HYPOT(3)

HYPOT(3) | Library Functions Manual | HYPOT(3)

# 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).

# SEE ALSO

math(3), sqrt(3)

# HISTORY

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

September 26, 2017 | NetBSD 9.0