RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-01-07_21:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.67 30.6124 0.977748 2 to 25 15.80 24.4869 0.893203 3 to 26 15.97 12.1110 0.206629 4 to 27 15.56 18.6026 0.648187 5 to 28 15.57 16.8152 0.533046 6 to 29 15.80 9.8706 0.091050 7 to 30 15.36 26.0966 0.927282 8 to 31 15.71 14.1810 0.345752 9 to 32 15.48 21.8700 0.810230 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.426907 Tough bday spacings test for dh-ranFile-2017-01-07_21:31: 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 9 52 61 94 102 78 56 25 10 8 5 (O-E)^2/E 0.0 6.4 2.1 0.1 0.2 0.0 0.3 0.8 1.6 0.3 0.2 Birthday Spacings: Sum(O-E)^2/E= 11.997, p= 0.715 RESULTS OF GCD FOR dh-ranFile-2017-01-07_21:31 Euclid's algorithm: p-value, steps to gcd: 0.836836 p-value, dist. of gcd's: 0.972782 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-01-07_21:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.838 0.652 0.830 0.079 0.099 0.428 0.357 0.234 Bits 8 to 15---> 0.424 0.886 0.178 0.379 0.821 0.500 0.030 0.264 Bits 16 to 23---> 0.639 0.481 0.170 0.866 0.365 0.763 0.848 0.685 Bits 24 to 31---> 0.246 0.015 0.601 0.040 0.165 0.480 0.897 0.967 KS test for the above 32 p values: 0.102 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-01-07_21:31, p-values for 5 runs: 0.7310, 0.5674, 0.8284, 0.4246, 0.3461 Rank test for binary matrices (31x31) for dh-ranFile-2017-01-07_21:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 209 211.4 0.028 0.028 r= 29 5178 5134.0 0.377 0.405 r= 30 23092 23103.0 0.005 0.410 r= 31 11521 11551.5 0.081 0.491 chi-square = 0.491 with df = 3; p-value = 0.079 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2017-01-07_21:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 212 211.4 0.002 0.002 r= 30 5220 5134.0 1.440 1.442 r= 31 23025 23103.0 0.264 1.706 r= 32 11543 11551.5 0.006 1.712 chi-square = 1.712 with df = 3; p-value = 0.366 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2017-01-07_21:31 b-rank test for bits 1 to 8, p=0.62500 b-rank test for bits 2 to 9, p=0.60328 b-rank test for bits 3 to 10, p=0.33643 b-rank test for bits 4 to 11, p=0.00907 b-rank test for bits 5 to 12, p=0.52680 b-rank test for bits 6 to 13, p=0.22932 b-rank test for bits 7 to 14, p=0.23403 b-rank test for bits 8 to 15, p=0.29595 b-rank test for bits 9 to 16, p=0.59292 b-rank test for bits 10 to 17, p=0.38004 b-rank test for bits 11 to 18, p=0.33774 b-rank test for bits 12 to 19, p=0.51361 b-rank test for bits 13 to 20, p=0.14855 b-rank test for bits 14 to 21, p=0.58885 b-rank test for bits 15 to 22, p=0.01738 b-rank test for bits 16 to 23, p=0.65328 b-rank test for bits 17 to 24, p=0.62916 b-rank test for bits 18 to 25, p=0.14863 b-rank test for bits 19 to 26, p=0.56275 b-rank test for bits 20 to 27, p=0.89268 b-rank test for bits 21 to 28, p=0.60599 b-rank test for bits 22 to 29, p=0.88142 b-rank test for bits 23 to 30, p=0.96172 b-rank test for bits 24 to 31, p=0.39924 b-rank test for bits 25 to 32, p=0.97419 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 = 0.692427 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-01-07_21:31 (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 142744 1.95 0.974422 2 141555 -0.83 0.203871 3 142711 1.87 0.969470 4 141784 -0.29 0.384827 5 142123 0.50 0.691191 6 142033 0.29 0.613690 7 141568 -0.80 0.212580 8 141718 -0.45 0.327426 9 141964 0.13 0.550820 10 142100 0.45 0.672017 11 141622 -0.67 0.251005 12 141892 -0.04 0.483851 13 141779 -0.30 0.380370 14 142317 0.95 0.829578 15 142195 0.67 0.747759 16 142021 0.26 0.602920 17 142139 0.54 0.704232 18 142161 0.59 0.721739 19 141648 -0.61 0.270738 20 141781 -0.30 0.382151 ---------------------------------------------------------------- OPSO test for dh-ranFile-2017-01-07_21:31 Bits used No. missing words z-score p-value 23 to 32 142204 1.0161 0.845210 22 to 31 141432 -1.6460 0.049885 21 to 30 141519 -1.3460 0.089157 20 to 29 142190 0.9678 0.833435 19 to 28 141644 -0.9149 0.180114 18 to 27 141991 0.2816 0.610883 17 to 26 141698 -0.7287 0.233085 16 to 25 141454 -1.5701 0.058196 15 to 24 141652 -0.8873 0.187447 14 to 23 141508 -1.3839 0.083195 13 to 22 142138 0.7885 0.784803 12 to 21 141652 -0.8873 0.187447 11 to 20 141798 -0.3839 0.350528 10 to 19 142181 0.9368 0.825568 9 to 18 141848 -0.2115 0.416255 8 to 17 142156 0.8506 0.802500 7 to 16 141789 -0.4149 0.339096 6 to 15 141659 -0.8632 0.194012 5 to 14 141502 -1.4046 0.080072 4 to 13 142072 0.5609 0.712578 3 to 12 141997 0.3023 0.618792 2 to 11 142334 1.4644 0.928455 1 to 10 142074 0.5678 0.714924 ----------------------------------------------------------------- OQSO test for dh-ranFile-2017-01-07_21:31 Bits used No. missing words z-score p-value 28 to 32 142195 0.9684 0.833571 27 to 31 141794 -0.3909 0.347917 26 to 30 142114 0.6938 0.756095 25 to 29 142076 0.5650 0.713957 24 to 28 142020 0.3752 0.646227 23 to 27 142061 0.5141 0.696421 22 to 26 141784 -0.4248 0.335474 21 to 25 141860 -0.1672 0.433598 20 to 24 142455 1.8497 0.967824 19 to 23 142495 1.9853 0.976446 18 to 22 142718 2.7413 0.996940 17 to 21 142112 0.6870 0.753964 16 to 20 142236 1.1074 0.865930 15 to 19 141491 -1.4181 0.078086 14 to 18 142108 0.6735 0.749672 13 to 17 141707 -0.6859 0.246399 12 to 16 141201 -2.4011 0.008173 11 to 15 142015 0.3582 0.639905 10 to 14 141950 0.1379 0.554826 9 to 13 141499 -1.3909 0.082120 8 to 12 142131 0.7514 0.773801 7 to 11 141345 -1.9130 0.027875 6 to 10 142145 0.7989 0.787820 5 to 9 141624 -0.9672 0.166717 4 to 8 142064 0.5243 0.699967 3 to 7 141580 -1.1164 0.132131 2 to 6 141988 0.2667 0.605141 1 to 5 141749 -0.5435 0.293396 ----------------------------------------------------------------- DNA test for dh-ranFile-2017-01-07_21:31 Bits used No. missing words z-score p-value 31 to 32 142137 0.6716 0.749079 30 to 31 142198 0.8515 0.802764 29 to 30 142074 0.4858 0.686429 28 to 29 142406 1.4651 0.928554 27 to 28 141647 -0.7738 0.219514 26 to 27 141982 0.2144 0.584869 25 to 26 142027 0.3471 0.635745 24 to 25 141630 -0.8240 0.204975 23 to 24 141893 -0.0482 0.480790 22 to 23 142845 2.7601 0.997111 21 to 22 141794 -0.3402 0.366851 20 to 21 142307 1.1731 0.879616 19 to 20 141834 -0.2222 0.412074 18 to 19 141694 -0.6352 0.262652 17 to 18 141963 0.1583 0.562897 16 to 17 142432 1.5418 0.938439 15 to 16 142388 1.4120 0.921026 14 to 15 141827 -0.2429 0.404056 13 to 14 141620 -0.8535 0.196696 12 to 13 142446 1.5831 0.943300 11 to 12 141849 -0.1780 0.429375 10 to 11 141703 -0.6086 0.271381 9 to 10 141893 -0.0482 0.480790 8 to 9 142046 0.4032 0.656583 7 to 8 141596 -0.9243 0.177671 6 to 7 141751 -0.4671 0.320232 5 to 6 141827 -0.2429 0.404056 4 to 5 141362 -1.6145 0.053205 3 to 4 142378 1.3825 0.916592 2 to 3 142077 0.4946 0.689559 1 to 2 141739 -0.5024 0.307676 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2017-01-07_21:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2485.38 -0.207 0.418118 Test results for specific bytes for dh-ranFile-2017-01-07_21:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2582.74 1.170 0.879023 2 to 9 2488.07 -0.169 0.433004 3 to 10 2627.13 1.798 0.963905 4 to 11 2533.33 0.471 0.681293 5 to 12 2560.20 0.851 0.802701 6 to 13 2590.09 1.274 0.898683 7 to 14 2522.00 0.311 0.622162 8 to 15 2540.34 0.571 0.715846 9 to 16 2463.51 -0.516 0.302935 10 to 17 2508.50 0.120 0.547831 11 to 18 2574.52 1.054 0.854043 12 to 19 2610.99 1.570 0.941742 13 to 20 2461.07 -0.551 0.290968 14 to 21 2393.02 -1.513 0.065155 15 to 22 2574.84 1.058 0.855063 16 to 23 2526.96 0.381 0.648501 17 to 24 2493.66 -0.090 0.464293 18 to 25 2537.09 0.525 0.700046 19 to 26 2543.40 0.614 0.730332 20 to 27 2605.67 1.494 0.932456 21 to 28 2581.69 1.155 0.876023 22 to 29 2313.61 -2.636 0.004194 23 to 30 2505.51 0.078 0.531034 24 to 31 2468.20 -0.450 0.326443 25 to 32 2476.92 -0.326 0.372043 CDPARK for dh-ranFile-2017-01-07_21:31: 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 3544 0.9589 0.831196 3532 0.4110 0.659449 3539 0.7306 0.767486 3546 1.0502 0.853193 3532 0.4110 0.659449 3541 0.8219 0.794438 3531 0.3653 0.642555 3556 1.5068 0.934075 3544 0.9589 0.831196 3578 2.5114 0.993988 Square side=100, avg. no. parked=3544.30 sample std.=13.39 p-value of the KSTEST for those 10 p-values: 0.001268 Results for the MINIMUM DISTANCE test for dh-ranFile-2017-01-07_21:31 0.4101,0.8395,0.7773,0.9910,0.5130,0.7279,0.1530,0.3906,0.0219,0.7210, The KS test for those 10 p-values: 0.766614 The 3DSPHERES test for dh-ranFile-2017-01-07_21:31 sample no r^3 equiv. uni. 1 49.776 0.809709 2 34.618 0.684601 3 28.907 0.618468 4 15.235 0.398210 5 1.927 0.062201 6 29.392 0.624589 7 27.021 0.593713 8 10.183 0.287829 9 67.383 0.894189 10 10.698 0.299946 11 0.612 0.020181 12 22.525 0.528022 13 43.724 0.767171 14 5.138 0.157393 15 5.684 0.172604 16 82.036 0.935076 17 25.745 0.576068 18 27.040 0.593970 19 26.824 0.591034 20 8.949 0.257928 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.878106 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-01-07_21:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -1.2 0.3 2.5 -0.3 -0.2 2.2 -1.5 -1.1 0.8 1.4 2.5 -0.2 -2.1 0.1 -0.6 -0.4 -0.3 1.1 -0.2 0.7 0.9 0.6 -1.9 -1.4 -0.8 -0.1 1.2 -1.6 -0.0 0.4 0.4 -0.3 2.2 -0.8 1.1 -1.4 -0.1 -0.8 -0.1 0.9 1.0 1.8 Chi-square with 42 degrees of freedom:58.381478 z-score=1.787366, p-value=0.952290 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2017-01-07_21:31 Test no p-value 1 0.046308 2 0.016647 3 0.055366 4 0.816964 5 0.592294 6 0.710857 7 0.055219 8 0.784227 9 0.217325 10 0.849667 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.104131 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-01-07_21:31: (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 66704 0.02 66698 0.01 3 25000.00 24899 0.41 25057 0.13 4 6666.67 6700 0.17 6529 2.84 5 1388.89 1415 0.49 1435 1.53 6 238.10 237 0.01 246 0.26 7 34.72 39 0.53 30 0.64 8 4.96 5 0.00 4 0.19 p=0.04883 p=0.53154 Number of rngs required: 687456, p-value: 0.136 RESULTS OF CRAPS TEST for dh-ranFile-2017-01-07_21:31 No. of wins: Observed Expected 98674 98585.9 z-score= 0.394, pvalue=0.65329 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66670 66666.7 0.000 0.000 2 37517 37654.3 0.501 0.501 3 27064 26954.7 0.443 0.944 4 19309 19313.5 0.001 0.945 5 13808 13851.4 0.136 1.081 6 10161 9943.5 4.756 5.837 7 7202 7145.0 0.454 6.291 8 5136 5139.1 0.002 6.293 9 3616 3699.9 1.901 8.194 10 2563 2666.3 4.002 12.196 11 1851 1923.3 2.720 14.916 12 1427 1388.7 1.054 15.970 13 971 1003.7 1.066 17.036 14 765 726.1 2.080 19.116 15 518 525.8 0.117 19.232 16 379 381.2 0.012 19.245 17 279 276.5 0.022 19.266 18 220 200.8 1.830 21.096 19 147 146.0 0.007 21.103 20 110 106.2 0.135 21.238 21 287 287.1 0.000 21.238 Chisq= 21.24 for 20 degrees of freedom, p= 0.61677 SUMMARY of craptest p-value for no. of wins: 0.653291 p-value for throws/game: 0.616771 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2017-01-07_21:31 No. of wins: Observed Expected 98480 98585.9 z-score=-0.473, pvalue=0.31794 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66401 66666.7 1.059 1.059 2 37515 37654.3 0.515 1.574 3 27128 26954.7 1.114 2.688 4 19492 19313.5 1.650 4.338 5 14013 13851.4 1.885 6.223 6 9958 9943.5 0.021 6.244 7 7126 7145.0 0.051 6.295 8 5146 5139.1 0.009 6.304 9 3673 3699.9 0.195 6.499 10 2688 2666.3 0.177 6.676 11 1926 1923.3 0.004 6.680 12 1389 1388.7 0.000 6.680 13 983 1003.7 0.428 7.107 14 719 726.1 0.070 7.177 15 525 525.8 0.001 7.179 16 361 381.2 1.065 8.244 17 242 276.5 4.314 12.558 18 196 200.8 0.116 12.674 19 139 146.0 0.334 13.008 20 112 106.2 0.315 13.323 21 268 287.1 1.272 14.596 Chisq= 14.60 for 20 degrees of freedom, p= 0.20096 SUMMARY of craptest p-value for no. of wins: 0.317942 p-value for throws/game: 0.200957 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0013,0.0042,0.0082,0.0091,0.0148,0.0166,0.0174,0.0202,0.0219,0.0279, 0.0297,0.0401,0.0463,0.0488,0.0499,0.0532,0.0552,0.0554,0.0582,0.0622, 0.0652,0.0781,0.0790,0.0791,0.0801,0.0821,0.0832,0.0892,0.0910,0.0987, 0.1021,0.1041,0.1321,0.1359,0.1485,0.1486,0.1530,0.1574,0.1648,0.1667, 0.1697,0.1726,0.1777,0.1782,0.1801,0.1874,0.1874,0.1940,0.1967,0.2010, 0.2039,0.2050,0.2066,0.2126,0.2173,0.2195,0.2293,0.2331,0.2340,0.2343, 0.2457,0.2464,0.2510,0.2579,0.2627,0.2644,0.2707,0.2714,0.2878,0.2910, 0.2934,0.2959,0.2999,0.3029,0.3077,0.3179,0.3202,0.3264,0.3274,0.3355, 0.3364,0.3377,0.3391,0.3458,0.3461,0.3479,0.3505,0.3570,0.3649,0.3657, 0.3669,0.3720,0.3792,0.3800,0.3804,0.3822,0.3848,0.3906,0.3982,0.3992, 0.4041,0.4041,0.4101,0.4121,0.4163,0.4181,0.4241,0.4246,0.4269,0.4281, 0.4294,0.4330,0.4336,0.4643,0.4795,0.4807,0.4808,0.4808,0.4839,0.5004, 0.5130,0.5136,0.5268,0.5280,0.5310,0.5315,0.5330,0.5478,0.5508,0.5548, 0.5628,0.5629,0.5674,0.5761,0.5849,0.5889,0.5910,0.5923,0.5929,0.5937, 0.5940,0.6009,0.6029,0.6033,0.6051,0.6060,0.6109,0.6137,0.6168,0.6185, 0.6188,0.6222,0.6246,0.6250,0.6292,0.6357,0.6392,0.6399,0.6426,0.6462, 0.6482,0.6485,0.6525,0.6533,0.6533,0.6566,0.6594,0.6594,0.6720,0.6813, 0.6846,0.6848,0.6864,0.6896,0.6912,0.6924,0.6964,0.7000,0.7000,0.7042, 0.7109,0.7126,0.7140,0.7148,0.7149,0.7158,0.7210,0.7217,0.7279,0.7303, 0.7310,0.7478,0.7491,0.7497,0.7540,0.7561,0.7629,0.7666,0.7672,0.7675, 0.7738,0.7773,0.7842,0.7848,0.7878,0.7944,0.8025,0.8027,0.8028,0.8097, 0.8102,0.8170,0.8211,0.8256,0.8284,0.8296,0.8300,0.8312,0.8312,0.8334, 0.8336,0.8368,0.8376,0.8395,0.8452,0.8478,0.8497,0.8532,0.8540,0.8551, 0.8656,0.8659,0.8760,0.8781,0.8790,0.8796,0.8814,0.8865,0.8927,0.8932, 0.8942,0.8969,0.8987,0.9166,0.9210,0.9273,0.9285,0.9286,0.9325,0.9341, 0.9351,0.9384,0.9417,0.9433,0.9523,0.9617,0.9639,0.9671,0.9678,0.9695, 0.9728,0.9742,0.9744,0.9764,0.9777,0.9910,0.9940,0.9969,0.9971, Overall p-value after applying KStest on 269 p-values = 0.163178 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.