218 lines
5.1 KiB
Groff
218 lines
5.1 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. 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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.\" from: @(#)lgamma.3 6.6 (Berkeley) 12/3/92
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.\" $FreeBSD$
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.\"
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.Dd December 8, 2017
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.Dt LGAMMA 3
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.Os
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.Sh NAME
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.Nm lgamma ,
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.Nm lgamma_r ,
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.Nm lgammaf ,
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.Nm lgammaf_r ,
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.Nm lgammal ,
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.Nm lgammal_r ,
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.Nm gamma ,
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.Nm gamma_r ,
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.Nm gammaf ,
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.Nm gammaf_r ,
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.Nm tgamma ,
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.Nm tgammaf ,
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.Nm tgammal ,
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.Nd log gamma functions, gamma function
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.Sh LIBRARY
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.Lb libm
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.Sh SYNOPSIS
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.In math.h
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.Ft extern int
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.Fa signgam ;
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.sp
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.Ft double
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.Fn lgamma "double x"
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.Ft double
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.Fn lgamma_r "double x" "int *signgamp"
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.Ft float
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.Fn lgammaf "float x"
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.Ft float
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.Fn lgammaf_r "float x" "int *signgamp"
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.Ft "long double"
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.Fn lgammal "long double x"
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.Ft "long double"
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.Fn lgammal_r "long double x" "int *signgamp"
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.Ft double
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.Fn gamma "double x"
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.Ft double
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.Fn gamma_r "double x" "int *signgamp"
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.Ft float
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.Fn gammaf "float x"
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.Ft float
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.Fn gammaf_r "float x" "int *signgamp"
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.Ft "long double"
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.Fn tgamma "double x"
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.Ft float
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.Fn tgammaf "float x"
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.Ft "long double"
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.Fn tgammal "long double x"
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.Sh DESCRIPTION
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.Fn lgamma x ,
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.Fn lgammaf x ,
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and
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.Fn lgammal x
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.if t \{\
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return 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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\(*G(x) = \(*p/(\(*G(1\-x)\|sin(\(*px)) for x < 1.
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.Ed
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.\}
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.if n \
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return ln\||\(*G(x)|.
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The external integer
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.Fa signgam
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returns the sign of \(*G(x).
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.Pp
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.Fn lgamma_r x signgamp ,
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.Fn lgammaf_r x signgamp ,
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and
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.Fn lgammal_r x signgamp
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provide the same functionality as
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.Fn lgamma x ,
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.Fn lgammaf x ,
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and
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.Fn lgammal x ,
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but the caller must provide an integer to store the sign of \(*G(x).
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.Pp
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The
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.Fn tgamma x ,
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.Fn tgammaf x ,
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and
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.Fn tgammal x
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functions return \(*G(x), with no effect on
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.Fa signgam .
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.Pp
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.Fn gamma ,
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.Fn gammaf ,
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.Fn gamma_r ,
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and
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.Fn gammaf_r
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are deprecated aliases for
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.Fn lgamma ,
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.Fn lgammaf ,
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.Fn lgamma_r ,
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and
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.Fn lgammaf_r ,
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respectively.
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.Sh IDIOSYNCRASIES
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Do not use the expression
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.Dq Li signgam\(**exp(lgamma(x))
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to compute g := \(*G(x).
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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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or
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.Fn lgammaf
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has returned can signgam be correct.
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.Pp
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For arguments in its range,
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.Fn tgamma
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is preferred, as for positive arguments
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it is accurate to within one unit in the last place.
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Exponentiation of
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.Fn lgamma
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will lose up to 10 significant bits.
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.Sh RETURN VALUES
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.Fn gamma ,
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.Fn gammaf ,
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.Fn gammal ,
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.Fn gamma_r ,
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.Fn gammaf_r ,
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.Fn gammal_r ,
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.Fn lgamma ,
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.Fn lgammaf ,
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.Fn lgammal ,
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.Fn lgamma_r ,
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.Fn lgammaf_r ,
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and
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.Fn lgammal_r
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return appropriate values unless an argument is out of range.
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Overflow will occur for sufficiently large positive values, and
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non-positive integers.
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For large non-integer negative values,
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.Fn tgamma
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will underflow.
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.Sh BUGS
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To conform with newer C/C++ standards, a stub implementation for
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.Nm tgammal
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was committed to the math library, where
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.Nm tgammal
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is mapped to
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.Nm tgamma .
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Thus, the numerical accuracy is at most that of the 53-bit double
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precision implementation.
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.Sh SEE ALSO
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.Xr math 3
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.Sh STANDARDS
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The
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.Fn lgamma ,
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.Fn lgammaf ,
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.Fn lgammal ,
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.Fn tgamma ,
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.Fn tgammaf ,
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and
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.Fn tgammal
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functions are expected to conform to
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.St -isoC-99 .
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.Sh HISTORY
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The
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.Fn lgamma
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function appeared in
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.Bx 4.3 .
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The
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.Fn gamma
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function appeared in
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.Bx 4.4
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as a function which computed \(*G(x).
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This version was used in
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.Fx 1.1 .
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The name
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.Fn gamma
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was originally dedicated to the
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.Fn lgamma
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function,
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and that usage was restored by switching to Sun's fdlibm in
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.Fx 1.1.5 .
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The
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.Fn tgamma
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function appeared in
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.Fx 5.0 .
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