RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-02-07_14:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.80 21.0199 0.774599 2 to 25 15.81 11.5052 0.170869 3 to 26 15.66 15.4955 0.440164 4 to 27 16.04 10.0771 0.099655 5 to 28 15.78 16.1302 0.485375 6 to 29 15.76 17.6375 0.587954 7 to 30 15.82 22.7893 0.843765 8 to 31 15.60 32.5258 0.987064 9 to 32 15.92 16.1449 0.486416 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.891187 Tough bday spacings test for dh-ranFile-2017-02-07_14:31: 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 42 75 93 102 90 36 29 16 7 2 (O-E)^2/E 0.1 0.8 0.0 0.2 0.2 1.8 5.0 0.0 0.1 0.0 1.0 Birthday Spacings: Sum(O-E)^2/E= 9.337, p= 0.500 RESULTS OF GCD FOR dh-ranFile-2017-02-07_14:31 Euclid's algorithm: p-value, steps to gcd: 0.746243 p-value, dist. of gcd's: 0.213802 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-02-07_14:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.809 0.926 0.312 0.087 0.261 0.943 0.136 0.221 Bits 8 to 15---> 0.376 0.713 0.200 0.008 0.216 0.458 0.397 0.586 Bits 16 to 23---> 0.316 0.847 0.510 0.105 0.154 0.696 0.152 0.284 Bits 24 to 31---> 0.327 0.886 0.559 0.787 0.923 0.079 0.777 0.772 KS test for the above 32 p values: 0.328 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-02-07_14:31, p-values for 5 runs: 0.3485, 0.9064, 0.8662, 0.3933, 0.5669 Rank test for binary matrices (31x31) for dh-ranFile-2017-02-07_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 198 211.4 0.852 0.852 r= 29 5015 5134.0 2.759 3.610 r= 30 23155 23103.0 0.117 3.727 r= 31 11632 11551.5 0.561 4.288 chi-square = 4.288 with df = 3; p-value = 0.768 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2017-02-07_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 211 211.4 0.001 0.001 r= 30 5136 5134.0 0.001 0.002 r= 31 23175 23103.0 0.224 0.226 r= 32 11478 11551.5 0.468 0.694 chi-square = 0.694 with df = 3; p-value = 0.125 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2017-02-07_14:31 b-rank test for bits 1 to 8, p=0.28208 b-rank test for bits 2 to 9, p=0.14359 b-rank test for bits 3 to 10, p=0.41047 b-rank test for bits 4 to 11, p=0.49837 b-rank test for bits 5 to 12, p=0.00849 b-rank test for bits 6 to 13, p=0.37518 b-rank test for bits 7 to 14, p=0.76466 b-rank test for bits 8 to 15, p=0.55722 b-rank test for bits 9 to 16, p=0.38884 b-rank test for bits 10 to 17, p=0.53784 b-rank test for bits 11 to 18, p=0.70435 b-rank test for bits 12 to 19, p=0.85227 b-rank test for bits 13 to 20, p=0.33510 b-rank test for bits 14 to 21, p=0.68087 b-rank test for bits 15 to 22, p=0.72464 b-rank test for bits 16 to 23, p=0.12133 b-rank test for bits 17 to 24, p=0.13317 b-rank test for bits 18 to 25, p=0.61261 b-rank test for bits 19 to 26, p=0.13476 b-rank test for bits 20 to 27, p=0.07960 b-rank test for bits 21 to 28, p=0.77579 b-rank test for bits 22 to 29, p=0.60469 b-rank test for bits 23 to 30, p=0.51462 b-rank test for bits 24 to 31, p=0.73753 b-rank test for bits 25 to 32, p=0.47839 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 = 0.409847 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-02-07_14:31 (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 141947 0.09 0.535067 2 142173 0.62 0.731070 3 142308 0.93 0.824195 4 141988 0.18 0.572918 5 141668 -0.56 0.286426 6 142156 0.58 0.717805 7 142311 0.94 0.826001 8 141696 -0.50 0.309089 9 141587 -0.75 0.225693 10 141215 -1.62 0.052373 11 141418 -1.15 0.125491 12 141473 -1.02 0.153992 13 142063 0.36 0.640218 14 142399 1.14 0.873707 15 141487 -0.99 0.161882 16 142135 0.53 0.700996 17 141796 -0.26 0.395586 18 141673 -0.55 0.290415 19 142101 0.45 0.672861 20 142590 1.59 0.944122 ---------------------------------------------------------------- OPSO test for dh-ranFile-2017-02-07_14:31 Bits used No. missing words z-score p-value 23 to 32 141814 -0.3287 0.371182 22 to 31 141843 -0.2287 0.409542 21 to 30 141516 -1.3563 0.087500 20 to 29 142076 0.5747 0.717261 19 to 28 141813 -0.3322 0.369880 18 to 27 141813 -0.3322 0.369880 17 to 26 141969 0.2058 0.581510 16 to 25 142096 0.6437 0.740112 15 to 24 141646 -0.9080 0.181930 14 to 23 142304 1.3609 0.913232 13 to 22 141644 -0.9149 0.180114 12 to 21 142017 0.3713 0.644784 11 to 20 142252 1.1816 0.881322 10 to 19 141664 -0.8460 0.198786 9 to 18 142046 0.4713 0.681278 8 to 17 141767 -0.4908 0.311786 7 to 16 141817 -0.3184 0.375099 6 to 15 142021 0.3851 0.649907 5 to 14 141805 -0.3598 0.359514 4 to 13 141580 -1.1356 0.128058 3 to 12 141728 -0.6253 0.265895 2 to 11 141397 -1.7667 0.038643 1 to 10 141185 -2.4977 0.006250 ----------------------------------------------------------------- OQSO test for dh-ranFile-2017-02-07_14:31 Bits used No. missing words z-score p-value 28 to 32 142335 1.4429 0.925483 27 to 31 142103 0.6565 0.744252 26 to 30 142000 0.3074 0.620714 25 to 29 141891 -0.0621 0.475227 24 to 28 142111 0.6836 0.752895 23 to 27 141737 -0.5842 0.279553 22 to 26 141936 0.0904 0.536018 21 to 25 141686 -0.7571 0.224510 20 to 24 141447 -1.5672 0.058532 19 to 23 142215 1.0362 0.849938 18 to 22 141984 0.2531 0.599912 17 to 21 141619 -0.9842 0.162516 16 to 20 142086 0.5989 0.725374 15 to 19 142515 2.0531 0.979969 14 to 18 141142 -2.6011 0.004646 13 to 17 141545 -1.2350 0.108412 12 to 16 141572 -1.1435 0.126417 11 to 15 142258 1.1819 0.881384 10 to 14 141871 -0.1299 0.448310 9 to 13 142077 0.5684 0.715109 8 to 12 142224 1.0667 0.856941 7 to 11 141813 -0.3265 0.372007 6 to 10 142071 0.5480 0.708166 5 to 9 141669 -0.8147 0.207628 4 to 8 141511 -1.3503 0.088465 3 to 7 141813 -0.3265 0.372007 2 to 6 141638 -0.9198 0.178848 1 to 5 142235 1.1040 0.865196 ----------------------------------------------------------------- DNA test for dh-ranFile-2017-02-07_14:31 Bits used No. missing words z-score p-value 31 to 32 142205 0.8722 0.808446 30 to 31 142083 0.5123 0.695780 29 to 30 141463 -1.3166 0.093985 28 to 29 142067 0.4651 0.679071 27 to 28 142187 0.8191 0.793631 26 to 27 141839 -0.2075 0.417824 25 to 26 141799 -0.3255 0.372418 24 to 25 142120 0.6214 0.732847 23 to 24 141605 -0.8977 0.184665 22 to 23 141294 -1.8151 0.034752 21 to 22 141955 0.1347 0.553583 20 to 21 142301 1.1554 0.876030 19 to 20 142095 0.5477 0.708051 18 to 19 141719 -0.5614 0.287247 17 to 18 141830 -0.2340 0.407488 16 to 17 142061 0.4474 0.672708 15 to 16 141934 0.0728 0.529007 14 to 15 141750 -0.4700 0.319178 13 to 14 142427 1.5271 0.936626 12 to 13 142057 0.4356 0.668438 11 to 12 142554 1.9017 0.971394 10 to 11 142747 2.4710 0.993263 9 to 10 141697 -0.6263 0.265545 8 to 9 142185 0.8132 0.791944 7 to 8 142032 0.3619 0.641271 6 to 7 141854 -0.1632 0.435174 5 to 6 142189 0.8250 0.795310 4 to 5 142238 0.9695 0.833859 3 to 4 142055 0.4297 0.666295 2 to 3 141853 -0.1662 0.434014 1 to 2 141549 -1.0629 0.143909 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2017-02-07_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2436.16 -0.903 0.183324 Test results for specific bytes for dh-ranFile-2017-02-07_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2495.35 -0.066 0.473785 2 to 9 2503.84 0.054 0.521631 3 to 10 2557.65 0.815 0.792537 4 to 11 2517.71 0.250 0.598872 5 to 12 2570.87 1.002 0.841874 6 to 13 2430.94 -0.977 0.164365 7 to 14 2501.60 0.023 0.509025 8 to 15 2483.61 -0.232 0.408333 9 to 16 2377.10 -1.738 0.041101 10 to 17 2456.86 -0.610 0.270903 11 to 18 2516.58 0.235 0.592710 12 to 19 2462.24 -0.534 0.296661 13 to 20 2629.95 1.838 0.966955 14 to 21 2444.85 -0.780 0.217732 15 to 22 2520.76 0.294 0.615465 16 to 23 2398.82 -1.431 0.076236 17 to 24 2538.11 0.539 0.705054 18 to 25 2492.95 -0.100 0.460294 19 to 26 2576.68 1.084 0.860916 20 to 27 2408.93 -1.288 0.098880 21 to 28 2734.87 3.322 0.999553 22 to 29 2381.21 -1.680 0.046481 23 to 30 2476.90 -0.327 0.371939 24 to 31 2488.62 -0.161 0.436065 25 to 32 2470.69 -0.415 0.339232 CDPARK for dh-ranFile-2017-02-07_14:31: 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 3492 -1.4155 0.078457 3560 1.6895 0.954438 3474 -2.2374 0.012629 3527 0.1826 0.572463 3539 0.7306 0.767486 3493 -1.3699 0.085365 3515 -0.3653 0.357445 3517 -0.2740 0.392053 3503 -0.9132 0.180558 3508 -0.6849 0.246694 Square side=100, avg. no. parked=3512.80 sample std.=23.64 p-value of the KSTEST for those 10 p-values: 0.202645 Results for the MINIMUM DISTANCE test for dh-ranFile-2017-02-07_14:31 0.5592,0.8440,0.9358,0.1532,0.7140,0.8188,0.9857,0.2903,0.1080,0.4531, The KS test for those 10 p-values: 0.553968 The 3DSPHERES test for dh-ranFile-2017-02-07_14:31 sample no r^3 equiv. uni. 1 4.578 0.141535 2 31.410 0.649010 3 44.648 0.774239 4 14.536 0.384008 5 28.688 0.615669 6 15.587 0.405216 7 18.044 0.452001 8 28.056 0.607497 9 31.224 0.646832 10 62.303 0.874667 11 5.169 0.158287 12 68.390 0.897683 13 7.737 0.227330 14 20.872 0.501291 15 3.046 0.096556 16 52.341 0.825300 17 7.292 0.215778 18 1.280 0.041783 19 24.605 0.559649 20 55.764 0.844140 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.962458 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-02-07_14:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 1.3 -0.7 2.5 -0.3 1.2 -1.0 1.0 1.3 1.2 -0.5 -1.9 -1.4 0.6 -0.0 0.6 0.7 -0.0 0.7 1.3 -1.4 -0.5 -1.0 -0.1 -1.2 0.6 0.3 0.1 1.0 0.5 -1.2 1.9 0.4 -1.2 -0.3 -0.9 -0.3 1.4 0.2 -0.4 1.5 0.1 1.0 -0.1 Chi-square with 42 degrees of freedom:43.489752 z-score=0.162545, p-value=0.592225 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2017-02-07_14:31 Test no p-value 1 0.005189 2 0.004957 3 0.000495 4 0.466763 5 0.032679 6 0.000423 7 0.572882 8 0.083689 9 0.578871 10 0.089007 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000001 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-02-07_14:31: (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 66782 0.20 66720 0.04 3 25000.00 24959 0.07 24932 0.18 4 6666.67 6554 1.90 6632 0.18 5 1388.89 1417 0.57 1420 0.70 6 238.10 249 0.50 251 0.70 7 34.72 34 0.01 39 0.53 8 4.96 4 0.19 5 0.00 p=0.24807 p=0.11324 Number of rngs required: 688439, p-value: 0.517 RESULTS OF CRAPS TEST for dh-ranFile-2017-02-07_14:31 No. of wins: Observed Expected 98246 98585.9 z-score=-1.520, pvalue=0.06425 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66364 66666.7 1.374 1.374 2 37868 37654.3 1.213 2.587 3 27206 26954.7 2.342 4.929 4 19374 19313.5 0.190 5.119 5 13771 13851.4 0.467 5.586 6 9826 9943.5 1.389 6.975 7 7152 7145.0 0.007 6.982 8 5224 5139.1 1.404 8.385 9 3624 3699.9 1.556 9.941 10 2649 2666.3 0.112 10.053 11 1900 1923.3 0.283 10.336 12 1394 1388.7 0.020 10.356 13 1018 1003.7 0.203 10.559 14 726 726.1 0.000 10.559 15 502 525.8 1.080 11.640 16 398 381.2 0.745 12.385 17 292 276.5 0.864 13.249 18 198 200.8 0.040 13.289 19 151 146.0 0.172 13.461 20 98 106.2 0.635 14.097 21 265 287.1 1.703 15.800 Chisq= 15.80 for 20 degrees of freedom, p= 0.27105 SUMMARY of craptest p-value for no. of wins: 0.064250 p-value for throws/game: 0.271048 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2017-02-07_14:31 No. of wins: Observed Expected 98349 98585.9 z-score=-1.059, pvalue=0.14472 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66857 66666.7 0.543 0.543 2 37458 37654.3 1.024 1.567 3 27005 26954.7 0.094 1.661 4 19339 19313.5 0.034 1.694 5 13743 13851.4 0.849 2.543 6 9974 9943.5 0.093 2.636 7 7141 7145.0 0.002 2.639 8 5078 5139.1 0.726 3.364 9 3707 3699.9 0.014 3.378 10 2751 2666.3 2.691 6.069 11 1911 1923.3 0.079 6.148 12 1416 1388.7 0.535 6.683 13 1016 1003.7 0.150 6.834 14 685 726.1 2.331 9.164 15 513 525.8 0.313 9.478 16 400 381.2 0.932 10.410 17 278 276.5 0.008 10.418 18 216 200.8 1.146 11.564 19 143 146.0 0.061 11.625 20 95 106.2 1.184 12.809 21 274 287.1 0.599 13.408 Chisq= 13.41 for 20 degrees of freedom, p= 0.14079 SUMMARY of craptest p-value for no. of wins: 0.144716 p-value for throws/game: 0.140787 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0000,0.0004,0.0005,0.0046,0.0050,0.0052,0.0063,0.0076,0.0085,0.0126, 0.0327,0.0348,0.0386,0.0411,0.0418,0.0465,0.0524,0.0585,0.0642,0.0762, 0.0785,0.0786,0.0796,0.0837,0.0854,0.0871,0.0875,0.0885,0.0890,0.0940, 0.0966,0.0989,0.0997,0.1046,0.1080,0.1084,0.1132,0.1213,0.1253,0.1255, 0.1264,0.1281,0.1332,0.1348,0.1361,0.1408,0.1415,0.1436,0.1439,0.1447, 0.1517,0.1532,0.1536,0.1540,0.1583,0.1619,0.1625,0.1644,0.1709,0.1788, 0.1801,0.1806,0.1819,0.1833,0.1847,0.1988,0.2004,0.2026,0.2076,0.2138, 0.2158,0.2162,0.2177,0.2211,0.2245,0.2257,0.2273,0.2467,0.2481,0.2611, 0.2655,0.2659,0.2709,0.2710,0.2796,0.2821,0.2842,0.2864,0.2872,0.2903, 0.2904,0.2967,0.3091,0.3118,0.3123,0.3160,0.3192,0.3268,0.3276,0.3351, 0.3392,0.3485,0.3574,0.3595,0.3699,0.3699,0.3712,0.3719,0.3720,0.3720, 0.3724,0.3751,0.3752,0.3758,0.3840,0.3888,0.3921,0.3933,0.3956,0.3967, 0.4052,0.4075,0.4083,0.4095,0.4098,0.4105,0.4178,0.4340,0.4352,0.4361, 0.4402,0.4483,0.4520,0.4531,0.4583,0.4603,0.4668,0.4738,0.4752,0.4784, 0.4854,0.4864,0.4984,0.4996,0.5013,0.5090,0.5096,0.5146,0.5165,0.5216, 0.5290,0.5351,0.5360,0.5378,0.5536,0.5540,0.5572,0.5592,0.5594,0.5596, 0.5669,0.5725,0.5729,0.5729,0.5789,0.5815,0.5864,0.5880,0.5922,0.5927, 0.5989,0.5999,0.6047,0.6075,0.6126,0.6155,0.6157,0.6207,0.6402,0.6413, 0.6448,0.6468,0.6490,0.6499,0.6663,0.6684,0.6727,0.6729,0.6791,0.6809, 0.6813,0.6958,0.6965,0.7010,0.7043,0.7051,0.7081,0.7082,0.7129,0.7140, 0.7151,0.7173,0.7178,0.7246,0.7254,0.7311,0.7328,0.7375,0.7401,0.7443, 0.7462,0.7529,0.7647,0.7675,0.7680,0.7722,0.7742,0.7746,0.7758,0.7771, 0.7873,0.7919,0.7925,0.7936,0.7953,0.8084,0.8094,0.8188,0.8242,0.8253, 0.8260,0.8339,0.8419,0.8438,0.8440,0.8441,0.8473,0.8499,0.8523,0.8569, 0.8609,0.8652,0.8662,0.8737,0.8747,0.8760,0.8813,0.8814,0.8862,0.8912, 0.8977,0.9064,0.9132,0.9234,0.9255,0.9257,0.9358,0.9366,0.9428,0.9441, 0.9544,0.9625,0.9670,0.9714,0.9800,0.9857,0.9871,0.9933,0.9996, Overall p-value after applying KStest on 269 p-values = 0.099476 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.