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.\" $Id: lgamma.3,v 1.1.1.1 1995/10/18 08:42:50 deraadt Exp $ 34.\" 35.Dd December 3, 1992 36.Dt LGAMMA 3 37.Os BSD 4.3 38.Sh NAME 39.Nm lgamma 40.Nd log gamma function 41.Sh SYNOPSIS 42.Fd #include <math.h> 43.Ft extern int 44.Fa signgam ; 45.sp 46.Ft double 47.Fn lgamma "double x" 48.Ft float 49.Fn lgammaf "float x" 50.Sh DESCRIPTION 51.Fn Lgamma x 52.if t \{\ 53returns ln\||\(*G(x)| where 54.Bd -unfilled -offset indent 55\(*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 56.br 57\(*G(x) = \(*p/(\(*G(1\-x)\|sin(\(*px)) for x < 1. 58.Ed 59.\} 60.if n \ 61returns ln\||\(*G(x)|. 62.Pp 63The external integer 64.Fa signgam 65returns the sign of \(*G(x). 66.Pp 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.Pp 80For arguments in its range, 81.Fn gamma 82is preferred, as for positive arguments 83it is accurate to within one unit in the last place. 84Exponentiation of 85.Fn lgamma 86will lose up to 10 significant bits. 87.Sh RETURN VALUES 88.Fn Gamma 89and 90.Fn lgamma 91return appropriate values unless an argument is out of range. 92Overflow will occur for sufficiently large positive values, and 93non-positive integers. 94On the 95.Tn VAX, 96the reserved operator is returned, 97and 98.Va errno 99is set to 100.Er ERANGE 101For large non-integer negative values, 102.Fn gamma 103will underflow. 104.Sh SEE ALSO 105.Xr math 3 , 106.Xr infnan 3 107.Sh HISTORY 108The 109.Nm lgamma 110function appeared in 111.Bx 4.3 . 112