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.\" Copyright (c) 1985, 1991, 1993
.\" The 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. All advertising materials mentioning features or use of this software
.\" must display the following acknowledgement:
.\" This product includes software developed by the University of
.\" California, Berkeley and its contributors.
.\" 4. 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.
.\"
.\" @(#)ieee.3 8.1 (Berkeley) 6/4/93
.\" $FreeBSD$
.\"
.Dd June 4, 1993
.Dt IEEE 3
.Os BSD 4.3
.Sh NAME
.Nm copysign ,
.Nm drem ,
.Nm finite ,
.Nm logb ,
.Nm scalb
.Nd "IEEE 754 floating point support
.Sh LIBRARY
.Lb libm
.Sh SYNOPSIS
.Fd #include <math.h>
.Ft double
.Fn copysign "double x" "double y"
.Ft double
.Fn drem "double x" "double y"
.Ft int
.Fn finite "double x"
.Ft double
.Fn logb "double x"
.Ft double
.Fn scalb "double x" "int n"
.Sh DESCRIPTION
These functions are required for, or recommended by the
.Tn IEEE
standard
754 for floating\-point arithmetic.
.Pp
The
.Fn copysign
function
returns
.Fa x
with its sign changed to
.Fa y Ns 's .
.Pp
The
.Fn drem
function
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 drem x 0
is exceptional.
(See below under
.Sx DIAGNOSTICS . )
.Pp
The
.Fn finite
function 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 or
is the
.Tn VAX Ns 's
reserved operand).
.Pp
The
.Fn logb
function returns
.Fa x Ns 's exponent
.Fa n ,
a signed integer converted to double\-precision floating\-point and so
chosen that
1 (<=
.Pf \\*(Ba Ns Fa x Ns \\*(Ba2** Ns Fa n
< 2
unless
.Fa x
= 0 or
(only on machines that conform to
.Tn IEEE
754)
.Pf \\*(Ba Fa x Ns \\*(Ba
= \*(If
or
.Fa x
lies between 0 and the Underflow Threshold.
(See below under
.Sx BUGS . )
.Pp
The
.Fn scalb
function returns
.Fa x Ns \(**(2** Ns Fa n )
computed, for integer n, without first computing
.Pf 2\(** Fa n .
.Sh RETURN VALUES
The
.Tn IEEE
standard
754 defines
.Fn drem x 0
and
.Fn drem \\*(If y
to be invalid operations that produce a \*(Na.
On the
.Tn VAX ,
.Fn drem x 0
generates a reserved operand fault. No \*(If
exists on a
.Tn VAX .
.Pp
.Tn IEEE
754 defines
.if n \
.Fn logb \(+-\\*(If
= \*(If and
.Fn logb 0
= \-\*(If, and
requires the latter to signal Division\-by\-Zero.
But on a
.Tn VAX ,
.Fn logb 0
= 1.0 \- 2.0**31 = \-2,147,483,647.0.
And if the correct value of
.Fn scalb
would overflow on a
.Tn VAX ,
it generates a reserved operand fault and sets the global variable
.Va errno
to
.Er ERANGE .
.Sh SEE ALSO
.Xr floor 3 ,
.Xr infnan 3 ,
.Xr math 3
.Sh HISTORY
The
.Nm ieee
functions appeared in
.Bx 4.3 .
.Sh BUGS
Should
.Fn drem x 0
and
.Fn logb 0
on a
.Tn VAX
signal invalidity
by setting
.Va errno No = Er EDOM ?
Should
.Fn logb 0
return \-1.7e38?
.Pp
.Tn IEEE
754 currently specifies that
.Fn logb "denormalized no.\&"
=
.Fn logb "tiniest normalized no. > 0"
but the consensus has changed to the specification in the new
proposed
.Tn IEEE
standard p854, namely that
.Fn logb x
satisfy
.Bd -ragged -offset indent
1 \(<=
.Fn scalb \\*(Bax\\*(Ba \-logb(x)
<
Radix\0 ... = 2
for
.Tn IEEE
754
.Ed
.Pp
for every x except 0,
\*(If
and \*(Na.
Almost every program that assumes 754's specification will work
correctly if
.Fn logb
follows 854's specification instead.
.Pp
.Tn IEEE
754 requires
.Fn copysign x \\*(Na)
=
.Pf \(+- Ns Fa x
but says nothing
else about the sign of a \*(Na. A \*(Na
.Em (N Ns ot
.Em a
.Em N Ns umber )
is
similar in spirit to the
.Tn VAX Ns 's
reserved operand, but very
different in important details. Since the sign bit of a
reserved operand makes it look negative,
.Bd -ragged -offset indent
.Fn copysign x "reserved operand"
=
.Pf \- Fa x ;
.Ed
.Pp
should this return the reserved operand instead?
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