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Manual Pages  — HYPOT


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



Math Library (libm, -lm)


#include <math.h>

hypot(double x, double y);

hypotf(float x, float y);

long double
hypotl(long double x, long double y);
#include <complex.h>

cabs(double complex z);

cabsf(float complex z);

long double
cabsl(long double complex z);


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(∞, v) = hypot(v, ∞) = +∞ 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.


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(±∞, NaN) = +∞. This is intentional; it happens because hypot(∞, v) = +∞ for all v, finite or infinite. Hence hypot(∞, 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(∞, NaN).


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


The hypot(), hypotf(), hypotl(), cabs(), cabsf(), and cabsl() functions conform to ISO/IEC 9899:1999 ("ISO C99").


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

HYPOT (3) March 30, 2008

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