NAME

hypot, hypotf, hypotl, cabs, cabsf, cabsl —

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 <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. The cabs(), cabsf() and cabsl() functions compute the complex absolute value of z.

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 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. But 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. 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).

STANDARDS

The hypot(), hypotf(), hypotl(), cabs(), cabsf(), and cabsl() functions conform to ISO/IEC 9899:1999 (“ISO C99”).

HISTORY

Both a hypot() function and a cabs() function appeared in Version 7 AT&T UNIX.