Manual page for HYPOT(3M)
hypot, cabs - Euclidean distance, complex absolute value
SYNOPSIS
#include <math.h>
double hypot(x,y)
double x,y;
double cabs(z)
struct {double x,y;} z;
DESCRIPTION
Hypot(x,y) and cabs(x,y) return sqrt(x*x+y*y)
computed in such a way that underflow will not happen, and overflow
occurs only if the final result deserves it.
hypot(\(if,v) = hypot(v,\(if) = +\(if for all v,
including NaN.
ERROR (due to Roundoff, etc.)
Below 0.97 ulps. Consequently hypot(5.0,12.0) = 13.0 exactly;
in general, hypot and cabs return an integer whenever an
integer might be expected.
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 ulps.
NOTES
As might be expected, hypot(v,NaN) and hypot(NaN,v) are NaN for all
finite v. But programmers
might be surprised at first to discover that
hypot(±\(if,NaN) = +\(if.
This is intentional; it happens because
hypot(\(if,v) = +\(if
for all v, finite or infinite.
Hence
hypot(\(if,v)
is independent of v.
The IEEE NaN is designed to
disappear when it turns out to be irrelevant, as it does in
hypot(\(if,NaN).
SEE ALSO
math(3M), sqrt(3M)
AUTHOR
W. Kahan
Created by unroff & hp-tools.
© somebody (See intro for details). All Rights Reserved.
Last modified 11/5/97
