ATAN2(3)                  OpenBSD Programmer's Manual                 ATAN2(3)

NAME
     atan2, atan2f - arc tangent functions of two variables



SYNOPSIS
     #include <math.h>

     double
     atan2(double y, double x);

     float
     atan2f(float y, float x);

DESCRIPTION
     The atan2() and atan2f() functions compute the principal value of the arc
     tangent of y/x, using the signs of both arguments to determine the quad-
     rant 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 inva-
                lidity on diverse computer systems.

           2.   The atan2() function is used mostly to convert from rectangu-
                lar (x,y) to polar (r,theta) coordinates that must satisfy x =
                r*cos theta and y = r*sin theta.  These equations are satis-
                fied 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 rea-
                sonable 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),  math(3),  sin(3),
     sinh(3),  tan(3),  tanh(3)

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

OpenBSD 2.6                       May 2, 1991                                1