Elementary Function Work

[Joseph Myers]

On Tue, 8 Dec 2020, N.G. Timmons wrote:

> I would be interested in setting up a test suite to provide ULP error
> information, error distribution information and number of known incorrectly
> rounded results that could be run to generate a documentation page or
> automatically update the function comment with the information for easy
> accessibility.

I suggest working with Paul Zimmermann since he's been working in that 
area, and it's naturally something separate from any particular libm 
implementation.  (Though different libm implementations may make different 
choices regarding the bounds on acceptable errors, requirements for 
correctness of floating-point exceptions raised, etc.)

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

There are obvious areas for extending his work, such as covering the 
ldbl-96 and ldbl-128ibm formats and <complex.h> functions and different 
rounding modes.

When function errors are found that are beyond the limits of those 
accepted for glibc, it's appropriate to file bug reports when such bug 
reports aren't already open for the functions in question (see his recent 
bug reports for lgamma and tgamma).  When function errors are found that 
are within the bounds of those accepted for glibc, but larger than those 
appearing in libm-test-ulps, it's appropriate to add the test inputs in 
question to auto-libm-test-in and regenerate the corresponding 
auto-libm-test-out-* file, so that the libm-test-ulps files (and thus the 
tables in the glibc manual generated from those files) more accurately 
reflect the largest known errors.

If a function gets reimplemented so as to reduce the largest errors (for 
most functions with errors larger than 1 or 2 ulps, I expect that could be 
done without making performance any worse), it then makes sense to remove 
entries for that function in libm-test-ulps files so they can be 
regenerated from scratch.

When large errors are found in other libm implementations, reporting bugs 
against those implementations is a good idea as well (depending on each 
implementation's policy on what errors count as bugs).

-- 
Joseph S. Myers
joseph@codesourcery.com