RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-01-28_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 15.58 12.4065 0.225075 2 to 25 15.64 22.1589 0.821315 3 to 26 15.89 12.1919 0.211622 4 to 27 15.77 21.0234 0.774756 5 to 28 15.78 15.3929 0.432798 6 to 29 15.84 15.7310 0.457020 7 to 30 16.08 13.0873 0.269674 8 to 31 15.83 15.0027 0.404710 9 to 32 15.80 21.3187 0.787640 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.672747 Tough bday spacings test for dh-ranFile-2016-01-28_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 7 35 80 103 101 76 59 29 6 1 3 (O-E)^2/E 0.5 0.1 0.6 0.3 0.1 0.1 0.9 0.0 5.3 4.8 0.3 Birthday Spacings: Sum(O-E)^2/E= 12.946, p= 0.773 RESULTS OF GCD FOR dh-ranFile-2016-01-28_14:31 Euclid's algorithm: p-value, steps to gcd: 0.337725 p-value, dist. of gcd's: 0.609035 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-01-28_14:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.937 0.509 0.184 0.935 0.030 0.173 0.976 0.887 Bits 8 to 15---> 0.917 0.122 0.464 0.115 0.071 0.560 0.895 0.298 Bits 16 to 23---> 0.096 0.998 0.495 0.798 0.945 0.780 0.433 0.592 Bits 24 to 31---> 0.529 0.202 0.520 0.005 0.942 0.428 0.433 0.004 KS test for the above 32 p values: 0.801 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-01-28_14:31, p-values for 5 runs: 0.7313, 0.0405, 0.9188, 0.3168, 0.5348 Rank test for binary matrices (31x31) for dh-ranFile-2016-01-28_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 230 211.4 1.633 1.633 r= 29 5093 5134.0 0.328 1.961 r= 30 23090 23103.0 0.007 1.968 r= 31 11587 11551.5 0.109 2.077 chi-square = 2.077 with df = 3; p-value = 0.443 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-01-28_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 187 211.4 2.820 2.820 r= 30 5272 5134.0 3.709 6.529 r= 31 23205 23103.0 0.450 6.979 r= 32 11336 11551.5 4.021 11.000 chi-square = 11.000 with df = 3; p-value = 0.988 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-01-28_14:31 b-rank test for bits 1 to 8, p=0.53697 b-rank test for bits 2 to 9, p=0.62908 b-rank test for bits 3 to 10, p=0.08947 b-rank test for bits 4 to 11, p=0.77540 b-rank test for bits 5 to 12, p=0.84173 b-rank test for bits 6 to 13, p=0.98540 b-rank test for bits 7 to 14, p=0.36434 b-rank test for bits 8 to 15, p=0.93191 b-rank test for bits 9 to 16, p=0.20594 b-rank test for bits 10 to 17, p=0.96701 b-rank test for bits 11 to 18, p=0.22641 b-rank test for bits 12 to 19, p=0.84479 b-rank test for bits 13 to 20, p=0.22516 b-rank test for bits 14 to 21, p=0.59793 b-rank test for bits 15 to 22, p=0.76794 b-rank test for bits 16 to 23, p=0.18493 b-rank test for bits 17 to 24, p=0.41548 b-rank test for bits 18 to 25, p=0.70889 b-rank test for bits 19 to 26, p=0.52311 b-rank test for bits 20 to 27, p=0.24718 b-rank test for bits 21 to 28, p=0.09031 b-rank test for bits 22 to 29, p=0.44941 b-rank test for bits 23 to 30, p=0.97065 b-rank test for bits 24 to 31, p=0.81646 b-rank test for bits 25 to 32, p=0.30527 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 = 0.589037 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-01-28_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 141631 -0.65 0.257748 2 142039 0.30 0.619043 3 141665 -0.57 0.284046 4 142203 0.69 0.753689 5 141657 -0.59 0.277744 6 142794 2.07 0.980632 7 141278 -1.48 0.070097 8 142144 0.55 0.708255 9 142429 1.21 0.887661 10 142440 1.24 0.892491 11 142804 2.09 0.981707 12 142395 1.13 0.871759 13 141727 -0.43 0.335052 14 142388 1.12 0.868299 15 141714 -0.46 0.324059 16 141552 -0.83 0.201892 17 141774 -0.32 0.375929 18 141967 0.13 0.553593 19 141697 -0.50 0.309913 20 142281 0.87 0.807409 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-01-28_14:31 Bits used No. missing words z-score p-value 23 to 32 141788 -0.4184 0.337835 22 to 31 141711 -0.6839 0.247020 21 to 30 142082 0.5954 0.724217 20 to 29 142466 1.9196 0.972543 19 to 28 142077 0.5782 0.718426 18 to 27 142710 2.7609 0.997118 17 to 26 142322 1.4230 0.922632 16 to 25 142046 0.4713 0.681278 15 to 24 141628 -0.9701 0.165998 14 to 23 141987 0.2678 0.605584 13 to 22 142015 0.3644 0.642213 12 to 21 141821 -0.3046 0.380341 11 to 20 141730 -0.6184 0.268163 10 to 19 141850 -0.2046 0.418948 9 to 18 141646 -0.9080 0.181930 8 to 17 141918 0.0299 0.511925 7 to 16 141946 0.1264 0.550312 6 to 15 141848 -0.2115 0.416255 5 to 14 141920 0.0368 0.514675 4 to 13 141903 -0.0218 0.491293 3 to 12 141615 -1.0149 0.155069 2 to 11 141831 -0.2701 0.393540 1 to 10 141680 -0.7908 0.214532 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-01-28_14:31 Bits used No. missing words z-score p-value 28 to 32 142309 1.3548 0.912262 27 to 31 142250 1.1548 0.875917 26 to 30 141965 0.1887 0.574841 25 to 29 141869 -0.1367 0.445629 24 to 28 141966 0.1921 0.576169 23 to 27 141967 0.1955 0.577496 22 to 26 142348 1.4870 0.931495 21 to 25 142932 3.4667 0.999737 20 to 24 142516 2.0565 0.980133 19 to 23 141834 -0.2554 0.399224 18 to 22 141790 -0.4045 0.342919 17 to 21 141877 -0.1096 0.456366 16 to 20 141651 -0.8757 0.190598 15 to 19 142125 0.7311 0.767636 14 to 18 142550 2.1718 0.985063 13 to 17 141626 -0.9604 0.168417 12 to 16 141814 -0.3232 0.373290 11 to 15 141610 -1.0147 0.155130 10 to 14 141868 -0.1401 0.444290 9 to 13 141662 -0.8384 0.200901 8 to 12 141890 -0.0655 0.473878 7 to 11 141775 -0.4554 0.324427 6 to 10 142298 1.3175 0.906169 5 to 9 142072 0.5514 0.709328 4 to 8 142459 1.8633 0.968789 3 to 7 141752 -0.5333 0.296905 2 to 6 142121 0.7175 0.763475 1 to 5 142211 1.0226 0.846754 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-01-28_14:31 Bits used No. missing words z-score p-value 31 to 32 141903 -0.0187 0.492551 30 to 31 142179 0.7955 0.786835 29 to 30 142194 0.8397 0.799471 28 to 29 141718 -0.5644 0.286243 27 to 28 142086 0.5212 0.698869 26 to 27 141604 -0.9007 0.183880 25 to 26 142239 0.9725 0.834594 24 to 25 141865 -0.1308 0.447980 23 to 24 142082 0.5094 0.694747 22 to 23 141640 -0.7945 0.213457 21 to 22 142017 0.3176 0.624610 20 to 21 141820 -0.2635 0.396079 19 to 20 142732 2.4268 0.992383 18 to 19 141900 -0.0275 0.489022 17 to 18 141920 0.0315 0.512555 16 to 17 142118 0.6155 0.730903 15 to 16 142713 2.3707 0.991123 14 to 15 141633 -0.8151 0.207498 13 to 14 141462 -1.3196 0.093491 12 to 13 141700 -0.6175 0.268455 11 to 12 141570 -1.0010 0.158420 10 to 11 141682 -0.6706 0.251241 9 to 10 141991 0.2409 0.595189 8 to 9 141501 -1.2045 0.114196 7 to 8 142057 0.4356 0.668438 6 to 7 142039 0.3825 0.648958 5 to 6 141814 -0.2812 0.389275 4 to 5 141841 -0.2016 0.420129 3 to 4 142014 0.3088 0.621248 2 to 3 141924 0.0433 0.517259 1 to 2 142151 0.7129 0.762043 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-01-28_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2328.40 -2.427 0.007617 Test results for specific bytes for dh-ranFile-2016-01-28_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2578.44 1.109 0.866364 2 to 9 2299.98 -2.829 0.002337 3 to 10 2327.49 -2.440 0.007350 4 to 11 2552.83 0.747 0.772521 5 to 12 2517.52 0.248 0.597832 6 to 13 2441.76 -0.824 0.205069 7 to 14 2473.35 -0.377 0.353125 8 to 15 2472.19 -0.393 0.347050 9 to 16 2556.04 0.793 0.785966 10 to 17 2536.34 0.514 0.696348 11 to 18 2429.79 -0.993 0.160380 12 to 19 2350.05 -2.121 0.016975 13 to 20 2512.37 0.175 0.569437 14 to 21 2478.93 -0.298 0.382862 15 to 22 2510.86 0.154 0.561036 16 to 23 2463.75 -0.513 0.304075 17 to 24 2477.74 -0.315 0.376471 18 to 25 2544.74 0.633 0.736563 19 to 26 2458.05 -0.593 0.276480 20 to 27 2567.09 0.949 0.828631 21 to 28 2463.51 -0.516 0.302932 22 to 29 2454.17 -0.648 0.258464 23 to 30 2606.76 1.510 0.934452 24 to 31 2467.89 -0.454 0.324885 25 to 32 2418.89 -1.147 0.125670 CDPARK for dh-ranFile-2016-01-28_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 3490 -1.5068 0.065925 3531 0.3653 0.642555 3485 -1.7352 0.041356 3528 0.2283 0.590298 3532 0.4110 0.659449 3537 0.6393 0.738676 3570 2.1461 0.984068 3531 0.3653 0.642555 3541 0.8219 0.794438 3541 0.8219 0.794438 Square side=100, avg. no. parked=3528.60 sample std.=23.47 p-value of the KSTEST for those 10 p-values: 0.227008 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-01-28_14:31 0.3454,0.4946,0.8938,0.4554,0.9060,0.9940,0.0853,0.2636,0.9315,0.0185, The KS test for those 10 p-values: 0.355407 The 3DSPHERES test for dh-ranFile-2016-01-28_14:31 sample no r^3 equiv. uni. 1 16.361 0.420380 2 6.298 0.189357 3 37.980 0.718044 4 14.273 0.378592 5 41.965 0.753115 6 9.554 0.272731 7 10.663 0.299127 8 41.662 0.750608 9 31.324 0.648003 10 58.936 0.859778 11 8.231 0.239940 12 17.373 0.439606 13 29.514 0.626114 14 50.174 0.812216 15 35.935 0.698154 16 15.929 0.411964 17 69.809 0.902410 18 13.315 0.358430 19 28.708 0.615930 20 6.931 0.206291 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.420943 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-01-28_14:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.1 -0.6 0.5 -2.6 0.6 0.1 -0.0 0.9 -0.3 -0.9 -1.3 0.5 1.6 0.1 -0.8 -0.2 0.8 0.3 -0.1 -0.6 -0.3 -0.1 0.7 0.4 0.8 -0.7 0.6 -2.0 -1.0 0.2 0.8 0.5 0.4 1.0 -1.2 -0.5 -0.4 0.1 -0.1 0.1 -1.0 1.8 Chi-square with 42 degrees of freedom:31.114873 z-score=-1.187665, p-value=0.108463 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-01-28_14:31 Test no p-value 1 0.139132 2 0.686461 3 0.717145 4 0.239672 5 0.001947 6 0.367895 7 0.837850 8 0.905521 9 0.460149 10 0.275327 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.812112 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-01-28_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 66574 0.13 66675 0.00 3 25000.00 25013 0.01 25074 0.22 4 6666.67 6723 0.48 6536 2.56 5 1388.89 1453 2.96 1440 1.88 6 238.10 195 7.80 239 0.00 7 34.72 34 0.01 31 0.40 8 4.96 7 0.84 4 0.19 p=0.94287 p=0.48782 Number of rngs required: 688392, p-value: 0.495 RESULTS OF CRAPS TEST for dh-ranFile-2016-01-28_14:31 No. of wins: Observed Expected 98357 98585.9 z-score=-1.024, pvalue=0.15301 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66673 66666.7 0.001 0.001 2 37528 37654.3 0.424 0.424 3 26857 26954.7 0.354 0.779 4 19466 19313.5 1.205 1.983 5 13993 13851.4 1.447 3.431 6 9873 9943.5 0.500 3.931 7 7055 7145.0 1.134 5.065 8 5196 5139.1 0.631 5.696 9 3781 3699.9 1.779 7.475 10 2653 2666.3 0.066 7.542 11 1921 1923.3 0.003 7.544 12 1329 1388.7 2.570 10.114 13 996 1003.7 0.059 10.174 14 750 726.1 0.784 10.958 15 515 525.8 0.223 11.181 16 399 381.2 0.836 12.017 17 278 276.5 0.008 12.024 18 207 200.8 0.190 12.214 19 149 146.0 0.062 12.276 20 102 106.2 0.167 12.444 21 279 287.1 0.229 12.673 Chisq= 12.67 for 20 degrees of freedom, p= 0.10903 SUMMARY of craptest p-value for no. of wins: 0.153015 p-value for throws/game: 0.109025 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-01-28_14:31 No. of wins: Observed Expected 98502 98585.9 z-score=-0.375, pvalue=0.35381 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66433 66666.7 0.819 0.819 2 37890 37654.3 1.475 2.294 3 27073 26954.7 0.519 2.813 4 19355 19313.5 0.089 2.902 5 13891 13851.4 0.113 3.015 6 9887 9943.5 0.322 3.337 7 7023 7145.0 2.084 5.421 8 5222 5139.1 1.338 6.759 9 3688 3699.9 0.038 6.797 10 2627 2666.3 0.579 7.376 11 1913 1923.3 0.055 7.432 12 1419 1388.7 0.659 8.091 13 955 1003.7 2.364 10.456 14 715 726.1 0.171 10.627 15 528 525.8 0.009 10.635 16 396 381.2 0.579 11.214 17 244 276.5 3.829 15.043 18 200 200.8 0.003 15.046 19 147 146.0 0.007 15.053 20 108 106.2 0.030 15.083 21 286 287.1 0.004 15.088 Chisq= 15.09 for 20 degrees of freedom, p= 0.22863 SUMMARY of craptest p-value for no. of wins: 0.353806 p-value for throws/game: 0.228625 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0019,0.0023,0.0041,0.0054,0.0074,0.0076,0.0170,0.0185,0.0302,0.0405, 0.0414,0.0659,0.0701,0.0707,0.0853,0.0895,0.0903,0.0935,0.0963,0.1085, 0.1090,0.1142,0.1149,0.1220,0.1257,0.1391,0.1530,0.1551,0.1551,0.1584, 0.1604,0.1660,0.1684,0.1733,0.1819,0.1839,0.1844,0.1849,0.1894,0.1906, 0.2009,0.2018,0.2019,0.2051,0.2059,0.2063,0.2075,0.2116,0.2135,0.2145, 0.2251,0.2252,0.2264,0.2270,0.2286,0.2397,0.2399,0.2470,0.2472,0.2512, 0.2577,0.2585,0.2636,0.2682,0.2685,0.2697,0.2727,0.2753,0.2765,0.2777, 0.2840,0.2862,0.2969,0.2980,0.2991,0.3029,0.3041,0.3053,0.3099,0.3168, 0.3241,0.3244,0.3249,0.3351,0.3377,0.3378,0.3429,0.3454,0.3470,0.3531, 0.3538,0.3554,0.3584,0.3643,0.3679,0.3733,0.3759,0.3765,0.3786,0.3803, 0.3829,0.3893,0.3935,0.3961,0.3992,0.4047,0.4120,0.4155,0.4163,0.4189, 0.4201,0.4204,0.4209,0.4276,0.4328,0.4330,0.4331,0.4396,0.4434,0.4443, 0.4456,0.4480,0.4494,0.4554,0.4564,0.4570,0.4601,0.4642,0.4739,0.4878, 0.4890,0.4913,0.4926,0.4946,0.4950,0.4952,0.5090,0.5119,0.5126,0.5147, 0.5173,0.5203,0.5231,0.5290,0.5348,0.5370,0.5503,0.5536,0.5600,0.5610, 0.5694,0.5748,0.5762,0.5775,0.5890,0.5903,0.5921,0.5952,0.5978,0.5979, 0.6056,0.6090,0.6159,0.6190,0.6212,0.6246,0.6261,0.6291,0.6422,0.6426, 0.6426,0.6480,0.6490,0.6594,0.6684,0.6727,0.6813,0.6865,0.6947,0.6963, 0.6982,0.6989,0.7083,0.7089,0.7093,0.7171,0.7180,0.7184,0.7242,0.7309, 0.7313,0.7366,0.7387,0.7506,0.7531,0.7537,0.7620,0.7635,0.7676,0.7679, 0.7725,0.7733,0.7748,0.7754,0.7803,0.7860,0.7868,0.7876,0.7944,0.7944, 0.7979,0.7995,0.8010,0.8074,0.8121,0.8122,0.8165,0.8213,0.8286,0.8346, 0.8379,0.8417,0.8448,0.8468,0.8598,0.8664,0.8683,0.8718,0.8759,0.8869, 0.8877,0.8925,0.8938,0.8948,0.9024,0.9055,0.9060,0.9062,0.9123,0.9174, 0.9188,0.9226,0.9315,0.9315,0.9319,0.9345,0.9347,0.9371,0.9417,0.9429, 0.9449,0.9670,0.9688,0.9707,0.9725,0.9762,0.9801,0.9806,0.9817,0.9841, 0.9851,0.9854,0.9883,0.9911,0.9924,0.9940,0.9971,0.9983,0.9997, Overall p-value after applying KStest on 269 p-values = 0.207121 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.