HYPOT

Section: Mathematical Library (3M)
Updated: May 12, 1986
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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; 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 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 on a VAX, the IEEE NaN is designed to disappear when it turns out to be irrelevant, as it does in hypot(infinity,NaN).

AUTHOR

W. Kahan

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