160 lines
3.5 KiB
Groff
160 lines
3.5 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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.\" 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: @(#)ieee.3 6.4 (Berkeley) 5/6/91
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.\" $FreeBSD$
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.\"
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.Dd March 30, 2008
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.Dt REMAINDER 3
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.Os
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.Sh NAME
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.Nm remainder ,
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.Nm remainderf ,
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.Nm remainderl ,
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.Nm remquo ,
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.Nm remquof ,
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.Nm remquol
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.Nd minimal residue functions
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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 double
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.Fn remainder "double x" "double y"
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.Ft float
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.Fn remainderf "float x" "float y"
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.Ft long double
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.Fn remainderl "long double x" "long double y"
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.Ft double
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.Fn remquo "double x" "double y" "int *quo"
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.Ft float
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.Fn remquof "float x" "float y" "int *quo"
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.Ft long double
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.Fn remquol "long double x" "long double y" "int *quo"
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.Sh DESCRIPTION
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.Fn remainder ,
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.Fn remainderf ,
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.Fn remainderl ,
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.Fn remquo ,
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.Fn remquof ,
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and
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.Fn remquol
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return the remainder
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.Fa r
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:=
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.Fa x
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\-
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.Fa n\(**y
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where
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.Fa n
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is the integer nearest the exact value of
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.Bk -words
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.Fa x Ns / Ns Fa y ;
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.Ek
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moreover if
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.Pf \*(Ba Fa n
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\-
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.Sm off
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.Fa x No / Fa y No \*(Ba
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.Sm on
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=
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1/2
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then
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.Fa n
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is even.
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Consequently
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the remainder is computed exactly and
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.Sm off
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.Pf \*(Ba Fa r No \*(Ba
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.Sm on
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\*(Le
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.Sm off
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.Pf \*(Ba Fa y No \*(Ba/2 .
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.Sm on
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But attempting to take the remainder when
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.Fa y
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is 0 or
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.Fa x
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is \*(Pm\*(If is an invalid operation that produces a \*(Na.
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.Pp
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The
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.Fn remquo ,
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.Fn remquof ,
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and
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.Fn remquol
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functions also store the last
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.Va k
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bits of
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.Fa n
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in the location pointed to by
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.Fa quo ,
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provided that
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.Fa n
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exists.
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The number of bits
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.Va k
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is platform-specific, but is guaranteed to be at least 3.
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.Sh SEE ALSO
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.Xr fmod 3 ,
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.Xr ieee 3 ,
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.Xr math 3
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.Sh STANDARDS
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The
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.Fn remainder ,
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.Fn remainderf ,
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.Fn remainderl ,
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.Fn remquo ,
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.Fn remquof ,
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and
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.Fn remquol
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routines conform to
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.St -isoC-99 .
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The remainder is as defined in
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.St -ieee754 .
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.Sh HISTORY
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The
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.Fn remainder
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and
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.Fn remainderf
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functions appeared in
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.Bx 4.3
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and
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.Fx 2.0 ,
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respectively.
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The
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.Fn remquo
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and
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.Fn remquof
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functions were added in
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.Fx 6.0 ,
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and
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.Fn remainderl
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and
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.Fn remquol
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were added in
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.Fx 8.0 .
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