correctly rounded mathematical functions

[Paul Zimmermann]

       Dear Joel,

thank you for your answer.

> From: Joel Sherrill <joel@rtems.org>
> Date: Mon, 3 Jan 2022 14:41:20 -0600
> 
> On Mon, Jan 3, 2022 at 6:58 AM Paul Zimmermann <Paul.Zimmermann@inria.fr> wrote:
> >
> >       Dear Newlib developers,
> >
> > the current C working draft [1, p392] has reserved names for correctly
> > rounded functions (cr_exp, cr_log, cr_sin, ...).
> >
> > We propose to provide such correctly rounded implementations
> > for the three IEEE formats (binary32, binary64, binary128) and the
> > "extended double" format (long double on x86_64).
> >
> > These implementations will be correctly rounded for all rounding modes,
> > for example one could do the following to emulate interval arithmetic:
> >
> >    fesetround (FE_DOWNWARD);
> >    y_lo = cr_exp (x_lo);
> >    fesetround (FE_UPWARD);
> >    y_hi = cr_exp (x_hi);
> >
> > Users who want a fast implementation will call the exp/log/sin/... functions,
> > users who want a correctly rounded function and thus reproducible results
> > (whatever the hardware, compiler or operating system) will use the
> > cr_exp/cr_log/cr_sin/... functions. Our goal is nevertheless to get the
> > best performance possible.
> >
> > Our objective is to provide open-source implementations that can be integrated
> > in the major mathematical libraries (GNU libc, Intel Math Library, AMD Libm,
> > Redhat Newlib, OpenLibm, Musl, llvm-libc, CUDA, ROCm).
> >
> > Are developers of Newlib interested by such functions?
> > If so, we could discuss what would be the requirements for integration in
> > Newlib in terms of license, table size, allowed operations.
> 
> Speaking from the RTEMS perspective, we are very interested
> in the addition of more POSIX and C Standard Library methods.
> We have been having GSoC students add them where possible
> for a few years.

great!

> The license has to be permissive and should have no advertising
> although based on COPYING.NEWLIB, some must have a BSD
> advertising clause still. Possibly those need review.
> 
> https://sourceware.org/git/?p=newlib-cygwin.git;a=blob_plain;f=COPYING.NEWLIB;hb=HEAD

since some Newlib files are already under LGPL v3+, for example
include/cgen/basic-ops.h, I guess the current
license we have (LGPL v3+) should be ok for Newlib.

> As long as the method's footprint only impacts applications that use
> it, there shouldn't be a huge concern on size but the target domain is
> mostly smaller single process, no-MMU embedded systems. That is
> ignoring Cygwin which has fewer constraints.  If you end up adding
> megabytes, that's going to be bad in general.

we'll try to have reasonable table sizes. And maybe for some functions
we'll provide several implementations, with different table sizes.

> > We have started to work on two functions (cbrt and acos), for which we
> > provide presumably correctly rounded implementations (up to the knowledge
> > of hard-to-round cases) [2].
> 
> Great! What's the size profile on those?

the binary32 cbrt code is quite small:

-rw-r--r-- 1 zimmerma caramba   2766 Dec 23 14:27 cbrtf.c

the binary128 code is larger:

-rw-r--r-- 1 zimmerma caramba  38450 Dec 22 18:06 cbrtf128-v2.patch

> What's the minimum compiler or C language version to build these?

good question. So far we work with current gcc versions (for example 11.2.0)
but did not exercise with older version. We don't use advanced C feature,
except the "glibc patches" use some GNU libc macros (for example mul_split
to split the product of two doubles into a+b, fast_two_sum, ...).

Best regards,
Paul