RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-10-06_21:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.56 19.2661 0.686528 2 to 25 15.64 24.4913 0.893312 3 to 26 15.63 20.3808 0.744782 4 to 27 15.88 16.5755 0.516538 5 to 28 15.96 14.4872 0.367635 6 to 29 15.68 13.3737 0.289165 7 to 30 15.86 14.1201 0.341417 8 to 31 15.96 14.2059 0.347525 9 to 32 16.20 13.2556 0.281088 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.543497 Tough bday spacings test for dh-ranFile-2016-10-06_21:31: 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 8 34 79 91 96 74 56 22 25 11 4 (O-E)^2/E 0.1 0.2 0.4 0.5 0.0 0.2 0.3 2.0 6.9 2.9 0.0 Birthday Spacings: Sum(O-E)^2/E= 13.592, p= 0.808 RESULTS OF GCD FOR dh-ranFile-2016-10-06_21:31 Euclid's algorithm: p-value, steps to gcd: 0.775136 p-value, dist. of gcd's: 0.434275 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-10-06_21:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.454 0.111 0.931 0.883 0.147 0.788 0.439 0.515 Bits 8 to 15---> 0.356 0.243 0.396 0.327 0.609 0.120 0.721 0.805 Bits 16 to 23---> 0.373 0.885 0.983 0.732 0.333 0.732 0.412 0.215 Bits 24 to 31---> 0.799 0.819 0.367 0.697 0.439 0.017 0.987 0.262 KS test for the above 32 p values: 0.224 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-10-06_21:31, p-values for 5 runs: 0.9332, 0.2132, 0.5432, 0.2550, 0.0244 Rank test for binary matrices (31x31) for dh-ranFile-2016-10-06_21:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 228 211.4 1.301 1.301 r= 29 5160 5134.0 0.132 1.432 r= 30 22991 23103.0 0.543 1.976 r= 31 11621 11551.5 0.418 2.393 chi-square = 2.393 with df = 3; p-value = 0.505 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-10-06_21:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 204 211.4 0.260 0.260 r= 30 5154 5134.0 0.078 0.338 r= 31 23175 23103.0 0.224 0.562 r= 32 11467 11551.5 0.618 1.181 chi-square = 1.181 with df = 3; p-value = 0.242 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-10-06_21:31 b-rank test for bits 1 to 8, p=0.71847 b-rank test for bits 2 to 9, p=0.39439 b-rank test for bits 3 to 10, p=0.90097 b-rank test for bits 4 to 11, p=0.66585 b-rank test for bits 5 to 12, p=0.84190 b-rank test for bits 6 to 13, p=0.15720 b-rank test for bits 7 to 14, p=0.60632 b-rank test for bits 8 to 15, p=0.71087 b-rank test for bits 9 to 16, p=0.85611 b-rank test for bits 10 to 17, p=0.76683 b-rank test for bits 11 to 18, p=0.21523 b-rank test for bits 12 to 19, p=0.81960 b-rank test for bits 13 to 20, p=0.83914 b-rank test for bits 14 to 21, p=0.72081 b-rank test for bits 15 to 22, p=0.27908 b-rank test for bits 16 to 23, p=0.62065 b-rank test for bits 17 to 24, p=0.24132 b-rank test for bits 18 to 25, p=0.64350 b-rank test for bits 19 to 26, p=0.63459 b-rank test for bits 20 to 27, p=0.99187 b-rank test for bits 21 to 28, p=0.72124 b-rank test for bits 22 to 29, p=0.21677 b-rank test for bits 23 to 30, p=0.24845 b-rank test for bits 24 to 31, p=0.00740 b-rank test for bits 25 to 32, p=0.70351 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 = 0.146257 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-10-06_21:31 (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 141826 -0.19 0.422815 2 142019 0.26 0.601117 3 142070 0.38 0.646317 4 142084 0.41 0.658403 5 142653 1.74 0.958855 6 141193 -1.67 0.047098 7 141532 -0.88 0.188993 8 142369 1.07 0.858588 9 141351 -1.30 0.096030 10 141781 -0.30 0.382151 11 142352 1.03 0.849496 12 142158 0.58 0.719381 13 141960 0.12 0.547120 14 141900 -0.02 0.491304 15 142392 1.13 0.870284 16 141785 -0.29 0.385720 17 141292 -1.44 0.074600 18 141688 -0.52 0.302534 19 141504 -0.95 0.171811 20 142462 1.29 0.901698 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-10-06_21:31 Bits used No. missing words z-score p-value 23 to 32 141642 -0.9218 0.178309 22 to 31 141882 -0.0942 0.462459 21 to 30 142258 1.2023 0.885378 20 to 29 141746 -0.5632 0.286647 19 to 28 141709 -0.6908 0.244848 18 to 27 141916 0.0230 0.509175 17 to 26 142024 0.3954 0.653731 16 to 25 142060 0.5196 0.698312 15 to 24 141854 -0.1908 0.424344 14 to 23 141760 -0.5149 0.303301 13 to 22 141148 -2.6253 0.004329 12 to 21 142099 0.6540 0.743455 11 to 20 142177 0.9230 0.821996 10 to 19 142246 1.1609 0.877165 9 to 18 141810 -0.3425 0.365981 8 to 17 141634 -0.9494 0.171205 7 to 16 141996 0.2989 0.617477 6 to 15 141965 0.1920 0.576115 5 to 14 141419 -1.6908 0.045438 4 to 13 141068 -2.9011 0.001859 3 to 12 141876 -0.1149 0.454250 2 to 11 141793 -0.4011 0.344159 1 to 10 142179 0.9299 0.823788 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-10-06_21:31 Bits used No. missing words z-score p-value 28 to 32 142112 0.6870 0.753964 27 to 31 141558 -1.1909 0.116837 26 to 30 141961 0.1752 0.569520 25 to 29 141508 -1.3604 0.086845 24 to 28 141674 -0.7977 0.212514 23 to 27 142216 1.0396 0.850728 22 to 26 141777 -0.4486 0.326869 21 to 25 141796 -0.3842 0.350426 20 to 24 141482 -1.4486 0.073728 19 to 23 141701 -0.7062 0.240031 18 to 22 141626 -0.9604 0.168417 17 to 21 142181 0.9209 0.821453 16 to 20 141678 -0.7842 0.216470 15 to 19 142176 0.9040 0.816993 14 to 18 141843 -0.2248 0.411049 13 to 17 142000 0.3074 0.620714 12 to 16 142034 0.4226 0.663710 11 to 15 142265 1.2057 0.886026 10 to 14 141241 -2.2655 0.011740 9 to 13 141927 0.0599 0.523882 8 to 12 141590 -1.0825 0.139521 7 to 11 141771 -0.4689 0.319565 6 to 10 142520 2.0701 0.980777 5 to 9 141999 0.3040 0.619423 4 to 8 141666 -0.8248 0.204729 3 to 7 141526 -1.2994 0.096899 2 to 6 141823 -0.2926 0.384897 1 to 5 141926 0.0565 0.522532 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-10-06_21:31 Bits used No. missing words z-score p-value 31 to 32 141755 -0.4553 0.324464 30 to 31 141866 -0.1278 0.449147 29 to 30 141805 -0.3078 0.379133 28 to 29 142238 0.9695 0.833859 27 to 28 141842 -0.1986 0.421283 26 to 27 141602 -0.9066 0.182315 25 to 26 141643 -0.7856 0.216041 24 to 25 141826 -0.2458 0.402914 23 to 24 142402 1.4533 0.926930 22 to 23 142011 0.2999 0.617878 21 to 22 141999 0.2645 0.604308 20 to 21 141498 -1.2134 0.112496 19 to 20 142057 0.4356 0.668438 18 to 19 142110 0.5919 0.723057 17 to 18 142026 0.3442 0.634637 16 to 17 141504 -1.1957 0.115914 15 to 16 142270 1.0639 0.856318 14 to 15 142257 1.0256 0.847454 13 to 14 141826 -0.2458 0.402914 12 to 13 141835 -0.2193 0.413223 11 to 12 142073 0.4828 0.685382 10 to 11 142164 0.7512 0.773746 9 to 10 141698 -0.6234 0.266513 8 to 9 141708 -0.5939 0.276292 7 to 8 141944 0.1023 0.540729 6 to 7 141735 -0.5142 0.303539 5 to 6 142341 1.2734 0.898555 4 to 5 142304 1.1642 0.877832 3 to 4 141554 -1.0482 0.147280 2 to 3 141437 -1.3933 0.081764 1 to 2 141977 0.1996 0.579110 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-10-06_21:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2510.95 0.155 0.561543 Test results for specific bytes for dh-ranFile-2016-10-06_21:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2395.79 -1.474 0.070272 2 to 9 2475.01 -0.353 0.361904 3 to 10 2552.40 0.741 0.770654 4 to 11 2464.91 -0.496 0.309835 5 to 12 2422.87 -1.091 0.137691 6 to 13 2583.74 1.184 0.881858 7 to 14 2516.30 0.231 0.591181 8 to 15 2604.23 1.474 0.929760 9 to 16 2499.04 -0.014 0.494598 10 to 17 2409.66 -1.278 0.100700 11 to 18 2595.23 1.347 0.910972 12 to 19 2413.35 -1.225 0.110199 13 to 20 2518.18 0.257 0.601424 14 to 21 2443.23 -0.803 0.211041 15 to 22 2523.76 0.336 0.631548 16 to 23 2433.66 -0.938 0.174081 17 to 24 2551.89 0.734 0.768493 18 to 25 2376.51 -1.746 0.040375 19 to 26 2571.76 1.015 0.844921 20 to 27 2486.91 -0.185 0.426542 21 to 28 2483.27 -0.237 0.406466 22 to 29 2578.30 1.107 0.865925 23 to 30 2473.75 -0.371 0.355212 24 to 31 2434.88 -0.921 0.178559 25 to 32 2511.87 0.168 0.566680 CDPARK for dh-ranFile-2016-10-06_21:31: 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 3512 -0.5023 0.307734 3532 0.4110 0.659449 3525 0.0913 0.536383 3479 -2.0091 0.022262 3509 -0.6393 0.261324 3521 -0.0913 0.463617 3548 1.1416 0.873180 3535 0.5479 0.708135 3505 -0.8219 0.205562 3505 -0.8219 0.205562 Square side=100, avg. no. parked=3517.10 sample std.=18.47 p-value of the KSTEST for those 10 p-values: 0.685427 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-10-06_21:31 0.8273,0.4723,0.9663,0.9532,0.8057,0.3841,0.3722,0.4398,0.8893,0.8015, The KS test for those 10 p-values: 0.045182 The 3DSPHERES test for dh-ranFile-2016-10-06_21:31 sample no r^3 equiv. uni. 1 77.852 0.925360 2 57.142 0.851138 3 36.636 0.705121 4 38.896 0.726521 5 41.435 0.748712 6 37.832 0.716646 7 3.947 0.123272 8 29.734 0.628844 9 80.214 0.931010 10 31.691 0.652286 11 98.599 0.962621 12 23.332 0.540556 13 80.148 0.930858 14 41.041 0.745396 15 4.790 0.147578 16 0.473 0.015637 17 5.978 0.180678 18 1.106 0.036206 19 7.222 0.213959 20 1.343 0.043792 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.235261 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-10-06_21:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 2.0 -1.2 -0.6 0.8 0.3 1.7 0.3 0.4 -0.2 -0.8 2.2 -0.5 1.7 -0.9 -0.7 -0.3 -1.6 -0.5 0.1 -0.8 0.9 0.6 0.2 3.0 -1.9 -0.4 0.1 0.5 -0.7 0.1 -0.2 1.2 0.1 -0.9 -0.1 0.2 0.0 -0.4 -0.8 -0.7 -0.6 -1.0 0.8 Chi-square with 42 degrees of freedom:43.173265 z-score=0.128014, p-value=0.579062 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-10-06_21:31 Test no p-value 1 0.405776 2 0.007946 3 0.030019 4 0.747818 5 0.029644 6 0.452705 7 0.161525 8 0.557575 9 0.016943 10 0.244121 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.004267 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-10-06_21:31: (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 66530 0.28 66620 0.03 3 25000.00 25048 0.09 25009 0.00 4 6666.67 6697 0.14 6687 0.06 5 1388.89 1461 3.74 1412 0.38 6 238.10 226 0.61 228 0.43 7 34.72 37 0.15 35 0.00 8 4.96 0 4.96 8 1.86 p=0.87443 p=0.16360 Number of rngs required: 689351, p-value: 0.864 RESULTS OF CRAPS TEST for dh-ranFile-2016-10-06_21:31 No. of wins: Observed Expected 98859 98585.9 z-score= 1.222, pvalue=0.88908 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66704 66666.7 0.021 0.021 2 37556 37654.3 0.257 0.278 3 27054 26954.7 0.366 0.643 4 19408 19313.5 0.463 1.106 5 13863 13851.4 0.010 1.116 6 9869 9943.5 0.559 1.674 7 7209 7145.0 0.573 2.247 8 5053 5139.1 1.442 3.689 9 3596 3699.9 2.916 6.605 10 2729 2666.3 1.475 8.079 11 1891 1923.3 0.543 8.623 12 1406 1388.7 0.215 8.837 13 1021 1003.7 0.298 9.135 14 712 726.1 0.275 9.410 15 527 525.8 0.003 9.413 16 371 381.2 0.270 9.683 17 288 276.5 0.475 10.158 18 215 200.8 1.000 11.158 19 133 146.0 1.155 12.313 20 101 106.2 0.256 12.569 21 294 287.1 0.165 12.734 Chisq= 12.73 for 20 degrees of freedom, p= 0.11149 SUMMARY of craptest p-value for no. of wins: 0.889080 p-value for throws/game: 0.111493 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-10-06_21:31 No. of wins: Observed Expected 98675 98585.9 z-score= 0.399, pvalue=0.65494 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66647 66666.7 0.006 0.006 2 37944 37654.3 2.229 2.234 3 26942 26954.7 0.006 2.240 4 19161 19313.5 1.204 3.444 5 13739 13851.4 0.912 4.356 6 10008 9943.5 0.418 4.774 7 6985 7145.0 3.584 8.358 8 5103 5139.1 0.253 8.611 9 3655 3699.9 0.544 9.155 10 2689 2666.3 0.193 9.349 11 1972 1923.3 1.232 10.580 12 1389 1388.7 0.000 10.580 13 977 1003.7 0.711 11.291 14 750 726.1 0.784 12.075 15 571 525.8 3.879 15.955 16 382 381.2 0.002 15.957 17 280 276.5 0.043 16.000 18 208 200.8 0.256 16.256 19 165 146.0 2.477 18.733 20 107 106.2 0.006 18.739 21 326 287.1 5.267 24.005 Chisq= 24.01 for 20 degrees of freedom, p= 0.75783 SUMMARY of craptest p-value for no. of wins: 0.654940 p-value for throws/game: 0.757833 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0019,0.0043,0.0043,0.0074,0.0079,0.0117,0.0156,0.0168,0.0169,0.0223, 0.0244,0.0296,0.0300,0.0362,0.0404,0.0438,0.0452,0.0454,0.0471,0.0703, 0.0737,0.0746,0.0818,0.0868,0.0960,0.0969,0.1007,0.1102,0.1108,0.1115, 0.1125,0.1159,0.1168,0.1196,0.1233,0.1377,0.1395,0.1463,0.1472,0.1473, 0.1476,0.1572,0.1615,0.1636,0.1684,0.1712,0.1718,0.1741,0.1783,0.1786, 0.1807,0.1823,0.1890,0.2047,0.2056,0.2056,0.2110,0.2125,0.2132,0.2140, 0.2152,0.2152,0.2160,0.2165,0.2168,0.2242,0.2353,0.2400,0.2413,0.2424, 0.2427,0.2441,0.2448,0.2485,0.2550,0.2613,0.2623,0.2665,0.2763,0.2791, 0.2811,0.2866,0.2892,0.3025,0.3033,0.3035,0.3077,0.3098,0.3196,0.3245, 0.3269,0.3269,0.3334,0.3414,0.3442,0.3475,0.3504,0.3552,0.3557,0.3619, 0.3660,0.3666,0.3676,0.3722,0.3728,0.3791,0.3822,0.3841,0.3849,0.3857, 0.3944,0.3964,0.4029,0.4029,0.4058,0.4065,0.4110,0.4117,0.4132,0.4213, 0.4228,0.4243,0.4265,0.4343,0.4387,0.4390,0.4398,0.4491,0.4527,0.4539, 0.4542,0.4625,0.4636,0.4723,0.4913,0.4946,0.5051,0.5092,0.5149,0.5165, 0.5225,0.5239,0.5364,0.5406,0.5407,0.5432,0.5435,0.5471,0.5576,0.5615, 0.5667,0.5695,0.5761,0.5791,0.5791,0.5912,0.6011,0.6014,0.6043,0.6063, 0.6092,0.6175,0.6179,0.6194,0.6206,0.6207,0.6288,0.6315,0.6346,0.6346, 0.6435,0.6463,0.6523,0.6537,0.6549,0.6584,0.6594,0.6637,0.6659,0.6684, 0.6854,0.6854,0.6865,0.6970,0.6983,0.7035,0.7051,0.7081,0.7109,0.7166, 0.7185,0.7194,0.7208,0.7212,0.7214,0.7231,0.7265,0.7321,0.7321,0.7435, 0.7448,0.7454,0.7478,0.7487,0.7540,0.7578,0.7668,0.7685,0.7707,0.7737, 0.7751,0.7877,0.7992,0.8015,0.8047,0.8057,0.8076,0.8170,0.8190,0.8196, 0.8215,0.8220,0.8238,0.8273,0.8339,0.8391,0.8419,0.8449,0.8475,0.8495, 0.8507,0.8511,0.8561,0.8563,0.8586,0.8643,0.8659,0.8703,0.8732,0.8744, 0.8772,0.8778,0.8819,0.8829,0.8848,0.8854,0.8860,0.8891,0.8893,0.8933, 0.8986,0.9010,0.9017,0.9110,0.9254,0.9269,0.9298,0.9309,0.9310,0.9315, 0.9332,0.9532,0.9589,0.9626,0.9663,0.9808,0.9829,0.9872,0.9919, Overall p-value after applying KStest on 269 p-values = 0.680614 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.