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. All advertising materials mentioning features or use of this software 13.\" must display the following acknowledgement: 14.\" This product includes software developed by the University of 15.\" California, Berkeley and its contributors. 16.\" 4. Neither the name of the University nor the names of its contributors 17.\" may be used to endorse or promote products derived from this software 18.\" without specific prior written permission. 19.\" 20.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 21.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 22.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 23.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 24.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 25.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 26.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 27.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 28.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 29.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 30.\" SUCH DAMAGE. 31.\" 32.\" from: @(#)lgamma.3 6.6 (Berkeley) 12/3/92 33.\" $NetBSD: lgamma.3,v 1.17 1999/08/16 12:35:18 kleink Exp $ 34.\" 35.Dd December 3, 1992 36.Dt LGAMMA 3 37.Os 38.Sh NAME 39.Nm lgamma , 40.Nm lgammaf , 41.Nm lgamma_r , 42.Nm lgammaf_r , 43.Nm gamma , 44.Nm gammaf , 45.Nm gamma_r , 46.Nm gammaf_r 47.Nd log gamma function 48.Sh LIBRARY 49.Lb libm 50.Sh SYNOPSIS 51.Fd #include <math.h> 52.Ft extern int 53.Fa signgam ; 54.sp 55.Ft double 56.Fn lgamma "double x" 57.Ft float 58.Fn lgammaf "float x" 59.Ft double 60.Fn lgamma_r "double x" "int *sign" 61.Ft float 62.Fn lgammaf_r "float x" "int *sign" 63.Ft double 64.Fn gamma "double x" 65.Ft float 66.Fn gammaf "float x" 67.Ft double 68.Fn gamma_r "double x" "int *sign" 69.Ft float 70.Fn gammaf_r "float x" "int *sign" 71.Sh DESCRIPTION 72.Fn lgamma x 73.if t \{\ 74returns ln\||\(*G(x)| where 75.Bd -unfilled -offset indent 76\(*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 77.br 78\(*G(x) = \(*p/(\(*G(1\-x)\|sin(\(*px)) for x < 1. 79.Ed 80.\} 81.if n \ 82returns ln\||\(*G(x)|. 83.Pp 84The external integer 85.Fa signgam 86returns the sign of \(*G(x). 87.Pp 88.Fn lgamma_r 89is a reentrant interface that performs identically to 90.Fn lgamma , 91differing in that the sign of \(*G(x) is stored in the location 92pointed to by the 93.Fa sign 94argument and 95.Fa signgam 96is not modified. 97.Sh IDIOSYNCRASIES 98Do not use the expression 99.Dq Li signgam\(**exp(lgamma(x)) 100to compute g := \(*G(x). 101Instead use a program like this (in C): 102.Bd -literal -offset indent 103lg = lgamma(x); g = signgam\(**exp(lg); 104.Ed 105.Pp 106Only after 107.Fn lgamma 108has returned can signgam be correct. 109.Pp 110.Sh RETURN VALUES 111.Fn lgamma 112returns appropriate values unless an argument is out of range. 113Overflow will occur for sufficiently large positive values, and 114non-positive integers. 115On the 116.Tn VAX, 117the reserved operator is returned, 118and 119.Va errno 120is set to 121.Er ERANGE . 122.Sh SEE ALSO 123.Xr math 3 124.Sh HISTORY 125The 126.Nm lgamma 127function appeared in 128.Bx 4.3 . 129