[musl] Accuracy of Mathematical Functions

[musl] Accuracy of Mathematical Functions

[Paul Zimmermann]

       Dear all,

we have updated our comparison with Musl 1.2.5:

https://members.loria.fr/PZimmermann/papers/accuracy.pdf

Large errors still there in 1.2.5:

* exp10l, expm1l, lgammal, sinhl, tgammal, powl

Paul

[musl] Accuracy of Mathematical Functions

[Paul Zimmermann]

       Dear all,

we have updated our comparison:

https://members.loria.fr/PZimmermann/papers/accuracy.pdf

This is a new version with updated versions of the different libraries, new corner
cases found, and the ARM Performance Library is now included.

There was no new release of Musl since our last update, thus it is still 1.2.4
that is tested.

Paul Zimmermann

[musl] Accuracy of Mathematical Functions

[Paul Zimmermann]

       Hi,

we have updated our comparison:

https://members.loria.fr/PZimmermann/papers/accuracy.pdf

This update uses Musl 1.2.4 (the previous one was for Musl 1.2.3).
The two reported issues in double-extended precision (end of page 15)
are already fixed in the development version (thanks Szabolcs).

This is a new version with updated versions of the different libraries and:

* the Microsoft math library is now included (it was clearly missing)
* we also added the FreeBSD math library
* and we added some new C23 functions (acospi, cospi, ...) which are available
  in the Intel and FreeBSD math libraries

Paul Zimmermann

Re: [musl] Accuracy of Mathematical Functions

[enh]

isn't Apple's libm (like Android's) largely the FreeBSD libm? are the
Apple vs FreeBSD differences you found really FreeBSD/arm64 vs
FreeBSD/x86-64 differences? (or differences between older and newer
FreeBSD libms?)

On Thu, Sep 21, 2023 at 12:31 AM Paul Zimmermann
<Paul.Zimmermann@inria.fr> wrote:
>
>        Hi,
>
> we have updated our comparison:
>
> https://members.loria.fr/PZimmermann/papers/accuracy.pdf
>
> This update uses Musl 1.2.4 (the previous one was for Musl 1.2.3).
> The two reported issues in double-extended precision (end of page 15)
> are already fixed in the development version (thanks Szabolcs).
>
> This is a new version with updated versions of the different libraries and:
>
> * the Microsoft math library is now included (it was clearly missing)
> * we also added the FreeBSD math library
> * and we added some new C23 functions (acospi, cospi, ...) which are available
>   in the Intel and FreeBSD math libraries
>
> Paul Zimmermann

Re: [musl] Accuracy of Mathematical Functions

[Szabolcs Nagy]

* enh <enh@google.com> [2023-09-21 09:30:10 -0700]:
> isn't Apple's libm (like Android's) largely the FreeBSD libm? are the
> Apple vs FreeBSD differences you found really FreeBSD/arm64 vs
> FreeBSD/x86-64 differences? (or differences between older and newer
> FreeBSD libms?)

freebsd is mostly c so behaves the same on x86 and arm
(fma usage can be different but that's about it)

in the apple libm neither x86 nor arm version looks freebsd based
(and this is old, they likely updated it for aarch64)

https://opensource.apple.com/source/Libm/Libm-2026/Source/

Re: [musl] Accuracy of Mathematical Functions

[enh]

oh, interesting... i see a lot of the files in the arm directory have
freebsd in the name but, yes, even there the majority seems to be
home-grown code.

On Thu, Sep 21, 2023 at 11:44 PM Szabolcs Nagy <nsz@port70.net> wrote:
>
> * enh <enh@google.com> [2023-09-21 09:30:10 -0700]:
> > isn't Apple's libm (like Android's) largely the FreeBSD libm? are the
> > Apple vs FreeBSD differences you found really FreeBSD/arm64 vs
> > FreeBSD/x86-64 differences? (or differences between older and newer
> > FreeBSD libms?)
>
> freebsd is mostly c so behaves the same on x86 and arm
> (fma usage can be different but that's about it)
>
> in the apple libm neither x86 nor arm version looks freebsd based
> (and this is old, they likely updated it for aarch64)
>
> https://opensource.apple.com/source/Libm/Libm-2026/Source/
>

[musl] Accuracy of Mathematical Functions

[Paul Zimmermann]

       Hi,

we have updated our comparison:

https://members.loria.fr/PZimmermann/papers/accuracy.pdf

This update uses Musl 1.2.3 (same version as the last update in August 2022).

The main change is that the LLVM library now implements more
correctly-rounded routines in single precision.

Best regards,
Paul

[musl] Accuracy of Mathematical Functions

[Paul Zimmermann]

       Hi,

we have updated our comparison:

https://members.loria.fr/PZimmermann/papers/accuracy.pdf

This update uses Musl 1.2.3. The acoshf and sinhf issues reported in 1.2.2
are fixed (thank you Szabolcs).

The main change is that the LLVM library now implements a few
correctly-rounded routines in single precision (log, log10, log2,
hypot), and hypot in double precision.

Best regards,
Paul

[musl] accuracy of mathematical functions

[Paul Zimmermann]

       Hi,

a new update is available:

https://members.loria.fr/PZimmermann/papers/#accuracy

It now considers Musl 1.2.2, and two new libraries: Apple and CUDA.

Best regards,
Paul Zimmermann

[musl] accuracy of mathematical functions

[Paul Zimmermann]

       Hi,

I am about to release a new update of the accuracy comparison of mathematical
functions [1]. It will mention Musl 1.2.2, the last release to date. The
following issues are still present in 1.2.2:

* acoshf and sinhf return a finite value instead of NaN (or the converse).
  Fixed by Szabolcs in February, but no new release since then.

* huge maximal errors for j0f, j1f, lgammaf, y0f, y1f

* huge maximal errors for j0, j1, lgamma, y0, y1

* large maximal known error for exp10l (40.1 ulps), expm1l (9.71e3 ulps),
  sinhl (9.71e3 ulps), powl (533 ulps), huge maximal known error for
  lgammal (9.08e19 ulps) and tgammal (3.69e19 ulps)

Best regards,
Paul

[1] https://members.loria.fr/PZimmermann/papers/accuracy.pdf

Re: [musl] accuracy of mathematical functions

[Morten Welinder]

* huge maximal errors for j0f, j1f, lgammaf, y0f, y1f

If anyone feels the urge to fix the bessel functions, the best
reference probably is John Harrison's:
https://www.cl.cam.ac.uk/~jrh13/papers/bessel.html  A certain amount
of tables will be needed, though.

M.

[musl] accuracy of mathematical functions

[Paul Zimmermann]

       Hi,

I have updated my comparison with the newly released glibc-2.33 version.
No big difference with the previous version, except that I included
the "long double" format (aka ldbl-96), including for musl (see pages
13 and 15):

https://members.loria.fr/PZimmermann/papers/#accuracy

Best regards,
Paul