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.\"     from: @(#)ieee.3	6.4 (Berkeley) 5/6/91
.\" $FreeBSD$
.\"
.Dd March 30, 2008
.Dt REMAINDER 3
.Os
.Sh NAME
.Nm remainder ,
.Nm remainderf ,
.Nm remainderl ,
.Nm remquo ,
.Nm remquof ,
.Nm remquol
.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 long double
.Fn remainderl "long double x" "long double y"
.Ft double
.Fn remquo "double x" "double y" "int *quo"
.Ft float
.Fn remquof "float x" "float y" "int *quo"
.Ft long double
.Fn remquol "long double x" "long double y" "int *quo"
.Sh DESCRIPTION
.Fn remainder ,
.Fn remainderf ,
.Fn remainderl ,
.Fn remquo ,
.Fn remquof ,
and
.Fn remquol
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 ,
.Fn remquof ,
and
.Fn remquol
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 remainderl ,
.Fn remquo ,
.Fn remquof ,
and
.Fn remquol
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 ,
and
.Fn remainderl
and
.Fn remquol
were added in
.Fx 8.0 .