05 September 2021 7:42:26.998 AM circle_monte_carlo_test(): FORTRAN90 version Test circle_monte_carlo(). circle01_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 3.03046 3.25273 1.46163 1.56883 1.68390 0.704962 2 6.28319 5.15307 1.13011 4.42867 0.724402 0.405709 3.96418 4 6.28319 2.96782 3.31537 2.51862 0.449202 2.86617 2.23921 8 6.28319 2.50513 3.77806 1.73649 0.768639 3.00942 1.37753 16 6.28319 2.61408 3.66910 1.62939 0.984696 2.68441 1.19223 32 6.28319 2.76071 3.52248 2.00169 0.759023 2.76345 1.58782 64 6.28319 2.91005 3.37313 1.97937 0.930683 2.44245 1.52582 128 6.28319 3.32680 2.95638 2.55944 0.767365 2.18902 2.16146 256 6.28319 3.07911 3.20407 2.28021 0.798902 2.40517 1.87908 512 6.28319 3.09361 3.18958 2.30635 0.787252 2.40233 1.92335 1024 6.28319 3.26815 3.01503 2.49095 0.777201 2.23783 2.09802 2048 6.28319 3.07191 3.21127 2.29916 0.772756 2.43852 1.91158 4096 6.28319 3.10765 3.17553 2.31182 0.795838 2.37969 1.91338 8192 6.28319 3.18346 3.09973 2.38454 0.798911 2.30082 1.98035 16384 6.28319 3.13603 3.14715 2.35485 0.781182 2.36597 1.96329 32768 6.28319 3.13853 3.14466 2.34854 0.789994 2.35466 1.95380 65536 6.28319 3.14427 3.13892 2.35959 0.784677 2.35424 1.96788 Exact 6.28319 3.14159 3.14159 2.35619 0.785398 2.35619 1.96350 circle01_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 0.00000 6.28319 0.00000 0.00000 6.28319 2 6.28319 4.84972 1.43347 4.07032 0.779395 0.654073 3.64655 4 6.28319 3.01837 3.26482 2.25052 0.767845 2.49697 1.90297 8 6.28319 3.04968 3.23351 2.30080 0.748871 2.48464 1.95871 16 6.28319 3.11752 3.16567 2.37908 0.738438 2.42723 2.01640 32 6.28319 3.21906 3.06412 2.43708 0.781985 2.28214 2.04792 64 6.28319 3.16393 3.11926 2.38392 0.780010 2.33925 1.99370 128 6.28319 3.16442 3.11877 2.38500 0.779418 2.33935 1.99556 256 6.28319 3.15606 3.12713 2.37107 0.784992 2.34214 1.97789 512 6.28319 3.14012 3.14307 2.35550 0.784619 2.35845 1.96372 1024 6.28319 3.14162 3.14157 2.35699 0.784632 2.35693 1.96467 2048 6.28319 3.14328 3.13990 2.35789 0.785389 2.35451 1.96516 4096 6.28319 3.14146 3.14173 2.35608 0.785374 2.35635 1.96344 8192 6.28319 3.14150 3.14168 2.35615 0.785351 2.35633 1.96351 16384 6.28319 3.14159 3.14159 2.35624 0.785350 2.35624 1.96357 32768 6.28319 3.14170 3.14149 2.35630 0.785398 2.35609 1.96360 65536 6.28319 3.14159 3.14160 2.35619 0.785397 2.35620 1.96349 Exact 6.28319 3.14159 3.14159 2.35619 0.785398 2.35619 1.96350 circle_monte_carlo_test(): Normal end of execution. 05 September 2021 7:42:27.022 AM