Fw: issue with tgamma

[C Howland]

> *From:* Paul Zimmermann <Paul.Zimmermann@inria.fr>
> *Sent:* Friday, January 5, 2024 5:49 AM
> *To:* newlib@sourceware.org <newlib@sourceware.org>
> *Subject:* issue with tgamma
>
>        Hi,
>
> I discovered the following issue with tgamma: for
> x=-0x1.13a5ccd87c9bbp+1008
> it yields +Inf instead of NaN:
>
> Checking tgamma with newlib-4.4.0.20231231
> tgamma 0 -1 -0x1.13a5ccd87c9bbp+1008 [-nan] [inf] inf inf
> libm gives inf
> mpfr gives -nan
>
> This issue was present in earlier versions of Newlib, but we only found it
> recently since we improved our testing framework.
>
> Paul
>
>      This strictly is OK, as the standards allow either a range or domain
error for negative integers, and domain errors may return an
implementation-defined value.   It most likely has been this way since the
1993 date in the source file, which includes
 *   5. Special Cases
 *              lgamma(2+s) ~ s*(1-Euler) for tiny s
 *              lgamma(1)=lgamma(2)=0
 *              lgamma(x) ~ -log(x) for tiny x
 *              lgamma(0) = lgamma(inf) = inf
 *              lgamma(-integer) = +-inf
(The tgamma function ends up using the lgamma function.)
     POSIX does have an implied preference of sorts for the NaN return, so
changing it could possibly be considered a small improvement even if not
necessary--although it is strange that they define the result for argument
0 differently, calling for INF there, seems inconsistent.
     (It's somewhat interesting that the MPFR return value you show is
-NaN.  I suppose they chose that to help reflect it being due to a negative
argument.)
                         Craig
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