HYPOT(3) Library Functions Manual HYPOT(3)
hypot, hypotf -- Euclidean distance and complex absolute value functions
Math Library (libm, -lm)
hypot(double x, double y);
hypotf(float x, float y);
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
hypot(infinity, v) = hypot(v, infinity) = +infinity for all v, including
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.
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).
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.
NetBSD 6.1.5 February 12, 2007 NetBSD 6.1.5