NAME    [Toc]    [Back]

     hypot, hypotf, cabs, cabsf - Euclidean distance and  complex
absolute value
 functions

SYNOPSIS    [Toc]    [Back]

     #include <math.h>

     double
     hypot(double x, double y);

     float
     hypotf(float x, float y);

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

     float
     cabsf(struct complex { float x; float y; } z);

DESCRIPTION    [Toc]    [Back]

     The  hypot()  and cabs() functions compute the sqrt(x*x+y*y)
in such a way
     that underflow will not happen, and overflow occurs only  if
the final result
  deserves  it.   The hypotf() and cabsf() functions are
single precision
 versions of hypot() and cabs(), respectively.

     hypot(Infinity, v) = hypot(v, Infinity) = +Infinity for  all
v, including
     NaN.

ERRORS (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    [Toc]    [Back]

     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 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).

SEE ALSO    [Toc]    [Back]

     math(3), sqrt(3)

HISTORY    [Toc]    [Back]

     Both  a  hypot()  function and a cabs() function appeared in
Version 7 AT&T
     UNIX.

BUGS    [Toc]    [Back]

     The cabs() and cabsf() functions use structures that are not
defined in
     any header and need to be defined by the user.  As such they
cannot be
     prototyped properly.

OpenBSD      3.6                            May      6,      1991