RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-02-14_09:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.74 21.5429 0.797056 2 to 25 15.56 16.8866 0.537925 3 to 26 15.93 16.0723 0.481288 4 to 27 15.93 16.5970 0.518022 5 to 28 15.84 6.2344 0.008533 6 to 29 15.84 21.2618 0.785203 7 to 30 15.96 26.6923 0.937262 8 to 31 15.91 12.6783 0.242558 9 to 32 15.93 15.7350 0.457305 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.789234 Tough bday spacings test for dh-ranFile-2017-02-14_09:31: 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 11 35 79 83 91 93 51 31 19 1 6 (O-E)^2/E 0.4 0.1 0.4 2.2 0.5 2.8 0.0 0.1 1.1 4.8 0.9 Birthday Spacings: Sum(O-E)^2/E= 13.278, p= 0.791 RESULTS OF GCD FOR dh-ranFile-2017-02-14_09:31 Euclid's algorithm: p-value, steps to gcd: 0.345094 p-value, dist. of gcd's: 0.770943 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-02-14_09:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.616 0.591 0.963 0.230 0.261 0.036 0.065 0.023 Bits 8 to 15---> 0.233 0.290 0.667 0.368 0.337 0.689 0.875 0.475 Bits 16 to 23---> 0.600 0.150 0.929 0.207 0.539 0.367 0.926 0.880 Bits 24 to 31---> 0.982 0.011 0.968 0.702 0.832 0.154 0.161 0.522 KS test for the above 32 p values: 0.244 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-02-14_09:31, p-values for 5 runs: 0.0582, 0.5926, 0.7135, 0.7200, 0.1425 Rank test for binary matrices (31x31) for dh-ranFile-2017-02-14_09:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 206 211.4 0.139 0.139 r= 29 5187 5134.0 0.547 0.686 r= 30 22986 23103.0 0.593 1.279 r= 31 11621 11551.5 0.418 1.697 chi-square = 1.697 with df = 3; p-value = 0.362 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2017-02-14_09:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 217 211.4 0.147 0.147 r= 30 5124 5134.0 0.020 0.167 r= 31 23191 23103.0 0.335 0.502 r= 32 11468 11551.5 0.604 1.106 chi-square = 1.106 with df = 3; p-value = 0.224 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2017-02-14_09:31 b-rank test for bits 1 to 8, p=0.68415 b-rank test for bits 2 to 9, p=0.78748 b-rank test for bits 3 to 10, p=0.13455 b-rank test for bits 4 to 11, p=0.02434 b-rank test for bits 5 to 12, p=0.79064 b-rank test for bits 6 to 13, p=0.96808 b-rank test for bits 7 to 14, p=0.53406 b-rank test for bits 8 to 15, p=0.34519 b-rank test for bits 9 to 16, p=0.79881 b-rank test for bits 10 to 17, p=0.56521 b-rank test for bits 11 to 18, p=0.56479 b-rank test for bits 12 to 19, p=0.88133 b-rank test for bits 13 to 20, p=0.17611 b-rank test for bits 14 to 21, p=0.15688 b-rank test for bits 15 to 22, p=0.16491 b-rank test for bits 16 to 23, p=0.62826 b-rank test for bits 17 to 24, p=0.20646 b-rank test for bits 18 to 25, p=0.69536 b-rank test for bits 19 to 26, p=0.08797 b-rank test for bits 20 to 27, p=0.27717 b-rank test for bits 21 to 28, p=0.50299 b-rank test for bits 22 to 29, p=0.45330 b-rank test for bits 23 to 30, p=0.57252 b-rank test for bits 24 to 31, p=0.14891 b-rank test for bits 25 to 32, p=0.37923 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 = 0.761927 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-02-14_09:31 (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 141929 0.05 0.518328 2 142010 0.24 0.592977 3 140714 -2.79 0.002612 4 142215 0.71 0.762443 5 141613 -0.69 0.244356 6 141533 -0.88 0.189626 7 142555 1.51 0.934296 8 141951 0.10 0.538780 9 141633 -0.65 0.259259 10 142264 0.83 0.796354 11 141649 -0.61 0.271512 12 142386 1.11 0.867299 13 141573 -0.79 0.215987 14 142111 0.47 0.681248 15 141945 0.08 0.533210 16 141564 -0.81 0.209878 17 142186 0.65 0.740998 18 142354 1.04 0.850586 19 141957 0.11 0.544342 20 142101 0.45 0.672861 ---------------------------------------------------------------- OPSO test for dh-ranFile-2017-02-14_09:31 Bits used No. missing words z-score p-value 23 to 32 141976 0.2299 0.590914 22 to 31 141683 -0.7804 0.217564 21 to 30 141667 -0.8356 0.201684 20 to 29 141846 -0.2184 0.413567 19 to 28 141345 -1.9460 0.025829 18 to 27 142014 0.3609 0.640925 17 to 26 142254 1.1885 0.882685 16 to 25 141725 -0.6356 0.262512 15 to 24 142008 0.3402 0.633163 14 to 23 142216 1.0575 0.854854 13 to 22 142174 0.9127 0.819288 12 to 21 141521 -1.3391 0.090274 11 to 20 142417 1.7506 0.959991 10 to 19 141995 0.2954 0.616161 9 to 18 141953 0.1506 0.559849 8 to 17 141248 -2.2804 0.011291 7 to 16 141814 -0.3287 0.371182 6 to 15 141334 -1.9839 0.023634 5 to 14 141780 -0.4460 0.327811 4 to 13 141651 -0.8908 0.186520 3 to 12 142141 0.7989 0.787815 2 to 11 141782 -0.4391 0.330306 1 to 10 141917 0.0264 0.510550 ----------------------------------------------------------------- OQSO test for dh-ranFile-2017-02-14_09:31 Bits used No. missing words z-score p-value 28 to 32 142266 1.2091 0.886678 27 to 31 142274 1.2362 0.891802 26 to 30 142283 1.2667 0.897365 25 to 29 141752 -0.5333 0.296905 24 to 28 142316 1.3785 0.915982 23 to 27 142378 1.5887 0.943937 22 to 26 141529 -1.2893 0.098655 21 to 25 141993 0.2836 0.611652 20 to 24 141809 -0.3401 0.366890 19 to 23 141646 -0.8926 0.186024 18 to 22 141592 -1.0757 0.141032 17 to 21 141303 -2.0554 0.019922 16 to 20 142045 0.4599 0.677205 15 to 19 142506 2.0226 0.978443 14 to 18 141853 -0.1909 0.424283 13 to 17 142072 0.5514 0.709328 12 to 16 141936 0.0904 0.536018 11 to 15 141855 -0.1842 0.426940 10 to 14 141913 0.0124 0.504963 9 to 13 141875 -0.1164 0.453679 8 to 12 142162 0.8565 0.804142 7 to 11 141537 -1.2621 0.103450 6 to 10 142076 0.5650 0.713957 5 to 9 141767 -0.4825 0.314734 4 to 8 141804 -0.3571 0.360527 3 to 7 141716 -0.6554 0.256119 2 to 6 141414 -1.6791 0.046568 1 to 5 141626 -0.9604 0.168417 ----------------------------------------------------------------- DNA test for dh-ranFile-2017-02-14_09:31 Bits used No. missing words z-score p-value 31 to 32 141797 -0.3314 0.370187 30 to 31 141717 -0.5673 0.285240 29 to 30 141184 -2.1396 0.016193 28 to 29 142496 1.7306 0.958238 27 to 28 142112 0.5978 0.725029 26 to 27 142182 0.8043 0.789399 25 to 26 142124 0.6332 0.736713 24 to 25 142437 1.5565 0.940211 23 to 24 141364 -1.6086 0.053847 22 to 23 141804 -0.3107 0.378011 21 to 22 141713 -0.5791 0.281246 20 to 21 142027 0.3471 0.635745 19 to 20 141988 0.2321 0.591756 18 to 19 141985 0.2232 0.588316 17 to 18 141893 -0.0482 0.480790 16 to 17 142075 0.4887 0.687474 15 to 16 141925 0.0462 0.518434 14 to 15 141982 0.2144 0.584869 13 to 14 141314 -1.7561 0.039533 12 to 13 141984 0.2203 0.587168 11 to 12 142009 0.2940 0.615626 10 to 11 141818 -0.2694 0.393807 9 to 10 141554 -1.0482 0.147280 8 to 9 141753 -0.4612 0.322345 7 to 8 142297 1.1436 0.873599 6 to 7 142251 1.0079 0.843243 5 to 6 141743 -0.4906 0.311837 4 to 5 141707 -0.5968 0.275306 3 to 4 142161 0.7424 0.771074 2 to 3 141718 -0.5644 0.286243 1 to 2 141486 -1.2488 0.105876 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2017-02-14_09:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2389.93 -1.557 0.059774 Test results for specific bytes for dh-ranFile-2017-02-14_09:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2552.80 0.747 0.772373 2 to 9 2618.88 1.681 0.953639 3 to 10 2477.50 -0.318 0.375180 4 to 11 2373.07 -1.795 0.036317 5 to 12 2523.82 0.337 0.631910 6 to 13 2471.73 -0.400 0.344663 7 to 14 2389.35 -1.565 0.058808 8 to 15 2441.60 -0.826 0.204439 9 to 16 2401.16 -1.398 0.081077 10 to 17 2572.72 1.028 0.848107 11 to 18 2524.24 0.343 0.634103 12 to 19 2385.88 -1.614 0.053272 13 to 20 2342.44 -2.228 0.012931 14 to 21 2490.60 -0.133 0.447101 15 to 22 2397.99 -1.443 0.074558 16 to 23 2441.33 -0.830 0.203335 17 to 24 2453.59 -0.656 0.255788 18 to 25 2340.87 -2.250 0.012209 19 to 26 2485.12 -0.210 0.416690 20 to 27 2460.02 -0.565 0.285903 21 to 28 2498.63 -0.019 0.492284 22 to 29 2486.73 -0.188 0.425549 23 to 30 2571.57 1.012 0.844253 24 to 31 2414.01 -1.216 0.111981 25 to 32 2452.52 -0.671 0.250965 CDPARK for dh-ranFile-2017-02-14_09:31: 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 3550 1.2329 0.891189 3526 0.1370 0.554479 3565 1.9178 0.972432 3534 0.5023 0.692266 3550 1.2329 0.891189 3573 2.2831 0.988788 3538 0.6849 0.753306 3543 0.9132 0.819442 3506 -0.7763 0.218799 3567 2.0091 0.977738 Square side=100, avg. no. parked=3545.20 sample std.=19.43 p-value of the KSTEST for those 10 p-values: 0.001633 Results for the MINIMUM DISTANCE test for dh-ranFile-2017-02-14_09:31 0.2300,0.4627,0.2683,0.5465,0.9437,0.9091,0.6778,0.2765,0.1074,0.0829, The KS test for those 10 p-values: 0.831280 The 3DSPHERES test for dh-ranFile-2017-02-14_09:31 sample no r^3 equiv. uni. 1 40.033 0.736689 2 13.472 0.361785 3 63.637 0.880117 4 8.381 0.243738 5 132.221 0.987813 6 139.562 0.990458 7 8.419 0.244706 8 4.614 0.142562 9 50.271 0.812822 10 18.041 0.451945 11 40.240 0.738500 12 28.952 0.619039 13 76.215 0.921173 14 28.456 0.612692 15 4.421 0.137032 16 2.683 0.085563 17 38.466 0.722571 18 49.154 0.805721 19 127.324 0.985652 20 31.810 0.653655 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.093778 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-02-14_09:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 0.9 1.1 -0.4 0.0 1.1 -0.4 0.6 0.1 -1.0 -0.7 0.9 1.3 0.0 1.1 0.0 0.3 0.4 0.4 -0.3 -0.0 -0.7 0.8 -1.5 -1.6 -2.4 1.2 0.3 1.0 -0.4 -0.4 -2.1 -1.0 -1.4 0.8 -0.7 2.6 0.2 0.1 -0.7 -0.6 0.0 -1.1 Chi-square with 42 degrees of freedom:41.671221 z-score=-0.035873, p-value=0.514718 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2017-02-14_09:31 Test no p-value 1 0.857035 2 0.514319 3 0.412276 4 0.241941 5 0.338149 6 0.112744 7 0.012948 8 0.805518 9 0.345964 10 0.280473 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.373954 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-02-14_09:31: (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 66572 0.13 66710 0.03 3 25000.00 25097 0.38 25056 0.13 4 6666.67 6642 0.09 6534 2.64 5 1388.89 1395 0.03 1430 1.22 6 238.10 251 0.70 230 0.28 7 34.72 37 0.15 36 0.05 8 4.96 5 0.00 3 0.77 p=0.03909 p=0.46991 Number of rngs required: 687896, p-value: 0.279 RESULTS OF CRAPS TEST for dh-ranFile-2017-02-14_09:31 No. of wins: Observed Expected 98205 98585.9 z-score=-1.703, pvalue=0.04424 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66476 66666.7 0.545 0.545 2 37534 37654.3 0.384 0.930 3 26944 26954.7 0.004 0.934 4 19342 19313.5 0.042 0.976 5 13908 13851.4 0.231 1.207 6 10077 9943.5 1.791 2.999 7 7247 7145.0 1.455 4.454 8 5028 5139.1 2.401 6.855 9 3686 3699.9 0.052 6.907 10 2742 2666.3 2.149 9.056 11 1889 1923.3 0.613 9.669 12 1402 1388.7 0.127 9.795 13 1011 1003.7 0.053 9.848 14 714 726.1 0.203 10.051 15 539 525.8 0.330 10.381 16 400 381.2 0.932 11.313 17 297 276.5 1.514 12.827 18 206 200.8 0.133 12.960 19 155 146.0 0.557 13.517 20 114 106.2 0.571 14.087 21 289 287.1 0.012 14.099 Chisq= 14.10 for 20 degrees of freedom, p= 0.17458 SUMMARY of craptest p-value for no. of wins: 0.044245 p-value for throws/game: 0.174583 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2017-02-14_09:31 No. of wins: Observed Expected 98496 98585.9 z-score=-0.402, pvalue=0.34388 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66909 66666.7 0.881 0.881 2 37652 37654.3 0.000 0.881 3 26940 26954.7 0.008 0.889 4 19154 19313.5 1.317 2.206 5 13818 13851.4 0.081 2.286 6 9836 9943.5 1.163 3.449 7 7388 7145.0 8.263 11.712 8 5229 5139.1 1.574 13.286 9 3599 3699.9 2.750 16.035 10 2628 2666.3 0.550 16.586 11 1924 1923.3 0.000 16.586 12 1346 1388.7 1.315 17.901 13 953 1003.7 2.562 20.464 14 769 726.1 2.530 22.993 15 507 525.8 0.675 23.668 16 379 381.2 0.012 23.680 17 270 276.5 0.155 23.835 18 172 200.8 4.139 27.973 19 145 146.0 0.007 27.980 20 115 106.2 0.727 28.707 21 267 287.1 1.409 30.116 Chisq= 30.12 for 20 degrees of freedom, p= 0.93200 SUMMARY of craptest p-value for no. of wins: 0.343879 p-value for throws/game: 0.932001 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0016,0.0026,0.0085,0.0113,0.0114,0.0122,0.0129,0.0129,0.0162,0.0199, 0.0230,0.0236,0.0243,0.0258,0.0363,0.0364,0.0391,0.0395,0.0442,0.0466, 0.0533,0.0538,0.0582,0.0588,0.0598,0.0653,0.0746,0.0811,0.0829,0.0856, 0.0880,0.0903,0.0938,0.0987,0.1035,0.1059,0.1074,0.1120,0.1127,0.1345, 0.1370,0.1410,0.1425,0.1426,0.1473,0.1489,0.1504,0.1543,0.1569,0.1610, 0.1649,0.1684,0.1746,0.1761,0.1860,0.1865,0.1896,0.2017,0.2033,0.2044, 0.2065,0.2065,0.2099,0.2160,0.2176,0.2188,0.2243,0.2298,0.2300,0.2326, 0.2419,0.2426,0.2437,0.2441,0.2444,0.2447,0.2510,0.2558,0.2561,0.2593, 0.2615,0.2625,0.2683,0.2715,0.2753,0.2765,0.2772,0.2794,0.2805,0.2812, 0.2852,0.2859,0.2862,0.2897,0.2969,0.3118,0.3147,0.3223,0.3278,0.3303, 0.3371,0.3381,0.3439,0.3447,0.3451,0.3452,0.3460,0.3605,0.3618,0.3623, 0.3669,0.3675,0.3681,0.3702,0.3712,0.3740,0.3752,0.3780,0.3792,0.3938, 0.4123,0.4136,0.4167,0.4243,0.4255,0.4269,0.4471,0.4519,0.4533,0.4537, 0.4573,0.4627,0.4699,0.4748,0.4808,0.4813,0.4923,0.5030,0.5050,0.5106, 0.5143,0.5147,0.5180,0.5183,0.5184,0.5224,0.5332,0.5341,0.5360,0.5379, 0.5388,0.5392,0.5443,0.5465,0.5545,0.5598,0.5648,0.5652,0.5725,0.5849, 0.5872,0.5883,0.5909,0.5913,0.5918,0.5926,0.5930,0.6001,0.6117,0.6127, 0.6156,0.6157,0.6162,0.6190,0.6283,0.6319,0.6332,0.6341,0.6357,0.6409, 0.6537,0.6673,0.6729,0.6772,0.6778,0.6812,0.6842,0.6875,0.6893,0.6923, 0.6954,0.7018,0.7093,0.7135,0.7140,0.7200,0.7226,0.7250,0.7367,0.7367, 0.7385,0.7410,0.7533,0.7619,0.7624,0.7709,0.7711,0.7724,0.7852,0.7875, 0.7878,0.7892,0.7894,0.7906,0.7915,0.7964,0.7971,0.7988,0.8041,0.8055, 0.8057,0.8128,0.8193,0.8194,0.8313,0.8324,0.8432,0.8443,0.8481,0.8506, 0.8549,0.8570,0.8673,0.8736,0.8751,0.8801,0.8802,0.8813,0.8827,0.8867, 0.8912,0.8912,0.8918,0.8974,0.9091,0.9160,0.9212,0.9261,0.9287,0.9320, 0.9343,0.9373,0.9402,0.9437,0.9439,0.9536,0.9582,0.9600,0.9631,0.9678, 0.9681,0.9724,0.9777,0.9784,0.9824,0.9857,0.9878,0.9888,0.9905, Overall p-value after applying KStest on 269 p-values = 0.338724 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.