Fritz Reese wrote: > Attached is a patch extending the GNU Fortran front-end to support > some additional math intrinsics, enabled with a new compile flag > -fdec-math. The flag adds the COTAN intrinsic (cotangent), as well as > degree versions of all trigonometric intrinsics (SIND, TAND, ACOSD, > etc...). > > + /* There is no builtin mpc_cot, so compute x = 1 / tan (x). */ > + val = &result->value.complex; > + mpc_tan (*val, *val, GFC_MPC_RND_MODE); > + mpc_div (*val, one, *val, GFC_MPC_RND_MODE);
The internet remarks: TAN(x) for x -> pi/2 goes to +inf or -inf - while COTAN(pi/2) == 0. For values near pi/2, using cos(x)/sin(x) should be numerically better than 1/tan(x). [Cf. mpfr_sin_cos and BUILT_IN_SINCOS.] I am not sure how big the prevision difference really is. A quick test showed results which didn't look to bad: implicit none real(8), volatile :: x x = 3.14159265358d0/2.0d0 print '(g0)', cotan(x), cos(x)/sin(x), cotan(x)-cos(x)/sin(x) end yields: 0.48965888601467483E-011 0.48965888601467475E-011 0.80779356694631609E-027 Usint N[1/Tan[314159265358/10^11/2],200], Mathematica shows 4.8966192313216916397514812338... * 10^12. I am not quite sure whether I should expect that already the 5th digit differs from the results above. > mpfr_set_d (tmp, 180.0l, GFC_RND_MODE); With some fonts the L after 180.0 looks like a one; I was initially puzzled why one uses not 180 but 180.01. Hence, I'd prefer an "L" instead of an "l". However, the second argument of mpfr_set_d is a "double" and 180.0 is already a double. Hence, one can even completely get rid of the "l". Regarding the decimal trigonometric functions, the internet suggests to use sin (fmod ((x), 360) * M_PI / 180) instead of sin (x * M_PI / 180) to yield better results for angles which are larger than +/-360 degrees. Cheers, Tobias
