124 lines
3.4 KiB
Groff
124 lines
3.4 KiB
Groff
.\" $OpenBSD: hypot.3,v 1.26 2021/06/29 14:47:33 schwarze Exp $
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.\" 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. 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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.\"
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.Dd $Mdocdate: June 29 2021 $
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.Dt HYPOT 3
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.Os
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.Sh NAME
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.Nm hypot ,
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.Nm hypotf ,
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.Nm hypotl ,
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.Nm cabs ,
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.Nm cabsf ,
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.Nm cabsl
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.Nd Euclidean distance and complex absolute value functions
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.Sh SYNOPSIS
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.In math.h
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.Ft double
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.Fn hypot "double x" "double y"
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.Ft float
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.Fn hypotf "float x" "float y"
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.Ft long double
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.Fn hypotl "long double x" "long double y"
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.In complex.h
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.Ft double
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.Fn cabs "double complex z"
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.Ft float
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.Fn cabsf "float complex z"
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.Ft long double
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.Fn cabsl "long double complex z"
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.Sh DESCRIPTION
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The
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.Fn hypot ,
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.Fn hypotf
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and
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.Fn hypotl
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functions
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compute 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 "infinity" "v" No = Fn hypot "v" "infinity" No = +infinity
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for all
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.Fa v ,
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including NaN.
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.Pp
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The
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.Fn cabs ,
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.Fn cabsf
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and
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.Fn cabsl
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functions return the absolute value of the complex number
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.Fa z .
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.Sh ERRORS (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" No = 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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.Sh NOTES
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As might be expected,
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.Fn hypot "v" "NaN"
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and
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.Fn hypot "NaN" "v"
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are NaN for all
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.Em finite
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.Fa v .
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Programmers might be surprised at first to discover that
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.Fn hypot "\(+-infinity" "NaN" No = +infinity .
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This is intentional; it happens because
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.Fn hypot "infinity" "v" No = +infinity
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for
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.Em all
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.Fa v ,
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finite or infinite.
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Hence
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.Fn hypot "infinity" "v"
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is independent of
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.Fa v .
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The IEEE NaN is designed to disappear
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when it turns out to be irrelevant, as it does in
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.Fn hypot "infinity" "NaN" .
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.Sh SEE ALSO
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.Xr fpclassify 3 ,
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.Xr sqrt 3
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.Sh HISTORY
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A
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.Fn hypot
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function first appeared in
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.At v2 ,
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and
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.Fn cabs
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in
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.At v7 .
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