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\" from: @(#)lgamma.3 6.6 (Berkeley) 12/3/92
\" $NetBSD: lgamma.3,v 1.24 2024/01/26 19:27:30 nros Exp $
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Dd January 24, 2024
Dt LGAMMA 3
Os
Sh NAME
Nm lgamma ,
Nm lgammaf ,
Nm lgammal ,
Nm lgamma_r ,
Nm lgammaf_r ,
Nm lgammal_r ,
Nm gamma ,
Nm gammaf ,
Nm gamma_r ,
Nm gammaf_r ,
Nm tgamma ,
Nm tgammaf ,
Nm tgammal
Nd log gamma function
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 long double
Fn lgammal "long double x"
Ft double
Fn lgamma_r "double x" "int *sign"
Ft float
Fn lgammaf_r "float x" "int *sign"
Ft long double
Fn lgammal_r "long double x" "int *sign"
Ft double
Fn gamma "double x"
Ft float
Fn gammaf "float x"
Ft double
Fn gamma_r "double x" "int *sign"
Ft float
Fn gammaf_r "float x" "int *sign"
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
if t \{\
returns 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 \
returns ln\||\(*G(x)|.
Pp
The external integer
Fa signgam
returns the sign of \(*G(x).
Pp
Fn lgamma_r
is a reentrant interface that performs identically to
Fn lgamma ,
differing in that the sign of \(*G(x) is stored in the location
pointed to by the
Fa sign
argument and
Fa signgam
is not modified.
Pp
The
Fn tgamma x
and
Fn tgammaf x
functions return \(*G(x), with no effect on
Fa signgam .
Pp
Fn gamma ,
Fn gammaf ,
Fn gamma_r ,
and
Fn gammaf_r
are deprecated aliases for
Fn lgamma ,
Fn lgammaf ,
Fn lgamma_r ,
and
Fn lgammaf_r ,
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
has returned can signgam be correct.
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.
On the
Tn VAX ,
the reserved operator is returned,
and
Va errno
is set to
Er ERANGE .
Sh SEE ALSO
Xr math 3
Sh HISTORY
The
Nm lgamma
function appeared in
Bx 4.3 .
The
Fn tgamma
function appeared in
Nx 6.0 .
