ATAN2(3)               FreeBSD Library Functions Manual               ATAN2(3)

NAME
     atan2, atan2f, atan2l, carg, cargf, cargl - arc tangent and complex phase
     angle functions

LIBRARY
     Math Library (libm, -lm)

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);

     #include <complex.h>

     double
     carg(double complex z);

     float
     cargf(float complex z);

     long double
     cargl(long double complex z);

DESCRIPTION
     The atan2(), atan2f(), and atan2l() functions compute 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 carg(), cargf(), and cargl() functions compute the complex argument
     (or phase angle) of z.  The complex argument is the number theta such
     that z = r * e^(I * theta), where r = cabs(z).  The call carg(z) is
     equivalent to atan2(cimag(z), creal(z)), and similarly for cargf() and
     cargl().

RETURN VALUES
     The atan2(), atan2f(), and atan2l() functions, if successful, return the
     arc tangent of y/x in the range [-pi, +pi] radians.  Here are some of the
     special cases:

     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 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).  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), cabs(3), cos(3), cosh(3), math(3), sin(3),
     sinh(3), tan(3), tanh(3)

STANDARDS
     The atan2(), atan2f(), atan2l(), carg(), cargf(), and cargl() functions
     conform to ISO/IEC 9899:1999 ("ISO C99").

FreeBSD 13.1-RELEASE-p6          July 31, 2008         FreeBSD 13.1-RELEASE-p6