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# Manual Reference Pages  -  HYPOTL (3)

### NAME

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

### CONTENTS

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

.Lb libm

### SYNOPSIS

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

### DESCRIPTION

The hypot, hypotf and hypotl 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, cabsf and cabsl functions compute the complex absolute value of z.

hypot oo v = hypot v oo = +oo 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.

### 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 ±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.

carg(3), math(3), sqrt(3)

### STANDARDS

The hypot, hypotf, hypotl, cabs, cabsf, and cabsl functions conform to -isoC-99.

### HISTORY

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