NAME

hypot, hypotf, hypotl — 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);

long double
hypotl(long double x, long double y);

#include <tgmath.h>

real-floating
hypot(real-floating, real-floating);

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).

HISTORY

The hypot() appeared in Version 7 AT&T UNIX.