10 December 2023 6:24:33.555 PM test_int_circle_test(): Fortran77 version Test test_int_circle(). TEST01 Use a simple Monte Carlo approach to estimate the integral of X^E over the circle of radius 1 centered at the origin. N E Exact Approximate Error 1 2 0.7854 0.6358 0.1496E+00 2 2 0.7854 1.3663 0.5809E+00 4 2 0.7854 1.0196 0.2342E+00 8 2 0.7854 0.8843 0.9887E-01 16 2 0.7854 0.5644 0.2210E+00 32 2 0.7854 0.6681 0.1173E+00 64 2 0.7854 0.6691 0.1163E+00 128 2 0.7854 0.8579 0.7251E-01 256 2 0.7854 0.7583 0.2706E-01 512 2 0.7854 0.8305 0.4508E-01 1024 2 0.7854 0.7848 0.6180E-03 2048 2 0.7854 0.7720 0.1336E-01 4096 2 0.7854 0.7898 0.4385E-02 8192 2 0.7854 0.7868 0.1412E-02 16384 2 0.7854 0.7793 0.6093E-02 32768 2 0.7854 0.7773 0.8072E-02 65536 2 0.7854 0.7823 0.3059E-02 131072 2 0.7854 0.7883 0.2910E-02 262144 2 0.7854 0.7849 0.5465E-03 524288 2 0.7854 0.7838 0.1616E-02 1048576 2 0.7854 0.7845 0.9346E-03 1 4 0.3927 0.1287 0.2640E+00 2 4 0.3927 1.0593 0.6666E+00 4 4 0.3927 0.6114 0.2187E+00 8 4 0.3927 0.4209 0.2817E-01 16 4 0.3927 0.2121 0.1806E+00 32 4 0.3927 0.3412 0.5151E-01 64 4 0.3927 0.2903 0.1024E+00 128 4 0.3927 0.4401 0.4739E-01 256 4 0.3927 0.3890 0.3711E-02 512 4 0.3927 0.4256 0.3291E-01 1024 4 0.3927 0.3961 0.3371E-02 2048 4 0.3927 0.3921 0.5916E-03 4096 4 0.3927 0.3967 0.4043E-02 8192 4 0.3927 0.3945 0.1801E-02 16384 4 0.3927 0.3882 0.4539E-02 32768 4 0.3927 0.3837 0.8995E-02 65536 4 0.3927 0.3897 0.2974E-02 131072 4 0.3927 0.3942 0.1525E-02 262144 4 0.3927 0.3916 0.1082E-02 524288 4 0.3927 0.3913 0.1422E-02 1048576 4 0.3927 0.3918 0.9252E-03 1 6 0.2454 0.0260 0.2194E+00 2 6 0.2454 0.8652 0.6198E+00 4 6 0.2454 0.4355 0.1900E+00 8 6 0.2454 0.2342 0.1120E-01 16 6 0.2454 0.1002 0.1453E+00 32 6 0.2454 0.2151 0.3033E-01 64 6 0.2454 0.1575 0.8791E-01 128 6 0.2454 0.2794 0.3395E-01 256 6 0.2454 0.2487 0.3251E-02 512 6 0.2454 0.2724 0.2696E-01 1024 6 0.2454 0.2477 0.2297E-02 2048 6 0.2454 0.2484 0.2976E-02 4096 6 0.2454 0.2480 0.2514E-02 8192 6 0.2454 0.2469 0.1488E-02 16384 6 0.2454 0.2418 0.3677E-02 32768 6 0.2454 0.2372 0.8262E-02 65536 6 0.2454 0.2429 0.2500E-02 131072 6 0.2454 0.2463 0.8614E-03 262144 6 0.2454 0.2441 0.1344E-02 524288 6 0.2454 0.2442 0.1192E-02 1048576 6 0.2454 0.2446 0.8064E-03 TEST02 Use a simple Monte Carlo approach to estimate the integral of R^E over the circle of radius 1 centered at the origin. N E Exact Approximate Error 1 1 2.0944 1.4682 0.6262E+00 2 1 2.0944 2.2702 0.1758E+00 4 1 2.0944 2.4391 0.3447E+00 8 1 2.0944 1.9031 0.1913E+00 16 1 2.0944 1.8081 0.2863E+00 32 1 2.0944 1.8511 0.2433E+00 64 1 2.0944 2.0076 0.8676E-01 128 1 2.0944 2.0655 0.2894E-01 256 1 2.0944 2.0406 0.5381E-01 512 1 2.0944 2.0992 0.4842E-02 1024 1 2.0944 2.0969 0.2487E-02 2048 1 2.0944 2.0838 0.1062E-01 4096 1 2.0944 2.0907 0.3705E-02 8192 1 2.0944 2.0918 0.2554E-02 16384 1 2.0944 2.0842 0.1017E-01 32768 1 2.0944 2.0876 0.6761E-02 65536 1 2.0944 2.0918 0.2579E-02 131072 1 2.0944 2.0909 0.3475E-02 262144 1 2.0944 2.0922 0.2168E-02 524288 1 2.0944 2.0928 0.1637E-02 1048576 1 2.0944 2.0937 0.6947E-03 1 3 1.2566 0.3207 0.9359E+00 2 3 1.2566 1.6293 0.3727E+00 4 3 1.2566 1.7387 0.4820E+00 8 3 1.2566 1.0468 0.2099E+00 16 3 1.2566 1.0049 0.2517E+00 32 3 1.2566 1.0750 0.1816E+00 64 3 1.2566 1.2028 0.5379E-01 128 3 1.2566 1.2677 0.1102E-01 256 3 1.2566 1.2077 0.4892E-01 512 3 1.2566 1.2717 0.1504E-01 1024 3 1.2566 1.2636 0.7004E-02 2048 3 1.2566 1.2464 0.1023E-01 4096 3 1.2566 1.2552 0.1448E-02 8192 3 1.2566 1.2565 0.1255E-03 16384 3 1.2566 1.2447 0.1194E-01 32768 3 1.2566 1.2473 0.9321E-02 65536 3 1.2566 1.2523 0.4319E-02 131072 3 1.2566 1.2518 0.4815E-02 262144 3 1.2566 1.2531 0.3571E-02 524288 3 1.2566 1.2543 0.2320E-02 1048576 3 1.2566 1.2555 0.1126E-02 1 5 0.8976 0.0700 0.8276E+00 2 5 0.8976 1.4399 0.5423E+00 4 5 0.8976 1.3978 0.5002E+00 8 5 0.8976 0.7578 0.1398E+00 16 5 0.8976 0.6972 0.2004E+00 32 5 0.8976 0.7776 0.1199E+00 64 5 0.8976 0.8619 0.3570E-01 128 5 0.8976 0.9254 0.2784E-01 256 5 0.8976 0.8485 0.4914E-01 512 5 0.8976 0.9072 0.9562E-02 1024 5 0.8976 0.9012 0.3624E-02 2048 5 0.8976 0.8885 0.9138E-02 4096 5 0.8976 0.8991 0.1480E-02 8192 5 0.8976 0.8992 0.1556E-02 16384 5 0.8976 0.8865 0.1106E-01 32768 5 0.8976 0.8880 0.9563E-02 65536 5 0.8976 0.8924 0.5164E-02 131072 5 0.8976 0.8925 0.5087E-02 262144 5 0.8976 0.8935 0.4068E-02 524288 5 0.8976 0.8951 0.2510E-02 1048576 5 0.8976 0.8963 0.1307E-02 TEST03 Use a simple Monte Carlo approach to estimate the integral of exp(X) over the circle of radius 1 centered at the origin. N Exact Approximate Error 1 ** 3.5510 4.9263 0.1375E+01 2 ** 3.5510 2.6002 0.9508E+00 4 ** 3.5510 4.5981 0.1047E+01 8 ** 3.5510 3.5564 0.5374E-02 16 ** 3.5510 4.0237 0.4727E+00 32 ** 3.5510 3.6086 0.5758E-01 64 ** 3.5510 3.6236 0.7260E-01 128 ** 3.5510 3.3051 0.2459E+00 256 ** 3.5510 3.5140 0.3704E-01 512 ** 3.5510 3.5148 0.3616E-01 1024 ** 3.5510 3.5882 0.3717E-01 2048 ** 3.5510 3.6017 0.5073E-01 4096 ** 3.5510 3.5718 0.2083E-01 8192 ** 3.5510 3.5401 0.1086E-01 16384 ** 3.5510 3.5274 0.2357E-01 32768 ** 3.5510 3.5328 0.1816E-01 65536 ** 3.5510 3.5461 0.4925E-02 131072 ** 3.5510 3.5427 0.8279E-02 262144 ** 3.5510 3.5512 0.1589E-03 524288 ** 3.5510 3.5489 0.2062E-02 1048576 ** 3.5510 3.5499 0.1103E-02 test_int_circle_test(): Normal end of execution. 10 December 2023 6:24:34.726 PM