RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-04-14_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 15.48 26.4065 0.932634 2 to 25 15.55 20.0913 0.730412 3 to 26 15.87 13.4969 0.297663 4 to 27 15.82 12.1420 0.208539 5 to 28 15.72 28.3747 0.959254 6 to 29 16.01 19.7938 0.715087 7 to 30 15.79 8.3494 0.041506 8 to 31 15.65 15.5547 0.444406 9 to 32 15.61 15.9070 0.469565 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.947762 Tough bday spacings test for dh-ranFile-2018-04-14_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 10 27 69 111 101 77 45 38 11 7 4 (O-E)^2/E 0.1 2.5 0.2 1.8 0.1 0.0 1.0 2.3 1.0 0.0 0.0 Birthday Spacings: Sum(O-E)^2/E= 9.082, p= 0.476 RESULTS OF GCD FOR dh-ranFile-2018-04-14_14:31 Euclid's algorithm: p-value, steps to gcd: 0.025325 p-value, dist. of gcd's: 0.963844 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-04-14_14:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.664 0.397 0.871 0.294 0.596 0.443 0.653 0.194 Bits 8 to 15---> 0.263 0.514 0.233 0.669 0.024 0.578 0.104 0.909 Bits 16 to 23---> 0.107 0.853 0.292 0.023 0.064 0.275 0.939 0.691 Bits 24 to 31---> 0.158 0.409 0.631 0.345 0.693 0.260 0.075 0.287 KS test for the above 32 p values: 0.789 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-04-14_14:31, p-values for 5 runs: 0.0003, 0.5590, 0.3082, 0.6844, 0.2252 Rank test for binary matrices (31x31) for dh-ranFile-2018-04-14_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 201 211.4 0.513 0.513 r= 29 5167 5134.0 0.212 0.725 r= 30 23236 23103.0 0.765 1.490 r= 31 11396 11551.5 2.094 3.584 chi-square = 3.584 with df = 3; p-value = 0.690 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-04-14_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 208 211.4 0.055 0.055 r= 30 5108 5134.0 0.132 0.187 r= 31 23164 23103.0 0.161 0.348 r= 32 11520 11551.5 0.086 0.434 chi-square = 0.434 with df = 3; p-value = 0.067 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-04-14_14:31 b-rank test for bits 1 to 8, p=0.32674 b-rank test for bits 2 to 9, p=0.94273 b-rank test for bits 3 to 10, p=0.36714 b-rank test for bits 4 to 11, p=0.12973 b-rank test for bits 5 to 12, p=0.11755 b-rank test for bits 6 to 13, p=0.57524 b-rank test for bits 7 to 14, p=0.48585 b-rank test for bits 8 to 15, p=0.30395 b-rank test for bits 9 to 16, p=0.31936 b-rank test for bits 10 to 17, p=0.89449 b-rank test for bits 11 to 18, p=0.86294 b-rank test for bits 12 to 19, p=0.91637 b-rank test for bits 13 to 20, p=0.04162 b-rank test for bits 14 to 21, p=0.61202 b-rank test for bits 15 to 22, p=0.54329 b-rank test for bits 16 to 23, p=0.81397 b-rank test for bits 17 to 24, p=0.16593 b-rank test for bits 18 to 25, p=0.62864 b-rank test for bits 19 to 26, p=0.27474 b-rank test for bits 20 to 27, p=0.19483 b-rank test for bits 21 to 28, p=0.28078 b-rank test for bits 22 to 29, p=0.60345 b-rank test for bits 23 to 30, p=0.57596 b-rank test for bits 24 to 31, p=0.89422 b-rank test for bits 25 to 32, p=0.82489 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 = 0.929254 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-04-14_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 141958 0.11 0.545268 2 142832 2.16 0.984449 3 141717 -0.45 0.326583 4 142573 1.55 0.939505 5 141914 0.01 0.504353 6 142018 0.25 0.600214 7 141638 -0.63 0.263057 8 141569 -0.80 0.213259 9 142251 0.80 0.787650 10 141812 -0.23 0.410054 11 142546 1.49 0.931565 12 142152 0.57 0.714638 13 142106 0.46 0.677066 14 141860 -0.12 0.454121 15 142011 0.24 0.593884 16 141695 -0.50 0.308266 17 141211 -1.63 0.051381 18 142691 1.83 0.966100 19 141583 -0.76 0.222895 20 142155 0.57 0.717015 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-04-14_14:31 Bits used No. missing words z-score p-value 23 to 32 141329 -2.0011 0.022689 22 to 31 141968 0.2023 0.580163 21 to 30 141954 0.1540 0.561209 20 to 29 142008 0.3402 0.633163 19 to 28 141621 -0.9942 0.160053 18 to 27 141700 -0.7218 0.235200 17 to 26 141844 -0.2253 0.410882 16 to 25 141684 -0.7770 0.218579 15 to 24 142128 0.7540 0.774586 14 to 23 141917 0.0264 0.510550 13 to 22 142635 2.5023 0.993831 12 to 21 141799 -0.3804 0.351806 11 to 20 142055 0.5023 0.692275 10 to 19 142015 0.3644 0.642213 9 to 18 141861 -0.1667 0.433821 8 to 17 141774 -0.4667 0.320373 7 to 16 142174 0.9127 0.819288 6 to 15 142163 0.8747 0.809138 5 to 14 141995 0.2954 0.616161 4 to 13 141851 -0.2011 0.420295 3 to 12 141421 -1.6839 0.046101 2 to 11 141451 -1.5804 0.057002 1 to 10 141491 -1.4425 0.074578 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-04-14_14:31 Bits used No. missing words z-score p-value 28 to 32 141511 -1.3503 0.088465 27 to 31 141548 -1.2248 0.110316 26 to 30 142106 0.6667 0.747511 25 to 29 142366 1.5480 0.939193 24 to 28 141856 -0.1808 0.428270 23 to 27 141991 0.2768 0.609051 22 to 26 142022 0.3819 0.648744 21 to 25 142470 1.9006 0.971321 20 to 24 141931 0.0735 0.529279 19 to 23 141779 -0.4418 0.329318 18 to 22 141855 -0.1842 0.426940 17 to 21 141549 -1.2215 0.110956 16 to 20 141695 -0.7265 0.233753 15 to 19 142425 1.7480 0.959771 14 to 18 141890 -0.0655 0.473878 13 to 17 141639 -0.9164 0.179736 12 to 16 142132 0.7548 0.774820 11 to 15 142390 1.6294 0.948385 10 to 14 142062 0.5175 0.697605 9 to 13 141880 -0.0994 0.460401 8 to 12 141997 0.2972 0.616838 7 to 11 141575 -1.1333 0.128540 6 to 10 141709 -0.6791 0.248542 5 to 9 141835 -0.2520 0.400534 4 to 8 142134 0.7616 0.776849 3 to 7 142007 0.3311 0.629710 2 to 6 142316 1.3785 0.915982 1 to 5 142525 2.0870 0.981557 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-04-14_14:31 Bits used No. missing words z-score p-value 31 to 32 142619 2.0934 0.981844 30 to 31 141617 -0.8623 0.194253 29 to 30 141738 -0.5054 0.306640 28 to 29 141456 -1.3373 0.090569 27 to 28 141686 -0.6588 0.255015 26 to 27 142203 0.8663 0.806833 25 to 26 142015 0.3117 0.622370 24 to 25 141982 0.2144 0.584869 23 to 24 142210 0.8869 0.812442 22 to 23 141998 0.2616 0.603171 21 to 22 142047 0.4061 0.657668 20 to 21 142264 1.0462 0.852271 19 to 20 141546 -1.0718 0.141912 18 to 19 142410 1.4769 0.930149 17 to 18 142281 1.0964 0.863542 16 to 17 141598 -0.9184 0.179211 15 to 16 142335 1.2557 0.895381 14 to 15 141640 -0.7945 0.213457 13 to 14 141968 0.1731 0.568701 12 to 13 141709 -0.5909 0.277279 11 to 12 141662 -0.7296 0.232821 10 to 11 142126 0.6391 0.738636 9 to 10 142295 1.1377 0.872371 8 to 9 142339 1.2675 0.897505 7 to 8 141965 0.1642 0.565220 6 to 7 141494 -1.2252 0.110257 5 to 6 141426 -1.4258 0.076970 4 to 5 141100 -2.3874 0.008484 3 to 4 142307 1.1731 0.879616 2 to 3 141469 -1.2989 0.096988 1 to 2 141128 -2.3048 0.010589 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-04-14_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2518.41 0.260 0.602697 Test results for specific bytes for dh-ranFile-2018-04-14_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2447.72 -0.739 0.229868 2 to 9 2606.68 1.509 0.934302 3 to 10 2335.02 -2.333 0.009821 4 to 11 2634.45 1.901 0.971378 5 to 12 2433.81 -0.936 0.174618 6 to 13 2567.73 0.958 0.830930 7 to 14 2590.86 1.285 0.900587 8 to 15 2581.23 1.149 0.874667 9 to 16 2468.60 -0.444 0.328487 10 to 17 2570.04 0.990 0.839028 11 to 18 2491.30 -0.123 0.451065 12 to 19 2505.10 0.072 0.528771 13 to 20 2422.15 -1.101 0.135443 14 to 21 2632.60 1.875 0.969620 15 to 22 2452.16 -0.676 0.249365 16 to 23 2494.68 -0.075 0.469991 17 to 24 2438.58 -0.869 0.192522 18 to 25 2418.32 -1.155 0.124021 19 to 26 2427.91 -1.019 0.153986 20 to 27 2628.08 1.811 0.964958 21 to 28 2504.03 0.057 0.522744 22 to 29 2570.68 1.000 0.841241 23 to 30 2470.03 -0.424 0.335834 24 to 31 2585.10 1.203 0.885595 25 to 32 2528.45 0.402 0.656279 CDPARK for dh-ranFile-2018-04-14_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 3549 1.1872 0.882429 3525 0.0913 0.536383 3543 0.9132 0.819442 3513 -0.4566 0.323972 3529 0.2740 0.607947 3518 -0.2283 0.409702 3513 -0.4566 0.323972 3519 -0.1826 0.427537 3528 0.2283 0.590298 3540 0.7763 0.781201 Square side=100, avg. no. parked=3527.70 sample std.=12.04 p-value of the KSTEST for those 10 p-values: 0.388769 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-04-14_14:31 0.0982,0.4637,0.6186,0.2423,0.4173,0.8039,0.0161,0.9976,0.9775,0.8058, The KS test for those 10 p-values: 0.425992 The 3DSPHERES test for dh-ranFile-2018-04-14_14:31 sample no r^3 equiv. uni. 1 5.908 0.178767 2 36.192 0.700728 3 0.249 0.008252 4 20.133 0.488849 5 1.418 0.046152 6 17.231 0.436945 7 79.881 0.930240 8 22.418 0.526339 9 62.897 0.877121 10 16.439 0.421871 11 20.004 0.486649 12 34.178 0.679950 13 11.514 0.318740 14 24.276 0.554790 15 46.956 0.790954 16 14.367 0.380538 17 4.829 0.148693 18 69.685 0.902006 19 4.380 0.135837 20 9.497 0.271362 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.909325 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-04-14_14:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 -2.0 0.3 1.6 -0.8 0.1 -0.2 1.7 1.6 3.1 -0.4 -2.2 1.0 0.0 1.8 -0.7 0.0 0.1 -0.3 -0.1 -0.8 -1.1 -1.4 2.7 -0.2 -0.1 -1.1 -0.0 -1.9 -0.0 -0.0 -2.4 1.2 1.0 -1.2 -0.5 0.0 -1.0 0.9 -0.1 -0.6 0.0 -0.1 Chi-square with 42 degrees of freedom:62.332735 z-score=2.218483, p-value=0.977618 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-04-14_14:31 Test no p-value 1 0.405026 2 0.366836 3 0.058416 4 0.744903 5 0.071535 6 0.512391 7 0.102658 8 0.426204 9 0.310882 10 0.445721 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.112711 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-04-14_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 66609 0.05 66669 0.00 3 25000.00 25165 1.09 24910 0.32 4 6666.67 6587 0.95 6788 2.21 5 1388.89 1375 0.14 1336 2.01 6 238.10 235 0.04 258 1.66 7 34.72 23 3.96 33 0.09 8 4.96 5 0.00 5 0.00 p=0.60171 p=0.60913 Number of rngs required: 687404, p-value: 0.123 RESULTS OF CRAPS TEST for dh-ranFile-2018-04-14_14:31 No. of wins: Observed Expected 98816 98585.9 z-score= 1.029, pvalue=0.84834 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67007 66666.7 1.737 1.737 2 37286 37654.3 3.603 5.340 3 27058 26954.7 0.396 5.736 4 19341 19313.5 0.039 5.775 5 13563 13851.4 6.006 11.781 6 10059 9943.5 1.341 13.121 7 7254 7145.0 1.662 14.783 8 5033 5139.1 2.189 16.973 9 3635 3699.9 1.137 18.110 10 2737 2666.3 1.875 19.985 11 1955 1923.3 0.522 20.506 12 1417 1388.7 0.575 21.081 13 1007 1003.7 0.011 21.092 14 717 726.1 0.115 21.207 15 523 525.8 0.015 21.222 16 392 381.2 0.309 21.531 17 267 276.5 0.329 21.860 18 201 200.8 0.000 21.860 19 135 146.0 0.827 22.687 20 112 106.2 0.315 23.002 21 301 287.1 0.672 23.674 Chisq= 23.67 for 20 degrees of freedom, p= 0.74306 SUMMARY of craptest p-value for no. of wins: 0.848337 p-value for throws/game: 0.743059 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-04-14_14:31 No. of wins: Observed Expected 98398 98585.9 z-score=-0.840, pvalue=0.20039 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66586 66666.7 0.098 0.098 2 37785 37654.3 0.454 0.551 3 27185 26954.7 1.967 2.518 4 19341 19313.5 0.039 2.558 5 13853 13851.4 0.000 2.558 6 9741 9943.5 4.126 6.683 7 7070 7145.0 0.788 7.471 8 5140 5139.1 0.000 7.471 9 3739 3699.9 0.414 7.885 10 2645 2666.3 0.170 8.055 11 1893 1923.3 0.478 8.534 12 1406 1388.7 0.215 8.748 13 1004 1003.7 0.000 8.748 14 771 726.1 2.771 11.520 15 508 525.8 0.605 12.125 16 375 381.2 0.099 12.224 17 270 276.5 0.155 12.378 18 198 200.8 0.040 12.418 19 121 146.0 4.276 16.694 20 97 106.2 0.800 17.494 21 272 287.1 0.796 18.289 Chisq= 18.29 for 20 degrees of freedom, p= 0.43165 SUMMARY of craptest p-value for no. of wins: 0.200394 p-value for throws/game: 0.431646 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0003,0.0083,0.0085,0.0098,0.0106,0.0161,0.0227,0.0234,0.0236,0.0253, 0.0415,0.0416,0.0461,0.0462,0.0514,0.0570,0.0584,0.0641,0.0668,0.0715, 0.0746,0.0747,0.0770,0.0885,0.0906,0.0970,0.0982,0.1027,0.1044,0.1072, 0.1103,0.1103,0.1110,0.1127,0.1175,0.1230,0.1240,0.1285,0.1297,0.1354, 0.1358,0.1419,0.1487,0.1540,0.1577,0.1601,0.1659,0.1746,0.1788,0.1792, 0.1797,0.1925,0.1939,0.1943,0.1948,0.2004,0.2085,0.2133,0.2135,0.2186, 0.2229,0.2252,0.2299,0.2328,0.2334,0.2338,0.2352,0.2423,0.2485,0.2494, 0.2550,0.2604,0.2629,0.2631,0.2714,0.2747,0.2747,0.2773,0.2808,0.2872, 0.2918,0.2940,0.2977,0.3039,0.3066,0.3082,0.3083,0.3109,0.3187,0.3194, 0.3204,0.3240,0.3240,0.3266,0.3267,0.3285,0.3293,0.3358,0.3454,0.3518, 0.3668,0.3671,0.3805,0.3888,0.3971,0.4005,0.4050,0.4092,0.4097,0.4101, 0.4109,0.4173,0.4203,0.4219,0.4260,0.4262,0.4269,0.4275,0.4283,0.4316, 0.4338,0.4369,0.4432,0.4444,0.4457,0.4511,0.4541,0.4604,0.4637,0.4696, 0.4700,0.4739,0.4757,0.4858,0.4866,0.4888,0.5044,0.5106,0.5124,0.5139, 0.5227,0.5263,0.5288,0.5293,0.5364,0.5433,0.5453,0.5548,0.5590,0.5612, 0.5652,0.5687,0.5752,0.5760,0.5780,0.5802,0.5849,0.5903,0.5939,0.5956, 0.6002,0.6017,0.6027,0.6032,0.6035,0.6079,0.6091,0.6091,0.6120,0.6162, 0.6168,0.6186,0.6224,0.6286,0.6297,0.6313,0.6332,0.6422,0.6487,0.6528, 0.6563,0.6577,0.6635,0.6694,0.6771,0.6799,0.6844,0.6900,0.6910,0.6923, 0.6930,0.6976,0.7007,0.7146,0.7151,0.7170,0.7304,0.7386,0.7431,0.7449, 0.7475,0.7746,0.7748,0.7768,0.7812,0.7877,0.7887,0.7910,0.8039,0.8058, 0.8068,0.8091,0.8124,0.8140,0.8193,0.8194,0.8249,0.8309,0.8390,0.8412, 0.8483,0.8523,0.8535,0.8629,0.8635,0.8711,0.8724,0.8747,0.8771,0.8796, 0.8824,0.8856,0.8942,0.8945,0.8954,0.8975,0.9006,0.9020,0.9093,0.9094, 0.9160,0.9164,0.9293,0.9301,0.9302,0.9316,0.9326,0.9343,0.9387,0.9392, 0.9395,0.9427,0.9478,0.9484,0.9593,0.9598,0.9638,0.9650,0.9661,0.9696, 0.9713,0.9714,0.9775,0.9776,0.9816,0.9818,0.9844,0.9938,0.9976, Overall p-value after applying KStest on 269 p-values = 0.860688 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.