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ATAN2(3)              DragonFly Library Functions Manual              ATAN2(3)


NAME

     atan2, atan2f, atan2l -- arc tangent functions of two variables


SYNOPSIS

     #include <math.h>

     double
     atan2(double y, double x);

     float
     atan2f(float y, float x);

     long double
     atan2l(long double y, long 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.  The atan2f() function is a single precision version of
     atan2().  The atan2l() function is an extended precision version of
     atan2().


RETURN VALUES

     The atan2(), atan2f() and atan2l() 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 != 0.


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)


STANDARDS

     The atan2() function conforms to ANSI X3.159-1989 (``ANSI C89'').

DragonFly 4.1                  January 15, 2015                  DragonFly 4.1

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