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.\"     from: @(#)hypot.3	6.7 (Berkeley) 5/6/91
.\" $FreeBSD$
.\"
.Dd May 6, 1991
.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
.Ar z .
.Pp
.Fn hypot "\*(If" "v"
=
.Fn hypot "v" "\*(If"
= +\*(If for all
.Ar 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
.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
(if 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 .