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.\"     from: @(#)ieee.3	6.4 (Berkeley) 5/6/91
.\"
.Dd February 25, 1994
.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 HISTORY
The
.Nm ieee
functions appeared in
.Bx 4.3 .
.Sh STANDARDS
.St -ieee754