issue with tgammaf

[Paul Zimmermann]

       Dear Keith,

> Are you able to share the code which performs these tests? I'd love to
> be able to run these on a regular basis to ensure that no regressions
> occur as we maintain the code.

I will send you privately the code, since it is not yet ready for a wide
distribution.

> > tgamma:
> > Total: errors=2028164922 (47.41%) errors2=1833526367 maxerr=2.39e+02 ulp(s)
> > Total: errors=2026865970 (47.38%) errors2=1832940352 maxerr=2.39e+02 ulp(s)
> 
> Given that around half of the possible input values (> 35, or near
> negative integers) generate an overflow, it seems like tgamma
> essentially *never* gives us an accurate finite result...

on a sample of 1/1000 of all values, it appears most errors come from exponents
(ilogbf) between -64 and -7. For example with exponent -64 I get no incorrect
rounding with glibc-2.32 out of 16776 samples, but 16410 with newlib.

For example for x=0x1.00e8p-64 newlib gives 0x1.fe31d6p+63 whereas the correct
rounding is 0x1.fe31a4p+63 according to MPFR.

Best regards,
Paul