157 lines
4.5 KiB
Groff
157 lines
4.5 KiB
Groff
.\" Copyright (c) 1985, 1991 Regents of the University of California.
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.\" All rights reserved.
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.\"
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.\" Redistribution and use in source and binary forms, with or without
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.\" modification, are permitted provided that the following conditions
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.\" are met:
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.\" 1. Redistributions of source code must retain the above copyright
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.\" notice, this list of conditions and the following disclaimer.
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.\" 2. Redistributions in binary form must reproduce the above copyright
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.\" notice, this list of conditions and the following disclaimer in the
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.\" documentation and/or other materials provided with the distribution.
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.\" 3. All advertising materials mentioning features or use of this software
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.\" must display the following acknowledgement:
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.\" This product includes software developed by the University of
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.\" California, Berkeley and its contributors.
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.\" 4. Neither the name of the University nor the names of its contributors
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.\" may be used to endorse or promote products derived from this software
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.\" without specific prior written permission.
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.\"
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.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
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.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
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.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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.\" SUCH DAMAGE.
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.\"
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.\" @(#)lgamma.3 6.4 (Berkeley) 5/6/91
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.\"
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.Dd May 6, 1991
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.Dt LGAMMA 3
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.Os BSD 4.3
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.Sh NAME
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.Nm lgamma
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.Nd log gamma function
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.Sh SYNOPSIS
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.Fd #include <math.h>
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.Ft double
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.Fn lgamma "double x"
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.Sh DESCRIPTION
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.ta \w'Lgamma returns ln\||\(*G(x)| where'u+1n +1.7i
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.if t \{\
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Lgamma returns ln\||\(*G(x)| where
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.Bd -unfilled -offset indent
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\(*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
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.br
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\(*G(x) = \(*p/(\(*G(1\-x)\|sin(\(*px)) for x < 1. \}
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.Ed
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.if n \
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Lgamma returns ln\||\(*G(x)|.
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.ta
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.Pp
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The external integer
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.Fa signgam
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returns the sign of
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\(*G(x) .
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.Sh IDIOSYNCRASIES
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Do
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.Em not
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use the expression
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.Dq Li signgam\(**exp(lgamma(x))
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to compute g := \(*G(x). Instead use a program like this (in C):
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.Bd -literal -offset indent
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lg = lgamma(x); g = signgam\(**exp(lg);
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.Ed
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.Pp
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Only after
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.Fn lgamma
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has returned can signgam be correct.
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Note too that \(*G(x) must overflow when x is large enough,
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underflow when \-x is large enough, and spawn a division by zero
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when x is a nonpositive integer.
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.Pp
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Only in the
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.Tn UNIX
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math library for C was the name gamma ever attached
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to ln\(*G. Elsewhere, for instance in
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.Tn IBM Ns 's
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.Tn FORTRAN
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library, the name
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.Tn GAMMA
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belongs to \(*G and the name
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.Tn ALGAMA
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to ln\(*G in single precision;
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in double the names are
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.Tn DGAMMA
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and
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.Tn DLGAMA .
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Why should C be different?
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.Pp
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Archaeological records suggest that C's
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.Em gamma
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originally delivered
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ln(\(*G(|x|)). Later, the program gamma was changed to
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cope with negative arguments x in a more conventional way, but
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the documentation did not reflect that change correctly. The most
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recent change corrects inaccurate values when x is almost a
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negative integer, and lets \(*G(x) be computed without
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conditional expressions. Programmers should not assume that
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.Fn lgamma
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has settled down.
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.Pp
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At some time in the future, the name
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.Em gamma
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will be rehabilitated
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and used for the gamma function, just as is done in
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.Tn FORTRAN .
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The reason for this is not so much compatibility with
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.Tn FORTRAN
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as a
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desire to achieve greater speed for smaller values of |x| and greater
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accuracy for larger values.
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.Pp
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Meanwhile, programmers who have to use the name
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.Em gamma
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in its former
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sense, for what is now
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.Fn lgamma ,
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have two choices:
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.Bl -enum -width indent
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.It
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Use the old math library,
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.Pa libom .
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.It
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Add the following program to your others:
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.Bd -literal -offset indent
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#include <math.h>
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double gamma(x)
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double x;
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{
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return (lgamma(x));
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}
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.Ed
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.Sh DIAGNOSTICS
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The reserved operand is returned on a
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.Tn VAX
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for negative integer arguments,
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.Va errno
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is set to
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.Er ERANGE ;
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for very large arguments over/underflows will
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occur inside the
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.Fn lgamma
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routine.
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.Sh SEE ALSO
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.Xr math 3 ,
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.Xr infnan 3
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.Sh HISTORY
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The
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.Nm
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function appeared in
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.Bx 4.3 .
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