NAME    [Toc]    [Back]

     atan2, atan2f - arc tangent functions of two variables

SYNOPSIS    [Toc]    [Back]

     #include <math.h>

     double
     atan2(double y, double x);

     float
     atan2f(float y, float x);

DESCRIPTION    [Toc]    [Back]

     The atan2() function computes the principal value of the arc
tangent of
     y/x,  using  the  signs  of  both arguments to determine the
quadrant of the
     return value.  The atan2f() function is a  single  precision
version of
     atan2().

RETURN VALUES    [Toc]    [Back]

     The  atan2()  and  atan2f() functions, if successful, return
the arc tangent
     of y/x in the range [-pi, +pi] radians.  If both x and y are
zero, the
     global variable errno is set to EDOM.  On the VAX:

     atan2(y, x):=        atan(y/x)            if x > 0,
                          sign(y)*(pi - atan(|y/x|))         if x
< 0,
                          0                    if x = y = 0, or
                          sign(y)*pi/2         if x = 0 y.

NOTES    [Toc]    [Back]

     The function atan2() defines "if x > 0," atan2(0, 0) = 0  on
a VAX despite
     that previously atan2(0, 0) may have generated an error message.  The
     reasons for assigning a value to atan2(0, 0) are these:

           1.   Programs that test arguments to  avoid  computing
atan2(0, 0)
                must  be indifferent to its value.  Programs that
require it to
                be invalid are vulnerable to diverse reactions to
that invalidity
 on diverse computer systems.

           2.    The  atan2()  function is used mostly to convert
from rectangular
 (x,y) to  polar  (r,theta)  coordinates  that
must satisfy x =
                r*cos theta and y = r*sin theta.  These equations
are satisfied
 when (x=0,y=0) is mapped to (r=0,theta=0) on
a VAX.  In
                general,  conversions to polar coordinates should
be computed
                thus:

                      r    := hypot(x,y);  ... := sqrt(x*x+y*y)
                      theta     := atan2(y,x).

           3.   The foregoing formulas need  not  be  altered  to
cope in a reasonable
 way with signed zeros and infinities on a
machine that
                conforms to IEEE 754; the  versions  of  hypot(3)
and atan2()
                provided  for such a machine are designed to handle all cases.
                That is why atan2(+-0, -0) = +-pi  for  instance.
In general
                the formulas above are equivalent to these:

                      r  :=  sqrt(x*x+y*y);  if  r  = 0 then x :=
copysign(1,x);

SEE ALSO    [Toc]    [Back]

     acos(3), asin(3), atan(3), cos(3), cosh(3), math(3), sin(3),
sinh(3),
     tan(3), tanh(3)

STANDARDS    [Toc]    [Back]

     The  atan2()  function  conforms to ANSI X3.159-1989 (``ANSI
C'').

OpenBSD      3.6                            May      2,      1991