145 lines
3.3 KiB
Groff
145 lines
3.3 KiB
Groff
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.\" $NetBSD: remainder.3,v 1.2 2011/09/18 05:33:14 jruoho Exp $
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.\"
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.\" Copyright (c) 2011 Jukka Ruohonen <jruohonen@iki.fi>
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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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.\"
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.\" THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS
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.\" ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
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.\" TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
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.\" PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS
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.\" BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
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.\" CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
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.\" SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
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.\" INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
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.\" CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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.\" ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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.\" POSSIBILITY OF SUCH DAMAGE.
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.\"
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.Dd September 18, 2011
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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 remquo ,
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.Nm remquof
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.Nd remainder 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 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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.Sh DESCRIPTION
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Provided that
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.Fa y
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\*(Ne 0 ,
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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 calculate the floating-point remainder
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.Fa r
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of
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.Bd -ragged -offset indent
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.Va r
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=
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.Va x - ny ,
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.Ed
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.Pp
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where
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.Fa n
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is the integral value nearest to the exact value of
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.Fa x
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/
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.Fa y .
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If
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.Bd -ragged -offset indent
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.Va | n
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-
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.Va x / y |
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= 1/2 ,
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.Ed
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.Pp
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the value
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.Fa n
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is chosen to be even.
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Consequently, the remainder is computed exactly and
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.Va | r |
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\*(Le
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.Fa | y |
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/ 2 .
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.Pp
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Also the
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.Fn remquo
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and
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.Fn remquof
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functions calculate the remainder as described above.
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But these additionally use
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.Fa quo
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to store a value whose sign is the sign of
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.Va x / y
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and whose magnitude is congruent modulo
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.Va 2^k
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to the magnitude of the integral quotient of
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.Va x / y ,
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where
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.Fa k
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is an implementation-defined integer greater than or equal to 3.
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.Pp
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The rationale of the
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.Fn remquo
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family of functions relates to situations where
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only few bits of the quotient are required.
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The exact representation of the quotient may not be meaningful when
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.Fa x
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is large in magnitude compared to
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.Fa y .
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.Sh RETURN VALUES
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The functions return the remainder independent of the rounding mode.
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If
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.Fa y
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is zero ,
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\*(Na
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is returned and a domain error occurs.
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A domain error occurs and a
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\*(Na
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is returned also when
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.Fa x
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is infinite but
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.Fa y
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is not a
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\*(Na.
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If either
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.Fa x
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or
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.Fa y
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is
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\*(Na,
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a
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\*(Na
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is always returned.
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.Sh SEE ALSO
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.Xr div 3 ,
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.Xr fast_remainder32 3 ,
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.Xr fmod 3 ,
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.Xr math 3
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.Sh STANDARDS
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The described functions conform to
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.St -isoC-99 .
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