RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-09-08_20:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 16.02 18.0803 0.616205 2 to 25 16.00 24.5923 0.895785 3 to 26 15.98 9.6339 0.081742 4 to 27 15.90 8.6011 0.048049 5 to 28 15.87 24.4504 0.892296 6 to 29 15.49 35.0097 0.993797 7 to 30 15.67 20.3971 0.745575 8 to 31 15.84 17.7427 0.594753 9 to 32 16.02 11.3573 0.162601 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.377613 Tough bday spacings test for dh-ranFile-2016-09-08_20:31: 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 14 34 71 88 101 86 58 18 19 7 4 (O-E)^2/E 2.6 0.2 0.1 1.0 0.1 0.8 0.7 4.7 1.1 0.0 0.0 Birthday Spacings: Sum(O-E)^2/E= 11.164, p= 0.655 RESULTS OF GCD FOR dh-ranFile-2016-09-08_20:31 Euclid's algorithm: p-value, steps to gcd: 0.120066 p-value, dist. of gcd's: 0.812268 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-09-08_20:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.266 0.195 0.004 0.527 0.709 0.859 0.427 0.283 Bits 8 to 15---> 0.197 0.121 0.597 0.622 0.380 0.548 0.201 0.230 Bits 16 to 23---> 0.199 0.526 0.442 0.269 0.312 0.315 0.234 0.652 Bits 24 to 31---> 0.539 0.861 0.818 0.092 0.364 0.817 0.670 0.312 KS test for the above 32 p values: 0.891 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-09-08_20:31, p-values for 5 runs: 0.9767, 0.0649, 0.7207, 0.7144, 0.9052 Rank test for binary matrices (31x31) for dh-ranFile-2016-09-08_20:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 242 211.4 4.424 4.424 r= 29 5212 5134.0 1.185 5.608 r= 30 23037 23103.0 0.189 5.797 r= 31 11509 11551.5 0.157 5.954 chi-square = 5.954 with df = 3; p-value = 0.886 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-09-08_20:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 202 211.4 0.420 0.420 r= 30 5179 5134.0 0.394 0.814 r= 31 23110 23103.0 0.002 0.816 r= 32 11509 11551.5 0.157 0.972 chi-square = 0.972 with df = 3; p-value = 0.192 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-09-08_20:31 b-rank test for bits 1 to 8, p=0.74105 b-rank test for bits 2 to 9, p=0.28644 b-rank test for bits 3 to 10, p=0.09189 b-rank test for bits 4 to 11, p=0.19312 b-rank test for bits 5 to 12, p=0.59164 b-rank test for bits 6 to 13, p=0.62836 b-rank test for bits 7 to 14, p=0.42601 b-rank test for bits 8 to 15, p=0.95972 b-rank test for bits 9 to 16, p=0.37234 b-rank test for bits 10 to 17, p=0.34338 b-rank test for bits 11 to 18, p=0.15016 b-rank test for bits 12 to 19, p=0.85853 b-rank test for bits 13 to 20, p=0.83053 b-rank test for bits 14 to 21, p=0.07115 b-rank test for bits 15 to 22, p=0.02493 b-rank test for bits 16 to 23, p=0.79298 b-rank test for bits 17 to 24, p=0.71275 b-rank test for bits 18 to 25, p=0.49468 b-rank test for bits 19 to 26, p=0.83004 b-rank test for bits 20 to 27, p=0.41713 b-rank test for bits 21 to 28, p=0.98667 b-rank test for bits 22 to 29, p=0.96950 b-rank test for bits 23 to 30, p=0.64472 b-rank test for bits 24 to 31, p=0.78002 b-rank test for bits 25 to 32, p=0.10467 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 = 0.840616 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-09-08_20:31 (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 142197 0.67 0.749248 2 142126 0.51 0.693655 3 141581 -0.77 0.221503 4 141682 -0.53 0.297659 5 142658 1.75 0.959874 6 142431 1.22 0.888550 7 141222 -1.61 0.054147 8 141821 -0.21 0.418248 9 142018 0.25 0.600214 10 142374 1.09 0.861189 11 142313 0.94 0.827199 12 141623 -0.67 0.251749 13 142131 0.52 0.697743 14 142317 0.95 0.829578 15 141376 -1.25 0.106364 16 141737 -0.40 0.343607 17 141629 -0.65 0.256241 18 141345 -1.32 0.093663 19 142156 0.58 0.717805 20 141499 -0.96 0.168851 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-09-08_20:31 Bits used No. missing words z-score p-value 23 to 32 142279 1.2747 0.898797 22 to 31 141642 -0.9218 0.178309 21 to 30 141939 0.1023 0.540745 20 to 29 141997 0.3023 0.618792 19 to 28 141544 -1.2598 0.103878 18 to 27 142110 0.6920 0.755521 17 to 26 142245 1.1575 0.876462 16 to 25 142693 2.7023 0.996557 15 to 24 142366 1.5747 0.942340 14 to 23 141854 -0.1908 0.424344 13 to 22 142052 0.4920 0.688628 12 to 21 141502 -1.4046 0.080072 11 to 20 141644 -0.9149 0.180114 10 to 19 141960 0.1747 0.569352 9 to 18 142346 1.5058 0.933935 8 to 17 141699 -0.7253 0.234141 7 to 16 141930 0.0713 0.528411 6 to 15 141601 -1.0632 0.143844 5 to 14 141545 -1.2563 0.104502 4 to 13 142005 0.3299 0.629261 3 to 12 141486 -1.4598 0.072178 2 to 11 142341 1.4885 0.931693 1 to 10 141792 -0.4046 0.342891 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-09-08_20:31 Bits used No. missing words z-score p-value 28 to 32 142568 2.2328 0.987218 27 to 31 142355 1.5107 0.934573 26 to 30 141686 -0.7571 0.224510 25 to 29 142129 0.7446 0.771757 24 to 28 141827 -0.2791 0.390090 23 to 27 141317 -2.0079 0.022327 22 to 26 141454 -1.5435 0.061356 21 to 25 142301 1.3277 0.907861 20 to 24 142552 2.1785 0.985317 19 to 23 142010 0.3413 0.633544 18 to 22 141477 -1.4655 0.071389 17 to 21 141503 -1.3774 0.084196 16 to 20 142108 0.6735 0.749672 15 to 19 142449 1.8294 0.966329 14 to 18 141262 -2.1943 0.014106 13 to 17 141840 -0.2350 0.407098 12 to 16 142372 1.5684 0.941603 11 to 15 141998 0.3006 0.618131 10 to 14 141810 -0.3367 0.368167 9 to 13 141810 -0.3367 0.368167 8 to 12 142106 0.6667 0.747511 7 to 11 142153 0.8260 0.795598 6 to 10 141838 -0.2418 0.404469 5 to 9 141837 -0.2452 0.403156 4 to 8 141612 -1.0079 0.156752 3 to 7 141755 -0.5232 0.300434 2 to 6 142065 0.5277 0.701145 1 to 5 142095 0.6294 0.735453 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-09-08_20:31 Bits used No. missing words z-score p-value 31 to 32 141427 -1.4228 0.077397 30 to 31 141881 -0.0836 0.466699 29 to 30 142267 1.0551 0.854304 28 to 29 142215 0.9017 0.816387 27 to 28 141891 -0.0541 0.478439 26 to 27 141096 -2.3992 0.008215 25 to 26 142542 1.8663 0.968999 24 to 25 141620 -0.8535 0.196696 23 to 24 142027 0.3471 0.635745 22 to 23 141816 -0.2753 0.391539 21 to 22 141558 -1.0364 0.150014 20 to 21 142390 1.4179 0.921891 19 to 20 141326 -1.7207 0.042649 18 to 19 141642 -0.7886 0.215178 17 to 18 141565 -1.0157 0.154881 16 to 17 141942 0.0964 0.538387 15 to 16 142586 1.9961 0.977037 14 to 15 141757 -0.4494 0.326589 13 to 14 142000 0.2675 0.605444 12 to 13 141611 -0.8800 0.189422 11 to 12 142053 0.4238 0.664146 10 to 11 141878 -0.0924 0.463183 9 to 10 142196 0.8456 0.801122 8 to 9 141388 -1.5378 0.062043 7 to 8 141479 -1.2694 0.102147 6 to 7 142225 0.9312 0.824120 5 to 6 142141 0.6834 0.752821 4 to 5 142116 0.6096 0.728952 3 to 4 142715 2.3766 0.991264 2 to 3 141669 -0.7089 0.239182 1 to 2 141822 -0.2576 0.398354 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-09-08_20:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2473.77 -0.371 0.355348 Test results for specific bytes for dh-ranFile-2016-09-08_20:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2459.22 -0.577 0.282064 2 to 9 2567.45 0.954 0.829914 3 to 10 2593.98 1.329 0.908083 4 to 11 2591.53 1.294 0.902250 5 to 12 2590.63 1.282 0.900022 6 to 13 2563.95 0.904 0.817090 7 to 14 2335.55 -2.326 0.010019 8 to 15 2513.08 0.185 0.573378 9 to 16 2436.91 -0.892 0.186153 10 to 17 2492.83 -0.101 0.459616 11 to 18 2475.59 -0.345 0.364985 12 to 19 2518.17 0.257 0.601377 13 to 20 2574.80 1.058 0.854927 14 to 21 2437.73 -0.881 0.189240 15 to 22 2545.89 0.649 0.741821 16 to 23 2545.22 0.639 0.738736 17 to 24 2474.61 -0.359 0.359751 18 to 25 2523.90 0.338 0.632310 19 to 26 2541.97 0.594 0.723591 20 to 27 2576.68 1.084 0.860900 21 to 28 2585.69 1.212 0.887219 22 to 29 2495.55 -0.063 0.474916 23 to 30 2452.21 -0.676 0.249552 24 to 31 2425.83 -1.049 0.147120 25 to 32 2502.36 0.033 0.513327 CDPARK for dh-ranFile-2016-09-08_20:31: 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 3510 -0.5936 0.276387 3518 -0.2283 0.409702 3548 1.1416 0.873180 3534 0.5023 0.692266 3497 -1.1872 0.117571 3528 0.2283 0.590298 3515 -0.3653 0.357445 3506 -0.7763 0.218799 3525 0.0913 0.536383 3496 -1.2329 0.108811 Square side=100, avg. no. parked=3517.70 sample std.=15.64 p-value of the KSTEST for those 10 p-values: 0.608670 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-09-08_20:31 0.6230,0.7988,0.0802,0.8637,0.6071,0.3511,0.1984,0.1544,0.7868,0.7122, The KS test for those 10 p-values: 0.893198 The 3DSPHERES test for dh-ranFile-2016-09-08_20:31 sample no r^3 equiv. uni. 1 22.706 0.530866 2 11.715 0.323284 3 9.629 0.274562 4 12.275 0.335807 5 2.427 0.077703 6 12.510 0.340980 7 37.838 0.716705 8 0.789 0.025959 9 83.227 0.937603 10 76.100 0.920870 11 149.837 0.993225 12 8.688 0.251444 13 16.259 0.418388 14 75.621 0.919596 15 6.719 0.200668 16 81.770 0.934498 17 88.097 0.946952 18 15.570 0.404878 19 18.387 0.458221 20 23.396 0.541528 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.363686 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-09-08_20:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 -0.7 2.0 0.8 0.6 0.9 -0.2 2.3 0.2 2.5 0.0 -0.3 -2.1 -0.0 0.1 -0.3 -1.0 -0.8 0.5 -0.8 0.2 -1.1 1.8 -0.3 1.2 0.5 0.5 0.7 -0.1 0.1 1.1 -1.5 -0.1 -0.9 -0.6 1.5 0.3 -1.0 -0.4 -0.1 -1.3 -1.0 -1.1 Chi-square with 42 degrees of freedom:44.799480 z-score=0.305448, p-value=0.644808 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-09-08_20:31 Test no p-value 1 0.000782 2 0.633232 3 0.015444 4 0.293530 5 0.017322 6 0.281525 7 0.191125 8 0.216372 9 0.136582 10 0.520206 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.001756 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-09-08_20:31: (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 66847 0.49 66557 0.18 3 25000.00 24889 0.49 25016 0.01 4 6666.67 6601 0.65 6710 0.28 5 1388.89 1389 0.00 1422 0.79 6 238.10 231 0.21 254 1.06 7 34.72 32 0.21 35 0.00 8 4.96 10 5.12 5 0.00 p=0.69488 p=0.11265 Number of rngs required: 688471, p-value: 0.531 RESULTS OF CRAPS TEST for dh-ranFile-2016-09-08_20:31 No. of wins: Observed Expected 98316 98585.9 z-score=-1.207, pvalue=0.11372 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66496 66666.7 0.437 0.437 2 37981 37654.3 2.834 3.271 3 26793 26954.7 0.970 4.242 4 19355 19313.5 0.089 4.331 5 13923 13851.4 0.370 4.701 6 9909 9943.5 0.120 4.821 7 7167 7145.0 0.068 4.888 8 5112 5139.1 0.143 5.031 9 3684 3699.9 0.068 5.099 10 2673 2666.3 0.017 5.116 11 1926 1923.3 0.004 5.120 12 1396 1388.7 0.038 5.157 13 989 1003.7 0.216 5.373 14 698 726.1 1.091 6.464 15 484 525.8 3.328 9.792 16 368 381.2 0.454 10.246 17 285 276.5 0.259 10.505 18 182 200.8 1.765 12.270 19 152 146.0 0.248 12.518 20 116 106.2 0.901 13.420 21 311 287.1 1.987 15.407 Chisq= 15.41 for 20 degrees of freedom, p= 0.24732 SUMMARY of craptest p-value for no. of wins: 0.113723 p-value for throws/game: 0.247321 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-09-08_20:31 No. of wins: Observed Expected 98409 98585.9 z-score=-0.791, pvalue=0.21447 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66589 66666.7 0.090 0.090 2 37762 37654.3 0.308 0.398 3 27236 26954.7 2.935 3.333 4 19018 19313.5 4.520 7.853 5 14017 13851.4 1.979 9.833 6 9816 9943.5 1.636 11.469 7 7141 7145.0 0.002 11.471 8 5149 5139.1 0.019 11.490 9 3625 3699.9 1.515 13.005 10 2572 2666.3 3.335 16.340 11 1945 1923.3 0.244 16.584 12 1410 1388.7 0.325 16.910 13 1043 1003.7 1.538 18.447 14 716 726.1 0.142 18.589 15 552 525.8 1.302 19.891 16 384 381.2 0.021 19.912 17 236 276.5 5.943 25.855 18 209 200.8 0.332 26.187 19 131 146.0 1.538 27.725 20 100 106.2 0.364 28.089 21 349 287.1 13.339 41.428 Chisq= 41.43 for 20 degrees of freedom, p= 0.99672 SUMMARY of craptest p-value for no. of wins: 0.214468 p-value for throws/game: 0.996719 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0008,0.0018,0.0038,0.0082,0.0100,0.0141,0.0154,0.0173,0.0223,0.0249, 0.0260,0.0426,0.0480,0.0541,0.0614,0.0620,0.0649,0.0712,0.0714,0.0722, 0.0774,0.0777,0.0801,0.0802,0.0817,0.0842,0.0916,0.0919,0.0937,0.1021, 0.1039,0.1045,0.1047,0.1064,0.1088,0.1127,0.1137,0.1176,0.1201,0.1207, 0.1366,0.1438,0.1471,0.1500,0.1502,0.1544,0.1549,0.1568,0.1626,0.1689, 0.1783,0.1801,0.1862,0.1892,0.1894,0.1911,0.1921,0.1931,0.1948,0.1967, 0.1974,0.1984,0.1988,0.2007,0.2012,0.2145,0.2152,0.2164,0.2188,0.2215, 0.2245,0.2299,0.2340,0.2341,0.2392,0.2473,0.2496,0.2514,0.2517,0.2562, 0.2662,0.2693,0.2746,0.2764,0.2815,0.2821,0.2826,0.2864,0.2935,0.2977, 0.3004,0.3115,0.3124,0.3152,0.3233,0.3266,0.3358,0.3410,0.3429,0.3434, 0.3436,0.3511,0.3553,0.3574,0.3598,0.3637,0.3642,0.3650,0.3682,0.3682, 0.3723,0.3776,0.3795,0.3901,0.3915,0.3984,0.4032,0.4045,0.4049,0.4071, 0.4097,0.4171,0.4182,0.4184,0.4243,0.4260,0.4270,0.4423,0.4582,0.4596, 0.4632,0.4667,0.4749,0.4784,0.4947,0.5133,0.5202,0.5263,0.5266,0.5284, 0.5309,0.5312,0.5364,0.5384,0.5387,0.5407,0.5415,0.5485,0.5694,0.5734, 0.5903,0.5916,0.5948,0.5967,0.6002,0.6014,0.6054,0.6071,0.6087,0.6162, 0.6181,0.6188,0.6216,0.6230,0.6284,0.6293,0.6323,0.6332,0.6335,0.6357, 0.6447,0.6448,0.6517,0.6551,0.6641,0.6701,0.6886,0.6923,0.6937,0.6949, 0.6977,0.7011,0.7087,0.7122,0.7127,0.7144,0.7167,0.7178,0.7207,0.7236, 0.7290,0.7355,0.7387,0.7411,0.7418,0.7456,0.7475,0.7492,0.7497,0.7528, 0.7555,0.7718,0.7800,0.7868,0.7930,0.7956,0.7988,0.8011,0.8123,0.8164, 0.8166,0.8171,0.8184,0.8241,0.8272,0.8296,0.8299,0.8300,0.8305,0.8406, 0.8543,0.8549,0.8585,0.8590,0.8609,0.8611,0.8612,0.8637,0.8732,0.8765, 0.8861,0.8872,0.8886,0.8915,0.8923,0.8932,0.8958,0.8988,0.9000,0.9023, 0.9052,0.9079,0.9081,0.9196,0.9209,0.9219,0.9317,0.9339,0.9345,0.9346, 0.9376,0.9416,0.9423,0.9470,0.9597,0.9599,0.9663,0.9690,0.9695,0.9767, 0.9770,0.9853,0.9867,0.9872,0.9913,0.9932,0.9938,0.9966,0.9967, Overall p-value after applying KStest on 269 p-values = 0.411697 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.