HYPOT(3)                  386BSD Programmer's Manual                  HYPOT(3)

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

SYNOPSIS
     #include <math.h>

     double
     hypot(double x, double y)

     struct {double x, y;} z;

     double
     cabs(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(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.

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

4th Berkeley Distribution         May 6, 1991                                1