80b8071609
. Hook e_lgammal[_r].c to the build.
. Create man page links for lgammal[-r].3.
* Symbol.map:
. Sort lgammal to its rightful place.
. Add FBSD_1.4 section for the new lgamal_r symbol.
* ld128/e_lgammal_r.c:
. 128-bit implementataion of lgammal_r().
* ld80/e_lgammal_r.c:
. Intel 80-bit format implementation of lgammal_r().
* src/e_lgamma.c:
. Expose lgammal as a weak reference to lgamma for platforms
where long double is mapped to double.
* src/e_lgamma_r.c:
. Use integer literal constants instead of real literal constants.
Let compiler(s) do the job of conversion to the appropriate type.
. Expose lgammal_r as a weak reference to lgamma_r for platforms
where long double is mapped to double.
* src/e_lgammaf_r.c:
. Fixed the Cygnus Support conversion of e_lgamma_r.c to float.
This includes the generation of new polynomial and rational
approximations with fewer terms. For each approximation, include
a comment on an estimate of the accuracy over the relevant domain.
. Use integer literal constants instead of real literal constants.
Let compiler(s) do the job of conversion to the appropriate type.
This allows the removal of several explicit casts of double values
to float.
* src/e_lgammal.c:
. Wrapper for lgammal() about lgammal_r().
* src/imprecise.c:
. Remove the lgamma.
* src/math.h:
. Add a prototype for lgammal_r().
* man/lgamma.3:
. Document the new functions.
Reviewed by: bde
205 lines
4.7 KiB
Groff
205 lines
4.7 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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.\" 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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.\" from: @(#)lgamma.3 6.6 (Berkeley) 12/3/92
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.\" $FreeBSD$
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.\"
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.Dd September 12, 2014
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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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.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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.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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and
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.Fn tgammaf 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 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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and
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.Fn tgammaf
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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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