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-- Begin comments from J.T. Conklin: The most significant improvement is the addition of "float" versions of the math functions that take float arguments, return floats, and do all operations in floating point. This doesn't help (performance) much on the i386, but they are still nice to have. The float versions were orginally done by Cygnus' Ian Taylor when fdlibm was integrated into the libm we support for embedded systems. I gave Ian a copy of my libm as a starting point since I had already fixed a lot of bugs & problems in Sun's original code. After he was done, I cleaned it up a bit and integrated the changes back into my libm. -- End comments Reviewed by: jkh Submitted by: jtc
126 lines
3.6 KiB
Groff
126 lines
3.6 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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.\" from: @(#)hypot.3 6.7 (Berkeley) 5/6/91
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.\" $Id: hypot.3,v 1.3 1993/08/14 13:42:48 mycroft Exp $
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.\"
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.Dd May 6, 1991
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.Dt HYPOT 3
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.Os BSD 4
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.Sh NAME
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.Nm hypot ,
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.Nm cabs
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.Nd euclidean distance and complex absolute value functions
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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 hypot "double x" "double y"
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.Fd struct {double x, y;} z;
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.Ft double
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.Fn cabs z
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.Sh DESCRIPTION
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The
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.Fn hypot
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and
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.Fn cabs
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functions
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computes the
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sqrt(x*x+y*y)
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in such a way that underflow will not happen, and overflow
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occurs only if the final result deserves it.
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.Pp
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.Fn hypot "\*(If" "v"
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=
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.Fn hypot "v" "\*(If"
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= +\*(If for all
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.Ar v ,
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including \*(Na.
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.Sh ERROR (due to Roundoff, etc.)
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Below 0.97
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.Em ulps .
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Consequently
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.Fn hypot "5.0" "12.0"
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= 13.0
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exactly;
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in general, hypot and cabs return an integer whenever an
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integer might be expected.
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.Pp
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The same cannot be said for the shorter and faster version of hypot
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and cabs that is provided in the comments in cabs.c; its error can
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exceed 1.2
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.Em ulps .
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.Sh NOTES
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As might be expected,
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.Fn hypot "v" "\*(Na"
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and
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.Fn hypot "\*(Na" "v"
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are \*(Na for all
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.Em finite
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.Ar v ;
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with "reserved operand" in place of "\*(Na", the
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same is true on a
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.Tn VAX .
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But programmers on machines other than a
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.Tn VAX
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(if has no \*(If)
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might be surprised at first to discover that
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.Fn hypot "\(+-\*(If" "\*(Na"
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= +\*(If.
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This is intentional; it happens because
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.Fn hypot "\*(If" "v"
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= +\*(If
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for
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.Em all
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.Ar v ,
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finite or infinite.
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Hence
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.Fn hypot "\*(If" "v"
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is independent of
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.Ar v .
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Unlike the reserved operand fault on a
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.Tn VAX ,
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the
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.Tn IEEE
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\*(Na is designed to
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disappear when it turns out to be irrelevant, as it does in
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.Fn hypot "\*(If" "\*(Na" .
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.Sh SEE ALSO
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.Xr math 3 ,
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.Xr sqrt 3
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.Sh HISTORY
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Both a
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.Fn hypot
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function and a
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.Fn cabs
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function
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appeared in
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.At v7 .
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