NAME
hypot, hypotf,
hypotl —
Euclidean distance and complex absolute
value functions
LIBRARY
library “libm”
SYNOPSIS
#include
<math.h>
double
hypot(double
x, double y);
float
hypotf(float
x, float y);
long double
hypotl(long
double x, long double
y);
#include
<tgmath.h>
real-floating
hypot(real-floating,
real-floating);
DESCRIPTION
Thehypot()
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
HISTORY
The hypot() appeared in
Version 7 AT&T UNIX.