Accuracy of Mathematical Functions in Single Precision for glibc 2.31

[Joseph Myers]

On Mon, 3 Feb 2020, paul zimmermann wrote:

>     https://homepages.loria.fr/PZimmermann/glibc/glibc231.pdf

lgamma testing should compare with mpfr_lgamma not mpfr_lngamma.

> - exp10 is close from being correctly rounded (only one exception)

That's an artifact of the simplistic implementation.  I expect it would be 
substantially faster if exp10f had an implementation along the lines of 
the expf / exp2f implementations rather than a wrapper round 
double-precision exp, at which point the accuracy would be similar to that 
of expf and exp2f.

> - j0, j1, y0, y1 are quite bad (this was already known, but the "Known
>   Maximum Errors in Math Functions" in the reference manual do not reflect it)

jn, yn, cpow are also known to have cases with large errors, but aren't 
covered by this testing because they aren't functions of a single real 
floating argument so aren't feasible to test exhaustively.

-- 
Joseph S. Myers
joseph@codesourcery.com