atan2(3) - NetBSD Manual Pages

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ATAN2(3)                NetBSD Library Functions Manual               ATAN2(3)


NAME

     atan2, atan2f -- arc tangent function of two variables


LIBRARY

     Math Library (libm, -lm)


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 vari-
     able 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 C89'').

NetBSD 3.0.1                      May 2, 1991                     NetBSD 3.0.1