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.\"     from: @(#)ieee.3	6.4 (Berkeley) 5/6/91
.\" $FreeBSD$
.\"
.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
and
.Fn copysignf
return
.Fa x
with its sign changed to
.Fa y Ns 's .
.Pp
.Fn finite
and
.Fn finitef
return 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
.Pp
.Fn ilogb
and
.Fn ilogbf
return
.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 .
.Pp
.Fn nextafter
and
.Fn nextafterf
return the next machine representable number from
.Fa x
in direction
.Fa y .
.Pp
.Fn remainder
and
.Fn remainderf
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
.Fn remainder x 0
and
.Fn remainder \*(If 0
are invalid operations that produce a \*(Na.
.Pp
.Fn scalbn
and
.Fn scalbnf
return
.Fa x Ns \(**(2** Ns Fa n )
computed by exponent manipulation.
.Sh SEE ALSO
.Xr math 3
.Sh HISTORY
The
.Nm ieee
functions appeared in
.Bx 4.3 .
.Sh STANDARDS
.St -ieee754