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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
Source: OpenBSD 2.6 man pages. Copyright: Portions are copyrighted by BERKELEY SOFTWARE DESIGN, INC., The Regents of the University of California, Massachusetts Institute of Technology, Free Software Foundation, FreeBSD Inc., and others. 
(Corrections, notes, and links courtesy of RocketAware.com)
FreeBSD Sources for hypot(3) functions FreeBSD Sources for hypot(3) functions OpenBSD sources for hypot(3)
Up to: Floating point math  Floating point math (including complex numbers)
Up to: Trigonometric  Trigonometric functions (sin, cos, tan, et al)
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