man-pages/man3/lgamma.3

.\" Copyright 2002 Walter Harms (walter.harms@informatik.uni-oldenburg.de)
.\" Distributed under GPL
.\" based on glibc infopages
.\" and Copyright 2008, Linux Foundation, written by Michael Kerrisk
.\"     <mtk.manpages@gmail.com>
.\"
.TH LGAMMA 3 2008-08-05 "" "Linux Programmer's Manual"
.SH NAME
lgamma, lgammaf, lgammal, lgamma_r, lgammaf_r, lgammal_r, signgam \-
log gamma function
.SH SYNOPSIS
.nf
.B #include <math.h>
.sp
.BI "double lgamma(double " x );
.br
.BI "float lgammaf(float " x );
.br
.BI "long double lgammal(long double " x );
.sp
.BI "double lgamma_r(double " x ", int *" signp );
.br
.BI "float lgammaf_r(float " x ", int *" signp );
.br
.BI "long double lgammal_r(long double " x ", int *" signp );
.sp
.BI "extern int " signgam ;
.fi
.sp
Link with \fI\-lm\fP.
.sp
.in -4n
Feature Test Macro Requirements for glibc (see
.BR feature_test_macros (7)):
.in
.sp
.ad l
.BR lgamma ():
_BSD_SOURCE || _SVID_SOURCE || _XOPEN_SOURCE || _ISOC99_SOURCE; or
.I cc\ -std=c99
.br
.BR lgammaf (),
.BR lgammal ():
_BSD_SOURCE || _SVID_SOURCE || _XOPEN_SOURCE\ >=\ 600 || _ISOC99_SOURCE; or
.I cc\ -std=c99
.br
.BR lgamma_r (),
.BR lgammaf_r (),
.BR lgammal_r ():
_BSD_SOURCE || _SVID_SOURCE
.br
.IR signgam :
_BSD_SOURCE || _SVID_SOURCE || _XOPEN_SOURCE
.ad b
.SH DESCRIPTION
For the definition of the Gamma function, see
.BR tgamma (3).
.PP
The
.BR lgamma ()
function returns the natural logarithm of
the absolute value of the Gamma function.
The sign of the Gamma function is returned in the
external integer \fIsigngam\fP declared in
.IR <math.h> .
It is 1 when the Gamma function is positive or zero, \-1
when it is negative.
.PP
Since using a constant location
.I signgam
is not thread-safe, the functions
.BR lgamma_r ()
etc. have
been introduced; they return the sign via the argument
.IR signp .
.SH RETURN VALUE
On success, these functions return the natural logarithm of Gamma(x).

If
.I x
is a NaN, a NaN is returned.

If
.I x
is 1 or 2, +0 is returned.

If
.I x
is positive infinity or negative infinity,
positive infinity is returned.

If
.I x
is a non-positive integer,
a pole error occurs,
and the functions return
.RB + HUGE_VAL ,
.RB + HUGE_VALF ,
or
.RB + HUGE_VALL ,
respectively.

If the result overflows,
a range error occurs,
.\" e.g., lgamma(DBL_MAX)
and the functions return
.BR HUGE_VAL ,
.BR HUGE_VALF ,
or
.BR HUGE_VALL ,
respectively, with the correct mathematical sign.
.SH ERRORS
See
.BR math_error (7)
for information on how to determine whether an error has occurred
when calling these functions.
.PP
The following errors can occur:
.TP
Pole error: \fIx\fP is a non-positive integer
.I errno
is set to
.\" FIXME . glibc 2.8 gives EDOM!
.BR ERANGE
(but see BUGS).
A divide-by-zero floating-point exception
.RB ( FE_DIVBYZERO )
is raised.
.TP
Range error: result overflow
.I errno
is set to
.BR ERANGE .
An overflow floating-point exception
.RB ( FE_OVERFLOW )
is raised.
.\" glibc (as at 2.8) also supports an inexact
.\" exception for various cases.
.SH "CONFORMING TO"
The
.BR lgamma ()
functions are specified in C99 and POSIX.1-2001.
.I signgam
is specified in POSIX.1-2001, but not in C99.
The
.BR lgamma_r ()
functions are non-standard, but present on several other systems.
.SH BUGS
For a pole error,
.\"
.\" FIXME . this is as at glibc 2.8; check later if this bug is fixed
.\" Bug raised: http://sources.redhat.com/bugzilla/show_bug.cgi?id=6777
.I errno
is set to
.BR EDOM ;
POSIX.1 says it should be set to
.BR ERANGE .
.SH "SEE ALSO"
.BR tgamma (3)