RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-01-28_04:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.79 10.7702 0.131742 2 to 25 15.75 10.4059 0.114269 3 to 26 15.99 16.6255 0.519998 4 to 27 15.61 19.2372 0.684911 5 to 28 15.66 26.6456 0.936526 6 to 29 15.62 17.9004 0.604852 7 to 30 15.65 11.6686 0.180221 8 to 31 15.70 29.1711 0.967019 9 to 32 15.78 25.2486 0.910718 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.506004 Tough bday spacings test for dh-ranFile-2016-01-28_04:31: 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 10 33 69 93 107 89 50 27 13 5 4 (O-E)^2/E 0.1 0.4 0.2 0.2 0.9 1.5 0.1 0.3 0.2 0.4 0.0 Birthday Spacings: Sum(O-E)^2/E= 4.282, p= 0.066 RESULTS OF GCD FOR dh-ranFile-2016-01-28_04:31 Euclid's algorithm: p-value, steps to gcd: 0.689830 p-value, dist. of gcd's: 0.827899 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-01-28_04:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.410 0.072 0.454 0.731 0.162 0.067 0.072 0.251 Bits 8 to 15---> 0.041 0.474 0.426 0.712 0.326 0.780 0.540 0.190 Bits 16 to 23---> 0.357 0.929 0.771 0.656 0.721 0.292 0.342 0.212 Bits 24 to 31---> 0.516 0.307 0.698 0.216 0.559 0.566 0.382 0.962 KS test for the above 32 p values: 0.643 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-01-28_04:31, p-values for 5 runs: 0.7141, 0.5542, 0.0363, 0.3586, 0.4252 Rank test for binary matrices (31x31) for dh-ranFile-2016-01-28_04:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 228 211.4 1.301 1.301 r= 29 5056 5134.0 1.185 2.486 r= 30 23231 23103.0 0.709 3.195 r= 31 11485 11551.5 0.383 3.578 chi-square = 3.578 with df = 3; p-value = 0.689 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-01-28_04:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 209 211.4 0.028 0.028 r= 30 5148 5134.0 0.038 0.066 r= 31 23244 23103.0 0.860 0.926 r= 32 11399 11551.5 2.014 2.940 chi-square = 2.940 with df = 3; p-value = 0.599 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-01-28_04:31 b-rank test for bits 1 to 8, p=0.84325 b-rank test for bits 2 to 9, p=0.91936 b-rank test for bits 3 to 10, p=0.79103 b-rank test for bits 4 to 11, p=0.31581 b-rank test for bits 5 to 12, p=0.83804 b-rank test for bits 6 to 13, p=0.05318 b-rank test for bits 7 to 14, p=0.20752 b-rank test for bits 8 to 15, p=0.59225 b-rank test for bits 9 to 16, p=0.88302 b-rank test for bits 10 to 17, p=0.28376 b-rank test for bits 11 to 18, p=0.29864 b-rank test for bits 12 to 19, p=0.07574 b-rank test for bits 13 to 20, p=0.77068 b-rank test for bits 14 to 21, p=0.69567 b-rank test for bits 15 to 22, p=0.64606 b-rank test for bits 16 to 23, p=0.39921 b-rank test for bits 17 to 24, p=0.88514 b-rank test for bits 18 to 25, p=0.67203 b-rank test for bits 19 to 26, p=0.70435 b-rank test for bits 20 to 27, p=0.26931 b-rank test for bits 21 to 28, p=0.54794 b-rank test for bits 22 to 29, p=0.82838 b-rank test for bits 23 to 30, p=0.65636 b-rank test for bits 24 to 31, p=0.69718 b-rank test for bits 25 to 32, p=0.23367 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 = 0.301925 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-01-28_04:31 (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 141916 0.02 0.506217 2 142055 0.34 0.633204 3 141488 -0.98 0.162456 4 142325 0.97 0.834274 5 142004 0.22 0.587528 6 141722 -0.44 0.330807 7 142211 0.70 0.759544 8 141280 -1.47 0.070727 9 141529 -0.89 0.187103 10 141339 -1.33 0.091340 11 142101 0.45 0.672861 12 142056 0.34 0.634083 13 141471 -1.02 0.152886 14 142022 0.26 0.603820 15 141789 -0.28 0.389300 16 141645 -0.62 0.268422 17 142753 1.97 0.975649 18 142105 0.46 0.676227 19 142528 1.45 0.925840 20 140861 -2.45 0.007155 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-01-28_04:31 Bits used No. missing words z-score p-value 23 to 32 141753 -0.5391 0.294920 22 to 31 142324 1.4299 0.923627 21 to 30 141702 -0.7149 0.237326 20 to 29 142021 0.3851 0.649907 19 to 28 142464 1.9127 0.972104 18 to 27 141617 -1.0080 0.156719 17 to 26 141764 -0.5011 0.308137 16 to 25 141322 -2.0253 0.021420 15 to 24 141781 -0.4425 0.329058 14 to 23 141539 -1.2770 0.100801 13 to 22 142111 0.6954 0.756602 12 to 21 142241 1.1437 0.873624 11 to 20 141765 -0.4977 0.309351 10 to 19 141959 0.1713 0.567997 9 to 18 141882 -0.0942 0.462459 8 to 17 142353 1.5299 0.936979 7 to 16 142047 0.4747 0.682508 6 to 15 141958 0.1678 0.566641 5 to 14 141710 -0.6873 0.245933 4 to 13 141791 -0.4080 0.341624 3 to 12 141983 0.2540 0.600266 2 to 11 141239 -2.3115 0.010403 1 to 10 141388 -1.7977 0.036113 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-01-28_04:31 Bits used No. missing words z-score p-value 28 to 32 141906 -0.0113 0.495497 27 to 31 142051 0.4802 0.684471 26 to 30 142155 0.8328 0.797516 25 to 29 142185 0.9345 0.824970 24 to 28 141660 -0.8452 0.199003 23 to 27 141731 -0.6045 0.272753 22 to 26 142075 0.5616 0.712803 21 to 25 142228 1.0802 0.859982 20 to 24 141843 -0.2248 0.411049 19 to 23 141920 0.0362 0.514426 18 to 22 141742 -0.5672 0.285282 17 to 21 141578 -1.1232 0.130686 16 to 20 141637 -0.9232 0.177964 15 to 19 142018 0.3684 0.643702 14 to 18 142068 0.5379 0.704665 13 to 17 141683 -0.7672 0.221475 12 to 16 141726 -0.6215 0.267149 11 to 15 141508 -1.3604 0.086845 10 to 14 141946 0.1243 0.549463 9 to 13 142248 1.1480 0.874523 8 to 12 141738 -0.5808 0.280695 7 to 11 141880 -0.0994 0.460401 6 to 10 141470 -1.4893 0.068210 5 to 9 142136 0.7684 0.778867 4 to 8 141743 -0.5638 0.286435 3 to 7 141892 -0.0587 0.476577 2 to 6 142091 0.6158 0.730997 1 to 5 142434 1.7785 0.962343 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-01-28_04:31 Bits used No. missing words z-score p-value 31 to 32 142512 1.7778 0.962281 30 to 31 142035 0.3707 0.644573 29 to 30 141448 -1.3609 0.086780 28 to 29 141262 -1.9095 0.028097 27 to 28 141818 -0.2694 0.393807 26 to 27 142289 1.1200 0.868637 25 to 26 141803 -0.3137 0.376891 24 to 25 141942 0.0964 0.538387 23 to 24 141856 -0.1573 0.437498 22 to 23 142317 1.2026 0.885428 21 to 22 141753 -0.4612 0.322345 20 to 21 141635 -0.8092 0.209191 19 to 20 141946 0.1082 0.543070 18 to 19 141784 -0.3697 0.355801 17 to 18 142078 0.4976 0.690600 16 to 17 141855 -0.1603 0.436336 15 to 16 141952 0.1259 0.550083 14 to 15 141856 -0.1573 0.437498 13 to 14 141402 -1.4965 0.067255 12 to 13 142018 0.3206 0.625728 11 to 12 141628 -0.8299 0.203303 10 to 11 141667 -0.7148 0.237355 9 to 10 142185 0.8132 0.791944 8 to 9 142015 0.3117 0.622370 7 to 8 142260 1.0344 0.849531 6 to 7 142101 0.5654 0.714099 5 to 6 142443 1.5742 0.942285 4 to 5 141696 -0.6293 0.264579 3 to 4 142349 1.2970 0.902678 2 to 3 141185 -2.1367 0.016313 1 to 2 141734 -0.5172 0.302509 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-01-28_04:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2444.24 -0.789 0.215175 Test results for specific bytes for dh-ranFile-2016-01-28_04:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2453.84 -0.653 0.256928 2 to 9 2457.32 -0.604 0.273049 3 to 10 2550.12 0.709 0.760760 4 to 11 2581.09 1.147 0.874258 5 to 12 2531.24 0.442 0.670669 6 to 13 2519.94 0.282 0.611005 7 to 14 2570.03 0.990 0.839003 8 to 15 2558.09 0.822 0.794327 9 to 16 2494.34 -0.080 0.468090 10 to 17 2504.20 0.059 0.523671 11 to 18 2517.30 0.245 0.596640 12 to 19 2544.10 0.624 0.733598 13 to 20 2462.53 -0.530 0.298089 14 to 21 2605.63 1.494 0.932384 15 to 22 2528.70 0.406 0.657579 16 to 23 2583.50 1.181 0.881168 17 to 24 2569.73 0.986 0.837973 18 to 25 2562.05 0.877 0.809879 19 to 26 2590.37 1.278 0.899386 20 to 27 2640.19 1.983 0.976297 21 to 28 2423.54 -1.081 0.139777 22 to 29 2623.19 1.742 0.959267 23 to 30 2467.51 -0.460 0.322937 24 to 31 2437.75 -0.880 0.189324 25 to 32 2465.92 -0.482 0.314911 CDPARK for dh-ranFile-2016-01-28_04:31: 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 3521 -0.0913 0.463617 3520 -0.1370 0.445521 3540 0.7763 0.781201 3544 0.9589 0.831196 3562 1.7808 0.962529 3531 0.3653 0.642555 3514 -0.4110 0.340551 3543 0.9132 0.819442 3493 -1.3699 0.085365 3501 -1.0046 0.157553 Square side=100, avg. no. parked=3526.90 sample std.=20.10 p-value of the KSTEST for those 10 p-values: 0.909798 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-01-28_04:31 0.2484,0.0334,0.6141,0.6286,0.0317,0.9391,0.6026,0.4008,0.7112,0.8499, The KS test for those 10 p-values: 0.795768 The 3DSPHERES test for dh-ranFile-2016-01-28_04:31 sample no r^3 equiv. uni. 1 80.377 0.931384 2 43.102 0.762296 3 25.188 0.568114 4 5.128 0.157109 5 66.235 0.890062 6 39.427 0.731322 7 2.088 0.067241 8 1.026 0.033615 9 22.098 0.521257 10 30.216 0.634754 11 116.262 0.979254 12 0.599 0.019765 13 20.582 0.496450 14 23.949 0.549906 15 56.009 0.845408 16 32.592 0.662567 17 2.345 0.075200 18 57.946 0.855075 19 60.526 0.867015 20 12.487 0.340477 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.399663 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-01-28_04:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.5 -0.6 0.8 1.4 0.1 -1.1 -1.4 -0.2 -0.1 1.2 -0.9 -0.0 0.8 2.1 1.0 0.2 -0.0 1.2 0.4 -1.3 -0.9 -1.3 -3.1 -0.9 1.2 -0.5 1.6 -0.2 -1.3 1.5 -0.1 -1.7 -0.3 1.0 -0.8 -0.2 -0.7 -0.8 0.4 -0.6 0.0 2.7 Chi-square with 42 degrees of freedom:53.036485 z-score=1.204179, p-value=0.881745 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-01-28_04:31 Test no p-value 1 0.181174 2 0.219142 3 0.032658 4 0.162125 5 0.118660 6 0.429927 7 0.988796 8 0.601829 9 0.278179 10 0.876441 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.244219 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-01-28_04:31: (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 66623 0.03 66738 0.08 3 25000.00 25122 0.60 24987 0.01 4 6666.67 6607 0.53 6661 0.00 5 1388.89 1361 0.56 1328 2.67 6 238.10 241 0.04 235 0.04 7 34.72 38 0.31 45 3.04 8 4.96 7 0.84 5 0.00 p=0.17901 p=0.55884 Number of rngs required: 688094, p-value: 0.361 RESULTS OF CRAPS TEST for dh-ranFile-2016-01-28_04:31 No. of wins: Observed Expected 98314 98585.9 z-score=-1.216, pvalue=0.11201 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66472 66666.7 0.568 0.568 2 37669 37654.3 0.006 0.574 3 26980 26954.7 0.024 0.598 4 19374 19313.5 0.190 0.788 5 13748 13851.4 0.772 1.560 6 10061 9943.5 1.387 2.947 7 7213 7145.0 0.647 3.594 8 5134 5139.1 0.005 3.599 9 3673 3699.9 0.195 3.794 10 2718 2666.3 1.003 4.797 11 1933 1923.3 0.049 4.845 12 1377 1388.7 0.099 4.944 13 998 1003.7 0.033 4.977 14 700 726.1 0.941 5.918 15 505 525.8 0.826 6.744 16 385 381.2 0.039 6.782 17 268 276.5 0.264 7.046 18 213 200.8 0.737 7.784 19 141 146.0 0.170 7.954 20 104 106.2 0.046 8.000 21 334 287.1 7.657 15.657 Chisq= 15.66 for 20 degrees of freedom, p= 0.26231 SUMMARY of craptest p-value for no. of wins: 0.112010 p-value for throws/game: 0.262313 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-01-28_04:31 No. of wins: Observed Expected 99000 98585.9 z-score= 1.852, pvalue=0.96801 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66516 66666.7 0.341 0.341 2 37707 37654.3 0.074 0.414 3 26909 26954.7 0.078 0.492 4 19460 19313.5 1.112 1.604 5 13847 13851.4 0.001 1.605 6 9859 9943.5 0.719 2.324 7 7158 7145.0 0.024 2.347 8 5173 5139.1 0.224 2.571 9 3592 3699.9 3.145 5.716 10 2714 2666.3 0.853 6.570 11 1985 1923.3 1.977 8.547 12 1353 1388.7 0.920 9.467 13 1045 1003.7 1.698 11.165 14 768 726.1 2.413 13.578 15 541 525.8 0.437 14.015 16 360 381.2 1.174 15.189 17 298 276.5 1.665 16.854 18 191 200.8 0.481 17.335 19 145 146.0 0.007 17.342 20 114 106.2 0.571 17.913 21 265 287.1 1.703 19.616 Chisq= 19.62 for 20 degrees of freedom, p= 0.51783 SUMMARY of craptest p-value for no. of wins: 0.968007 p-value for throws/game: 0.517828 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0072,0.0104,0.0163,0.0198,0.0214,0.0281,0.0317,0.0327,0.0334,0.0336, 0.0361,0.0363,0.0406,0.0532,0.0663,0.0672,0.0673,0.0675,0.0682,0.0707, 0.0719,0.0725,0.0752,0.0757,0.0854,0.0868,0.0868,0.0913,0.1008,0.1120, 0.1143,0.1187,0.1307,0.1317,0.1398,0.1529,0.1567,0.1571,0.1576,0.1621, 0.1623,0.1625,0.1780,0.1790,0.1802,0.1812,0.1871,0.1893,0.1902,0.1990, 0.2033,0.2075,0.2092,0.2123,0.2152,0.2165,0.2191,0.2215,0.2337,0.2373, 0.2374,0.2442,0.2459,0.2484,0.2507,0.2569,0.2623,0.2646,0.2671,0.2684, 0.2693,0.2728,0.2730,0.2782,0.2807,0.2838,0.2853,0.2864,0.2920,0.2949, 0.2981,0.2986,0.3019,0.3025,0.3072,0.3081,0.3094,0.3149,0.3158,0.3223, 0.3229,0.3256,0.3291,0.3308,0.3405,0.3406,0.3416,0.3419,0.3558,0.3569, 0.3586,0.3610,0.3769,0.3818,0.3893,0.3938,0.3992,0.3997,0.4008,0.4104, 0.4110,0.4252,0.4260,0.4299,0.4363,0.4375,0.4375,0.4455,0.4541,0.4604, 0.4625,0.4636,0.4681,0.4743,0.4766,0.4955,0.4965,0.5060,0.5062,0.5144, 0.5155,0.5178,0.5200,0.5213,0.5237,0.5384,0.5403,0.5431,0.5479,0.5495, 0.5499,0.5501,0.5542,0.5588,0.5592,0.5665,0.5666,0.5680,0.5681,0.5875, 0.5923,0.5966,0.5990,0.6003,0.6018,0.6026,0.6038,0.6049,0.6110,0.6141, 0.6224,0.6257,0.6286,0.6332,0.6341,0.6348,0.6426,0.6434,0.6437,0.6446, 0.6461,0.6499,0.6562,0.6564,0.6576,0.6626,0.6707,0.6720,0.6729,0.6762, 0.6825,0.6845,0.6849,0.6892,0.6898,0.6906,0.6957,0.6972,0.6983,0.7044, 0.7047,0.7112,0.7125,0.7128,0.7141,0.7141,0.7208,0.7307,0.7310,0.7313, 0.7336,0.7566,0.7595,0.7608,0.7623,0.7707,0.7708,0.7789,0.7804,0.7812, 0.7910,0.7919,0.7943,0.7958,0.7975,0.8099,0.8194,0.8250,0.8279,0.8284, 0.8312,0.8343,0.8380,0.8380,0.8390,0.8433,0.8454,0.8495,0.8499,0.8551, 0.8600,0.8670,0.8686,0.8736,0.8743,0.8745,0.8764,0.8812,0.8817,0.8830, 0.8851,0.8854,0.8901,0.8994,0.9027,0.9098,0.9107,0.9194,0.9236,0.9258, 0.9289,0.9314,0.9324,0.9365,0.9370,0.9391,0.9423,0.9593,0.9620,0.9623, 0.9623,0.9625,0.9670,0.9680,0.9721,0.9756,0.9763,0.9793,0.9888, Overall p-value after applying KStest on 269 p-values = 0.900981 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.