1.\" $OpenBSD: lgamma.3,v 1.10 2000/04/15 02:15:28 aaron Exp $ 2.\" Copyright (c) 1985, 1991 Regents of the University of California. 3.\" All rights reserved. 4.\" 5.\" Redistribution and use in source and binary forms, with or without 6.\" modification, are permitted provided that the following conditions 7.\" are met: 8.\" 1. Redistributions of source code must retain the above copyright 9.\" notice, this list of conditions and the following disclaimer. 10.\" 2. Redistributions in binary form must reproduce the above copyright 11.\" notice, this list of conditions and the following disclaimer in the 12.\" documentation and/or other materials provided with the distribution. 13.\" 3. All advertising materials mentioning features or use of this software 14.\" must display the following acknowledgement: 15.\" This product includes software developed by the University of 16.\" California, Berkeley and its contributors. 17.\" 4. Neither the name of the University nor the names of its contributors 18.\" may be used to endorse or promote products derived from this software 19.\" without specific prior written permission. 20.\" 21.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 22.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 23.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 24.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 25.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 26.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 27.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 28.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 29.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 30.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 31.\" SUCH DAMAGE. 32.\" 33.\" from: @(#)lgamma.3 6.6 (Berkeley) 12/3/92 34.\" 35.Dd December 3, 1992 36.Dt LGAMMA 3 37.Os 38.Sh NAME 39.Nm lgamma , 40.Nm lgammaf 41.Nd log gamma functions 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.Sh IDIOSYNCRASIES 68Do not use the expression 69.Dq Li signgam\(**exp(lgamma(x)) 70to compute g := \(*G(x). 71Instead use a program like this (in C): 72.Bd -literal -offset indent 73lg = lgamma(x); g = signgam\(**exp(lg); 74.Ed 75.Pp 76Only after 77.Fn lgamma 78has returned can signgam be correct. 79.Sh RETURN VALUES 80.Fn lgamma 81returns appropriate values unless an argument is out of range. 82Overflow will occur for sufficiently large positive values, and 83non-positive integers. 84On the 85.Tn VAX , 86the reserved operator is returned, 87and 88.Va errno 89is set to 90.Er ERANGE . 91.Sh SEE ALSO 92.Xr infnan 3 , 93.Xr math 3 94.Sh HISTORY 95The 96.Fn lgamma 97function appeared in 98.Bx 4.3 . 99