cabs man page on NeXTSTEP

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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.  But programmers 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.  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)
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