1.\" $OpenBSD: lgamma.3,v 1.27 2016/04/26 19:49:22 tb 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 $Mdocdate: April 26 2016 $ 32.Dt LGAMMA 3 33.Os 34.Sh NAME 35.Nm lgamma , 36.Nm lgammaf , 37.Nm lgammal , 38.Nm lgamma_r , 39.Nm lgammaf_r , 40.Nm lgammal_r , 41.Nm tgamma , 42.Nm tgammaf , 43.Nm tgammal , 44.Nm gamma , 45.Nm gammaf 46.Nd log gamma functions 47.Sh SYNOPSIS 48.In math.h 49.Vt extern int signgam ; 50.Ft double 51.Fn lgamma "double x" 52.Ft float 53.Fn lgammaf "float x" 54.Ft long double 55.Fn lgammal "long double x" 56.Ft double 57.Fn lgamma_r "double x" "int *signgamp" 58.Ft float 59.Fn lgammaf_r "float x" "int *signgamp" 60.Ft long double 61.Fn lgammal_r "long double x" "int *signgamp" 62.Ft double 63.Fn tgamma "double x" 64.Ft float 65.Fn tgammaf "float x" 66.Ft long double 67.Fn tgammal "long double x" 68.Sh DESCRIPTION 69.Fn lgamma x 70.if t \{\ 71returns ln\||\(*G(x)| where 72.Bd -unfilled -offset indent 73\(*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 74.br 75\(*G(x) = \(*p/(\(*G(1\-x)\|sin(\(*px)) for x < 1. 76.Ed 77.\} 78.if n \ 79returns ln\||\(*G(x)|. 80.Pp 81The external integer 82.Va signgam 83returns the sign of \(*G(x). 84The 85.Fn lgammaf 86function is a single precision version of 87.Fn lgamma . 88The 89.Fn lgammal 90function is an extended precision version of 91.Fn lgamma . 92.Pp 93The 94.Fn lgamma_r , 95.Fn lgammaf_r , 96and 97.Fn lgammal_r 98functions are thread-safe versions of 99.Fn lgamma , 100.Fn lgammaf , 101and 102.Fn lgammal 103that return the sign via the 104.Fa signgamp 105pointer instead of modifying 106.Va signgam . 107.Pp 108The 109.Fn tgamma x , 110.Fn tgammaf x 111and 112.Fn tgammal x 113functions return \(*G(x), with no effect on 114.Va signgam . 115.Sh IDIOSYNCRASIES 116Do not use the expression 117.Sq Li signgam*exp(lgamma(x)) 118to compute g := \(*G(x). 119Instead use a program like this (in C): 120.Bd -literal -offset indent 121lg = lgamma(x); g = signgam*exp(lg); 122.Ed 123.Pp 124Only after 125.Fn lgamma 126has returned can 127.Va signgam 128be correct. 129.Pp 130For arguments in its range, 131.Fn tgamma 132is preferred, as for positive arguments 133it is accurate to within one unit in the last place. 134.Sh RETURN VALUES 135.Fn lgamma 136returns appropriate values unless an argument is out of range. 137Overflow will occur for sufficiently large positive values, and 138non-positive integers. 139For large non-integer negative values, 140.Fn tgamma 141will underflow. 142.Sh STANDARDS 143The 144.Fn lgamma , 145.Fn lgammaf , 146.Fn lgammal , 147.Fn tgamma , 148.Fn tgammaf , 149and 150.Fn tgammal 151functions are expected to conform to 152.St -isoC-99 . 153.Pp 154The 155.Fn lgamma_r , 156.Fn lgammaf_r , 157and 158.Fn lgammal_r 159functions are 160.Bx 161extensions. 162.Pp 163.Fn gamma 164and 165.Fn gammaf 166are deprecated aliases for 167.Fn lgamma 168and 169.Fn lgammaf , 170respectively. 171.Sh HISTORY 172A 173.Fn gamma 174function first appeared in 175.At v5 . 176The 177.Fn lgamma 178function first appeared in 179.Bx 4.3 . 180The 181.Fn tgamma 182function first appeared in 183.Ox 4.4 , 184and is based on the 185.Fn gamma 186function that appeared in 187.Bx 4.4 188as a function to compute \(*G(x). 189