Re: Accuracy of Mathematical Functions

On 25 Sep 2023, at 15:50, Paul Zimmermann <Paul.Zimmermann@inria.fr> wrote:
> 
> I hope this is not off-topic for this list (Technical discussions relating
> to FreeBSD).

The freebsd-numerics@ list might have been a better match, but it
receives very low traffic, and the audience on this list will be larger.


> We have updated our comparison:
> 
> https://members.loria.fr/PZimmermann/papers/accuracy.pdf
> 
> This new update includes for the first time the FreeBSD math library,
> whose accuracy is quite good, except:
> 
> * single precision: the Bessel functions, lgammaf, cospif, sinpif, tanpif, powf
> * double precision: the Bessel functions, lgammaf, tgammaf, cospi, sinpi,
>  tanpi, pow
> * double-extended precision: erfcl, lgammal, tgammal, cospil, sinpil, tanpil,
>  powl
> 
> Some issues have already been fixed in the development version by Steve
> Kargl (we used FreeBSD 13.2).

Very interesting paper! Of course we are always interested in
improvements for libm, and Steve semi-regularly posts patches in our bug
tracker. (Steve's no longer a committer, but usually these get committed
by others quickly enough.)

At the moment FreeBSD 14.0 is in beta phase, and there have been a
number of updates to libm, so it would be interesting to see if it makes
the ulp situation a bit better.

-Dimitry