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HYPOT(3) Library Functions Manual HYPOT(3)


hypot, hypotf, hypotl, cabs, cabsf, cabslEuclidean distance and complex absolute value functions


#include <math.h>
hypot(double x, double y);
hypotf(float x, float y);
long double
hypotl(long double x, long double y);
#include <complex.h>
cabs(double complex z);
cabsf(float complex z);
long double
cabsl(long double complex z);


The hypot(), hypotf() and hypotl() 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.
The cabs(), cabsf() and cabsl() functions return the absolute value of the complex number z.

ERRORS (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.


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).




A hypot() function first appeared in Version 3 AT&T UNIX, and cabs() in Version 7 AT&T UNIX.
July 17, 2013 OpenBSD-5.6