[PATCH] aarch64: Improve SVE sin polynomial

[Vincent Lefevre]

On 2023-08-04 09:28:53 +0200, Paul Zimmermann via Libc-alpha wrote:
>        Hi Szabolcs,
> 
> > i'd say we want to minimize the maximum of
> > 
> >  (poly(x) - sin(x))/ulp(sin(x))
> > 
> > instead of
> > 
> >  (poly(x) - sin(x))/sin(x)
> 
> interesting question! I have asked the Sollya developers if this is
> possible.

I would say that a large change of the weight function (e.g.
a discontinuity point) is likely to generate an extrema for
the error function, which could affect the quality of the
minimax approximation. That's from the theory. In practice,
it is still possible that this works by chance, but I suppose
that this depends on the considered function and domain.

Concerning Sollya, doesn't it uses the derivative of the
error function (making the direct use of ulp impossible)?

-- 
Vincent Lefèvre <vincent@vinc17.net> - Web: <https://www.vinc17.net/>
100% accessible validated (X)HTML - Blog: <https://www.vinc17.net/blog/>
Work: CR INRIA - computer arithmetic / AriC project (LIP, ENS-Lyon)