RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-12-14_10:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.65 13.9292 0.327896 2 to 25 15.49 19.5711 0.703249 3 to 26 15.54 18.6536 0.651226 4 to 27 15.72 15.4742 0.438635 5 to 28 15.73 16.5332 0.513599 6 to 29 15.64 29.0081 0.965548 7 to 30 15.62 16.3572 0.501334 8 to 31 16.01 16.0185 0.477477 9 to 32 15.69 16.1687 0.488088 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.254833 Tough bday spacings test for dh-ranFile-2015-12-14_10:31: 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 28 74 100 114 76 43 25 14 8 7 (O-E)^2/E 0.4 2.0 0.0 0.1 2.7 0.1 1.6 0.8 0.1 0.3 2.1 Birthday Spacings: Sum(O-E)^2/E= 10.063, p= 0.565 RESULTS OF GCD FOR dh-ranFile-2015-12-14_10:31 Euclid's algorithm: p-value, steps to gcd: 0.783190 p-value, dist. of gcd's: 0.037192 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-12-14_10:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.145 0.489 0.862 0.570 0.396 0.626 0.661 0.457 Bits 8 to 15---> 0.295 0.509 0.110 0.696 0.455 0.305 0.115 0.740 Bits 16 to 23---> 0.287 0.668 0.158 0.276 0.310 0.051 0.568 0.582 Bits 24 to 31---> 0.713 0.671 0.147 0.194 0.071 0.824 0.563 0.292 KS test for the above 32 p values: 0.853 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-12-14_10:31, p-values for 5 runs: 0.1126, 0.6182, 0.8871, 0.0174, 0.9943 Rank test for binary matrices (31x31) for dh-ranFile-2015-12-14_10:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 227 211.4 1.148 1.148 r= 29 5194 5134.0 0.701 1.849 r= 30 23092 23103.0 0.005 1.855 r= 31 11487 11551.5 0.360 2.215 chi-square = 2.215 with df = 3; p-value = 0.471 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-12-14_10:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 213 211.4 0.012 0.012 r= 30 5109 5134.0 0.122 0.134 r= 31 22956 23103.0 0.936 1.070 r= 32 11722 11551.5 2.516 3.585 chi-square = 3.585 with df = 3; p-value = 0.690 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-12-14_10:31 b-rank test for bits 1 to 8, p=0.92155 b-rank test for bits 2 to 9, p=0.00562 b-rank test for bits 3 to 10, p=0.74535 b-rank test for bits 4 to 11, p=0.13640 b-rank test for bits 5 to 12, p=0.67327 b-rank test for bits 6 to 13, p=0.97143 b-rank test for bits 7 to 14, p=0.83555 b-rank test for bits 8 to 15, p=0.05630 b-rank test for bits 9 to 16, p=0.93978 b-rank test for bits 10 to 17, p=0.74178 b-rank test for bits 11 to 18, p=0.35360 b-rank test for bits 12 to 19, p=0.33806 b-rank test for bits 13 to 20, p=0.76718 b-rank test for bits 14 to 21, p=0.58412 b-rank test for bits 15 to 22, p=0.15579 b-rank test for bits 16 to 23, p=0.80870 b-rank test for bits 17 to 24, p=0.36977 b-rank test for bits 18 to 25, p=0.40040 b-rank test for bits 19 to 26, p=0.23711 b-rank test for bits 20 to 27, p=0.74621 b-rank test for bits 21 to 28, p=0.29333 b-rank test for bits 22 to 29, p=0.15021 b-rank test for bits 23 to 30, p=0.19310 b-rank test for bits 24 to 31, p=0.67623 b-rank test for bits 25 to 32, p=0.58823 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 = 0.964075 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-12-14_10:31 (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 141403 -1.18 0.118402 2 142147 0.56 0.710657 3 142069 0.37 0.645448 4 142019 0.26 0.601117 5 141520 -0.91 0.181504 6 141512 -0.93 0.176615 7 141818 -0.21 0.415512 8 142143 0.55 0.707453 9 142048 0.32 0.627029 10 141693 -0.51 0.306624 11 142688 1.82 0.965569 12 142040 0.31 0.619933 13 141937 0.06 0.525774 14 142557 1.51 0.934892 15 142136 0.53 0.701806 16 141988 0.18 0.572918 17 141975 0.15 0.560972 18 141659 -0.58 0.279313 19 141449 -1.08 0.141067 20 141946 0.09 0.534139 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-12-14_10:31 Bits used No. missing words z-score p-value 23 to 32 141406 -1.7356 0.041315 22 to 31 141651 -0.8908 0.186520 21 to 30 141162 -2.5770 0.004983 20 to 29 141883 -0.0908 0.463829 19 to 28 141886 -0.0804 0.467940 18 to 27 141462 -1.5425 0.061474 17 to 26 142254 1.1885 0.882685 16 to 25 142271 1.2471 0.893827 15 to 24 141891 -0.0632 0.474801 14 to 23 141679 -0.7942 0.213528 13 to 22 141760 -0.5149 0.303301 12 to 21 142356 1.5402 0.938249 11 to 20 142207 1.0264 0.847660 10 to 19 141711 -0.6839 0.247020 9 to 18 141604 -1.0529 0.146202 8 to 17 142539 2.1713 0.985045 7 to 16 142265 1.2264 0.889985 6 to 15 141990 0.2782 0.609560 5 to 14 141992 0.2851 0.612204 4 to 13 141746 -0.5632 0.286647 3 to 12 142530 2.1402 0.983832 2 to 11 141614 -1.0184 0.154249 1 to 10 142008 0.3402 0.633163 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-12-14_10:31 Bits used No. missing words z-score p-value 28 to 32 141815 -0.3198 0.374574 27 to 31 141579 -1.1198 0.131407 26 to 30 141813 -0.3265 0.372007 25 to 29 141972 0.2124 0.584118 24 to 28 142266 1.2091 0.886678 23 to 27 141871 -0.1299 0.448310 22 to 26 141509 -1.3571 0.087383 21 to 25 141869 -0.1367 0.445629 20 to 24 141511 -1.3503 0.088465 19 to 23 142234 1.1006 0.864459 18 to 22 141823 -0.2926 0.384897 17 to 21 142089 0.6091 0.728755 16 to 20 142090 0.6124 0.729877 15 to 19 141416 -1.6723 0.047232 14 to 18 141341 -1.9265 0.027018 13 to 17 142016 0.3616 0.641172 12 to 16 141935 0.0870 0.534671 11 to 15 141428 -1.6316 0.051379 10 to 14 141945 0.1209 0.548121 9 to 13 141976 0.2260 0.589399 8 to 12 141927 0.0599 0.523882 7 to 11 142403 1.6735 0.952881 6 to 10 141573 -1.1401 0.127122 5 to 9 141882 -0.0926 0.463093 4 to 8 141968 0.1989 0.578822 3 to 7 142267 1.2124 0.887328 2 to 6 142414 1.7107 0.956436 1 to 5 141636 -0.9265 0.177082 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-12-14_10:31 Bits used No. missing words z-score p-value 31 to 32 142224 0.9282 0.823356 30 to 31 141388 -1.5378 0.062043 29 to 30 141458 -1.3314 0.091536 28 to 29 142699 2.3294 0.990081 27 to 28 141862 -0.1396 0.444482 26 to 27 142061 0.4474 0.672708 25 to 26 141880 -0.0865 0.465527 24 to 25 142008 0.2911 0.614498 23 to 24 142107 0.5831 0.720086 22 to 23 141659 -0.7384 0.230125 21 to 22 141888 -0.0629 0.474915 20 to 21 141981 0.2114 0.583719 19 to 20 142199 0.8545 0.803582 18 to 19 141959 0.1465 0.558244 17 to 18 141810 -0.2930 0.384758 16 to 17 141844 -0.1927 0.423592 15 to 16 141972 0.1849 0.573333 14 to 15 141745 -0.4847 0.313927 13 to 14 142048 0.4091 0.658751 12 to 13 141671 -0.7030 0.241016 11 to 12 142725 2.4061 0.991938 10 to 11 142456 1.6126 0.946584 9 to 10 142043 0.3943 0.653323 8 to 9 142020 0.3265 0.627962 7 to 8 142521 1.8043 0.964411 6 to 7 141504 -1.1957 0.115914 5 to 6 142223 0.9253 0.822590 4 to 5 141941 0.0934 0.537216 3 to 4 142175 0.7837 0.783388 2 to 3 141538 -1.0954 0.136678 1 to 2 141873 -0.1072 0.457328 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-12-14_10:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2520.82 0.294 0.615791 Test results for specific bytes for dh-ranFile-2015-12-14_10:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2497.39 -0.037 0.485251 2 to 9 2756.00 3.620 0.999853 3 to 10 2514.19 0.201 0.579533 4 to 11 2397.93 -1.443 0.074442 5 to 12 2553.46 0.756 0.775192 6 to 13 2486.35 -0.193 0.423451 7 to 14 2526.11 0.369 0.644014 8 to 15 2421.92 -1.104 0.134738 9 to 16 2589.38 1.264 0.896889 10 to 17 2528.74 0.406 0.657767 11 to 18 2468.57 -0.444 0.328345 12 to 19 2426.61 -1.038 0.149669 13 to 20 2438.96 -0.863 0.194012 14 to 21 2459.92 -0.567 0.285396 15 to 22 2546.57 0.659 0.744912 16 to 23 2453.62 -0.656 0.255931 17 to 24 2321.47 -2.525 0.005789 18 to 25 2396.37 -1.466 0.071387 19 to 26 2592.04 1.302 0.903470 20 to 27 2487.67 -0.174 0.430796 21 to 28 2535.95 0.508 0.694393 22 to 29 2596.79 1.369 0.914465 23 to 30 2491.10 -0.126 0.449938 24 to 31 2495.99 -0.057 0.477408 25 to 32 2462.44 -0.531 0.297665 CDPARK for dh-ranFile-2015-12-14_10:31: 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 3548 1.1416 0.873180 3544 0.9589 0.831196 3524 0.0457 0.518210 3474 -2.2374 0.012629 3513 -0.4566 0.323972 3524 0.0457 0.518210 3505 -0.8219 0.205562 3513 -0.4566 0.323972 3557 1.5525 0.939730 3514 -0.4110 0.340551 Square side=100, avg. no. parked=3521.60 sample std.=22.83 p-value of the KSTEST for those 10 p-values: 0.882265 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-12-14_10:31 0.4522,0.5320,0.0818,0.4255,0.7041,0.8207,0.2981,0.8045,0.0534,0.8280, The KS test for those 10 p-values: 0.906096 The 3DSPHERES test for dh-ranFile-2015-12-14_10:31 sample no r^3 equiv. uni. 1 14.331 0.379791 2 73.652 0.914142 3 18.132 0.453591 4 35.647 0.695245 5 45.804 0.782768 6 33.078 0.667991 7 6.221 0.187278 8 42.994 0.761437 9 2.891 0.091879 10 18.596 0.461983 11 35.971 0.698517 12 3.006 0.095329 13 53.956 0.834456 14 20.242 0.490704 15 11.338 0.314722 16 0.187 0.006209 17 6.600 0.197471 18 94.471 0.957106 19 30.090 0.633228 20 28.165 0.608914 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.975542 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-12-14_10:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.5 0.1 1.1 -0.8 0.9 -0.1 -0.2 2.1 0.4 0.5 -1.5 -0.5 -0.8 -0.1 0.9 1.1 -0.1 -1.6 0.1 -0.5 0.5 0.2 -0.4 -0.6 -1.1 0.7 -0.2 -0.6 1.7 0.7 2.3 2.2 2.2 0.6 -0.3 1.2 -0.7 0.5 0.4 -1.3 1.0 -1.1 Chi-square with 42 degrees of freedom:43.109364 z-score=0.121042, p-value=0.576385 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-12-14_10:31 Test no p-value 1 0.312044 2 0.393297 3 0.066192 4 0.046340 5 0.042364 6 0.135152 7 0.416307 8 0.881845 9 0.002902 10 0.558923 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.013385 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-12-14_10:31: (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 66781 0.20 66813 0.32 3 25000.00 24902 0.38 24784 1.87 4 6666.67 6626 0.25 6670 0.00 5 1388.89 1404 0.16 1442 2.03 6 238.10 253 0.93 249 0.50 7 34.72 28 1.30 36 0.05 8 4.96 5 0.00 5 0.00 p=0.22010 p=0.42596 Number of rngs required: 687888, p-value: 0.276 RESULTS OF CRAPS TEST for dh-ranFile-2015-12-14_10:31 No. of wins: Observed Expected 98450 98585.9 z-score=-0.608, pvalue=0.27171 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66430 66666.7 0.840 0.840 2 37633 37654.3 0.012 0.852 3 27016 26954.7 0.139 0.991 4 19361 19313.5 0.117 1.109 5 13845 13851.4 0.003 1.111 6 9823 9943.5 1.461 2.573 7 7265 7145.0 2.015 4.587 8 5157 5139.1 0.063 4.650 9 3719 3699.9 0.099 4.749 10 2714 2666.3 0.853 5.602 11 1948 1923.3 0.316 5.919 12 1436 1388.7 1.608 7.527 13 990 1003.7 0.187 7.714 14 716 726.1 0.142 7.856 15 518 525.8 0.117 7.973 16 400 381.2 0.932 8.905 17 290 276.5 0.655 9.560 18 197 200.8 0.073 9.633 19 150 146.0 0.110 9.744 20 105 106.2 0.014 9.758 21 287 287.1 0.000 9.758 Chisq= 9.76 for 20 degrees of freedom, p= 0.02764 SUMMARY of craptest p-value for no. of wins: 0.271714 p-value for throws/game: 0.027643 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-12-14_10:31 No. of wins: Observed Expected 98134 98585.9 z-score=-2.021, pvalue=0.02164 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66577 66666.7 0.121 0.121 2 37678 37654.3 0.015 0.135 3 26979 26954.7 0.022 0.157 4 19280 19313.5 0.058 0.215 5 13853 13851.4 0.000 0.215 6 9783 9943.5 2.592 2.808 7 7120 7145.0 0.088 2.895 8 5300 5139.1 5.039 7.935 9 3642 3699.9 0.905 8.840 10 2723 2666.3 1.206 10.045 11 1941 1923.3 0.162 10.208 12 1450 1388.7 2.702 12.910 13 996 1003.7 0.059 12.969 14 755 726.1 1.147 14.116 15 531 525.8 0.051 14.167 16 377 381.2 0.045 14.212 17 273 276.5 0.045 14.258 18 209 200.8 0.332 14.590 19 133 146.0 1.155 15.745 20 104 106.2 0.046 15.791 21 296 287.1 0.275 16.066 Chisq= 16.07 for 20 degrees of freedom, p= 0.28748 SUMMARY of craptest p-value for no. of wins: 0.021641 p-value for throws/game: 0.287479 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0029,0.0050,0.0056,0.0058,0.0062,0.0126,0.0134,0.0174,0.0216,0.0270, 0.0276,0.0372,0.0413,0.0424,0.0463,0.0472,0.0508,0.0514,0.0534,0.0563, 0.0615,0.0620,0.0662,0.0714,0.0714,0.0744,0.0818,0.0874,0.0885,0.0915, 0.0919,0.0953,0.1099,0.1126,0.1145,0.1159,0.1184,0.1271,0.1314,0.1347, 0.1352,0.1364,0.1367,0.1411,0.1447,0.1462,0.1474,0.1497,0.1502,0.1542, 0.1558,0.1577,0.1766,0.1771,0.1815,0.1865,0.1873,0.1931,0.1940,0.1941, 0.1975,0.2056,0.2135,0.2201,0.2301,0.2371,0.2410,0.2470,0.2548,0.2559, 0.2717,0.2757,0.2763,0.2793,0.2854,0.2866,0.2873,0.2875,0.2919,0.2933, 0.2947,0.2977,0.2981,0.3033,0.3048,0.3066,0.3104,0.3120,0.3139,0.3147, 0.3240,0.3240,0.3279,0.3283,0.3381,0.3406,0.3536,0.3698,0.3720,0.3746, 0.3798,0.3848,0.3849,0.3933,0.3962,0.4004,0.4155,0.4163,0.4235,0.4236, 0.4255,0.4260,0.4308,0.4386,0.4445,0.4456,0.4483,0.4499,0.4522,0.4536, 0.4547,0.4573,0.4573,0.4620,0.4631,0.4638,0.4655,0.4679,0.4710,0.4748, 0.4749,0.4774,0.4775,0.4853,0.4881,0.4886,0.4907,0.5013,0.5090,0.5136, 0.5182,0.5182,0.5239,0.5258,0.5320,0.5341,0.5347,0.5372,0.5481,0.5582, 0.5589,0.5610,0.5625,0.5651,0.5677,0.5704,0.5729,0.5733,0.5764,0.5788, 0.5795,0.5821,0.5837,0.5841,0.5841,0.5882,0.5894,0.6011,0.6089,0.6096, 0.6122,0.6145,0.6158,0.6182,0.6199,0.6263,0.6270,0.6280,0.6332,0.6332, 0.6412,0.6440,0.6454,0.6512,0.6533,0.6578,0.6588,0.6608,0.6680,0.6685, 0.6706,0.6727,0.6733,0.6762,0.6902,0.6944,0.6952,0.6956,0.6985,0.7018, 0.7032,0.7041,0.7075,0.7107,0.7134,0.7201,0.7288,0.7299,0.7397,0.7418, 0.7449,0.7453,0.7462,0.7614,0.7672,0.7752,0.7828,0.7832,0.7834,0.8036, 0.8045,0.8087,0.8207,0.8226,0.8234,0.8241,0.8280,0.8312,0.8345,0.8355, 0.8477,0.8531,0.8618,0.8645,0.8732,0.8818,0.8823,0.8827,0.8867,0.8871, 0.8873,0.8900,0.8938,0.8969,0.9035,0.9061,0.9141,0.9145,0.9215,0.9349, 0.9382,0.9397,0.9398,0.9466,0.9529,0.9564,0.9571,0.9641,0.9644,0.9655, 0.9656,0.9714,0.9755,0.9838,0.9850,0.9901,0.9919,0.9943,0.9999, Overall p-value after applying KStest on 269 p-values = 0.619528 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.