HYPOT(3) BSD Programmer's Manual HYPOT(3)
hypot, hypotf - Euclidean distance and complex absolute value functions
#include <math.h> double hypot(double x, double y); float hypotf(float x, float y);
The hypot() 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 all v, including NaN.
Below 0.97 ulps. Consequently hypot(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 1.2 ulps.
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) = +In- finity. This is intentional; it happens because hypot(Infinity, v) = +In- finity for all v, finite or infinite. Hence hypot(Infinity, v) is in- dependent 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(Infinity, NaN).
Both a hypot() function and a cabs() 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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