ATAN2(3)                  386BSD Programmer's Manual                  ATAN2(3)

NAME
     atan2 - arc tangent function of two variables

SYNOPSIS
     #include <math.h>

     double
     atan2(double y, double x)

DESCRIPTION
     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.

RETURN VALUES
     The atan2 function, if successful, returns 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
     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
     acos(3),  asin(3),  atan(3),  cos(3),  cosh(3),  sin(3),  sinh(3),
     tan(3),  tanh(3),  math(3),

STANDARDS
     The atan2() function conforms to ANSI C3.159-1989 (``ANSI C'').

BSD Experimental                  May 2, 1991                                1