The
hypot ();
and
hypotf ();
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.
The
cabs ();
and
cabsf ();
functions compute the complex absolute value of
Fa z .
hypot ( v);
=
hypot (v );
= + for all
Fa v ,
including .
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 );
and
hypot ( v);
are for all
finite
Fa v .
But programmers
might be surprised at first to discover that
hypot (± );
= +.
This is intentional; it happens because
hypot ( v);
= +
for
all
Fa v ,
finite or infinite.
Hence
hypot ( v);
is independent of
Fa v .
Unlike the reserved operand fault on a
VAX
the
IEEE
is designed to
disappear when it turns out to be irrelevant, as it does in
hypot ( .);
