27 February 2022 08:53:59 AM CIRCLE_MONTE_CARLO_TEST C++ version Test the CIRCLE_MONTE_CARLO library. CIRCLE0_SAMPLE_RANDOM_TEST CIRCLE01_SAMPLE_RANDOM randomly samples the unit circle. Use it to estimate integrals. N 1 X^2 Y^2 X^4 X^2Y^2 Y^4 X^6 1 6.28319 0.244176 6.03901 0.00948912 0.234687 5.80432 0.000368764 2 6.28319 3.63178 2.65141 2.86244 0.76933 1.88208 2.53685 4 6.28319 3.83126 2.45192 3.12087 0.710389 1.74154 2.5537 8 6.28319 3.51264 2.77054 2.67251 0.840136 1.93041 2.15783 16 6.28319 3.0875 3.19568 2.17034 0.917164 2.27852 1.7465 32 6.28319 2.69825 3.58493 1.86613 0.832123 2.75281 1.42816 64 6.28319 3.08747 3.19572 2.31135 0.776114 2.4196 1.93519 128 6.28319 3.48751 2.79568 2.66339 0.824118 1.97156 2.22291 256 6.28319 3.15363 3.12956 2.41053 0.743103 2.38645 2.04418 512 6.28319 3.24432 3.03887 2.45557 0.788744 2.25012 2.06643 1024 6.28319 3.09144 3.19174 2.31783 0.773612 2.41813 1.93114 2048 6.28319 3.11979 3.16339 2.37492 0.744877 2.41852 2.00411 4096 6.28319 3.13302 3.15017 2.33952 0.793495 2.35668 1.93821 8192 6.28319 3.14973 3.13346 2.36981 0.779918 2.35354 1.97784 16384 6.28319 3.14761 3.13557 2.36642 0.781195 2.35438 1.97398 32768 6.28319 3.13992 3.14326 2.35215 0.787771 2.35549 1.95857 65536 6.28319 3.14611 3.13708 2.36048 0.785628 2.35145 1.96673 Exact 6.28319 3.14159 3.14159 2.35619 0.785398 2.35619 1.9635 CIRCLE0_SAMPLE_ERGODIC_TEST CIRCLE01_SAMPLE_ERGODIC ergodically samples the unit circle. Use it to estimate integrals. N 1 X^2 Y^2 X^4 X^2Y^2 Y^4 X^6 1 6.28319 6.28319 0 6.28319 0 0 6.28319 2 6.28319 1.73214 4.55105 0.928913 0.803224 3.74783 0.504963 4 6.28319 3.32879 2.95439 2.49547 0.833325 2.12107 2.07908 8 6.28319 3.33924 2.94395 2.49259 0.846651 2.0973 2.08161 16 6.28319 3.21222 3.07096 2.46158 0.750642 2.32032 2.06962 32 6.28319 2.99983 3.28336 2.20654 0.793287 2.49007 1.82489 64 6.28319 3.1503 3.13289 2.35915 0.791154 2.34173 1.96008 128 6.28319 3.16408 3.1191 2.38431 0.77977 2.33933 1.99449 256 6.28319 3.13653 3.14666 2.35008 0.786446 2.36021 1.95658 512 6.28319 3.14507 3.13811 2.35878 0.786289 2.35182 1.96566 1024 6.28319 3.14151 3.14167 2.35688 0.784633 2.35704 1.96458 2048 6.28319 3.1403 3.14288 2.35488 0.785426 2.35746 1.96213 4096 6.28319 3.14181 3.14137 2.35635 0.785462 2.35591 1.96363 8192 6.28319 3.14181 3.14138 2.35635 0.785455 2.35592 1.96363 16384 6.28319 3.1416 3.14159 2.35625 0.78535 2.35624 1.96357 32768 6.28319 3.1415 3.14168 2.3561 0.785399 2.35628 1.9634 65536 6.28319 3.1416 3.14158 2.3562 0.7854 2.35618 1.9635 Exact 6.28319 3.14159 3.14159 2.35619 0.785398 2.35619 1.9635 CIRCLE_MONTE_CARLO_TEST Normal end of execution. 27 February 2022 08:53:59 AM