HYPOT(3M)HYPOT(3M)NAME
hypot, cabs - Euclidean distance, complex absolute value
SYNOPSIS
#include <math.h>
double hypot(x,y)
double x,y;
double cabs(z)
struct {double x,y;} z;
DESCRIPTION
Hypot(x,y) and cabs(x,y) return sqrt(x∗x+y∗y) computed 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.
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,NaN) and hypot(NaN,v) are NaN for all
finite v. But programmers 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. The IEEE NaN is designed
to disappear when it turns out to be irrelevant, as it does in
hypot(infinity,NaN).
SEE ALSOmath(3M), sqrt(3M)AUTHOR
W. Kahan
4th Berkeley Distribution May 12, 1986 HYPOT(3M)