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.\" $FreeBSD$ 34.\" 35.Dd December 3, 1992 36.Dt LGAMMA 3 37.Os 38.Sh NAME 39.Nm lgamma , 40.Nm lgammaf , 41.Nm gamma , 42.Nm gammaf 43.Nd log gamma functions, gamma functions 44.Sh LIBRARY 45.Lb libm 46.Sh SYNOPSIS 47.In math.h 48.Ft extern int 49.Fa signgam ; 50.sp 51.Ft double 52.Fn lgamma "double x" 53.Ft float 54.Fn lgammaf "float x" 55.Ft double 56.Fn gamma "double x" 57.Ft float 58.Fn gammaf "float x" 59.Sh DESCRIPTION 60.Fn lgamma x 61and 62.Fn lgammaf x 63.if t \{\ 64return ln\||\(*G(x)| where 65.Bd -unfilled -offset indent 66\(*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 67.br 68\(*G(x) = \(*p/(\(*G(1\-x)\|sin(\(*px)) for x < 1. 69.Ed 70.\} 71.if n \ 72return ln\||\(*G(x)|. 73.Pp 74The external integer 75.Fa signgam 76returns the sign of \(*G(x). 77.Pp 78.Fn gamma x 79and 80.Fn gammaf x 81return \(*G(x), with no effect on 82.Fa signgam . 83.Sh IDIOSYNCRASIES 84Do not use the expression 85.Dq Li signgam\(**exp(lgamma(x)) 86to compute g := \(*G(x). 87Instead use a program like this (in C): 88.Bd -literal -offset indent 89lg = lgamma(x); g = signgam\(**exp(lg); 90.Ed 91.Pp 92Only after 93.Fn lgamma 94or 95.Fn lgammaf 96has returned can signgam be correct. 97.Pp 98For arguments in its range, 99.Fn gamma 100and 101.Fn gammaf 102is preferred, as for positive arguments 103it is accurate to within one unit in the last place. 104Exponentiation of 105.Fn lgamma 106will lose up to 10 significant bits. 107.Sh RETURN VALUES 108.Fn gamma , 109.Fn gammaf , 110.Fn lgamma , 111and 112.Fn lgammaf 113return appropriate values unless an argument is out of range. 114Overflow will occur for sufficiently large positive values, and 115non-positive integers. 116On the 117.Tn VAX , 118the reserved operator is returned, 119and 120.Va errno 121is set to 122.Er ERANGE . 123For large non-integer negative values, 124.Fn gamma 125will underflow. 126.Sh SEE ALSO 127.Xr math 3 128.Sh HISTORY 129The 130.Fn lgamma 131function appeared in 132.Bx 4.3 . 133The 134.Fn gamma 135function appeared in 136.Bx 4.4 . 137The name 138.Fn gamma 139was originally dedicated to the 140.Fn lgamma 141function, so some old code may no longer be compatible. 142