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.\" 4. Neither the name of the University nor the names of its contributors 13.\" may be used to endorse or promote products derived from this software 14.\" without specific prior written permission. 15.\" 16.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 17.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 18.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 19.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 20.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 21.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 22.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 23.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 24.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 25.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 26.\" SUCH DAMAGE. 27.\" 28.\" from: @(#)lgamma.3 6.6 (Berkeley) 12/3/92 29.\" $FreeBSD$ 30.\" 31.Dd January 14, 2005 32.Dt LGAMMA 3 33.Os 34.Sh NAME 35.Nm lgamma , 36.Nm lgamma_r , 37.Nm lgammaf , 38.Nm lgammaf_r , 39.Nm gamma , 40.Nm gamma_r , 41.Nm gammaf , 42.Nm gammaf_r , 43.Nm tgamma , 44.Nm tgammaf 45.Nd log gamma functions, gamma function 46.Sh LIBRARY 47.Lb libm 48.Sh SYNOPSIS 49.In math.h 50.Ft extern int 51.Fa signgam ; 52.sp 53.Ft double 54.Fn lgamma "double x" 55.Ft double 56.Fn lgamma_r "double x" "int *signgamp" 57.Ft float 58.Fn lgammaf "float x" 59.Ft float 60.Fn lgammaf_r "float x" "int *signgamp" 61.Ft double 62.Fn gamma "double x" 63.Ft double 64.Fn gamma_r "double x" "int *signgamp" 65.Ft float 66.Fn gammaf "float x" 67.Ft float 68.Fn gammaf_r "float x" "int *signgamp" 69.Ft double 70.Fn tgamma "double x" 71.Ft float 72.Fn tgammaf "float x" 73.Sh DESCRIPTION 74.Fn lgamma x 75and 76.Fn lgammaf x 77.if t \{\ 78return ln\||\(*G(x)| where 79.Bd -unfilled -offset indent 80\(*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 81\(*G(x) = \(*p/(\(*G(1\-x)\|sin(\(*px)) for x < 1. 82.Ed 83.\} 84.if n \ 85return ln\||\(*G(x)|. 86The external integer 87.Fa signgam 88returns the sign of \(*G(x). 89.Pp 90.Fn lgamma_r x signgamp 91and 92.Fn lgammaf_r x signgamp 93provide the same functionality as 94.Fn lgamma x 95and 96.Fn lgammaf x 97but the caller must provide an integer to store the sign of \(*G(x). 98.Pp 99The 100.Fn tgamma x 101and 102.Fn tgammaf x 103functions return \(*G(x), with no effect on 104.Fa signgam . 105.Pp 106.Fn gamma , 107.Fn gammaf , 108.Fn gamma_r , 109and 110.Fn gammaf_r 111are deprecated aliases for 112.Fn lgamma , 113.Fn lgammaf , 114.Fn lgamma_r , 115and 116.Fn lgammaf_r , 117respectively. 118.Sh IDIOSYNCRASIES 119Do not use the expression 120.Dq Li signgam\(**exp(lgamma(x)) 121to compute g := \(*G(x). 122Instead use a program like this (in C): 123.Bd -literal -offset indent 124lg = lgamma(x); g = signgam\(**exp(lg); 125.Ed 126.Pp 127Only after 128.Fn lgamma 129or 130.Fn lgammaf 131has returned can signgam be correct. 132.Pp 133For arguments in its range, 134.Fn tgamma 135is preferred, as for positive arguments 136it is accurate to within one unit in the last place. 137Exponentiation of 138.Fn lgamma 139will lose up to 10 significant bits. 140.Sh RETURN VALUES 141.Fn gamma , 142.Fn gamma_r , 143.Fn gammaf , 144.Fn gammaf_r , 145.Fn lgamma , 146.Fn lgamma_r , 147.Fn lgammaf , 148and 149.Fn lgammaf_r 150return appropriate values unless an argument is out of range. 151Overflow will occur for sufficiently large positive values, and 152non-positive integers. 153For large non-integer negative values, 154.Fn tgamma 155will underflow. 156.Sh SEE ALSO 157.Xr math 3 158.Sh STANDARDS 159The 160.Fn lgamma , 161.Fn lgammaf , 162.Fn tgamma , 163and 164.Fn tgammaf 165functions are expected to conform to 166.St -isoC-99 . 167.Sh HISTORY 168The 169.Fn lgamma 170function appeared in 171.Bx 4.3 . 172The 173.Fn gamma 174function appeared in 175.Bx 4.4 176as a function which computed \(*G(x). 177This version was used in 178.Fx 1.1 . 179The name 180.Fn gamma 181was originally dedicated to the 182.Fn lgamma 183function, 184and that usage was restored by switching to Sun's fdlibm in 185.Fx 1.1.5 . 186The 187.Fn tgamma 188function appeared in 189.Fx 5.0 . 190