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from: @(#)lgamma.3 6.6 (Berkeley) 12/3/92
$FreeBSD: src/lib/msun/man/lgamma.3,v 1.22 2005/01/16 16:46:14 ru Exp $
.Dd January 14, 2005 .Dt LGAMMA 3 .Os .Sh NAME .Nm lgamma , .Nm lgamma_r , .Nm lgammaf , .Nm lgammaf_r , .Nm gamma , .Nm gamma_r , .Nm gammaf , .Nm gammaf_r , .Nm tgamma .Nd log gamma functions, gamma function .Sh LIBRARY .Lb libm .Sh SYNOPSIS n math.h .Ft extern int .Fa signgam ; .Ft double .Fn lgamma "double x" .Ft double .Fn lgamma_r "double x" "int *signgamp" .Ft float .Fn lgammaf "float x" .Ft float .Fn lgammaf_r "float x" "int *signgamp" .Ft double .Fn gamma "double x" .Ft double .Fn gamma_r "double x" "int *signgamp" .Ft float .Fn gammaf "float x" .Ft float .Fn gammaf_r "float x" "int *signgamp" .Ft double .Fn tgamma "double x" .Sh DESCRIPTION .Fn lgamma x and .Fn lgammaf x return ln\||\(*G(x)| where d -unfilled -offset indent \(*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 \(*G(x) = \(*p/(\(*G(1-x)\|sin(\(*px)) for x < 1. .Ed .\} return ln\||\(*G(x)|.
p The external integer .Fa signgam returns the sign of \(*G(x).
p .Fn lgamma_r x signgamp and .Fn lgammaf_r x signgamp provide the same functionality as .Fn lgamma x and .Fn lgammaf x but the caller must provide an integer to store the sign of \(*G(x).
p .Fn gamma , .Fn gammaf , .Fn gamma_r , and .Fn gammaf_r are deprecated aliases for .Fn lgamma , .Fn lgammaf , .Fn lgamma_r , and .Fn lgammaf_r , respectively. .Fn tgamma x returns \(*G(x), with no effect on .Fa signgam . .Sh IDIOSYNCRASIES Do not use the expression .Dq Li signgam\(**exp(lgamma(x)) to compute g := \(*G(x). Instead use a program like this (in C): d -literal -offset indent lg = lgamma(x); g = signgam\(**exp(lg); .Ed
p Only after .Fn lgamma or .Fn lgammaf has returned can signgam be correct.
p For arguments in its range, .Fn tgamma is preferred, as for positive arguments it is accurate to within one unit in the last place. Exponentiation of .Fn lgamma will lose up to 10 significant bits. .Sh RETURN VALUES .Fn gamma , .Fn gamma_r , .Fn gammaf , .Fn gammaf_r , .Fn lgamma , .Fn lgamma_r , .Fn lgammaf , and .Fn lgammaf_r return appropriate values unless an argument is out of range. Overflow will occur for sufficiently large positive values, and non-positive integers. For large non-integer negative values, .Fn tgamma will underflow. .Sh SEE ALSO .Xr math 3 .Sh STANDARDS The .Fn lgamma and .Fn tgamma functions are expected to conform to .St -isoC-99 . .Sh HISTORY The .Fn lgamma function appeared in x 4.3 . The .Fn gamma function appeared in x 4.4 as a function which computed \(*G(x). This version was used in .Fx 1.1 . The name .Fn gamma was originally dedicated to the .Fn lgamma function, and that usage was restored by switching to Sun's fdlibm in .Fx 1.1.5 . The .Fn tgamma function appeared in .Fx 5.0 .
