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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 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
+.Dv 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 = Dv 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 -filled -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 -filled -offset indent
+.Fn copysign x "reserved operand"
+=
+.Pf \- Fa x ;
+.Ed
+.Pp
+should this return the reserved operand instead?