'\" e
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.\"     from: @(#)lgamma.3	6.6 (Berkeley) 12/3/92
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.Dd $Mdocdate: August 26 2017 $
.Dt LGAMMA 3
.Os
.Sh NAME
.Nm lgamma ,
.Nm lgammaf ,
.Nm lgammal ,
.Nm lgamma_r ,
.Nm lgammaf_r ,
.Nm lgammal_r ,
.Nm tgamma ,
.Nm tgammaf ,
.Nm tgammal ,
.Nm gamma ,
.Nm gammaf
.Nd log gamma functions
.Sh SYNOPSIS
.In math.h
.Vt extern int signgam ;
.Ft double
.Fn lgamma "double x"
.Ft float
.Fn lgammaf "float x"
.Ft long double
.Fn lgammal "long double x"
.Ft double
.Fn lgamma_r "double x" "int *signgamp"
.Ft float
.Fn lgammaf_r "float x" "int *signgamp"
.Ft long double
.Fn lgammal_r "long double x" "int *signgamp"
.Ft double
.Fn tgamma "double x"
.Ft float
.Fn tgammaf "float x"
.Ft long double
.Fn tgammal "long double x"
.Sh DESCRIPTION
.Fn lgamma x
returns ln\||\(*G(x)| where
.Bd -filled -offset indent
.EQ
GAMMA left ( x right ) =
int from 0 to inf t sup {x - 1} e sup -t dt
.EN
\ \ \ for x > 0 and
.br
.EQ
GAMMA left ( x right ) =
pi over { GAMMA left ( 1 - x right ) sin left ( pi x right ) }
.EN
\ \ \ for x < 1.
.Ed
.Pp
The external integer
.Va signgam
returns the sign of \(*G(x).
The
.Fn lgammaf
function is a single precision version of
.Fn lgamma .
The
.Fn lgammal
function is an extended precision version of
.Fn lgamma .
.Pp
The
.Fn lgamma_r ,
.Fn lgammaf_r ,
and
.Fn lgammal_r
functions are thread-safe versions of
.Fn lgamma ,
.Fn lgammaf ,
and
.Fn lgammal
that return the sign via the
.Fa signgamp
pointer instead of modifying
.Va signgam .
.Pp
The
.Fn tgamma x ,
.Fn tgammaf x
and
.Fn tgammal x
functions return \(*G(x), with no effect on
.Va signgam .
.Sh IDIOSYNCRASIES
Do not use the expression
.Sq Li signgam*exp(lgamma(x))
to compute g := \(*G(x).
Instead use a program like this (in C):
.Bd -literal -offset indent
lg = lgamma(x); g = signgam*exp(lg);
.Ed
.Pp
Only after
.Fn lgamma
has returned can
.Va signgam
be correct.
.Pp
For arguments in its range,
.Fn tgamma
is preferred, as for positive arguments
it is accurate to within one unit in the last place.
.Sh RETURN VALUES
.Fn lgamma
returns appropriate values unless an argument is out of range.
Overflow will occur for sufficiently large positive values, and
non-positive integers.
For large non-integer negative values,
.Fn tgamma
will underflow.
.Sh STANDARDS
The
.Fn lgamma ,
.Fn lgammaf ,
.Fn lgammal ,
.Fn tgamma ,
.Fn tgammaf ,
and
.Fn tgammal
functions are expected to conform to
.St -isoC-99 .
.Pp
The
.Fn lgamma_r ,
.Fn lgammaf_r ,
and
.Fn lgammal_r
functions are
.Bx
extensions.
.Pp
.Fn gamma
and
.Fn gammaf
are deprecated aliases for
.Fn lgamma
and
.Fn lgammaf ,
respectively.
.Sh HISTORY
A
.Fn gamma
function first appeared in
.At v5 .
The
.Fn lgamma
function first appeared in
.Bx 4.3 .
The
.Fn tgamma
function first appeared in
.Ox 4.4 ,
and is based on the
.Fn gamma
function that appeared in
.Bx 4.4
as a function to compute \(*G(x).