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 1.24 2024/01/26 19:27:30 nros Exp $ 30.\" 31.Dd January 24, 2024 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 gamma , 42.Nm gammaf , 43.Nm gamma_r , 44.Nm gammaf_r , 45.Nm tgamma , 46.Nm tgammaf , 47.Nm tgammal 48.Nd log gamma function 49.Sh LIBRARY 50.Lb libm 51.Sh SYNOPSIS 52.In math.h 53.Ft extern int 54.Fa signgam ; 55.sp 56.Ft double 57.Fn lgamma "double x" 58.Ft float 59.Fn lgammaf "float x" 60.Ft long double 61.Fn lgammal "long double x" 62.Ft double 63.Fn lgamma_r "double x" "int *sign" 64.Ft float 65.Fn lgammaf_r "float x" "int *sign" 66.Ft long double 67.Fn lgammal_r "long double x" "int *sign" 68.Ft double 69.Fn gamma "double x" 70.Ft float 71.Fn gammaf "float x" 72.Ft double 73.Fn gamma_r "double x" "int *sign" 74.Ft float 75.Fn gammaf_r "float x" "int *sign" 76.Ft double 77.Fn tgamma "double x" 78.Ft float 79.Fn tgammaf "float x" 80.Ft long double 81.Fn tgammal "long double x" 82.Sh DESCRIPTION 83.Fn lgamma x 84.if t \{\ 85returns ln\||\(*G(x)| where 86.Bd -unfilled -offset indent 87\(*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 88.br 89\(*G(x) = \(*p/(\(*G(1\-x)\|sin(\(*px)) for x < 1. 90.Ed 91.\} 92.if n \ 93returns ln\||\(*G(x)|. 94.Pp 95The external integer 96.Fa signgam 97returns the sign of \(*G(x). 98.Pp 99.Fn lgamma_r 100is a reentrant interface that performs identically to 101.Fn lgamma , 102differing in that the sign of \(*G(x) is stored in the location 103pointed to by the 104.Fa sign 105argument and 106.Fa signgam 107is not modified. 108.Pp 109The 110.Fn tgamma x 111and 112.Fn tgammaf x 113functions return \(*G(x), with no effect on 114.Fa signgam . 115.Pp 116.Fn gamma , 117.Fn gammaf , 118.Fn gamma_r , 119and 120.Fn gammaf_r 121are deprecated aliases for 122.Fn lgamma , 123.Fn lgammaf , 124.Fn lgamma_r , 125and 126.Fn lgammaf_r , 127respectively. 128.Sh IDIOSYNCRASIES 129Do not use the expression 130.Dq Li signgam\(**exp(lgamma(x)) 131to compute g := \(*G(x). 132Instead use a program like this (in C): 133.Bd -literal -offset indent 134lg = lgamma(x); g = signgam\(**exp(lg); 135.Ed 136.Pp 137Only after 138.Fn lgamma 139has returned can signgam be correct. 140.Sh RETURN VALUES 141.Fn lgamma 142returns appropriate values unless an argument is out of range. 143Overflow will occur for sufficiently large positive values, and 144non-positive integers. 145For large non-integer negative values, 146.Fn tgamma 147will underflow. 148On the 149.Tn VAX , 150the reserved operator is returned, 151and 152.Va errno 153is set to 154.Er ERANGE . 155.Sh SEE ALSO 156.Xr math 3 157.Sh HISTORY 158The 159.Nm lgamma 160function appeared in 161.Bx 4.3 . 162The 163.Fn tgamma 164function appeared in 165.Nx 6.0 . 166