Tobias, Many thanks for the comments. I will adjust the patch according to your advice shortly.
- Fritz On Mon, Sep 26, 2016, 11:59 Tobias Burnus <tobias.bur...@physik.fu-berlin.de> wrote: > > 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
