RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-03-16_16:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.78 23.8357 0.876031 2 to 25 15.92 18.9683 0.669645 3 to 26 15.68 8.5767 0.047388 4 to 27 15.96 16.9521 0.542385 5 to 28 15.67 17.7008 0.592051 6 to 29 15.86 18.4214 0.637267 7 to 30 16.17 10.7831 0.132386 8 to 31 15.83 12.9142 0.258089 9 to 32 15.47 31.6526 0.983386 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.926995 Tough bday spacings test for dh-ranFile-2016-03-16_16:31: 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 10 39 64 80 107 98 51 24 16 8 3 (O-E)^2/E 0.1 0.2 1.2 3.2 0.9 5.0 0.0 1.1 0.1 0.3 0.3 Birthday Spacings: Sum(O-E)^2/E= 12.329, p= 0.736 RESULTS OF GCD FOR dh-ranFile-2016-03-16_16:31 Euclid's algorithm: p-value, steps to gcd: 0.643124 p-value, dist. of gcd's: 0.210954 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-03-16_16:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.053 0.536 0.897 0.032 0.530 0.996 0.974 0.298 Bits 8 to 15---> 0.224 0.112 0.437 0.816 0.786 0.081 0.529 0.552 Bits 16 to 23---> 0.624 0.511 0.043 0.229 0.512 0.972 0.935 0.990 Bits 24 to 31---> 0.417 0.138 0.907 0.380 0.114 0.998 0.502 0.525 KS test for the above 32 p values: 0.827 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-03-16_16:31, p-values for 5 runs: 0.5368, 0.2470, 0.6702, 0.6152, 0.8758 Rank test for binary matrices (31x31) for dh-ranFile-2016-03-16_16:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 197 211.4 0.983 0.983 r= 29 5084 5134.0 0.487 1.470 r= 30 23227 23103.0 0.665 2.135 r= 31 11492 11551.5 0.307 2.442 chi-square = 2.442 with df = 3; p-value = 0.514 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-03-16_16:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 215 211.4 0.061 0.061 r= 30 5053 5134.0 1.278 1.339 r= 31 23074 23103.0 0.037 1.375 r= 32 11658 11551.5 0.981 2.357 chi-square = 2.357 with df = 3; p-value = 0.498 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-03-16_16:31 b-rank test for bits 1 to 8, p=0.33368 b-rank test for bits 2 to 9, p=0.84344 b-rank test for bits 3 to 10, p=0.07056 b-rank test for bits 4 to 11, p=0.78538 b-rank test for bits 5 to 12, p=0.42152 b-rank test for bits 6 to 13, p=0.22765 b-rank test for bits 7 to 14, p=0.78451 b-rank test for bits 8 to 15, p=0.85629 b-rank test for bits 9 to 16, p=0.05994 b-rank test for bits 10 to 17, p=0.25987 b-rank test for bits 11 to 18, p=0.66536 b-rank test for bits 12 to 19, p=0.29793 b-rank test for bits 13 to 20, p=0.52256 b-rank test for bits 14 to 21, p=0.95004 b-rank test for bits 15 to 22, p=0.67594 b-rank test for bits 16 to 23, p=0.14646 b-rank test for bits 17 to 24, p=0.74166 b-rank test for bits 18 to 25, p=0.52060 b-rank test for bits 19 to 26, p=0.23321 b-rank test for bits 20 to 27, p=0.08666 b-rank test for bits 21 to 28, p=0.57627 b-rank test for bits 22 to 29, p=0.72138 b-rank test for bits 23 to 30, p=0.36926 b-rank test for bits 24 to 31, p=0.38568 b-rank test for bits 25 to 32, p=0.27307 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 = 0.873411 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-03-16_16:31 (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 142681 1.80 0.964303 2 141585 -0.76 0.224291 3 141602 -0.72 0.236360 4 141587 -0.75 0.225693 5 142344 1.02 0.845086 6 142086 0.41 0.660116 7 141916 0.02 0.506217 8 142617 1.65 0.950879 9 140778 -2.64 0.004105 10 141200 -1.66 0.048728 11 140688 -2.85 0.002162 12 141352 -1.30 0.096429 13 141708 -0.47 0.319036 14 141707 -0.47 0.318202 15 142229 0.75 0.772436 16 141542 -0.86 0.195378 17 142203 0.69 0.753689 18 141803 -0.25 0.401899 19 142660 1.75 0.960276 20 141426 -1.13 0.129391 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-03-16_16:31 Bits used No. missing words z-score p-value 23 to 32 141775 -0.4632 0.321608 22 to 31 141945 0.1230 0.548947 21 to 30 141893 -0.0563 0.477547 20 to 29 142184 0.9471 0.828216 19 to 28 142454 1.8782 0.969821 18 to 27 141948 0.1333 0.553040 17 to 26 142144 0.8092 0.790802 16 to 25 141725 -0.6356 0.262512 15 to 24 141876 -0.1149 0.454250 14 to 23 141613 -1.0218 0.153431 13 to 22 141927 0.0609 0.524293 12 to 21 141911 0.0058 0.502297 11 to 20 141416 -1.7011 0.044459 10 to 19 142051 0.4885 0.687408 9 to 18 141694 -0.7425 0.228887 8 to 17 141538 -1.2804 0.100194 7 to 16 141502 -1.4046 0.080072 6 to 15 141519 -1.3460 0.089157 5 to 14 142537 2.1644 0.984782 4 to 13 141752 -0.5425 0.293731 3 to 12 141732 -0.6115 0.270440 2 to 11 141875 -0.1184 0.452884 1 to 10 142296 1.3333 0.908791 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-03-16_16:31 Bits used No. missing words z-score p-value 28 to 32 141493 -1.4113 0.079080 27 to 31 142260 1.1887 0.882723 26 to 30 141884 -0.0859 0.465787 25 to 29 142197 0.9752 0.835258 24 to 28 142385 1.6124 0.946567 23 to 27 142285 1.2735 0.898572 22 to 26 141771 -0.4689 0.319565 21 to 25 141927 0.0599 0.523882 20 to 24 141761 -0.5028 0.307548 19 to 23 141985 0.2565 0.601221 18 to 22 141888 -0.0723 0.471180 17 to 21 142270 1.2226 0.889262 16 to 20 142170 0.8836 0.811551 15 to 19 142256 1.1752 0.880033 14 to 18 142416 1.7175 0.957058 13 to 17 142047 0.4667 0.679635 12 to 16 142139 0.7785 0.781875 11 to 15 142301 1.3277 0.907861 10 to 14 142052 0.4836 0.685675 9 to 13 142058 0.5040 0.692857 8 to 12 142552 2.1785 0.985317 7 to 11 141970 0.2057 0.581472 6 to 10 141932 0.0768 0.530628 5 to 9 142086 0.5989 0.725374 4 to 8 142131 0.7514 0.773801 3 to 7 141699 -0.7130 0.237928 2 to 6 141662 -0.8384 0.200901 1 to 5 141684 -0.7638 0.222484 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-03-16_16:31 Bits used No. missing words z-score p-value 31 to 32 141549 -1.0629 0.143909 30 to 31 141651 -0.7620 0.223019 29 to 30 142122 0.6273 0.734784 28 to 29 141905 -0.0128 0.494905 27 to 28 141634 -0.8122 0.208343 26 to 27 141815 -0.2783 0.390407 25 to 26 141732 -0.5231 0.300453 24 to 25 141572 -0.9951 0.159850 23 to 24 141833 -0.2252 0.410927 22 to 23 141815 -0.2783 0.390407 21 to 22 142180 0.7984 0.787691 20 to 21 141957 0.1406 0.555915 19 to 20 141657 -0.7443 0.228337 18 to 19 141779 -0.3845 0.350321 17 to 18 141902 -0.0216 0.491375 16 to 17 141871 -0.1131 0.454988 15 to 16 142009 0.2940 0.615626 14 to 15 142178 0.7925 0.785976 13 to 14 142011 0.2999 0.617878 12 to 13 141124 -2.3166 0.010263 11 to 12 141576 -0.9833 0.162736 10 to 11 142090 0.5329 0.702966 9 to 10 141680 -0.6765 0.249365 8 to 9 141576 -0.9833 0.162736 7 to 8 142124 0.6332 0.736713 6 to 7 141833 -0.2252 0.410927 5 to 6 141564 -1.0187 0.154179 4 to 5 141933 0.0698 0.527833 3 to 4 141933 0.0698 0.527833 2 to 3 141699 -0.6204 0.267483 1 to 2 142469 1.6509 0.950625 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-03-16_16:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2588.28 1.248 0.894076 Test results for specific bytes for dh-ranFile-2016-03-16_16:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2570.31 0.994 0.839966 2 to 9 2559.68 0.844 0.800657 3 to 10 2513.93 0.197 0.578112 4 to 11 2612.63 1.593 0.944407 5 to 12 2586.76 1.227 0.890075 6 to 13 2416.17 -1.185 0.117913 7 to 14 2444.10 -0.790 0.214620 8 to 15 2463.91 -0.510 0.304886 9 to 16 2493.11 -0.097 0.461182 10 to 17 2592.81 1.313 0.905325 11 to 18 2516.35 0.231 0.591438 12 to 19 2518.60 0.263 0.603734 13 to 20 2446.02 -0.763 0.222624 14 to 21 2641.43 2.000 0.977257 15 to 22 2452.60 -0.670 0.251326 16 to 23 2415.33 -1.197 0.115585 17 to 24 2609.02 1.542 0.938427 18 to 25 2378.73 -1.715 0.043165 19 to 26 2554.22 0.767 0.778379 20 to 27 2569.79 0.987 0.838179 21 to 28 2474.11 -0.366 0.357121 22 to 29 2456.22 -0.619 0.267907 23 to 30 2433.68 -0.938 0.174139 24 to 31 2495.02 -0.070 0.471920 25 to 32 2287.96 -2.999 0.001356 CDPARK for dh-ranFile-2016-03-16_16:31: 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 3473 -2.2831 0.011212 3534 0.5023 0.692266 3480 -1.9635 0.024796 3510 -0.5936 0.276387 3527 0.1826 0.572463 3520 -0.1370 0.445521 3523 0.0000 0.500000 3519 -0.1826 0.427537 3558 1.5982 0.944998 3513 -0.4566 0.323972 Square side=100, avg. no. parked=3515.70 sample std.=23.39 p-value of the KSTEST for those 10 p-values: 0.432387 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-03-16_16:31 0.5429,0.8037,0.8639,0.3942,0.3846,0.9082,0.9037,0.1310,0.7416,0.5709, The KS test for those 10 p-values: 0.282040 The 3DSPHERES test for dh-ranFile-2016-03-16_16:31 sample no r^3 equiv. uni. 1 9.063 0.260745 2 49.193 0.805973 3 19.238 0.473381 4 143.357 0.991592 5 14.850 0.390428 6 4.121 0.128352 7 8.493 0.246567 8 77.146 0.923581 9 7.529 0.221941 10 6.367 0.191237 11 13.914 0.371113 12 21.280 0.508028 13 2.392 0.076649 14 11.598 0.320642 15 54.283 0.836254 16 69.097 0.900065 17 37.078 0.709439 18 74.728 0.917166 19 47.012 0.791344 20 10.344 0.291631 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.721309 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-03-16_16:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 0.1 0.3 -0.5 0.0 0.1 0.4 -0.3 0.7 0.6 -1.9 0.2 -1.4 1.7 -0.3 -0.6 -1.9 -0.9 1.3 -2.2 0.7 0.8 2.0 1.9 -0.3 0.4 0.5 -0.2 -0.7 -0.4 2.2 -0.3 0.2 2.2 -0.6 -0.5 1.0 1.8 -1.6 -0.1 0.1 -1.0 0.8 Chi-square with 42 degrees of freedom:50.388318 z-score=0.915241, p-value=0.824393 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-03-16_16:31 Test no p-value 1 0.881487 2 0.541036 3 0.782534 4 0.200882 5 0.628939 6 0.245347 7 0.003135 8 0.830910 9 0.004761 10 0.000835 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.021178 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-03-16_16:31: (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 66516 0.34 66764 0.14 3 25000.00 25141 0.80 24968 0.04 4 6666.67 6660 0.01 6664 0.00 5 1388.89 1406 0.21 1304 5.19 6 238.10 239 0.00 256 1.35 7 34.72 30 0.64 39 0.53 8 4.96 7 0.84 4 0.19 p=0.17103 p=0.71731 Number of rngs required: 687691, p-value: 0.205 RESULTS OF CRAPS TEST for dh-ranFile-2016-03-16_16:31 No. of wins: Observed Expected 98818 98585.9 z-score= 1.038, pvalue=0.85043 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66724 66666.7 0.049 0.049 2 37354 37654.3 2.395 2.445 3 27082 26954.7 0.601 3.045 4 19387 19313.5 0.280 3.325 5 13900 13851.4 0.170 3.496 6 9879 9943.5 0.419 3.915 7 7201 7145.0 0.439 4.353 8 5081 5139.1 0.656 5.010 9 3710 3699.9 0.028 5.037 10 2579 2666.3 2.858 7.896 11 2006 1923.3 3.553 11.449 12 1399 1388.7 0.076 11.525 13 1006 1003.7 0.005 11.530 14 701 726.1 0.870 12.400 15 537 525.8 0.237 12.637 16 370 381.2 0.326 12.964 17 303 276.5 2.532 15.495 18 217 200.8 1.302 16.797 19 166 146.0 2.744 19.542 20 117 106.2 1.095 20.637 21 281 287.1 0.130 20.767 Chisq= 20.77 for 20 degrees of freedom, p= 0.58904 SUMMARY of craptest p-value for no. of wins: 0.850428 p-value for throws/game: 0.589041 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-03-16_16:31 No. of wins: Observed Expected 98511 98585.9 z-score=-0.335, pvalue=0.36888 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66960 66666.7 1.291 1.291 2 37559 37654.3 0.241 1.532 3 26930 26954.7 0.023 1.555 4 19327 19313.5 0.009 1.564 5 13934 13851.4 0.492 2.056 6 9907 9943.5 0.134 2.191 7 7184 7145.0 0.213 2.403 8 5074 5139.1 0.824 3.227 9 3796 3699.9 2.498 5.725 10 2544 2666.3 5.610 11.335 11 1849 1923.3 2.873 14.207 12 1349 1388.7 1.137 15.345 13 991 1003.7 0.161 15.506 14 696 726.1 1.251 16.757 15 526 525.8 0.000 16.757 16 364 381.2 0.772 17.528 17 263 276.5 0.663 18.191 18 199 200.8 0.017 18.208 19 141 146.0 0.170 18.378 20 99 106.2 0.490 18.868 21 308 287.1 1.519 20.388 Chisq= 20.39 for 20 degrees of freedom, p= 0.56607 SUMMARY of craptest p-value for no. of wins: 0.368884 p-value for throws/game: 0.566074 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0008,0.0014,0.0022,0.0031,0.0041,0.0048,0.0103,0.0112,0.0212,0.0248, 0.0318,0.0432,0.0434,0.0445,0.0474,0.0487,0.0526,0.0599,0.0706,0.0766, 0.0791,0.0801,0.0810,0.0867,0.0892,0.0964,0.1002,0.1122,0.1144,0.1156, 0.1179,0.1284,0.1294,0.1310,0.1324,0.1383,0.1439,0.1465,0.1534,0.1542, 0.1599,0.1627,0.1627,0.1710,0.1741,0.1912,0.1954,0.2009,0.2009,0.2052, 0.2083,0.2110,0.2146,0.2219,0.2225,0.2226,0.2230,0.2243,0.2243,0.2257, 0.2276,0.2283,0.2286,0.2289,0.2332,0.2364,0.2379,0.2453,0.2466,0.2470, 0.2494,0.2513,0.2581,0.2599,0.2607,0.2625,0.2675,0.2679,0.2704,0.2731, 0.2764,0.2820,0.2916,0.2937,0.2979,0.2982,0.3005,0.3049,0.3075,0.3182, 0.3190,0.3196,0.3206,0.3216,0.3240,0.3337,0.3503,0.3571,0.3689,0.3693, 0.3711,0.3795,0.3846,0.3857,0.3904,0.3904,0.3904,0.3942,0.4019,0.4109, 0.4109,0.4172,0.4215,0.4275,0.4324,0.4371,0.4455,0.4529,0.4542,0.4550, 0.4612,0.4658,0.4712,0.4719,0.4734,0.4775,0.4914,0.4949,0.4983,0.5000, 0.5018,0.5023,0.5062,0.5080,0.5115,0.5124,0.5142,0.5206,0.5226,0.5239, 0.5243,0.5247,0.5278,0.5278,0.5290,0.5304,0.5306,0.5357,0.5368,0.5410, 0.5424,0.5429,0.5489,0.5517,0.5530,0.5559,0.5661,0.5709,0.5725,0.5763, 0.5781,0.5815,0.5890,0.5914,0.5921,0.6012,0.6037,0.6152,0.6156,0.6179, 0.6239,0.6289,0.6373,0.6431,0.6601,0.6654,0.6696,0.6702,0.6759,0.6796, 0.6857,0.6874,0.6923,0.6929,0.7030,0.7094,0.7173,0.7213,0.7214,0.7254, 0.7348,0.7364,0.7367,0.7416,0.7417,0.7537,0.7724,0.7738,0.7784,0.7819, 0.7825,0.7845,0.7854,0.7858,0.7860,0.7877,0.7908,0.7913,0.8007,0.8037, 0.8060,0.8116,0.8164,0.8244,0.8275,0.8282,0.8309,0.8353,0.8363,0.8382, 0.8400,0.8434,0.8451,0.8504,0.8563,0.8639,0.8734,0.8758,0.8760,0.8800, 0.8815,0.8827,0.8893,0.8901,0.8941,0.8970,0.8986,0.9001,0.9037,0.9053, 0.9069,0.9079,0.9082,0.9088,0.9172,0.9236,0.9270,0.9351,0.9384,0.9444, 0.9450,0.9466,0.9500,0.9506,0.9509,0.9571,0.9603,0.9643,0.9698,0.9718, 0.9735,0.9773,0.9834,0.9848,0.9853,0.9896,0.9916,0.9961,0.9978, Overall p-value after applying KStest on 269 p-values = 0.661407 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.