hypot, hypotf, cabs, cabsf  euclidean distance and complex absolute
value functions
Math Library (libm, lm)
#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);
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.
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.
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).
math(3), sqrt(3)
Both a hypot() function and a cabs() function appeared in Version 7 AT&T
UNIX.
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
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