HYPOT(3) BSD Programmer's Manual HYPOT(3)
NAME
hypot, cabs  euclidean distance and complex absolute value functions
SYNOPSIS
#include <<math.h>>
double
hypot(double x, double y);
struct {double x, y;} z;
double
cabs(z);
DESCRIPTION
The hypot() and cabs() functions computes the sqrt(x*x+y*y) in such a way
that underflow will not happen, and overflow occurs only if the final re
sult deserves it.
hypot(infinity, v) = hypot(v, infinity) = +infinity for all v, including
NaN.
ERROR (due to Roundoff, etc.)
Below 0.97 ulps. Consequently hypot(5.0, 12.0) = 13.0 exactly; in gener
al, hypot and cabs return an integer whenever an integer might be expect
ed.
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; with "reserved operand" in place of "NaN", the same is true on
a VAX. But programmers on machines other than a VAX (if 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 in
dependent 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.
4th Berkeley Distribution June 4, 1993 1
