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.\"     from: @(#)hypot.3	6.7 (Berkeley) 5/6/91
.\"
.Dd $Mdocdate: April 27 2016 $
.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 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.
.Pp
.Fn hypot "infinity" "v" No = Fn hypot "v" "infinity" No = +infinity
for all
.Ar v ,
including NaN.
.Pp
The
.Fn cabs ,
.Fn cabsf
and
.Fn cabsl
functions return the absolute value of the complex number
.Fa z .
.Sh ERRORS (due to Roundoff, etc.)
Below 0.97
.Em ulps .
Consequently
.Fn hypot "5.0" "12.0" No = 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" "NaN"
and
.Fn hypot "NaN" "v"
are NaN for all
.Em finite
.Ar v .
Programmers might be surprised at first to discover that
.Fn hypot "\(+-infinity" "NaN" No = +infinity .
This is intentional; it happens because
.Fn hypot "infinity" "v" No = +infinity
for
.Em all
.Ar v ,
finite or infinite.
Hence
.Fn hypot "infinity" "v"
is independent of
.Ar v .
The IEEE NaN is designed to disappear
when it turns out to be irrelevant, as it does in
.Fn hypot "infinity" "NaN" .
.Sh SEE ALSO
.Xr fpclassify 3 ,
.Xr sqrt 3
.Sh HISTORY
A
.Fn hypot
function first appeared in
.At v3 ,
and
.Fn cabs
in
.At v7 .