RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-01-26_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 15.85 20.6450 0.757428 2 to 25 15.86 10.1702 0.103679 3 to 26 15.91 8.0351 0.034210 4 to 27 15.75 18.5350 0.644134 5 to 28 16.04 13.4580 0.294972 6 to 29 15.60 22.2876 0.826091 7 to 30 15.89 16.2625 0.494692 8 to 31 15.56 14.7614 0.387335 9 to 32 16.15 15.6772 0.453179 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.864127 Tough bday spacings test for dh-ranFile-2016-01-26_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 6 42 60 86 105 90 60 25 16 5 5 (O-E)^2/E 1.1 0.8 2.4 1.4 0.5 1.8 1.2 0.8 0.1 0.4 0.2 Birthday Spacings: Sum(O-E)^2/E= 10.675, p= 0.617 RESULTS OF GCD FOR dh-ranFile-2016-01-26_09:31 Euclid's algorithm: p-value, steps to gcd: 0.786916 p-value, dist. of gcd's: 0.881650 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-01-26_09:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.571 0.842 0.430 0.768 0.852 0.343 0.374 0.743 Bits 8 to 15---> 0.480 0.074 0.543 0.415 0.497 0.072 0.805 0.041 Bits 16 to 23---> 0.173 0.328 0.888 0.672 0.504 0.128 0.465 0.342 Bits 24 to 31---> 0.295 0.081 0.060 0.009 0.464 0.503 0.564 0.102 KS test for the above 32 p values: 0.866 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-01-26_09:31, p-values for 5 runs: 0.3621, 0.8217, 0.6612, 0.8188, 0.6014 Rank test for binary matrices (31x31) for dh-ranFile-2016-01-26_09:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 203 211.4 0.335 0.335 r= 29 5153 5134.0 0.070 0.405 r= 30 23204 23103.0 0.441 0.847 r= 31 11440 11551.5 1.077 1.923 chi-square = 1.923 with df = 3; p-value = 0.412 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-01-26_09:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 190 211.4 2.170 2.170 r= 30 5239 5134.0 2.147 4.317 r= 31 23223 23103.0 0.623 4.940 r= 32 11348 11551.5 3.586 8.525 chi-square = 8.525 with df = 3; p-value = 0.964 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-01-26_09:31 b-rank test for bits 1 to 8, p=0.53084 b-rank test for bits 2 to 9, p=0.12883 b-rank test for bits 3 to 10, p=0.02866 b-rank test for bits 4 to 11, p=0.31252 b-rank test for bits 5 to 12, p=0.99869 b-rank test for bits 6 to 13, p=0.10531 b-rank test for bits 7 to 14, p=0.16947 b-rank test for bits 8 to 15, p=0.37925 b-rank test for bits 9 to 16, p=0.74153 b-rank test for bits 10 to 17, p=0.76699 b-rank test for bits 11 to 18, p=0.72264 b-rank test for bits 12 to 19, p=0.90488 b-rank test for bits 13 to 20, p=0.56416 b-rank test for bits 14 to 21, p=0.08428 b-rank test for bits 15 to 22, p=0.15206 b-rank test for bits 16 to 23, p=0.14659 b-rank test for bits 17 to 24, p=0.10006 b-rank test for bits 18 to 25, p=0.23156 b-rank test for bits 19 to 26, p=0.11276 b-rank test for bits 20 to 27, p=0.41523 b-rank test for bits 21 to 28, p=0.47110 b-rank test for bits 22 to 29, p=0.07366 b-rank test for bits 23 to 30, p=0.30726 b-rank test for bits 24 to 31, p=0.28767 b-rank test for bits 25 to 32, p=0.93864 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 = 0.046888 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-01-26_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 141204 -1.65 0.049680 2 141164 -1.74 0.040805 3 141585 -0.76 0.224291 4 140924 -2.30 0.010663 5 142175 0.62 0.732610 6 141994 0.20 0.578410 7 141873 -0.08 0.466177 8 142229 0.75 0.772436 9 142446 1.25 0.895061 10 142781 2.04 0.979156 11 141856 -0.12 0.450419 12 142334 0.99 0.839455 13 142384 1.11 0.866294 14 141946 0.09 0.534139 15 141877 -0.08 0.469894 16 142471 1.31 0.905293 17 141077 -1.94 0.025906 18 142061 0.35 0.638469 19 141826 -0.19 0.422815 20 142110 0.47 0.680413 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-01-26_09:31 Bits used No. missing words z-score p-value 23 to 32 141794 -0.3977 0.345430 22 to 31 142435 1.8127 0.965058 21 to 30 141411 -1.7184 0.042864 20 to 29 141978 0.2368 0.593591 19 to 28 142771 2.9713 0.998517 18 to 27 142349 1.5161 0.935253 17 to 26 141479 -1.4839 0.068918 16 to 25 141600 -1.0667 0.143064 15 to 24 142179 0.9299 0.823788 14 to 23 142293 1.3230 0.907082 13 to 22 141800 -0.3770 0.353087 12 to 21 142100 0.6575 0.744565 11 to 20 142262 1.2161 0.888027 10 to 19 141887 -0.0770 0.469312 9 to 18 142526 2.1264 0.983267 8 to 17 141433 -1.6425 0.050241 7 to 16 141787 -0.4218 0.336575 6 to 15 142020 0.3816 0.648629 5 to 14 141928 0.0644 0.525666 4 to 13 141669 -0.8287 0.203630 3 to 12 142183 0.9437 0.827336 2 to 11 142369 1.5851 0.943525 1 to 10 142505 2.0540 0.980014 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-01-26_09:31 Bits used No. missing words z-score p-value 28 to 32 141964 0.1853 0.573512 27 to 31 142196 0.9718 0.834416 26 to 30 141839 -0.2384 0.405783 25 to 29 142091 0.6158 0.730997 24 to 28 141469 -1.4926 0.067765 23 to 27 142135 0.7650 0.777859 22 to 26 142086 0.5989 0.725374 21 to 25 141937 0.0938 0.537365 20 to 24 141704 -0.6960 0.243204 19 to 23 142018 0.3684 0.643702 18 to 22 142796 3.0057 0.998675 17 to 21 141608 -1.0215 0.153519 16 to 20 142453 1.8429 0.967332 15 to 19 142369 1.5582 0.940407 14 to 18 142383 1.6057 0.945826 13 to 17 142101 0.6497 0.742066 12 to 16 141963 0.1819 0.572182 11 to 15 142392 1.6362 0.949098 10 to 14 141751 -0.5367 0.295733 9 to 13 141961 0.1752 0.569520 8 to 12 142080 0.5785 0.718551 7 to 11 141977 0.2294 0.590717 6 to 10 141531 -1.2825 0.099838 5 to 9 141828 -0.2757 0.391391 4 to 8 141738 -0.5808 0.280695 3 to 7 142322 1.3989 0.919076 2 to 6 141998 0.3006 0.618131 1 to 5 141547 -1.2282 0.109679 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-01-26_09:31 Bits used No. missing words z-score p-value 31 to 32 142158 0.7335 0.768385 30 to 31 142103 0.5713 0.716101 29 to 30 141696 -0.6293 0.264579 28 to 29 141835 -0.2193 0.413223 27 to 28 141746 -0.4818 0.314974 26 to 27 141733 -0.5201 0.301480 25 to 26 141872 -0.1101 0.456158 24 to 25 142109 0.5890 0.722068 23 to 24 142542 1.8663 0.968999 22 to 23 141709 -0.5909 0.277279 21 to 22 142169 0.7660 0.778158 20 to 21 141471 -1.2930 0.098004 19 to 20 141872 -0.1101 0.456158 18 to 19 141344 -1.6676 0.047694 17 to 18 142448 1.5890 0.943969 16 to 17 142152 0.7158 0.762955 15 to 16 141803 -0.3137 0.376891 14 to 15 142187 0.8191 0.793631 13 to 14 141572 -0.9951 0.159850 12 to 13 141939 0.0875 0.534872 11 to 12 142368 1.3530 0.911974 10 to 11 141653 -0.7561 0.224784 9 to 10 141573 -0.9921 0.160569 8 to 9 141582 -0.9656 0.167128 7 to 8 142306 1.1701 0.879023 6 to 7 142282 1.0993 0.864186 5 to 6 141726 -0.5408 0.294324 4 to 5 142315 1.1967 0.884282 3 to 4 141847 -0.1839 0.427060 2 to 3 141952 0.1259 0.550083 1 to 2 142022 0.3324 0.630191 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-01-26_09:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2604.94 1.484 0.931102 Test results for specific bytes for dh-ranFile-2016-01-26_09:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2460.79 -0.554 0.289628 2 to 9 2492.83 -0.101 0.459643 3 to 10 2527.51 0.389 0.651387 4 to 11 2429.84 -0.992 0.160555 5 to 12 2515.37 0.217 0.586017 6 to 13 2648.09 2.094 0.981884 7 to 14 2483.41 -0.235 0.407235 8 to 15 2566.09 0.935 0.825015 9 to 16 2514.08 0.199 0.578917 10 to 17 2376.68 -1.744 0.040582 11 to 18 2488.71 -0.160 0.436547 12 to 19 2518.03 0.255 0.600646 13 to 20 2656.20 2.209 0.986414 14 to 21 2479.69 -0.287 0.386985 15 to 22 2604.79 1.482 0.930823 16 to 23 2499.71 -0.004 0.498375 17 to 24 2479.60 -0.289 0.386459 18 to 25 2600.96 1.428 0.923315 19 to 26 2576.74 1.085 0.861097 20 to 27 2502.04 0.029 0.511484 21 to 28 2525.80 0.365 0.642402 22 to 29 2411.35 -1.254 0.104963 23 to 30 2508.02 0.113 0.545138 24 to 31 2513.53 0.191 0.575872 25 to 32 2639.13 1.968 0.975446 CDPARK for dh-ranFile-2016-01-26_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 3546 1.0502 0.853193 3498 -1.1416 0.126820 3558 1.5982 0.944998 3511 -0.5479 0.291865 3503 -0.9132 0.180558 3489 -1.5525 0.060270 3515 -0.3653 0.357445 3507 -0.7306 0.232514 3512 -0.5023 0.307734 3527 0.1826 0.572463 Square side=100, avg. no. parked=3516.60 sample std.=20.31 p-value of the KSTEST for those 10 p-values: 0.338972 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-01-26_09:31 0.4603,0.3323,0.5872,0.7192,0.5435,0.1131,0.4346,0.3110,0.8551,0.5565, The KS test for those 10 p-values: 0.585837 The 3DSPHERES test for dh-ranFile-2016-01-26_09:31 sample no r^3 equiv. uni. 1 11.553 0.319628 2 9.272 0.265860 3 17.654 0.444831 4 16.135 0.415981 5 57.768 0.854212 6 112.368 0.976379 7 27.151 0.595467 8 22.416 0.526305 9 114.325 0.977870 10 127.591 0.985779 11 10.294 0.290466 12 17.300 0.438236 13 45.651 0.781660 14 21.196 0.506645 15 9.320 0.267053 16 5.543 0.168712 17 19.299 0.474445 18 119.487 0.981368 19 59.101 0.860547 20 55.304 0.841734 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.077495 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-01-26_09:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -1.6 0.3 0.5 -1.1 -1.4 1.8 -0.2 0.1 -1.7 1.5 0.6 -0.5 0.4 -2.2 0.5 -0.3 0.3 -1.0 2.2 -0.7 0.9 -0.9 0.1 0.8 1.2 0.3 -0.6 -0.5 -1.4 0.2 -1.1 -0.3 -0.6 0.5 0.4 -0.7 -0.1 -0.4 2.1 0.1 0.0 -1.1 Chi-square with 42 degrees of freedom:41.748320 z-score=-0.027461, p-value=0.518082 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-01-26_09:31 Test no p-value 1 0.460249 2 0.973246 3 0.000142 4 0.000369 5 0.837521 6 0.018118 7 0.959841 8 0.144113 9 0.916800 10 0.281218 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.007908 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-01-26_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 66453 0.68 66594 0.08 3 25000.00 25358 5.13 25076 0.23 4 6666.67 6514 3.50 6705 0.22 5 1388.89 1388 0.00 1334 2.17 6 238.10 243 0.10 248 0.41 7 34.72 38 0.31 36 0.05 8 4.96 5 0.00 6 0.22 p=0.86302 p=0.23977 Number of rngs required: 690994, p-value: 0.999 RESULTS OF CRAPS TEST for dh-ranFile-2016-01-26_09:31 No. of wins: Observed Expected 98529 98585.9 z-score=-0.254, pvalue=0.39963 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66800 66666.7 0.267 0.267 2 37311 37654.3 3.130 3.397 3 26844 26954.7 0.455 3.852 4 19371 19313.5 0.171 4.023 5 13931 13851.4 0.457 4.480 6 9758 9943.5 3.462 7.943 7 7249 7145.0 1.513 9.456 8 5259 5139.1 2.799 12.254 9 3718 3699.9 0.089 12.343 10 2701 2666.3 0.452 12.795 11 1930 1923.3 0.023 12.818 12 1386 1388.7 0.005 12.823 13 1070 1003.7 4.377 17.201 14 685 726.1 2.331 19.532 15 557 525.8 1.847 21.379 16 359 381.2 1.287 22.666 17 323 276.5 7.806 30.472 18 208 200.8 0.256 30.728 19 152 146.0 0.248 30.976 20 99 106.2 0.490 31.466 21 289 287.1 0.012 31.478 Chisq= 31.48 for 20 degrees of freedom, p= 0.95081 SUMMARY of craptest p-value for no. of wins: 0.399630 p-value for throws/game: 0.950814 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-01-26_09:31 No. of wins: Observed Expected 98579 98585.9 z-score=-0.031, pvalue=0.48776 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66923 66666.7 0.986 0.986 2 37641 37654.3 0.005 0.990 3 26920 26954.7 0.045 1.035 4 19139 19313.5 1.576 2.611 5 13832 13851.4 0.027 2.638 6 9952 9943.5 0.007 2.645 7 7219 7145.0 0.766 3.411 8 5108 5139.1 0.188 3.599 9 3690 3699.9 0.026 3.625 10 2608 2666.3 1.275 4.900 11 1946 1923.3 0.267 5.167 12 1367 1388.7 0.340 5.508 13 1035 1003.7 0.975 6.483 14 718 726.1 0.091 6.574 15 493 525.8 2.050 8.625 16 372 381.2 0.220 8.844 17 269 276.5 0.206 9.050 18 193 200.8 0.305 9.355 19 143 146.0 0.061 9.416 20 103 106.2 0.097 9.513 21 329 287.1 6.111 15.624 Chisq= 15.62 for 20 degrees of freedom, p= 0.26034 SUMMARY of craptest p-value for no. of wins: 0.487764 p-value for throws/game: 0.260338 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0001,0.0004,0.0079,0.0090,0.0107,0.0181,0.0259,0.0287,0.0342,0.0406, 0.0408,0.0412,0.0429,0.0469,0.0477,0.0497,0.0502,0.0603,0.0603,0.0678, 0.0689,0.0716,0.0737,0.0738,0.0775,0.0807,0.0843,0.0980,0.0998,0.1001, 0.1022,0.1037,0.1050,0.1053,0.1097,0.1128,0.1131,0.1268,0.1282,0.1288, 0.1431,0.1441,0.1466,0.1521,0.1535,0.1599,0.1606,0.1606,0.1671,0.1687, 0.1695,0.1728,0.1806,0.2036,0.2243,0.2248,0.2316,0.2325,0.2398,0.2432, 0.2603,0.2646,0.2659,0.2671,0.2773,0.2807,0.2812,0.2877,0.2896,0.2905, 0.2919,0.2943,0.2950,0.2952,0.2957,0.3015,0.3073,0.3077,0.3110,0.3125, 0.3150,0.3196,0.3277,0.3323,0.3366,0.3390,0.3422,0.3427,0.3454,0.3531, 0.3574,0.3621,0.3744,0.3769,0.3793,0.3865,0.3870,0.3873,0.3914,0.3996, 0.4058,0.4072,0.4115,0.4132,0.4149,0.4152,0.4160,0.4228,0.4271,0.4300, 0.4346,0.4365,0.4382,0.4448,0.4504,0.4532,0.4562,0.4562,0.4596,0.4602, 0.4603,0.4641,0.4655,0.4662,0.4693,0.4699,0.4711,0.4744,0.4803,0.4878, 0.4947,0.4972,0.4984,0.5026,0.5040,0.5066,0.5115,0.5181,0.5257,0.5263, 0.5308,0.5341,0.5349,0.5374,0.5428,0.5435,0.5451,0.5501,0.5565,0.5638, 0.5642,0.5695,0.5706,0.5722,0.5725,0.5735,0.5759,0.5784,0.5789,0.5858, 0.5860,0.5872,0.5907,0.5936,0.5955,0.6006,0.6014,0.6166,0.6181,0.6302, 0.6385,0.6424,0.6437,0.6441,0.6486,0.6514,0.6612,0.6724,0.6804,0.7161, 0.7186,0.7192,0.7221,0.7226,0.7254,0.7310,0.7326,0.7415,0.7421,0.7428, 0.7446,0.7574,0.7630,0.7670,0.7680,0.7684,0.7724,0.7779,0.7782,0.7817, 0.7869,0.7936,0.8053,0.8188,0.8217,0.8238,0.8250,0.8261,0.8273,0.8344, 0.8375,0.8395,0.8417,0.8419,0.8518,0.8532,0.8542,0.8551,0.8605,0.8611, 0.8630,0.8641,0.8642,0.8662,0.8663,0.8790,0.8816,0.8843,0.8878,0.8880, 0.8951,0.9049,0.9053,0.9071,0.9120,0.9168,0.9191,0.9233,0.9308,0.9311, 0.9353,0.9386,0.9404,0.9435,0.9440,0.9450,0.9458,0.9491,0.9508,0.9598, 0.9637,0.9651,0.9673,0.9690,0.9732,0.9754,0.9764,0.9779,0.9792,0.9800, 0.9814,0.9819,0.9833,0.9858,0.9864,0.9985,0.9987,0.9987,0.9991, Overall p-value after applying KStest on 269 p-values = 0.141263 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.