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