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. 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.\" $NetBSD: lgamma.3,v 1.23 2017/07/03 21:32:50 wiz Exp $ 30.\" 31.Dd May 4, 2012 32.Dt LGAMMA 3 33.Os 34.Sh NAME 35.Nm lgamma , 36.Nm lgammaf , 37.Nm lgamma_r , 38.Nm lgammaf_r , 39.Nm gamma , 40.Nm gammaf , 41.Nm gamma_r , 42.Nm gammaf_r , 43.Nm tgamma , 44.Nm tgammaf 45.Nd log 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 float 56.Fn lgammaf "float x" 57.Ft double 58.Fn lgamma_r "double x" "int *sign" 59.Ft float 60.Fn lgammaf_r "float x" "int *sign" 61.Ft double 62.Fn gamma "double x" 63.Ft float 64.Fn gammaf "float x" 65.Ft double 66.Fn gamma_r "double x" "int *sign" 67.Ft float 68.Fn gammaf_r "float x" "int *sign" 69.Ft double 70.Fn tgamma "double x" 71.Ft float 72.Fn tgammaf "float x" 73.Sh DESCRIPTION 74.Fn lgamma x 75.if t \{\ 76returns ln\||\(*G(x)| where 77.Bd -unfilled -offset indent 78\(*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 79.br 80\(*G(x) = \(*p/(\(*G(1\-x)\|sin(\(*px)) for x < 1. 81.Ed 82.\} 83.if n \ 84returns ln\||\(*G(x)|. 85.Pp 86The external integer 87.Fa signgam 88returns the sign of \(*G(x). 89.Pp 90.Fn lgamma_r 91is a reentrant interface that performs identically to 92.Fn lgamma , 93differing in that the sign of \(*G(x) is stored in the location 94pointed to by the 95.Fa sign 96argument and 97.Fa signgam 98is not modified. 99.Pp 100The 101.Fn tgamma x 102and 103.Fn tgammaf x 104functions return \(*G(x), with no effect on 105.Fa signgam . 106.Pp 107.Fn gamma , 108.Fn gammaf , 109.Fn gamma_r , 110and 111.Fn gammaf_r 112are deprecated aliases for 113.Fn lgamma , 114.Fn lgammaf , 115.Fn lgamma_r , 116and 117.Fn lgammaf_r , 118respectively. 119.Sh IDIOSYNCRASIES 120Do not use the expression 121.Dq Li signgam\(**exp(lgamma(x)) 122to compute g := \(*G(x). 123Instead use a program like this (in C): 124.Bd -literal -offset indent 125lg = lgamma(x); g = signgam\(**exp(lg); 126.Ed 127.Pp 128Only after 129.Fn lgamma 130has returned can signgam be correct. 131.Sh RETURN VALUES 132.Fn lgamma 133returns appropriate values unless an argument is out of range. 134Overflow will occur for sufficiently large positive values, and 135non-positive integers. 136For large non-integer negative values, 137.Fn tgamma 138will underflow. 139On the 140.Tn VAX , 141the reserved operator is returned, 142and 143.Va errno 144is set to 145.Er ERANGE . 146.Sh SEE ALSO 147.Xr math 3 148.Sh HISTORY 149The 150.Nm lgamma 151function appeared in 152.Bx 4.3 . 153The 154.Fn tgamma 155function appeared in 156.Nx 6.0 . 157