HYPOT(3)                System Library Functions Manual               HYPOT(3)

NAME
     hypot, hypotf, cabs, cabsf, z_abs - Euclidean distance and complex abso-
     lute value functions

SYNOPSIS
     #include 

     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);

     double
     z_abs(struct complex { double x; double y; } *z);

DESCRIPTION
     The hypot(), cabs() and z_abs() 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.

     The z_abs() function works the same as the cabs() function but the argu-
     ment is a pointer.

DIAGNOSTICS
     On success all of the functions return the length of a right-angle trian-
     gle's hypotenuse with the other two sides being x and y.

     On error or overflow then the return value will be Nan with errno being
     set.

ERRORS (due to Roundoff, etc.)
     Below 0.97 ulps.  Consequently hypot(5.0, 12.0) = 13.0 exactly; in gen-
     eral, 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 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
     math(3), sqrt(3)

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

Interix                           May 31 2007                          Interix