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.\" Copyright (c) 2011 Jukka Ruohonen <jruohonen@iki.fi>
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.Dd September 18, 2011
.Dt REMAINDER 3
.Os
.Sh NAME
.Nm remainder ,
.Nm remainderf ,
.Nm remquo ,
.Nm remquof
.Nd remainder 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
Provided that
.Fa y
\*(Ne 0 ,
the
.Fn remainder
and
.Fn remainderf
functions calculate the floating-point remainder
.Fa r
of
.Bd -ragged -offset indent
.Va r
=
.Va x - ny ,
.Ed
.Pp
where
.Fa n
is the integral value nearest to the exact value of
.Fa x
/
.Fa y .
If
.Bd -ragged -offset indent
.Va | n
-
.Va x / y |
= 1/2 ,
.Ed
.Pp
the value
.Fa n
is chosen to be even.
Consequently, the remainder is computed exactly and
.Va | r |
\*(Le
.Fa | y |
/ 2 .
.Pp
Also the
.Fn remquo
and
.Fn remquof
functions calculate the remainder as described above.
But these additionally use
.Fa quo
to store a value whose sign is the sign of
.Va x / y
and whose magnitude is congruent modulo
.Va 2^k
to the magnitude of the integral quotient of
.Va x / y ,
where
.Fa k
is an implementation-defined integer greater than or equal to 3.
.Pp
The rationale of the
.Fn remquo
family of functions relates to situations where
only few bits of the quotient are required.
The exact representation of the quotient may not be meaningful when
.Fa x
is large in magnitude compared to
.Fa y .
.Sh RETURN VALUES
The functions return the remainder independent of the rounding mode.
If
.Fa y
is zero ,
\*(Na
is returned and a domain error occurs.
A domain error occurs and a
\*(Na
is returned also when
.Fa x
is infinite but
.Fa y
is not a
\*(Na.
If either
.Fa x
or
.Fa y
is
\*(Na,
a
\*(Na
is always returned.
.Sh SEE ALSO
.Xr div 3 ,
.Xr fast_remainder32 3 ,
.Xr fmod 3 ,
.Xr math 3
.Sh STANDARDS
The described functions conform to
.St -isoC-99 .