Re: Accuracy of Mathematical Functions

[Paul Zimmermann <Paul.Zimmermann@inria.fr>]

       Dear Joseph,

> Date: Fri, 11 Feb 2022 18:23:58 +0000
> From: Joseph Myers <joseph@codesourcery.com>
> 
> On Fri, 11 Feb 2022, Paul Zimmermann wrote:
> 
> >        Hi,
> > 
> > with the release of GNU libc 2.35, we have published a new version of our
> > comparison of the accuracy of mathematical libraries:
> > 
> > https://members.loria.fr/PZimmermann/papers/accuracy.pdf
> > 
> > For the GNU libc, with respect to 2.34, we observed an improvement in j0f,
> > tgamma, hypot, hypotl and hypotf128.
> > 
> > With respect to the previous update, we compare two new libraries: LLVM libc
> > and ROCm.
> 
> Thanks for the update.  A few remarks on things it might be interesting to 
> add to the analysis:
> 
> 1. I don't know if any of those libraries include any of the new functions 
> C23 adds from TS 18661-4 (beyond exp10), but if they do, it might be worth 
> adding them to the comparison.  (My remarks from 
> <https://sourceware.org/pipermail/libc-alpha/2022-January/135006.html> 
> apply regarding adding them to glibc - when I get time I hope to add them, 
> as with other new C23 features, if no-one else has done them by then.)

is http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1946.pdf the correct
reference for the list of these functions? Most of them are available in
MPFR, when they will be available in glibc we might indeed add them.

> 2. I don't know if any of those libraries have IEEE binary16 functions (C 
> _Float16), but again, if any do, they might be worth testing (in that 
> case, exhaustive testing should be possible for functions of two 
> arguments, not just functions of a single argument).
>
> 3. As previously remarked, FreeBSD libm is another implementation that 
> might be worth testing (though that would require running the tests on a 
> FreeBSD system).
> 
> 4. As previously remarked, it would be interesting to see similar data for 
> complex functions (real and imaginary parts of the result of a function 
> with one complex argument being essentially the same as the case of a 
> function with a real result and two real arguments).

for points 2-4, I agree this would be interesting, but we have limited
manpower. If anyone wants to help us, she/he is welcome!

Best regards,
Paul