270 lines
5.4 KiB
Groff
270 lines
5.4 KiB
Groff
.\" Copyright (c) 1985, 1991 Regents of the University of California.
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.\" All rights reserved.
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.\"
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.\" Redistribution and use in source and binary forms, with or without
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.\" modification, are permitted provided that the following conditions
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.\" are met:
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.\" 1. Redistributions of source code must retain the above copyright
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.\" notice, this list of conditions and the following disclaimer.
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.\" 2. Redistributions in binary form must reproduce the above copyright
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.\" notice, this list of conditions and the following disclaimer in the
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.\" documentation and/or other materials provided with the distribution.
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.\" 3. All advertising materials mentioning features or use of this software
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.\" must display the following acknowledgement:
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.\" This product includes software developed by the University of
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.\" California, Berkeley and its contributors.
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.\" 4. Neither the name of the University nor the names of its contributors
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.\" may be used to endorse or promote products derived from this software
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.\" without specific prior written permission.
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.\"
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.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
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.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
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.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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.\" SUCH DAMAGE.
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.\"
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.\" @(#)ieee.3 6.4 (Berkeley) 5/6/91
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.\"
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.Dd May 6, 1991
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.Dt IEEE 3
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.Os BSD 4.3
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.Sh NAME
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.Nm copysign ,
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.Nm drem ,
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.Nm finite ,
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.Nm logb ,
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.Nm scalb
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.Nm copysign ,
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.Nm remainder,
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.Nd exponent manipulations
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.Sh SYNOPSIS
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.Fd #include <math.h>
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.Ft double
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.Fn copysign "double x" "double y"
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.Ft double
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.Fn drem "double x" "double y"
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.Ft int
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.Fn finite "double x"
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.Ft double
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.Fn logb "double x"
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.Ft double
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.Fn scalb "double x" "int n"
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.Sh DESCRIPTION
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These functions are required for, or recommended by the
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.Tn IEEE
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standard
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754 for floating\-point arithmetic.
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.Pp
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The
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.Fn copysign
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function
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returns
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.Fa x
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with its sign changed to
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.Fa y Ns 's.
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.Pp
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The
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.Fn drem
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function
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returns the remainder
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.Fa r
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:=
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.Fa x
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\-
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.Fa n\(**y
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where
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.Fa n
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is the integer nearest the exact value of
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.Bk -words
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.Fa x Ns / Ns Fa y ;
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.Ek
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moreover if
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.Pf \\*(Ba Fa n
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\-
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.Sm off
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.Fa x No / Fa y No \\*(Ba
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.Sm on
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=
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1/2
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then
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.Fa n
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is even. Consequently
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the remainder is computed exactly and
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.Sm off
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.Pf \\*(Ba Fa r No \\*(Ba
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.Sm on
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\*(Le
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.Sm off
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.Pf \\*(Ba Fa y No \\*(Ba/2.
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.Sm on
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But
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.Fn drem x 0
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is exceptional.
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(See below under
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.Sx DIAGNOSTICS . )
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.Pp
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The
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.Fn finite
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function returns the value 1 just when
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\-\*(If \*(Lt
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.Fa x
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\*(Lt +\*(If;
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otherwise a
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zero is returned
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(when
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.Pf \\*(Ba Ns Fa x Ns \\*(Ba
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= \*(If or
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.Fa x
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is \*(Na or
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is the
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.Tn VAX Ns 's
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reserved operand).
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.Pp
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The
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.Fn logb
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function returns
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.Fa x Ns 's exponent
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.Fa n ,
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a signed integer converted to double\-precision floating\-point and so
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chosen that
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1 (<=
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.Pf \\*(Ba Ns Fa x Ns \\*(Ba2** Ns Fa n
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< 2
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unless
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.Fa x
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= 0 or
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(only on machines that conform to
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.Tn IEEE
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754)
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.Pf \\*(Ba Fa x Ns \\*(Ba
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= \*(If
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or
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.Fa x
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lies between 0 and the Underflow Threshold.
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(See below under
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.Sx BUGS . )
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.Pp
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The
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Fn calb
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returns
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.Fa x Ns \(**(2** Ns Fa n )
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computed, for integer n, without first computing
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.Pf 2\(** Fa n .
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.Sh RETURN VALUES
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The
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.Tn IEEE
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standard
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754 defines
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.Fn drem x 0
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and
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.Fn drem \\*(If y
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to be invalid operations that produce a \*(Na.
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On the
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.Tn VAX ,
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.Fn drem x 0
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generates a reserved operand fault. No \*(If
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exists on a
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.Tn VAX .
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.Pp
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.Tn IEEE
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754 defines
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.if n \
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.Fn logb \(+-\\*(If
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= \*(If and
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.Fn logb 0
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= \-\*(If, and
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requires the latter to signal Division\-by\-Zero.
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But on a
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.Tn VAX ,
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.Fn logb 0
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= 1.0 \- 2.0**31 = \-2,147,483,647.0.
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And if the correct value of
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.Fn scalb
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would overflow on a
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.Tn VAX ,
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it generates a reserved operand fault and sets the global variable
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.Va errno
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to
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.Dv ERANGE .
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.Sh SEE ALSO
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.Xr floor 3 ,
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.Xr math 3 ,
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.Xr infnan 3
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.Sh HISTORY
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The
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.Nm ieee
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functions appeared in
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.Bx 4.3 .
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.Sh BUGS
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Should
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.Fn drem x 0
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and
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.Fn logb 0
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on a
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.Tn VAX
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signal invalidity
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by setting
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.Va errno No = Dv EDOM ?
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Should
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.Fn logb 0
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return \-1.7e38?
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.Pp
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.Tn IEEE
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754 currently specifies that
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.Fn logb "denormalized no."
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=
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.Fn logb "tiniest normalized no. > 0"
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but the consensus has changed to the specification in the new
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proposed
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.Tn IEEE
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standard p854, namely that
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.Fn logb x
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satisfy
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.Bd -filled -offset indent
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1 \(<=
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.Fn scalb \\*(Bax\\*(Ba \-logb(x)
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<
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Radix\0 ... = 2
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for
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.Tn IEEE
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754
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.Ed
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.Pp
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for every x except 0,
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\*(If
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and \*(Na.
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Almost every program that assumes 754's specification will work
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correctly if
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.Fn logb
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follows 854's specification instead.
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.Pp
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.Tn IEEE
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754 requires
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.Fn copysign x \\*(Na)
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=
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.Pf \(+- Ns Fa x
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but says nothing
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else about the sign of a \*(Na. A \*(Na
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.Em N Ns ot
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.Em a
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.Em N Ns umber )
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is
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similar in spirit to the
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.Tn VAX Ns 's
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reserved operand, but very
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different in important details. Since the sign bit of a
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reserved operand makes it look negative,
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.Bd -filled -offset indent
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.Fn copysign x "reserved operand"
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=
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.Pf \- Fa x ;
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.Ed
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.Pp
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should this return the reserved operand instead?
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