[Bug 1837] New: tgamma() is incorrectly implemented

[bugzilla at busybox.net]

https://bugs.busybox.net/show_bug.cgi?id=1837

           Summary: tgamma() is incorrectly implemented
           Product: uClibc
           Version: 0.9.32
          Platform: All
        OS/Version: All
            Status: NEW
          Severity: major
          Priority: P5
         Component: Standard Compliance
        AssignedTo: unassigned at uclibc.org
        ReportedBy: r.c.poss at uva.nl
                CC: uclibc-cvs at uclibc.org
   Estimated Hours: 0.0


As per the ISO standard, tgamma(x) should compute Gamma(x), while lgamma(x)
computes ln(Gamma(x)). The current implementation aliases tgamma and lgamma,
which is incorrect.

This was identified in Sept 2009, as per the comment in e_lgamma_r.c:

"""
/* FIXME! Looks like someone just used __ieee754_gamma_r,
 * believing it's a "true" gamma function, but it was not!
 * Our tgamma is WRONG.
 */
"""

(Denis Vlasenko, 2009-09-18)

The function tgamma() thus needs to be replaced entirely.

A "quick and dirty" fix is to rewrite as follows:

"""
        double y;
        int local_signgam;
        y = __ieee754_lgamma_r(x, &local_signgam);
        return local_signgam * exp(y);
"""

This provides relatively accurate results for small inputs, but diverges for
large inputs.

An alternate implementation can be found in FreeBSD's source, in
/scratch/usr/src/lib/msun/bsdsrc/b_tgamma.c.

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