HYPOT(3M)																 HYPOT(3M)

NAME

       hypot, cabs - Euclidean distance, complex absolute value

SYNOPSIS

       #include <math.h>

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

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

DESCRIPTION

       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, 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.

       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 ulps.

NOTES

       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(+-infin-
       ity,NaN) = +infinity.  This is intentional; it happens because hypot(infinity,v)  =  +infinity  for  all  v,  finite  or  infinite.   Hence
       hypot(infinity,v) is independent of v.  Unlike the reserved operand on a VAX, the IEEE NaN is designed to disappear when it turns out to be
       irrelevant, as it does in hypot(infinity,NaN).

SEE ALSO

       math(3M), sqrt(3M)

AUTHOR

       W. Kahan

4th Berkeley Distribution					   May 12, 1986 							 HYPOT(3M)