xref: /freebsd/lib/msun/man/lgamma.3 (revision a9dbc63dc2a2c6866b650af62ab04bc59da50d30)

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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 x
and
.Fn gammaf x
return ln\||\(*G(x)|, with no effect on
.Fa signgam .
.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
.\and
.\.Fn gammaf
.\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).
In many older libraries the function
.Fn gamma
calculated the same value as
.Fn lgamma .
Now
.Fn gamma
computes ln\||\(*G(x)|,
but it uses a different algorithm,
and it does not set
.Fa signgam .
The
.St -isoC-99
standard specifies a function
.Fn tgamma
for computing \(*G(x).
This function is currently unimplimented in this library.