update for ANSI C from Alex Zliu and John Gilmore

[unix-history] / usr / src / lib / libm / common_source / lgamma.3

.\" Copyright (c) 1985 Regents of the University of California.
.\" All rights reserved.  The Berkeley software License Agreement
.\" specifies the terms and conditions for redistribution.
.\"
.\"	@(#)lgamma.3	6.2 (Berkeley) %G%
.\"
.TH LGAMMA 3M  ""
.UC 6
.SH NAME
lgamma \- log gamma function
.SH SYNOPSIS
.nf
.B #include <math.h>
.PP
.B double lgamma(x)
.B double x;
.fi
.SH DESCRIPTION
.nf
.ta \w'Lgamma returns ln\||\(*G(x)| where'u+1n +1.7i
.if t \{\
Lgamma returns ln\||\(*G(x)| where	\(*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
.br
	\(*G(x) = \(*p/(\(*G(1\-x)\|sin(\(*px))	for x < 1.  \}
.if n \
Lgamma returns ln\||\(*G(x)|.
.ta
.fi
.PP
The external integer signgam returns the sign of
\(*G(x) .
.SH IDIOSYNCRASIES
Do \fBnot\fR use the expression signgam\(**exp(lgamma(x))
to compute g := \(*G(x).  Instead use a program like this (in C):
.RS
lg = lgamma(x); g = signgam\(**exp(lg);
.RE
.PP
Only after lgamma has returned can signgam be correct.
Note too that \(*G(x) must overflow when x is large enough,
underflow when \-x is large enough, and spawn a division by zero
when x is a nonpositive integer.
.PP
Only in the UNIX math library for C was the name gamma ever attached
to ln\(*G.  Elsewhere, for instance in IBM's FORTRAN library, the name
GAMMA belongs to \(*G and the name ALGAMA to ln\(*G in single precision;
in double the names are DGAMMA and DLGAMA.  Why should C be different?
.PP
Archaeological records suggest that C's gamma originally delivered
ln(\(*G(|x|)).  Later, the program gamma was changed to
cope with negative arguments x in a more conventional way, but
the documentation did not reflect that change correctly.  The most
recent change corrects inaccurate values when x is almost a
negative integer, and lets \(*G(x) be computed without
conditional expressions.  Programmers should not assume that
lgamma has settled down.
.PP
At some time in the future, the name \fIgamma\fR will be rehabilitated
and used for the gamma function, just as is done in FORTRAN.
The reason for this is not so much compatibility with FORTRAN as a
desire to achieve greater speed for smaller values of |x| and greater
accuracy for larger values.
.PP
Meanwhile, programmers who have to use the name \fIgamma\fR in its former
sense, for what is now \fIlgamma\fR, have two choices:
.IP 1) \w'1)\0'u
Use the old math library, \fIlibom\fR.
.IP 2) \w'1)\0'u
Add the following program to your others:
.RS
.nf
\fB#include <math.h>
double gamma(x)
double x;
{
.RS
\fBreturn (lgamma(x));
.RE
}\fR
.RE
.fi
.SH DIAGNOSTICS
The reserved operand is returned on a VAX for negative integer arguments,
\fIerrno\fR is set to ERANGE; for very large arguments over/underflows will
occur inside the \fIlgamma\fP routine.
.SH SEE ALSO
math(3M), infnan(3M)