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.\"     from: @(#)lgamma.3	6.6 (Berkeley) 12/3/92
.\" $FreeBSD$
.\"
.Dd December 3, 1992
.Dt LGAMMA 3
.Os
.Sh NAME
.Nm lgamma ,
.Nm lgammaf ,
.Nm gamma ,
.Nm gammaf
.Nd log gamma functions, gamma functions
.Sh LIBRARY
.Lb libm
.Sh SYNOPSIS
.In math.h
.Ft extern int
.Fa signgam ;
.sp
.Ft double
.Fn lgamma "double x"
.Ft float
.Fn lgammaf "float x"
.Ft double
.Fn gamma "double x"
.Ft float
.Fn gammaf "float x"
.Sh DESCRIPTION
.Fn lgamma x
and
.Fn lgammaf x
.if t \{\
return ln\||\(*G(x)| where
.Bd -unfilled -offset indent
\(*G(x) = \(is\d\s8\z0\s10\u\u\s8\(if\s10\d t\u\s8x\-1\s10\d e\u\s8\-t\s10\d dt	for x > 0 and
.br
\(*G(x) = \(*p/(\(*G(1\-x)\|sin(\(*px))	for x < 1.
.Ed
.\}
.if n \
return ln\||\(*G(x)|.
.Pp
The external integer
.Fa signgam
returns the sign of \(*G(x).
.Pp
.Fn gamma
and
.Fn gammaf
are deprecated aliases for
.Fn lgamma
and
.Fn lgammaf ,
respectively.
.Sh IDIOSYNCRASIES
Do not use the expression
.Dq 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
or
.Fn lgammaf
has returned can signgam be correct.
.\".Pp
.\"For arguments in its range,
.\".Fn gamma
.\"is preferred, as for positive arguments
.\"it is accurate to within one unit in the last place.
.\"Exponentiation of
.\".Fn lgamma
.\"will lose up to 10 significant bits.
.Sh RETURN VALUES
.Fn gamma ,
.Fn gammaf ,
.Fn lgamma ,
and
.Fn lgammaf
return appropriate values unless an argument is out of range.
Overflow will occur for sufficiently large positive values, and
non-positive integers.
On the
.Tn VAX ,
the reserved operator is returned,
and
.Va errno
is set to
.Er ERANGE .
\."For large non-integer negative values,
\.".Fn gamma
\."will underflow.
.Sh SEE ALSO
.Xr math 3
.Sh HISTORY
The
.Fn lgamma
function appeared in
.Bx 4.3 .
The
.Fn gamma
function appeared in
.Bx 4.4
as a function which computed \(*G(x).
This version was used in
.Fx 1.1 .
The name
.Fn gamma
was originally dedicated to the
.Fn lgamma
function,
and that usage was restored by switching to Sun's fdlibm in
.Fx 1.1.5 .
The
.St -isoC-99
standard specifies a function
.Fn tgamma
for computing \(*G(x).
This function is currently unimplemented in this library.