66864 b-rank test for bits 13 to 20, p=0.95428 b-rank test for bits 14 to 21, p=0.97842 b-rank test for bits 15 to 22, p=0.83520 b-rank test for bits 16 to 23, p=0.87415 b-rank test for bits 17 to 24, p=0.06143 b-rank test for bits 18 to 25, p=0.18177 b-rank test for bits 19 to 26, p=0.16019 b-rank test for bits 20 to 27, p=0.39267 b-rank test for bits 21 to 28, p=0.88964 b-rank test for bits 22 to 29, p=0.87347 b-rank test for bits 23 to 30, p=0.96533 b-rank test for bits 24 to 31, p=0.82313 b-rank test for bits 25 to 32, p=0.40388 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 = 0.039274 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-08-17_15:31 (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 142443 1.25 0.893782 2 141714 -0.46 0.324059 3 141264 -1.51 0.065805 4 141628 -0.66 0.255490 5 141373 -1.25 0.105083 6 141845 -0.15 0.440263 7 142175 0.62 0.732610 8 142139 0.54 0.704232 9 141600 -0.72 0.234922 10 141169 -1.73 0.041838 11 141946 0.09 0.534139 12 141742 -0.39 0.347914 13 142312 0.94 0.826601 14 141421 -1.14 0.126944 15 142050 0.33 0.628797 16 142242 0.78 0.781499 17 142037 0.30 0.617261 18 141803 -0.25 0.401899 19 142411 1.17 0.879427 20 142389 1.12 0.868797 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-08-17_15:31 Bits used No. missing words z-score p-value 23 to 32 141768 -0.4873 0.313007 22 to 31 141891 -0.0632 0.474801 21 to 30 141707 -0.6977 0.242686 20 to 29 142154 0.8437 0.800579 19 to 28 141541 -1.2701 0.102024 18 to 27 142195 0.9851 0.837705 17 to 26 141521 -1.3391 0.090274 16 to 25 141662 -0.8529 0.196868 15 to 24 142086 0.6092 0.728806 14 to 23 142049 0.4816 0.684962 13 to 22 141646 -0.9080 0.181930 12 to 21 141983 0.2540 0.600266 11 to 20 141665 -0.8425 0.199749 10 to 19 142563 2.2540 0.987903 9 to 18 141621 -0.9942 0.160053 8 to 17 141896 -0.0460 0.481669 7 to 16 142112 0.6989 0.757681 6 to 15 142315 1.3989 0.919073 5 to 14 141946 0.1264 0.550312 4 to 13 141675 -0.8080 0.209535 3 to 12 141464 -1.5356 0.062316 2 to 11 141770 -0.4804 0.315454 1 to 10 141457 -1.5598 0.059408 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-08-17_15:31 Bits used No. missing words z-score p-value 28 to 32 142556 2.1921 0.985814 27 to 31 141565 -1.1672 0.121561 26 to 30 141990 0.2735 0.607749 25 to 29 141896 -0.0452 0.481979 24 to 28 142174 0.8972 0.815190 23 to 27 142024 0.3887 0.651255 22 to 26 141829 -0.2723 0.392694 21 to 25 141748 -0.5469 0.292230 20 to 24 141891 -0.0621 0.475227 19 to 23 142220 1.0531 0.853857 18 to 22 141767 -0.4825 0.314734 17 to 21 141814 -0.3232 0.373290 16 to 20 141736 -0.5876 0.278414 15 to 19 141466 -1.5028 0.066444 14 to 18 141728 -0.6147 0.269384 13 to 17 141853 -0.1909 0.424283 12 to 16 141903 -0.0215 0.491440 11 to 15 142009 0.3379 0.632267 10 to 14 141589 -1.0859 0.138770 9 to 13 141943 0.1141 0.545435 8 to 12 141833 -0.2587 0.397916 7 to 11 142026 0.3955 0.653760 6 to 10 142035 0.4260 0.664946 5 to 9 141633 -0.9367 0.174453 4 to 8 141961 0.1752 0.569520 3 to 7 142087 0.6023 0.726503 2 to 6 141964 0.1853 0.573512 1 to 5 142351 1.4972 0.932828 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-08-17_15:31 Bits used No. missing words z-score p-value 31 to 32 141539 -1.0924 0.137325 30 to 31 142569 1.9459 0.974168 29 to 30 142158 0.7335 0.768385 28 to 29 141789 -0.3550 0.361311 27 to 28 141823 -0.2547 0.399493 26 to 27 142155 0.7247 0.765679 25 to 26 141420 -1.4435 0.074447 24 to 25 141958 0.1436 0.557080 23 to 24 142055 0.4297 0.666295 22 to 23 141498 -1.2134 0.112496 21 to 22 142613 2.0757 0.981040 20 to 21 142237 0.9666 0.833123 19 to 20 142041 0.3884 0.651143 18 to 19 141219 -2.0364 0.020857 17 to 18 142555 1.9046 0.971586 16 to 17 142177 0.7896 0.785116 15 to 16 142180 0.7984 0.787691 14 to 15 142121 0.6244 0.733816 13 to 14 142420 1.5064 0.934018 12 to 13 141591 -0.9390 0.173859 11 to 12 141516 -1.1603 0.122970 10 to 11 141702 -0.6116 0.270404 9 to 10 141502 -1.2016 0.114766 8 to 9 142212 0.8928 0.814026 7 to 8 142139 0.6775 0.750953 6 to 7 141812 -0.2871 0.387014 5 to 6 141977 0.1996 0.579110 4 to 5 141797 -0.3314 0.370187 3 to 4 142037 0.3766 0.646767 2 to 3 142805 2.6421 0.995880 1 to 2 142350 1.2999 0.903184 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-08-17_15:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2531.72 0.449 0.673159 Test results for specific bytes for dh-ranFile-2016-08-17_15:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2536.35 0.514 0.696418 2 to 9 2531.36 0.444 0.671313 3 to 10 2458.24 -0.591 0.277402 4 to 11 2458.81 -0.583 0.280090 5 to 12 2556.00 0.792 0.785805 6 to 13 2515.27 0.216 0.585466 7 to 14 2415.28 -1.198 0.115421 8 to 15 2527.12 0.384 0.649337 9 to 16 2516.66 0.236 0.593127 10 to 17 2432.94 -0.948 0.171460 11 to 18 2543.71 0.618 0.731758 12 to 19 2504.31 0.061 0.524276 13 to 20 2485.95 -0.199 0.421250 14 to 21 2525.47 0.360 0.640639 15 to 22 2569.44 0.982 0.836966 16 to 23 2487.36 -0.179 0.429061 17 to 24 2549.47 0.700 0.757915 18 to 25 2495.69 -0.061 0.475711 19 to 26 2473.42 -0.376 0.353501 20 to 27 2669.40 2.396 0.991706 21 to 28 2561.44 0.869 0.807529 22 to 29 2419.64 -1.136 0.127890 23 to 30 2570.68 1.000 0.841240 24 to 31 2499.77 -0.003 0.498690 25 to 32 2455.68 -0.627 0.265393 CDPARK for dh-ranFile-2016-08-17_15:31: 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 3513 -0.4566 0.323972 3526 0.1370 0.554479 3500 -1.0502 0.146807 3540 0.7763 0.781201 3482 -1.8721 0.030593 3530 0.3196 0.625377 3539 0.7306 0.767486 3519 -0.1826 0.427537 3498 -1.1416 0.126820 3527 0.1826 0.572463 Square side=100, avg. no. parked=3517.40 sample std.=18.05 p-value of the KSTEST for those 10 p-values: 0.714876 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-08-17_15:31 0.9814,0.0484,0.6748,0.8078,0.8866,0.2941,0.5849,0.3774,0.0415,0.1767, The KS test for those 10 p-values: 0.875113 The 3DSPHERES test for dh-ranFile-2016-08-17_15:31 sample no r^3 equiv. uni. 1 10.353 0.291854 2 1.122 0.036711 3 19.824 0.483555 4 13.777 0.368241 5 24.554 0.558891 6 7.437 0.219567 7 9.106 0.261783 8 31.060 0.644892 9 1.509 0.049065 10 35.079 0.689415 11 8.161 0.238178 12 17.322 0.438637 13 8.429 0.244938 14 3.213 0.101560 15 16.208 0.417399 16 5.964 0.180289 17 141.987 0.991199 18 5.396 0.164618 19 57.652 0.853645 20 109.871 0.974328 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.212501 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-08-17_15:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.5 -1.8 0.8 0.0 0.5 0.7 -0.4 2.1 1.4 1.0 -0.7 1.4 -0.2 -0.9 1.0 -0.9 -0.9 -0.5 0.6 -1.8 0.1 1.3 -1.2 0.2 0.6 0.4 -2.8 1.8 0.4 -0.6 -0.7 0.6 0.4 0.2 0.4 1.0 0.5 -0.4 0.4 0.9 1.0 0.8 Chi-square with 42 degrees of freedom:42.962416 z-score=0.105008, p-value=0.570207 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-08-17_15:31 Test no p-value 1 0.001250 2 0.645592 3 0.428602 4 0.079257 5 0.043243 6 0.060772 7 0.482441 8 0.559943 9 0.406079 10 0.055584 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.007153 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-08-17_15:31: (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 66490 0.47 66541 0.24 3 25000.00 25015 0.01 25054 0.12 4 6666.67 6788 2.21 6741 0.83 5 1388.89 1414 0.45 1375 0.14 6 238.10 242 0.06 256 1.35 7 34.72 40 0.80 28 1.30 8 4.96 10 5.12 4 0.19 p=0.83347 p=0.34417 Number of rngs required: 688142, p-value: 0.382 RESULTS OF CRAPS TEST for dh-ranFile-2016-08-17_15:31 No. of wins: Observed Expected 98858 98585.9 z-score= 1.217, pvalue=0.88823 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66726 66666.7 0.053 0.053 2 37609 37654.3 0.055 0.107 3 26824 26954.7 0.634 0.741 4 19412 19313.5 0.503 1.244 5 13903 13851.4 0.192 1.436 6 9783 9943.5 2.592 4.028 7 7321 7145.0 4.334 8.362 8 5191 5139.1 0.525 8.887 9 3659 3699.9 0.451 9.338 10 2644 2666.3 0.186 9.525 11 1838 1923.3 3.786 13.311 12 1437 1388.7 1.677 14.988 13 992 1003.7 0.137 15.124 14 715 726.1 0.171 15.295 15 527 525.8 0.003 15.298 16 360 381.2 1.174 16.471 17 291 276.5 0.756 17.228 18 218 200.8 1.468 18.696 19 163 146.0 1.983 20.679 20 120 106.2 1.789 22.468 21 267 287.1 1.409 23.877 Chisq= 23.88 for 20 degrees of freedom, p= 0.75219 SUMMARY of craptest p-value for no. of wins: 0.888231 p-value for throws/game: 0.752195 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-08-17_15:31 No. of wins: Observed Expected 98435 98585.9 z-score=-0.675, pvalue=0.24992 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66613 66666.7 0.043 0.043 2 37614 37654.3 0.043 0.086 3 27122 26954.7 1.038 1.124 4 19365 19313.5 0.138 1.262 5 13893 13851.4 0.125 1.387 6 9744 9943.5 4.004 5.391 7 7040 7145.0 1.544 6.935 8 5153 5139.1 0.038 6.973 9 3693 3699.9 0.013 6.985 10 2743 2666.3 2.207 9.192 11 1955 1923.3 0.522 9.713 12 1422 1388.7 0.797 10.510 13 1024 1003.7 0.410 10.920 14 695 726.1 1.335 12.255 15 547 525.8 0.852 13.107 16 395 381.2 0.503 13.610 17 249 276.5 2.743 16.353 18 184 200.8 1.410 17.763 19 158 146.0 0.989 18.752 20 113 106.2 0.433 19.186 21 278 287.1 0.289 19.475 Chisq= 19.48 for 20 degrees of freedom, p= 0.50883 SUMMARY of craptest p-value for no. of wins: 0.249924 p-value for throws/game: 0.508830 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0013,0.0062,0.0072,0.0197,0.0205,0.0209,0.0210,0.0306,0.0367,0.0393, 0.0415,0.0418,0.0432,0.0463,0.0484,0.0491,0.0556,0.0594,0.0608,0.0614, 0.0623,0.0658,0.0664,0.0744,0.0793,0.0879,0.0903,0.0971,0.1013,0.1016, 0.1020,0.1051,0.1125,0.1147,0.1148,0.1154,0.1195,0.1214,0.1216,0.1230, 0.1268,0.1269,0.1279,0.1299,0.1373,0.1388,0.1468,0.1500,0.1601,0.1602, 0.1646,0.1713,0.1715,0.1739,0.1745,0.1767,0.1803,0.1818,0.1819,0.1866, 0.1932,0.1969,0.1994,0.1997,0.2095,0.2125,0.2196,0.2349,0.2382,0.2427, 0.2449,0.2475,0.2499,0.2555,0.2618,0.2654,0.2694,0.2696,0.2704,0.2774, 0.2784,0.2801,0.2834,0.2882,0.2906,0.2919,0.2922,0.2941,0.3130,0.3147, 0.3155,0.3185,0.3240,0.3241,0.3306,0.3370,0.3442,0.3479,0.3535,0.3613, 0.3631,0.3682,0.3702,0.3733,0.3774,0.3775,0.3819,0.3870,0.3927,0.3927, 0.3979,0.3995,0.4019,0.4039,0.4061,0.4174,0.4186,0.4212,0.4243,0.4275, 0.4286,0.4291,0.4386,0.4403,0.4649,0.4720,0.4748,0.4752,0.4757,0.4760, 0.4779,0.4817,0.4820,0.4824,0.4836,0.4914,0.4965,0.4976,0.4987,0.5088, 0.5215,0.5243,0.5341,0.5454,0.5503,0.5545,0.5571,0.5589,0.5599,0.5660, 0.5695,0.5702,0.5725,0.5735,0.5744,0.5781,0.5791,0.5849,0.5852,0.5855, 0.5931,0.6003,0.6064,0.6077,0.6173,0.6185,0.6254,0.6288,0.6323,0.6406, 0.6449,0.6456,0.6468,0.6493,0.6511,0.6513,0.6538,0.6649,0.6663,0.6683, 0.6686,0.6713,0.6732,0.6748,0.6850,0.6894,0.6964,0.7042,0.7064,0.7122, 0.7149,0.7265,0.7288,0.7318,0.7326,0.7338,0.7359,0.7390,0.7510,0.7522, 0.7577,0.7579,0.7581,0.7607,0.7657,0.7675,0.7684,0.7812,0.7815,0.7851, 0.7858,0.7877,0.8003,0.8006,0.8075,0.8078,0.8140,0.8152,0.8231,0.8266, 0.8331,0.8335,0.8339,0.8352,0.8370,0.8377,0.8412,0.8456,0.8536,0.8539, 0.8567,0.8688,0.8709,0.8735,0.8742,0.8751,0.8794,0.8866,0.8882,0.8896, 0.8938,0.9032,0.9033,0.9054,0.9191,0.9316,0.9328,0.9340,0.9409,0.9448, 0.9479,0.9522,0.9543,0.9653,0.9660,0.9662,0.9716,0.9732,0.9742,0.9743, 0.9784,0.9810,0.9814,0.9850,0.9858,0.9879,0.9912,0.9917,0.9959, Overall p-value after applying KStest on 269 p-values = 0.806711 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.