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 1.11 1997/11/12 00:48:01 mrg Exp $ 34.\" 35.Dd December 3, 1992 36.Dt LGAMMA 3 37.Os BSD 4.3 38.Sh NAME 39.Nm lgamma , 40.Nm gamma 41.Nd log gamma function 42.Sh SYNOPSIS 43.Fd #include <math.h> 44.Ft extern int 45.Fa signgam ; 46.sp 47.Ft double 48.Fn lgamma "double x" 49.Ft float 50.Fn lgammaf "float x" 51.Sh DESCRIPTION 52.Fn Lgamma x 53.if t \{\ 54returns ln\||\(*G(x)| where 55.Bd -unfilled -offset indent 56\(*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 57.br 58\(*G(x) = \(*p/(\(*G(1\-x)\|sin(\(*px)) for x < 1. 59.Ed 60.\} 61.if n \ 62returns ln\||\(*G(x)|. 63.Pp 64The external integer 65.Fa signgam 66returns the sign of \(*G(x). 67.Pp 68.Sh IDIOSYNCRASIES 69Do not use the expression 70.Dq Li signgam\(**exp(lgamma(x)) 71to compute g := \(*G(x). 72Instead use a program like this (in C): 73.Bd -literal -offset indent 74lg = lgamma(x); g = signgam\(**exp(lg); 75.Ed 76.Pp 77Only after 78.Fn lgamma 79has returned can signgam be correct. 80.Pp 81.Sh RETURN VALUES 82.Fn Lgamma 83returns appropriate values unless an argument is out of range. 84Overflow will occur for sufficiently large positive values, and 85non-positive integers. 86On the 87.Tn VAX, 88the reserved operator is returned, 89and 90.Va errno 91is set to 92.Er ERANGE . 93.Sh SEE ALSO 94.Xr math 3 95.Sh HISTORY 96The 97.Nm lgamma 98function appeared in 99.Bx 4.3 . 100