Re: Accuracy of Mathematical Functions

[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.)

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).

-- 
Joseph S. Myers
joseph@codesourcery.com