Re: Accuracy of Mathematical Functions

[Joseph Myers <josmyers@redhat.com>]

On Wed, 7 Aug 2024, Paul Zimmermann wrote:

>        Dear Joseph,
> 
> > > we have updated our comparison:
> > > 
> > > https://members.loria.fr/PZimmermann/papers/accuracy.pdf
> > > 
> > > This update is for GNU libc 2.40:
> > > 
> > > * it includes the new functions exp10m1, exp2m1, log10p1, log2p1
> > >   added in 2.40 (for all formats)
> > 
> > The table for single precision only has exp10m1, not the other three 
> > functions.
> 
> sorry, I have fixed that in a new version (same link).

Thanks.  Some further comments on the document (some of which I may have 
made before):

* The bug referenced as a reason for not testing other rounding modes was 
fixed long ago, results in other rounding modes would be interesting as 
well (they would of course make the document longer), and worst-case 
inputs for other rounding modes would be worth adding to the glibc tests.

* I don't think "dummy implementations" is a useful description for 
implementations that do actually implement the function (within a few 
ulp).  There are many possible ways to implement a function, including 
building on other functions, and those ones are optimized for getting the 
APIs into glibc for all supported formats rather than for speed or 
accuracy (and replacing by faster, more accurate implementations for 
particular formats is welcome).

* As previously mentioned, I still think it would be of interest to see 
such data for complex functions (a function with one complex argument and 
a complex result is effectively two bivariate real functions.

-- 
Joseph S. Myers
josmyers@redhat.com