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.Dd March 1, 2024 29.Dt LGAMMA 3 30.Os 31.Sh NAME 32.Nm lgamma , 33.Nm lgamma_r , 34.Nm lgammaf , 35.Nm lgammaf_r , 36.Nm lgammal , 37.Nm lgammal_r , 38.Nm gamma , 39.Nm gamma_r , 40.Nm gammaf , 41.Nm gammaf_r , 42.Nm tgamma , 43.Nm tgammaf , 44.Nm tgammal , 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 "long double" 62.Fn lgammal "long double x" 63.Ft "long double" 64.Fn lgammal_r "long double x" "int *signgamp" 65.Ft double 66.Fn gamma "double x" 67.Ft double 68.Fn gamma_r "double x" "int *signgamp" 69.Ft float 70.Fn gammaf "float x" 71.Ft float 72.Fn gammaf_r "float x" "int *signgamp" 73.Ft "long double" 74.Fn tgamma "double x" 75.Ft float 76.Fn tgammaf "float x" 77.Ft "long double" 78.Fn tgammal "long double x" 79.Sh DESCRIPTION 80.Fn lgamma x , 81.Fn lgammaf x , 82and 83.Fn lgammal x 84.if t \{\ 85return 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\(*G(x) = \(*p/(\(*G(1\-x)\|sin(\(*px)) for x < 1. 89.Ed 90.\} 91.if n \ 92return ln\||\(*G(x)|. 93The external integer 94.Fa signgam 95returns the sign of \(*G(x). 96.Pp 97.Fn lgamma_r x signgamp , 98.Fn lgammaf_r x signgamp , 99and 100.Fn lgammal_r x signgamp 101provide the same functionality as 102.Fn lgamma x , 103.Fn lgammaf x , 104and 105.Fn lgammal x , 106but the caller must provide an integer to store the sign of \(*G(x). 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.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 139or 140.Fn lgammaf 141has returned can signgam be correct. 142.Pp 143For arguments in its range, 144.Fn tgamma 145is preferred, as for positive arguments 146it is accurate to within one unit in the last place. 147Exponentiation of 148.Fn lgamma 149will lose up to 10 significant bits. 150.Sh RETURN VALUES 151.Fn gamma , 152.Fn gammaf , 153.Fn gammal , 154.Fn gamma_r , 155.Fn gammaf_r , 156.Fn gammal_r , 157.Fn lgamma , 158.Fn lgammaf , 159.Fn lgammal , 160.Fn lgamma_r , 161.Fn lgammaf_r , 162and 163.Fn lgammal_r 164return appropriate values unless an argument is out of range. 165Overflow will occur for sufficiently large positive values, and 166non-positive integers. 167For large non-integer negative values, 168.Fn tgamma 169will underflow. 170.Sh SEE ALSO 171.Xr math 3 172.Sh STANDARDS 173The 174.Fn lgamma , 175.Fn lgammaf , 176.Fn lgammal , 177.Fn tgamma , 178.Fn tgammaf , 179and 180.Fn tgammal 181functions are expected to conform to 182.St -isoC-99 . 183.Sh HISTORY 184The 185.Fn lgamma 186function appeared in 187.Bx 4.3 . 188The 189.Fn gamma 190function appeared in 191.Bx 4.4 192as a function which computed \(*G(x). 193This version was used in 194.Fx 1.1 . 195The name 196.Fn gamma 197was originally dedicated to the 198.Fn lgamma 199function, 200and that usage was restored by switching to Sun's fdlibm in 201.Fx 1.1.5 . 202The 203.Fn tgamma 204function appeared in 205.Fx 5.0 . 206The 128-bit 207.Ft long double 208version of 209.Fn tgammal 210replaced the 80-bit stub version in 211version in 212.Fx 16 , 213thanks to an appropriate implementation from Arm. 214