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

NAME
     hypot, hypotf, cabs, cabsf - euclidean distance and complex absolute val-
     ue functions



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 { double x; double 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 re-
     sult 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 gener-
     al, hypot and cabs return an integer whenever an integer might be expect-
     ed.

     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 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).

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 Version 7 AT&T
     UNIX.

OpenBSD 2.6                       May 6, 1991                                1