146 lines
3.5 KiB
Groff
146 lines
3.5 KiB
Groff
.\" 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.
|
|
.\"
|
|
.\" from: @(#)ieee.3 6.4 (Berkeley) 5/6/91
|
|
.\" $FreeBSD: src/lib/msun/man/remainder.3,v 1.4 2005/11/24 09:25:10 joel Exp $
|
|
.\"
|
|
.Dd March 24, 2005
|
|
.Dt REMAINDER 3
|
|
.Os
|
|
.Sh NAME
|
|
.Nm remainder ,
|
|
.Nm remainderf ,
|
|
.Nm remquo ,
|
|
.Nm remquof
|
|
.Nd minimal residue functions
|
|
.Sh LIBRARY
|
|
.Lb libm
|
|
.Sh SYNOPSIS
|
|
.In math.h
|
|
.Ft double
|
|
.Fn remainder "double x" "double y"
|
|
.Ft float
|
|
.Fn remainderf "float x" "float y"
|
|
.Ft double
|
|
.Fn remquo "double x" "double y" "int *quo"
|
|
.Ft float
|
|
.Fn remquof "float x" "float y" "int *quo"
|
|
.Sh DESCRIPTION
|
|
.Fn remainder ,
|
|
.Fn remainderf ,
|
|
.Fn remquo ,
|
|
and
|
|
.Fn remquof
|
|
return the remainder
|
|
.Fa r
|
|
:=
|
|
.Fa x
|
|
\-
|
|
.Fa n\(**y
|
|
where
|
|
.Fa n
|
|
is the integer nearest the exact value of
|
|
.Bk -words
|
|
.Fa x Ns / Ns Fa y ;
|
|
.Ek
|
|
moreover if
|
|
.Pf \\*(Ba Fa n
|
|
\-
|
|
.Sm off
|
|
.Fa x No / Fa y No \\*(Ba
|
|
.Sm on
|
|
=
|
|
1/2
|
|
then
|
|
.Fa n
|
|
is even.
|
|
Consequently
|
|
the remainder is computed exactly and
|
|
.Sm off
|
|
.Pf \\*(Ba Fa r No \\*(Ba
|
|
.Sm on
|
|
\*(Le
|
|
.Sm off
|
|
.Pf \\*(Ba Fa y No \\*(Ba/2 .
|
|
.Sm on
|
|
But attempting to take the remainder when
|
|
.Fa y
|
|
is 0 or
|
|
.Fa x
|
|
is \*(Pm\*(If is an invalid operation that produces a \*(Na.
|
|
.Pp
|
|
The
|
|
.Fn remquo
|
|
and
|
|
.Fn remquof
|
|
functions also store the last
|
|
.Va k
|
|
bits of
|
|
.Fa n
|
|
in the location pointed to by
|
|
.Fa quo ,
|
|
provided that
|
|
.Fa n
|
|
exists.
|
|
The number of bits
|
|
.Va k
|
|
is platform-specific, but is guaranteed to be at least 3.
|
|
.Sh SEE ALSO
|
|
.Xr fmod 3 ,
|
|
.Xr ieee 3 ,
|
|
.Xr math 3
|
|
.Sh STANDARDS
|
|
The
|
|
.Fn remainder ,
|
|
.Fn remainderf ,
|
|
.Fn remquo ,
|
|
and
|
|
.Fn remquof
|
|
routines conform to
|
|
.St -isoC-99 .
|
|
The remainder is as defined in
|
|
.St -ieee754 .
|
|
.Sh HISTORY
|
|
The
|
|
.Fn remainder
|
|
and
|
|
.Fn remainderf
|
|
functions appeared in
|
|
.Bx 4.3
|
|
and
|
|
.Fx 2.0 ,
|
|
respectively.
|
|
The
|
|
.Fn remquo
|
|
and
|
|
.Fn remquof
|
|
functions were added in
|
|
.Fx 6.0 .
|