.\"	$OpenBSD: hypot.3,v 1.15 2007/05/31 19:19:35 jmc Exp $
.\" 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. 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
.\"
.Dd $Mdocdate: May 31 2007 $
.Dt HYPOT 3
.Os
.Sh NAME
.Nm hypot ,
.Nm hypotf ,
.Nm cabs ,
.Nm cabsf
.Nd Euclidean distance and complex absolute value functions
.Sh SYNOPSIS
.Fd #include <math.h>
.Ft double
.Fn hypot "double x" "double y"
.Ft float
.Fn hypotf "float x" "float y"
.Ft double
.Fn cabs "struct complex { double x; double y; } z"
.Ft float
.Fn cabsf "struct complex { float x; float y; } z"
.Sh DESCRIPTION
The
.Fn hypot
and
.Fn cabs
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 hypotf
and
.Fn cabsf
functions are single precision versions of
.Fn hypot
and
.Fn cabs ,
respectively.
.Pp
.Fn hypot "\*(If" "v"
=
.Fn hypot "v" "\*(If"
= +\*(If for all
.Ar v ,
including \*(Na.
.Sh ERRORS (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
.Ar v ;
with "reserved operand" in place of "\*(Na", the
same is true on a
.Tn VAX .
But programmers on machines other than a
.Tn VAX
(it has no \*(If)
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
.Ar v ,
finite or infinite.
Hence
.Fn hypot "\*(If" "v"
is independent of
.Ar 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 .
.Sh BUGS
The
.Fn cabs
and
.Fn cabsf
functions use structures that are not defined in any header and need to
be defined by the user.
As such they cannot be prototyped properly.