1.\" $OpenBSD: lgamma.3,v 1.12 2003/06/02 20:18:41 millert 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. Neither the name of the University nor the names of its contributors 14.\" may be used to endorse or promote products derived from this software 15.\" without specific prior written permission. 16.\" 17.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 18.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 19.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 20.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 21.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 22.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 23.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 24.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 25.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 26.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 27.\" SUCH DAMAGE. 28.\" 29.\" from: @(#)lgamma.3 6.6 (Berkeley) 12/3/92 30.\" 31.Dd December 3, 1992 32.Dt LGAMMA 3 33.Os 34.Sh NAME 35.Nm lgamma , 36.Nm lgammaf 37.Nd log gamma functions 38.Sh SYNOPSIS 39.Fd #include <math.h> 40.Ft extern int 41.Fa signgam ; 42.sp 43.Ft double 44.Fn lgamma "double x" 45.Ft float 46.Fn lgammaf "float x" 47.Sh DESCRIPTION 48.Fn lgamma x 49.if t \{\ 50returns ln\||\(*G(x)| where 51.Bd -unfilled -offset indent 52\(*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 53.br 54\(*G(x) = \(*p/(\(*G(1\-x)\|sin(\(*px)) for x < 1. 55.Ed 56.\} 57.if n \ 58returns ln\||\(*G(x)|. 59.Pp 60The external integer 61.Fa signgam 62returns the sign of \(*G(x). 63The 64.Fn lgammaf 65function is a single precision version of 66.Fn lgamma . 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