RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-09-13_08:31 (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 20.6303 0.756734 2 to 25 15.82 13.2647 0.281708 3 to 26 15.58 20.9369 0.770874 4 to 27 15.55 20.3560 0.743576 5 to 28 15.75 14.6460 0.379036 6 to 29 15.80 25.8181 0.922162 7 to 30 15.48 23.1521 0.855637 8 to 31 15.94 10.2578 0.107546 9 to 32 15.80 20.1595 0.733847 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.284900 Tough bday spacings test for dh-ranFile-2015-09-13_08:31: 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 32 82 99 105 67 56 22 16 4 3 (O-E)^2/E 2.6 0.6 1.0 0.0 0.5 1.6 0.3 2.0 0.1 1.0 0.3 Birthday Spacings: Sum(O-E)^2/E= 10.061, p= 0.565 RESULTS OF GCD FOR dh-ranFile-2015-09-13_08:31 Euclid's algorithm: p-value, steps to gcd: 0.659780 p-value, dist. of gcd's: 0.465221 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-09-13_08:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.499 0.525 0.351 0.784 0.484 0.806 0.897 0.103 Bits 8 to 15---> 0.758 0.579 0.732 0.083 0.214 0.652 0.158 0.783 Bits 16 to 23---> 0.813 0.805 0.195 0.751 0.502 0.158 0.316 0.721 Bits 24 to 31---> 0.738 0.900 0.909 0.704 0.569 0.306 0.493 0.403 KS test for the above 32 p values: 0.741 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-09-13_08:31, p-values for 5 runs: 0.7811, 0.6133, 0.1900, 0.4068, 0.0962 Rank test for binary matrices (31x31) for dh-ranFile-2015-09-13_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 212 211.4 0.002 0.002 r= 29 5103 5134.0 0.187 0.189 r= 30 23092 23103.0 0.005 0.194 r= 31 11593 11551.5 0.149 0.343 chi-square = 0.343 with df = 3; p-value = 0.048 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-09-13_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 218 211.4 0.205 0.205 r= 30 5213 5134.0 1.215 1.420 r= 31 22976 23103.0 0.699 2.119 r= 32 11593 11551.5 0.149 2.268 chi-square = 2.268 with df = 3; p-value = 0.481 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-09-13_08:31 b-rank test for bits 1 to 8, p=0.79201 b-rank test for bits 2 to 9, p=0.38441 b-rank test for bits 3 to 10, p=0.41666 b-rank test for bits 4 to 11, p=0.09416 b-rank test for bits 5 to 12, p=0.55588 b-rank test for bits 6 to 13, p=0.28132 b-rank test for bits 7 to 14, p=0.05335 b-rank test for bits 8 to 15, p=0.33176 b-rank test for bits 9 to 16, p=0.55408 b-rank test for bits 10 to 17, p=0.93535 b-rank test for bits 11 to 18, p=0.41587 b-rank test for bits 12 to 19, p=0.62248 b-rank test for bits 13 to 20, p=0.86080 b-rank test for bits 14 to 21, p=0.28213 b-rank test for bits 15 to 22, p=0.00789 b-rank test for bits 16 to 23, p=0.81643 b-rank test for bits 17 to 24, p=0.43186 b-rank test for bits 18 to 25, p=0.49093 b-rank test for bits 19 to 26, p=0.08428 b-rank test for bits 20 to 27, p=0.60126 b-rank test for bits 21 to 28, p=0.05419 b-rank test for bits 22 to 29, p=0.71886 b-rank test for bits 23 to 30, p=0.93236 b-rank test for bits 24 to 31, p=0.38971 b-rank test for bits 25 to 32, p=0.13078 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 = 0.615187 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-09-13_08:31 (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 141539 -0.87 0.193449 2 141836 -0.17 0.431981 3 141757 -0.36 0.360954 4 142065 0.36 0.641965 5 142798 2.08 0.981068 6 141327 -1.36 0.086823 7 141823 -0.20 0.420073 8 142097 0.44 0.669481 9 142730 1.92 0.972410 10 141526 -0.90 0.185225 11 141983 0.17 0.568331 12 142111 0.47 0.681248 13 142105 0.46 0.676227 14 141541 -0.86 0.194734 15 142243 0.78 0.782188 16 141736 -0.40 0.342747 17 142484 1.34 0.910313 18 141545 -0.85 0.197319 19 141913 0.01 0.503421 20 141804 -0.25 0.402803 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-09-13_08:31 Bits used No. missing words z-score p-value 23 to 32 142023 0.3920 0.652458 22 to 31 142206 1.0230 0.846846 21 to 30 141999 0.3092 0.621418 20 to 29 141890 -0.0667 0.473428 19 to 28 141349 -1.9322 0.026669 18 to 27 142164 0.8782 0.810075 17 to 26 141714 -0.6736 0.250298 16 to 25 142283 1.2885 0.901217 15 to 24 141798 -0.3839 0.350528 14 to 23 142237 1.1299 0.870740 13 to 22 141726 -0.6322 0.263637 12 to 21 141508 -1.3839 0.083195 11 to 20 141696 -0.7356 0.230981 10 to 19 142037 0.4402 0.670119 9 to 18 142057 0.5092 0.694696 8 to 17 141744 -0.5701 0.284304 7 to 16 142607 2.4058 0.991931 6 to 15 142355 1.5368 0.937828 5 to 14 142076 0.5747 0.717261 4 to 13 141581 -1.1322 0.128781 3 to 12 141587 -1.1115 0.133180 2 to 11 142199 0.9989 0.841069 1 to 10 141664 -0.8460 0.198786 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-09-13_08:31 Bits used No. missing words z-score p-value 28 to 32 141885 -0.0825 0.467135 27 to 31 141547 -1.2282 0.109679 26 to 30 142633 2.4531 0.992919 25 to 29 141714 -0.6621 0.253942 24 to 28 142354 1.5074 0.934140 23 to 27 142014 0.3548 0.638635 22 to 26 142410 1.6972 0.955169 21 to 25 142206 1.0057 0.842711 20 to 24 141982 0.2463 0.597290 19 to 23 141173 -2.4960 0.006280 18 to 22 142136 0.7684 0.778867 17 to 21 141576 -1.1299 0.129252 16 to 20 142195 0.9684 0.833571 15 to 19 141794 -0.3909 0.347917 14 to 18 141251 -2.2316 0.012820 13 to 17 141700 -0.7096 0.238978 12 to 16 141553 -1.2079 0.113543 11 to 15 141852 -0.1943 0.422955 10 to 14 141726 -0.6215 0.267149 9 to 13 142049 0.4735 0.682057 8 to 12 141778 -0.4452 0.328093 7 to 11 141992 0.2802 0.610352 6 to 10 142159 0.8463 0.801318 5 to 9 141907 -0.0079 0.496849 4 to 8 141984 0.2531 0.599912 3 to 7 142444 1.8124 0.965041 2 to 6 142053 0.4870 0.686877 1 to 5 142071 0.5480 0.708166 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-09-13_08:31 Bits used No. missing words z-score p-value 31 to 32 141772 -0.4051 0.342701 30 to 31 142799 2.6244 0.995660 29 to 30 141584 -0.9597 0.168609 28 to 29 142279 1.0905 0.862247 27 to 28 142612 2.0728 0.980903 26 to 27 141966 0.1672 0.566381 25 to 26 141454 -1.3432 0.089611 24 to 25 141994 0.2498 0.598615 23 to 24 141652 -0.7591 0.223901 22 to 23 141987 0.2291 0.590610 21 to 22 141652 -0.7591 0.223901 20 to 21 141272 -1.8800 0.030052 19 to 20 142416 1.4946 0.932491 18 to 19 141511 -1.1750 0.119994 17 to 18 141849 -0.1780 0.429375 16 to 17 141733 -0.5201 0.301480 15 to 16 142182 0.8043 0.789399 14 to 15 141526 -1.1308 0.129077 13 to 14 141698 -0.6234 0.266513 12 to 13 141744 -0.4877 0.312882 11 to 12 141677 -0.6853 0.246565 10 to 11 142059 0.4415 0.670576 9 to 10 142152 0.7158 0.762955 8 to 9 142348 1.2940 0.902169 7 to 8 141780 -0.3815 0.351415 6 to 7 141795 -0.3373 0.367962 5 to 6 141530 -1.1190 0.131577 4 to 5 142237 0.9666 0.833123 3 to 4 142319 1.2085 0.886566 2 to 3 141382 -1.5555 0.059908 1 to 2 141552 -1.0541 0.145925 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-09-13_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2510.21 0.144 0.557400 Test results for specific bytes for dh-ranFile-2015-09-13_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2591.62 1.296 0.902460 2 to 9 2509.98 0.141 0.556116 3 to 10 2483.13 -0.239 0.405705 4 to 11 2465.84 -0.483 0.314495 5 to 12 2388.30 -1.580 0.057086 6 to 13 2448.66 -0.726 0.233885 7 to 14 2502.00 0.028 0.511298 8 to 15 2503.94 0.056 0.522197 9 to 16 2405.33 -1.339 0.090304 10 to 17 2390.63 -1.547 0.060968 11 to 18 2473.32 -0.377 0.352972 12 to 19 2441.11 -0.833 0.202460 13 to 20 2391.54 -1.534 0.062533 14 to 21 2430.12 -0.988 0.161520 15 to 22 2448.93 -0.722 0.235066 16 to 23 2448.30 -0.731 0.232343 17 to 24 2467.01 -0.467 0.320399 18 to 25 2571.46 1.011 0.843884 19 to 26 2483.48 -0.234 0.407621 20 to 27 2594.43 1.335 0.909136 21 to 28 2620.72 1.707 0.956110 22 to 29 2449.05 -0.721 0.235605 23 to 30 2467.85 -0.455 0.324694 24 to 31 2418.05 -1.159 0.123243 25 to 32 2578.70 1.113 0.867128 CDPARK for dh-ranFile-2015-09-13_08:31: 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 3490 -1.5068 0.065925 3510 -0.5936 0.276387 3534 0.5023 0.692266 3505 -0.8219 0.205562 3506 -0.7763 0.218799 3519 -0.1826 0.427537 3541 0.8219 0.794438 3525 0.0913 0.536383 3501 -1.0046 0.157553 3490 -1.5068 0.065925 Square side=100, avg. no. parked=3512.10 sample std.=16.50 p-value of the KSTEST for those 10 p-values: 0.143490 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-09-13_08:31 0.4787,0.5079,0.0255,0.2807,0.6828,0.7190,0.9047,0.1944,0.7936,0.1553, The KS test for those 10 p-values: 0.988575 The 3DSPHERES test for dh-ranFile-2015-09-13_08:31 sample no r^3 equiv. uni. 1 3.645 0.114397 2 0.844 0.027739 3 25.524 0.572928 4 14.501 0.383288 5 9.172 0.263417 6 1.777 0.057519 7 74.023 0.915197 8 4.783 0.147368 9 54.818 0.839150 10 12.277 0.335843 11 25.925 0.578600 12 32.962 0.666708 13 14.088 0.374754 14 24.675 0.560668 15 6.264 0.188436 16 1.076 0.035225 17 36.452 0.703305 18 48.367 0.800559 19 158.316 0.994893 20 13.373 0.359676 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.668532 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-09-13_08:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 1.8 0.3 -1.7 -0.5 0.1 2.0 -0.6 0.8 0.0 0.2 2.0 -0.8 -0.3 1.1 -1.6 0.0 0.2 -1.2 1.5 -0.6 0.7 -0.6 -1.7 1.7 -0.4 1.1 -1.3 -1.0 0.5 -1.5 0.1 0.7 -0.8 -0.4 2.0 -1.2 -0.7 -0.8 -0.1 0.9 0.0 -0.1 Chi-square with 42 degrees of freedom:46.073618 z-score=0.444468, p-value=0.692558 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-09-13_08:31 Test no p-value 1 0.679125 2 0.260054 3 0.014870 4 0.001206 5 0.550565 6 0.484080 7 0.955881 8 0.422901 9 0.636472 10 0.042164 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.147459 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-09-13_08:31: (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 66802 0.27 66804 0.28 3 25000.00 25018 0.01 24955 0.08 4 6666.67 6521 3.18 6617 0.37 5 1388.89 1391 0.00 1351 1.03 6 238.10 217 1.87 229 0.35 7 34.72 44 2.48 39 0.53 8 4.96 6 0.22 4 0.19 p=0.76491 p=0.16995 Number of rngs required: 687843, p-value: 0.259 RESULTS OF CRAPS TEST for dh-ranFile-2015-09-13_08:31 No. of wins: Observed Expected 98311 98585.9 z-score=-1.229, pvalue=0.10947 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66332 66666.7 1.680 1.680 2 37902 37654.3 1.629 3.309 3 27071 26954.7 0.502 3.811 4 19262 19313.5 0.137 3.948 5 13974 13851.4 1.085 5.033 6 9932 9943.5 0.013 5.046 7 7062 7145.0 0.965 6.011 8 5057 5139.1 1.311 7.321 9 3688 3699.9 0.038 7.360 10 2637 2666.3 0.322 7.681 11 1936 1923.3 0.083 7.765 12 1394 1388.7 0.020 7.785 13 1116 1003.7 12.561 20.346 14 740 726.1 0.265 20.611 15 510 525.8 0.477 21.088 16 381 381.2 0.000 21.088 17 270 276.5 0.155 21.242 18 200 200.8 0.003 21.246 19 144 146.0 0.027 21.273 20 115 106.2 0.727 21.999 21 277 287.1 0.356 22.355 Chisq= 22.36 for 20 degrees of freedom, p= 0.67846 SUMMARY of craptest p-value for no. of wins: 0.109474 p-value for throws/game: 0.678463 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-09-13_08:31 No. of wins: Observed Expected 98650 98585.9 z-score= 0.287, pvalue=0.61290 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66774 66666.7 0.173 0.173 2 37380 37654.3 1.998 2.171 3 26830 26954.7 0.577 2.748 4 19264 19313.5 0.127 2.875 5 13822 13851.4 0.062 2.938 6 10043 9943.5 0.995 3.932 7 7012 7145.0 2.477 6.409 8 5191 5139.1 0.525 6.934 9 3702 3699.9 0.001 6.935 10 2769 2666.3 3.956 10.891 11 1920 1923.3 0.006 10.897 12 1450 1388.7 2.702 13.599 13 1028 1003.7 0.588 14.187 14 793 726.1 6.156 20.343 15 559 525.8 2.092 22.434 16 391 381.2 0.255 22.689 17 280 276.5 0.043 22.732 18 194 200.8 0.232 22.964 19 141 146.0 0.170 23.135 20 126 106.2 3.685 26.820 21 331 287.1 6.708 33.528 Chisq= 33.53 for 20 degrees of freedom, p= 0.97050 SUMMARY of craptest p-value for no. of wins: 0.612897 p-value for throws/game: 0.970500 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0012,0.0063,0.0079,0.0128,0.0149,0.0255,0.0267,0.0277,0.0301,0.0352, 0.0422,0.0483,0.0534,0.0542,0.0571,0.0575,0.0599,0.0610,0.0625,0.0659, 0.0659,0.0828,0.0832,0.0843,0.0868,0.0896,0.0903,0.0942,0.0962,0.1029, 0.1075,0.1095,0.1097,0.1135,0.1144,0.1200,0.1232,0.1288,0.1291,0.1293, 0.1308,0.1316,0.1332,0.1435,0.1459,0.1474,0.1475,0.1553,0.1576,0.1579, 0.1584,0.1615,0.1686,0.1700,0.1852,0.1884,0.1900,0.1934,0.1944,0.1947, 0.1953,0.1973,0.1988,0.2025,0.2056,0.2135,0.2188,0.2239,0.2239,0.2310, 0.2323,0.2339,0.2351,0.2356,0.2390,0.2466,0.2503,0.2539,0.2591,0.2601, 0.2634,0.2636,0.2665,0.2671,0.2764,0.2807,0.2813,0.2817,0.2821,0.2843, 0.2849,0.3015,0.3056,0.3129,0.3145,0.3158,0.3204,0.3247,0.3281,0.3318, 0.3358,0.3427,0.3427,0.3479,0.3505,0.3514,0.3515,0.3530,0.3597,0.3610, 0.3680,0.3748,0.3790,0.3833,0.3844,0.3897,0.4028,0.4033,0.4057,0.4068, 0.4076,0.4159,0.4167,0.4201,0.4229,0.4230,0.4275,0.4294,0.4319,0.4320, 0.4652,0.4671,0.4734,0.4787,0.4813,0.4838,0.4841,0.4909,0.4928,0.4968, 0.4989,0.5023,0.5034,0.5079,0.5113,0.5222,0.5250,0.5364,0.5506,0.5541, 0.5559,0.5561,0.5574,0.5607,0.5648,0.5664,0.5683,0.5686,0.5729,0.5786, 0.5793,0.5906,0.5973,0.5986,0.5999,0.6013,0.6104,0.6129,0.6133,0.6152, 0.6214,0.6225,0.6365,0.6386,0.6420,0.6518,0.6525,0.6598,0.6667,0.6685, 0.6695,0.6701,0.6706,0.6762,0.6785,0.6791,0.6812,0.6821,0.6828,0.6869, 0.6923,0.6926,0.6947,0.7033,0.7038,0.7082,0.7173,0.7189,0.7190,0.7215, 0.7322,0.7338,0.7384,0.7412,0.7436,0.7512,0.7567,0.7580,0.7630,0.7649, 0.7709,0.7789,0.7811,0.7822,0.7829,0.7835,0.7894,0.7920,0.7936,0.7944, 0.8006,0.8013,0.8046,0.8062,0.8101,0.8131,0.8164,0.8331,0.8336,0.8391, 0.8411,0.8427,0.8439,0.8468,0.8556,0.8608,0.8622,0.8671,0.8707,0.8866, 0.8969,0.9002,0.9012,0.9022,0.9025,0.9047,0.9091,0.9092,0.9103,0.9152, 0.9222,0.9324,0.9325,0.9341,0.9354,0.9378,0.9552,0.9559,0.9561,0.9650, 0.9705,0.9724,0.9809,0.9811,0.9886,0.9919,0.9929,0.9949,0.9957, Overall p-value after applying KStest on 269 p-values = 0.514544 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.