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.\" Copyright (c) 1985, 1991 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.
.\" 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.
.\"
.\" from: @(#)hypot.3 6.7 (Berkeley) 5/6/91
.\" $FreeBSD$
.\"
.Dd March 30, 2008
.Dt HYPOT 3
.Os
.Sh NAME
.Nm hypot ,
.Nm hypotf ,
.Nm hypotl ,
.Nm cabs ,
.Nm cabsf ,
.Nm cabsl
.Nd Euclidean distance and complex absolute value functions
.Sh LIBRARY
.Lb libm
.Sh SYNOPSIS
.In math.h
.Ft double
.Fn hypot "double x" "double y"
.Ft float
.Fn hypotf "float x" "float y"
.Ft "long double"
.Fn hypotl "long double x" "long double y"
.In complex.h
.Ft double
.Fn cabs "double complex z"
.Ft float
.Fn cabsf "float complex z"
.Ft "long double"
.Fn cabsl "long double complex z"
.Sh DESCRIPTION
The
.Fn hypot ,
.Fn hypotf
and
.Fn hypotl
functions
compute the
sqrt(x*x+y*y)
in such a way that underflow will not happen, and overflow
occurs only if the final result deserves it.
The
.Fn cabs ,
.Fn cabsf
and
.Fn cabsl
functions compute the complex absolute value of
.Fa z .
.Pp
.Fn hypot "\*(If" "v"
=
.Fn hypot "v" "\*(If"
= +\*(If for all
.Fa v ,
including \*(Na.
.Sh ERROR (due to Roundoff, etc.)
Below 0.97
.Em ulps .
Consequently
.Fn hypot "5.0" "12.0"
= 13.0
exactly;
in general, hypot and cabs return an integer whenever an
integer might be expected.
.Sh NOTES
As might be expected,
.Fn hypot "v" "\*(Na"
and
.Fn hypot "\*(Na" "v"
are \*(Na for all
.Em finite
.Fa v .
But programmers
might be surprised at first to discover that
.Fn hypot "\(+-\*(If" "\*(Na"
= +\*(If.
This is intentional; it happens because
.Fn hypot "\*(If" "v"
= +\*(If
for
.Em all
.Fa v ,
finite or infinite.
Hence
.Fn hypot "\*(If" "v"
is independent of
.Fa v .
Unlike the reserved operand fault on a
.Tn VAX ,
the
.Tn IEEE
\*(Na is designed to
disappear when it turns out to be irrelevant, as it does in
.Fn hypot "\*(If" "\*(Na" .
.Sh SEE ALSO
.Xr carg 3 ,
.Xr math 3 ,
.Xr sqrt 3
.Sh HISTORY
Both a
.Fn hypot
function and a
.Fn cabs
function
appeared in
.At v7 .
.Sh STANDARDS
The
.Fn hypot ,
.Fn hypotf ,
.Fn hypotl ,
.Fn cabs ,
.Fn cabsf ,
and
.Fn cabsl
functions conform to
.St -isoC-99 .
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