HYPOT(3) BSD Programmer's Manual HYPOT(3)

hypot,hypotf- Euclidean distance and complex absolute value functions

libm

#include <math.h>doublehypot(double x,double y);floathypotf(float x,float y);

Thehypot() functions compute the sqrt(x*x+y*y) in such a way that under- flow will not happen, and overflow occurs only if the final result deserves it.hypot(Infinity,v) =hypot(v,Infinity) = +Infinity for allv, includingNaN.

Below 0.97ulps. Consequentlyhypot(5.0,12.0) = 13.0 exactly; in gen- eral, hypot returns an integer whenever an integer might be expected. The same cannot be said for the shorter and faster version of hypot that is provided in the comments in cabs.c; its error can exceed 1.2ulps.

As might be expected,hypot(v,NaN) andhypot(NaN,v) areNaNfor allfinite 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 thathypot(±Infinity,NaN) = +In- finity. This is intentional; it happens becausehypot(Infinity,v) = +In- finity forall v, finite or infinite. Hencehypot(Infinity,v) is in- dependent ofv. Unlike the reserved operand fault on a VAX, the IEEENaNis designed to disappear when it turns out to be irrelevant, as it does inhypot(Infinity,NaN).

math(3), sqrt(3)

Both ahypot() function and acabs() function appeared in Version 7 AT&T UNIX.cabs() was removed from public namespace in NetBSD 5.0 to avoid conflicts with the complex function in C99. MirOS BSD #10-current February 12, 2007 1

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