NAME

hypot, hypotf, hypotl, cabs, cabsf, cabsl — Euclidean distance and complex absolute value functions

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 <complex.h>

double
cabs(double complex z);

float
cabsf(float complex z);

long double
cabsl(long double complex z);

DESCRIPTION

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.

NOTES

As might be expected, hypot(v, NaN) and hypot(NaN, v) are NaN for all finite v. Programmers 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. The IEEE NaN is designed to disappear when it turns out to be irrelevant, as it does in hypot(infinity, NaN).

SEE ALSO

fpclassify(3), sqrt(3)

HISTORY

A hypot() function first appeared in Version 2 AT&T UNIX, and cabs() in Version 7 AT&T UNIX.