HYPOT(3) BSD Programmer's Manual HYPOT(3)

**hypot**, **hypotf** - Euclidean distance and complex absolute value functions

libm

**#include <math.h>**
*double*
**hypot**(*double x*, *double y*);
*float*
**hypotf**(*float x*, *float y*);

The **hypot**() functions compute the sqrt(x*x+y*y) in such a way that under-
flow 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*.

Below 0.97 *ulps*. Consequently **hypot**(*5.0*, *12.0*) = 13.0 exactly; in gen-
eral, 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*.

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*) = +In-
finity. This is intentional; it happens because **hypot**(*Infinity*, *v*) = +In-
finity for *all v*, finite or infinite. Hence **hypot**(*Infinity*, *v*) is in-
dependent 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*).

math(3), sqrt(3)

Both a **hypot**() function and a **cabs**() function appeared in Version 7 AT&T
UNIX. **cabs**() was removed from public namespace in NetBSD 5.0 to avoid
conflicts with the complex function in C99.
MirBSD #10-current February 12, 2007 1