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@(#)hypot.3 6.4 (Berkeley) 09/11/85

C 4 hypot, cabs - Euclidean distance, complex absolute value

 #include <math.h> 

 double hypot(x,y)  double x,y; 

 double cabs(z)  struct {double x,y;} z; 

Hypot(x,y) and cabs(x,y) return sqrt(x\(**x+y\(**y) computed in such a way that underflow will not happen, and overflow occurs only if the final result deserves it.

hypot(infinity,v) = hypot(v,infinity) = +infinity for all v, hypot(\(if,v) = hypot(v,\(if) = +\(if for all v, including \*(nn.

intro(3M), sqrt(3M) Below 0.97 \*(ups. Consequently hypot(5.0,12.0)\0=\013.0 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 \*(ups.

As might be expected, hypot(v,\*(nn) and hypot(\*(nn,v) are \*(nn for all finite v; with "reserved operand" in place of "\*(nn", the same is true on a VAX. But programmers on machines other than a VAX (it has no infinity) \(if) might be surprised at first to discover that hypot(\(+-infinity,\*(nn) = +infinity. hypot(\(+-\(if,\*(nn) = +\(if. This is intentional; it happens because hypot(infinity,v) = +infinity hypot(\(if,v) = +\(if for all v, finite or infinite. Hence hypot(infinity,v) hypot(\(if,v) is independent of v. Unlike the reserved operand on a VAX, the IEEE \*(nn is designed to disappear when it turns out to be irrelevant, as it does in hypot(infinity,\*(nn). hypot(\(if,\*(nn). W. Kahan