NetBSD/lib/libm/man/lgamma.3

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.\" from: @(#)lgamma.3 6.6 (Berkeley) 12/3/92
.\" $NetBSD: lgamma.3,v 1.17 1999/08/16 12:35:18 kleink Exp $
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.\"
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.Dd December 3, 1992
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.Dt LGAMMA 3
.Os
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.Sh NAME
.Nm lgamma ,
.Nm lgammaf ,
.Nm lgamma_r ,
.Nm lgammaf_r ,
.Nm gamma ,
.Nm gammaf ,
.Nm gamma_r ,
.Nm gammaf_r
.Nd log gamma function
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.Sh LIBRARY
.Lb libm
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.Sh SYNOPSIS
.Fd #include <math.h>
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.Ft extern int
.Fa signgam ;
.sp
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.Ft double
.Fn lgamma "double x"
.Ft float
.Fn lgammaf "float x"
.Ft double
.Fn lgamma_r "double x" "int *sign"
.Ft float
.Fn lgammaf_r "float 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"
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.Sh DESCRIPTION
.Fn lgamma x
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.if t \{\
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returns ln\||\(*G(x)| where
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.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
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\(*G(x) = \(*p/(\(*G(1\-x)\|sin(\(*px)) for x < 1.
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.Ed
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.\}
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.if n \
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returns ln\||\(*G(x)|.
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.Pp
The external integer
.Fa signgam
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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.
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.Sh IDIOSYNCRASIES
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Do not use the expression
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.Dq Li signgam\(**exp(lgamma(x))
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to compute g := \(*G(x).
Instead use a program like this (in C):
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.Bd -literal -offset indent
lg = lgamma(x); g = signgam\(**exp(lg);
.Ed
.Pp
Only after
.Fn lgamma
has returned can signgam be correct.
.Pp
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.Sh RETURN VALUES
.Fn lgamma
returns appropriate values unless an argument is out of range.
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Overflow will occur for sufficiently large positive values, and
non-positive integers.
On the
.Tn VAX,
the reserved operator is returned,
and
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.Va errno
is set to
.Er ERANGE .
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.Sh SEE ALSO
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.Xr math 3
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.Sh HISTORY
The
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.Nm lgamma
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function appeared in
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.Bx 4.3 .