[J3] C TS 18661

[Bill Long]

> On Jan 30, 2019, at 11:29 AM, Steven G. Kargl via J3 <j3 at mailman.j3-fortran.org> wrote:
> 
> In time harmonic analysis, one often computes exp(cmplx(0.,tau)).
> Many people, including me, do cmplx(cos(tau),sin(tau)).  Thus,
> cos() and sin() are computed in pairs, and the argument reduction
> for large arguments (tau > pi/4) is performed twice.  With
> sincos() argument reduction is done once and the number of function
> calls is cut in half.  As I happen to be the person who wrote the
> sincos() implementation that appears in FreeBSD's libm, I have timing
> codes


Compilers can see that sin(x) and cos(x) with the same value of x are both computed, and replace it with an internal sincos(x) call that does exactly what you describe.  This problem was solved long ago. 

Fro this example:

subroutine sub (x, z)
real(8),intent(in) :: x
complex(8),intent(out) :: z

z = cmplx(cos(x), sin(x), 8)

end subroutine sub


the internal dump of the compiled code is (Cray compiler, default options) is

    1.       subroutine sub( x, z )
    5.       0[loc( z ),0].L = coss( 0[loc( x ),0].L )
    7.       return

where coss is the internal name for what you call sincos. 

I assume other compilers do this obvious optimization as well. 


Cheers,
Bill


Bill Long                                                                       longb at cray.com
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