06 October 2025 6:02:47.521 PM 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 2.46590 3.81729 0.967767 1.49813 2.31915 0.379810 2 6.28319 0.873996 5.40919 0.232091 0.641905 4.76728 0.630300E-01 4 6.28319 3.60407 2.67911 2.55819 1.04589 1.63323 2.08680 8 6.28319 3.05152 3.23167 2.58857 0.462942 2.76873 2.44803 16 6.28319 3.33377 2.94941 2.62165 0.712128 2.23728 2.23678 32 6.28319 3.57250 2.71069 2.83646 0.736039 1.97465 2.49617 64 6.28319 2.76573 3.51745 2.02850 0.737234 2.78022 1.69700 128 6.28319 2.69283 3.59035 1.85412 0.838710 2.75164 1.45921 256 6.28319 3.09384 3.18935 2.30241 0.791431 2.39792 1.92462 512 6.28319 3.14208 3.14110 2.38394 0.758147 2.38295 2.01165 1024 6.28319 3.19514 3.08805 2.39251 0.802626 2.28542 1.99583 2048 6.28319 3.26105 3.02213 2.48064 0.780410 2.24172 2.08457 4096 6.28319 3.17436 3.10882 2.38890 0.785465 2.32336 1.99268 8192 6.28319 3.11202 3.17117 2.31813 0.793887 2.37728 1.92377 16384 6.28319 3.16241 3.12077 2.37968 0.782726 2.33805 1.98804 32768 6.28319 3.13511 3.14808 2.35291 0.782194 2.36589 1.96042 65536 6.28319 3.14332 3.13986 2.35750 0.785822 2.35404 1.96364 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. 06 October 2025 6:02:47.545 PM