1.\" Copyright (c) 1985, 1991 Regents of the University of California. 2.\" All rights reserved. 3.\" 4.\" Redistribution and use in source and binary forms, with or without 5.\" modification, are permitted provided that the following conditions 6.\" are met: 7.\" 1. Redistributions of source code must retain the above copyright 8.\" notice, this list of conditions and the following disclaimer. 9.\" 2. Redistributions in binary form must reproduce the above copyright 10.\" notice, this list of conditions and the following disclaimer in the 11.\" documentation and/or other materials provided with the distribution. 12.\" 3. Neither the name of the University nor the names of its contributors 13.\" may be used to endorse or promote products derived from this software 14.\" without specific prior written permission. 15.\" 16.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 17.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 18.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 19.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 20.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 21.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 22.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 23.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 24.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 25.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 26.\" SUCH DAMAGE. 27.\" 28.\" from: @(#)lgamma.3 6.6 (Berkeley) 12/3/92 29.\" $NetBSD: lgamma.3,v 1.21 2003/08/07 16:44:48 agc Exp $ 30.\" 31.Dd December 3, 1992 32.Dt LGAMMA 3 33.Os 34.Sh NAME 35.Nm lgamma , 36.Nm lgammaf , 37.Nm lgamma_r , 38.Nm lgammaf_r , 39.Nm gamma , 40.Nm gammaf , 41.Nm gamma_r , 42.Nm gammaf_r 43.Nd log gamma function 44.Sh LIBRARY 45.Lb libm 46.Sh SYNOPSIS 47.In math.h 48.Ft extern int 49.Fa signgam ; 50.sp 51.Ft double 52.Fn lgamma "double x" 53.Ft float 54.Fn lgammaf "float x" 55.Ft double 56.Fn lgamma_r "double x" "int *sign" 57.Ft float 58.Fn lgammaf_r "float x" "int *sign" 59.Ft double 60.Fn gamma "double x" 61.Ft float 62.Fn gammaf "float x" 63.Ft double 64.Fn gamma_r "double x" "int *sign" 65.Ft float 66.Fn gammaf_r "float x" "int *sign" 67.Sh DESCRIPTION 68.Fn lgamma x 69.if t \{\ 70returns ln\||\(*G(x)| where 71.Bd -unfilled -offset indent 72\(*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 \*[Gt] 0 and 73.br 74\(*G(x) = \(*p/(\(*G(1\-x)\|sin(\(*px)) for x \*[Lt] 1. 75.Ed 76.\} 77.if n \ 78returns ln\||\(*G(x)|. 79.Pp 80The external integer 81.Fa signgam 82returns the sign of \(*G(x). 83.Pp 84.Fn lgamma_r 85is a reentrant interface that performs identically to 86.Fn lgamma , 87differing in that the sign of \(*G(x) is stored in the location 88pointed to by the 89.Fa sign 90argument and 91.Fa signgam 92is not modified. 93.Sh IDIOSYNCRASIES 94Do not use the expression 95.Dq Li signgam\(**exp(lgamma(x)) 96to compute g := \(*G(x). 97Instead use a program like this (in C): 98.Bd -literal -offset indent 99lg = lgamma(x); g = signgam\(**exp(lg); 100.Ed 101.Pp 102Only after 103.Fn lgamma 104has returned can signgam be correct. 105.Sh RETURN VALUES 106.Fn lgamma 107returns appropriate values unless an argument is out of range. 108Overflow will occur for sufficiently large positive values, and 109non-positive integers. 110On the 111.Tn VAX , 112the reserved operator is returned, 113and 114.Va errno 115is set to 116.Er ERANGE . 117.Sh SEE ALSO 118.Xr math 3 119.Sh HISTORY 120The 121.Nm lgamma 122function appeared in 123.Bx 4.3 . 124