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(+infinity,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

     ORIGIN
          MIPS Computer Systems





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