hypot, hypotf, cabs, cabsf - Euclidean distance and complex absolute value functions

CONTENTS

Library
Synopsis
Description
ERROR (due to Roundoff, etc.)
Notes
See Also
History

.Lb libm

.In math.h double hypot double x double y float hypotf float x float y
.In complex.h double cabs double complex z float cabsf float complex z

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 z.

hypot oo v = hypot v oo = +oo 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. But programmers might be surprised at first to discover that hypot ±oo NaN = +oo. This is intentional; it happens because hypot oo v = +oo for all v, finite or infinite. Hence hypot oo 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 oo NaN.

math(3), sqrt(3)

Both a hypot function and a cabs function appeared in AT&T v7 .

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