HYPOT(3)

NAME
hypot, cabs - euclidean distance and complex absolute value functions

LIBRARY
libm

SYNOPSIS
#include <math.h>
double
hypot(double x, double y);
float
hypotf(float x, float y);
double
cabs(struct complex { double x; double y; } z);
float
cabsf(struct complex { float x; float y; } z);

DESCRIPTION
The hypot() and cabs() functions computes 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(, v) = hypot(v, ) = + for all v, including .

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.

The same cannot be said for the shorter and faster version of hypot and cabs that is provided in the comments in cabs.c; its error can exceed 1.2 ulps.

NOTES
As might be expected, hypot(v, ) and hypot(, v) are for all finite v; with "reserved operand" in place of "", the same is true on a VAX. But programmers on machines other than a VAX (if has no ) might be surprised at first to discover that hypot(±, ) = +. This is intentional; it happens because hypot(, v) = + for all v, finite or infinite. Hence hypot(, v) is independent of v. Unlike the reserved operand fault on a VAX, the IEEE is designed to disappear when it turns out to be irrelevant, as it does in hypot(, ).

BUGS
The cabs() and cabsf() functions use structures that are not defined in any header and need to be defined by the user. As such they cannot be prototyped properly.

SEE ALSO
math(3), sqrt(3)

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