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. All advertising materials mentioning features or use of this software 13.\" must display the following acknowledgement: 14.\" This product includes software developed by the University of 15.\" California, Berkeley and its contributors. 16.\" 4. Neither the name of the University nor the names of its contributors 17.\" may be used to endorse or promote products derived from this software 18.\" without specific prior written permission. 19.\" 20.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 21.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 22.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 23.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 24.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 25.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 26.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 27.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 28.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 29.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 30.\" SUCH DAMAGE. 31.\" 32.\" from: @(#)lgamma.3 6.6 (Berkeley) 12/3/92 33.\" $FreeBSD$ 34.\" 35.Dd December 3, 1992 36.Dt LGAMMA 3 37.Os 38.Sh NAME 39.Nm lgamma , 40.Nm lgammaf , 41.Nm gamma , 42.Nm gammaf , 43.Nm tgamma 44.Nd log gamma functions, gamma function 45.Sh LIBRARY 46.Lb libm 47.Sh SYNOPSIS 48.In math.h 49.Ft extern int 50.Fa signgam ; 51.sp 52.Ft double 53.Fn lgamma "double x" 54.Ft float 55.Fn lgammaf "float x" 56.Ft double 57.Fn gamma "double x" 58.Ft float 59.Fn gammaf "float x" 60.Ft double 61.Fn tgamma "double x" 62.Sh DESCRIPTION 63.Fn lgamma x 64and 65.Fn lgammaf x 66.if t \{\ 67return ln\||\(*G(x)| where 68.Bd -unfilled -offset indent 69\(*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 70.br 71\(*G(x) = \(*p/(\(*G(1\-x)\|sin(\(*px)) for x < 1. 72.Ed 73.\} 74.if n \ 75return ln\||\(*G(x)|. 76.Pp 77The external integer 78.Fa signgam 79returns the sign of \(*G(x). 80.Pp 81.Fn gamma 82and 83.Fn gammaf 84are deprecated aliases for 85.Fn lgamma 86and 87.Fn lgammaf , 88respectively. 89.Fn tgamma x 90returns \(*G(x), with no effect on 91.Fa signgam . 92.Sh IDIOSYNCRASIES 93Do not use the expression 94.Dq Li signgam\(**exp(lgamma(x)) 95to compute g := \(*G(x). 96Instead use a program like this (in C): 97.Bd -literal -offset indent 98lg = lgamma(x); g = signgam\(**exp(lg); 99.Ed 100.Pp 101Only after 102.Fn lgamma 103or 104.Fn lgammaf 105has returned can signgam be correct. 106.Pp 107For arguments in its range, 108.Fn tgamma 109is preferred, as for positive arguments 110it is accurate to within one unit in the last place. 111Exponentiation of 112.Fn lgamma 113will lose up to 10 significant bits. 114.Sh RETURN VALUES 115.Fn gamma , 116.Fn gammaf , 117.Fn lgamma , 118and 119.Fn lgammaf 120return appropriate values unless an argument is out of range. 121Overflow will occur for sufficiently large positive values, and 122non-positive integers. 123On the 124.Tn VAX , 125the reserved operator is returned, 126and 127.Va errno 128is set to 129.Er ERANGE . 130For large non-integer negative values, 131.Fn tgamma 132will underflow. 133.Sh SEE ALSO 134.Xr math 3 135.Sh STANDARDS 136The 137.Fn lgamma 138and 139.Fn tgamma 140functions are expected to conform to 141.St -isoC-99 . 142.Sh HISTORY 143The 144.Fn lgamma 145function appeared in 146.Bx 4.3 . 147The 148.Fn gamma 149function appeared in 150.Bx 4.4 151as a function which computed \(*G(x). 152This version was used in 153.Fx 1.1 . 154The name 155.Fn gamma 156was originally dedicated to the 157.Fn lgamma 158function, 159and that usage was restored by switching to Sun's fdlibm in 160.Fx 1.1.5 . 161The 162.Fn tgamma 163function appeared in 164.Fx 5.0 . 165