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.\" $OpenBSD: ieee.3,v 1.12 2008/06/10 23:56:21 martynas Exp $
.\" 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. 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
.\"
.Dd $Mdocdate: June 10 2008 $
.Dt IEEE 3
.Os
.Sh NAME
.Nm copysign ,
.Nm copysignf ,
.Nm finite ,
.Nm finitef ,
.Nm ilogb ,
.Nm ilogbf ,
.Nm nextafter ,
.Nm nextafterf ,
.Nm remainder ,
.Nm remainderf ,
.Nm scalbn ,
.Nm scalbnf
.Nd functions for IEEE arithmetic
.Sh SYNOPSIS
.Fd #include <math.h>
.Ft double
.Fn copysign "double x" "double y"
.Ft float
.Fn copysignf "float x" "float y"
.Ft int
.Fn finite "double x"
.Ft int
.Fn finitef "float x"
.Ft int
.Fn ilogb "double x"
.Ft int
.Fn ilogbf "float x"
.Ft double
.Fn nextafter "double x" "double y"
.Ft float
.Fn nextafterf "float x" "float y"
.Ft double
.Fn remainder "double x" "double y"
.Ft float
.Fn remainderf "float x" "float y"
.Ft double
.Fn scalbn "double x" "int n"
.Ft float
.Fn scalbnf "float x" "int n"
.Sh DESCRIPTION
These functions are required or recommended by
.St -ieee754 .
.Pp
.Fn copysign
returns
.Fa x
with its sign changed to
.Fa y Ns 's.
The
.Fn copysignf
function is a single precision version of
.Fn copysign .
.Pp
.Fn finite
returns the value 1 just when
\-\*(If \*(Lt
.Fa x
\*(Lt +\*(If;
otherwise a
zero is returned
(when
.Pf \\*(Ba Ns Fa x Ns \\*(Ba
= \*(If or
.Fa x
is \*(Na.
The
.Fn finitef
function is a single precision version of
.Fn finite .
.Pp
.Fn ilogb
returns
.Fa x Ns 's exponent
.Fa n ,
in integer format.
.Fn ilogb \*(Pm\*(If
returns
.Dv INT_MAX
and
.Fn ilogb 0
returns
.Dv INT_MIN .
The
.Fn ilogbf
function is a single precision version of
.Fn ilogb .
.Pp
.Fn nextafter
returns the next machine representable number from
.Fa x
in direction
.Fa y .
The
.Fn nextafterf
function is a single precision version of
.Fn nextafter .
.Pp
.Fn remainder
returns 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
.Fn remainder x 0
and
.Fn remainder \*(If 0
are invalid operations that produce a \*(Na.
The
.Fn remainderf
function is a single precision version of
.Fn remainder .
.Pp
.Fn scalbn
returns
.Fa x Ns \(**(2** Ns Fa n )
computed by exponent manipulation.
The
.Fn scalbnf
function is a single precision version of
.Fn scalbn .
.Sh SEE ALSO
.Xr math 3
.Sh STANDARDS
.St -ieee754
.Sh HISTORY
The
.Nm ieee
functions appeared in
.Bx 4.3 .
.Sh BUGS
.Tn VAX
floating point does not have distinguished values
for either infinity or not-a-number.
The
.Fn finite
function always returns 1 on that architecture.
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