135 lines
3.7 KiB
Groff
135 lines
3.7 KiB
Groff
.\" 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.
|
|
.\" 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.
|
|
.\"
|
|
.\" from: @(#)hypot.3 6.7 (Berkeley) 5/6/91
|
|
.\" $FreeBSD: src/lib/msun/man/hypot.3,v 1.13 2005/01/14 23:28:28 das Exp $
|
|
.\"
|
|
.Dd January 14, 2005
|
|
.Dt HYPOT 3
|
|
.Os
|
|
.Sh NAME
|
|
.Nm hypot ,
|
|
.Nm hypotf ,
|
|
.Nm cabs ,
|
|
.Nm cabsf
|
|
.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"
|
|
.In complex.h
|
|
.Ft double
|
|
.Fn cabs "double complex z"
|
|
.Ft float
|
|
.Fn cabsf "float complex z"
|
|
.Sh DESCRIPTION
|
|
The
|
|
.Fn hypot
|
|
and
|
|
.Fn hypotf
|
|
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
|
|
and
|
|
.Fn cabsf
|
|
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.
|
|
.Pp
|
|
The same cannot be said for the shorter and faster version of hypot
|
|
and cabs that is provided in the comments in cabs.c; its error can
|
|
exceed 1.2
|
|
.Em ulps .
|
|
.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 math 3 ,
|
|
.Xr sqrt 3
|
|
.Sh HISTORY
|
|
Both a
|
|
.Fn hypot
|
|
function and a
|
|
.Fn cabs
|
|
function
|
|
appeared in
|
|
.At v7 .
|