[Bug libfortran/93871] COTAN is slow for complex types

[sgk at troutmask dot apl.washington.edu]

https://gcc.gnu.org/bugzilla/show_bug.cgi?id=93871

--- Comment #30 from Steve Kargl <sgk at troutmask dot apl.washington.edu> ---
On Thu, Feb 27, 2020 at 07:31:43AM +0000, thenlich at gcc dot gnu.org wrote:
> https://gcc.gnu.org/bugzilla/show_bug.cgi?id=93871
> 
> --- Comment #29 from Thomas Henlich <thenlich at gcc dot gnu.org> ---
> (In reply to Steve Kargl from comment #28)
> >          ! Fold  into [0,90] range
> ...
> >          if (arg == 180) then
> 
> I don't understand how (arg == 180) could be true after folding into [0,90]
> range.
> 

Whoops.  I quickly threw that code together to
investigate the symmetry needed to fold [0,360]
into [0:90].  My guess is that I did a last
minute edit and moved the (arg == 180) condition
without checking or there is a subtle rounding
issue with (180 - nearest(180,+-1)).  That code
certainly isn't production quality as there is
no special handling of +-Inf or NaN or tiny x.

We should also consider the upper normal x
limit where x > xmax=2**(p-e) where p is the
precision and e is some value where modulo(x,360)
is always integral.  This is similar to the
radian sin(x) for REAL x and x > 2.**22. 

I suppose that the point is that it is likely that 
gfortran should not in-line the sind(x) function.
Creating the if-statement is doable in trans-intrinsic.c,
but may drive someone nuts to get right.  For cosd(x),
your suggestion of cosd(x) = sind(90 - module(x,360))
looks promising and could be in-lined.