09 May 2025 8:57:26.139 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 6.27104 0.121447E-01 6.25892 0.121213E-01 0.234745E-04 6.24682 2 6.28319 0.982557 5.30063 0.306757 0.675801 4.62483 0.958551E-01 4 6.28319 3.11861 3.16458 2.56218 0.556428 2.60815 2.27758 8 6.28319 3.92479 2.35839 2.99293 0.931860 1.42653 2.47769 16 6.28319 3.10799 3.17520 2.54431 0.563682 2.61151 2.25620 32 6.28319 4.02716 2.25603 3.48079 0.546370 1.70966 3.14713 64 6.28319 3.31359 2.96959 2.52314 0.790447 2.17915 2.13296 128 6.28319 3.00317 3.28001 2.19999 0.803178 2.47684 1.79698 256 6.28319 3.29258 2.99060 2.56338 0.729197 2.26141 2.18564 512 6.28319 3.10363 3.17955 2.36738 0.736251 2.44330 2.00569 1024 6.28319 3.13303 3.15016 2.33987 0.793159 2.35700 1.93390 2048 6.28319 3.09528 3.18790 2.30267 0.792615 2.39529 1.90779 4096 6.28319 3.13598 3.14720 2.35691 0.779073 2.36813 1.96639 8192 6.28319 3.12728 3.15591 2.34072 0.786556 2.36935 1.94789 16384 6.28319 3.12241 3.16077 2.32920 0.793209 2.36756 1.93217 32768 6.28319 3.14458 3.13860 2.36058 0.784007 2.35460 1.96997 65536 6.28319 3.14013 3.14305 2.35470 0.785434 2.35762 1.96213 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. 09 May 2025 8:57:26.163 PM