HYPOT(3) BSD Library Functions Manual HYPOT(3)NAME
hypot, hypotf, cabs, cabsf — Euclidean distance and complex absolute
value functions
LIBRARY
Math Library (libm, -lm)
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 compute 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 NaN.
ERRORS
Below 0.97 ulps. Consequently hypot(5.0, 12.0) = 13.0 exactly; in gen‐
eral, 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 (it has no ∞) might
be surprised at first to discover that hypot(±∞, NaN) = +∞. 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 NaN is designed to disappear when it
turns out to be irrelevant, as it does in hypot(∞, NaN).
SEE ALSOmath(3), sqrt(3)HISTORY
Both a hypot() function and a cabs() function appeared in Version 7 AT&T
UNIX.
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.
BSD May 6, 1991 BSD
