NAME
hypot,
hypotf —
Euclidean distance and complex absolute value
functions
LIBRARY
Math Library (libm, -lm)
SYNOPSIS
#include <math.h>
double
hypot(
double
x,
double y);
float
hypotf(
float
x,
float y);
DESCRIPTION
The
hypot() 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.
hypot(
infinity,
v)
=
hypot(
v,
infinity) = +infinity for all
v,
including NaN.
ERRORS
Below 0.97
ulps. Consequently
hypot(
5.0,
12.0)
= 13.0 exactly; in general, hypot returns an integer whenever an integer might
be expected.
The same cannot be said for the shorter and faster version of hypot 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; with
"reserved operand" in place of "NaN", the same is true on
a VAX. But programmers on machines other than a VAX (it has no infinity) might
be surprised at first to discover that
hypot(
±infinity,
NaN) = +infinity. This is intentional; it happens
because
hypot(
infinity,
v) = +infinity for
all
v, finite or infinite. Hence
hypot(
infinity,
v) is independent of
v. Unlike the
reserved operand fault on a VAX, the IEEE NaN is designed to disappear when it
turns out to be irrelevant, as it does in
hypot(
infinity,
NaN).
SEE ALSO
math(3),
sqrt(3)
HISTORY
Both a
hypot() function and a
cabs()
function appeared in
Version 7 AT&T UNIX.
cabs() was removed from public namespace in
NetBSD 5.0 to avoid conflicts with the complex
function in C99.