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



PPRROOLLOOGG
       This manual page is part of the POSIX Programmer's Manual.  The OS
       implementation of this interface may differ (consult the corresponding
       OS manual page for details of OS behavior), or the interface may not be
       implemented on OS.

NNAAMMEE
       atan2, atan2f, atan2l -- arc tangent functions

SSYYNNOOPPSSIISS
       #include <math.h>

       double atan2(double _y, double _x);
       float atan2f(float _y, float _x);
       long double atan2l(long double _y, long double _x);

DDEESSCCRRIIPPTTIIOONN
       The functionality described on this reference page is aligned with the
       ISO C standard. Any conflict between the requirements described here
       and the ISO C standard is unintentional. This volume of POSIX.1-2017
       defers to the ISO C standard.

       These functions shall 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.

       An application wishing to check for error situations should set _e_r_r_n_o
       to zero and call _f_e_c_l_e_a_r_e_x_c_e_p_t(FE_ALL_EXCEPT) before calling these
       functions. On return, if _e_r_r_n_o is non-zero or _f_e_t_e_s_t_e_x_c_e_p_t(FE_INVALID |
       FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW) is non-zero, an error has
       occurred.

RREETTUURRNN VVAALLUUEE
       Upon successful completion, these functions shall return the arc
       tangent of _y/_x in the range [-<pi>,<pi>] radians.

       If _y is +-0 and _x is < 0, +-<pi> shall be returned.

       If _y is +-0 and _x is > 0, +-0 shall be returned.

       If _y is < 0 and _x is +-0, -<pi>/2 shall be returned.

       If _y is > 0 and _x is +-0, <pi>/2 shall be returned.

       If _x is 0, a pole error shall not occur.

       If either _x or _y is NaN, a NaN shall be returned.

       If the correct value would cause underflow, a range error may occur,
       and _a_t_a_n(), _a_t_a_n_2_f(), and _a_t_a_n_2_l() shall return an implementation-
       defined value no greater in magnitude than DBL_MIN, FLT_MIN, and
       LDBL_MIN, respectively.

       If the IEC 60559 Floating-Point option is supported, _y/_x should be
       returned.

       If _y is +-0 and _x is -0, +-<pi> shall be returned.

       If _y is +-0 and _x is +0, +-0 shall be returned.

       For finite values of +-_y > 0, if _x is -Inf, +-<pi> shall be returned.

       For finite values of +-_y > 0, if _x is +Inf, +-0 shall be returned.

       For finite values of _x, if _y is +-Inf, +-<pi>/2 shall be returned.

       If _y is +-Inf and _x is -Inf, +-3<pi>/4 shall be returned.

       If _y is +-Inf and _x is +Inf, +-<pi>/4 shall be returned.

       If both arguments are 0, a domain error shall not occur.

EERRRROORRSS
       These functions may fail if:

       Range Error The result underflows.

                   If the integer expression (_m_a_t_h___e_r_r_h_a_n_d_l_i_n_g & MATH_ERRNO)
                   is non-zero, then _e_r_r_n_o shall be set to [[EERRAANNGGEE]].  If the
                   integer expression (_m_a_t_h___e_r_r_h_a_n_d_l_i_n_g & MATH_ERREXCEPT) is
                   non-zero, then the underflow floating-point exception shall
                   be raised.

       _T_h_e _f_o_l_l_o_w_i_n_g _s_e_c_t_i_o_n_s _a_r_e _i_n_f_o_r_m_a_t_i_v_e_.

EEXXAAMMPPLLEESS
   CCoonnvveerrttiinngg CCaarrtteessiiaann ttoo PPoollaarr CCoooorrddiinnaatteess SSyysstteemm
       The function below uses _a_t_a_n_2() to convert a 2d vector expressed in
       cartesian coordinates (_x,_y) to the polar coordinates (_r_h_o,_t_h_e_t_a).
       There are other ways to compute the angle _t_h_e_t_a, using _a_s_i_n() _a_c_o_s(),
       or _a_t_a_n().  However, _a_t_a_n_2() presents here two advantages:

        *  The angle's quadrant is automatically determined.

        *  The singular cases (0,_y) are taken into account.

       Finally, this example uses _h_y_p_o_t() rather than _s_q_r_t() since it is
       better for special cases; see _h_y_p_o_t() for more information.


           #include <math.h>

           void
           cartesian_to_polar(const double x, const double y,
                              double *rho, double *theta
               )
           {
               *rho   = hypot (x,y); /* better than sqrt(x*x+y*y) */
               *theta = atan2 (y,x);
           }

AAPPPPLLIICCAATTIIOONN UUSSAAGGEE
       On error, the expressions (_m_a_t_h___e_r_r_h_a_n_d_l_i_n_g & MATH_ERRNO) and
       (_m_a_t_h___e_r_r_h_a_n_d_l_i_n_g & MATH_ERREXCEPT) are independent of each other, but
       at least one of them must be non-zero.

RRAATTIIOONNAALLEE
       None.

FFUUTTUURREE DDIIRREECCTTIIOONNSS
       None.

SSEEEE AALLSSOO
       _a_c_o_s(), _a_s_i_n(), _a_t_a_n(), _f_e_c_l_e_a_r_e_x_c_e_p_t(), _f_e_t_e_s_t_e_x_c_e_p_t(), _h_y_p_o_t(),
       _i_s_n_a_n(), _s_q_r_t(), _t_a_n()

       The Base Definitions volume of POSIX.1-2017, _S_e_c_t_i_o_n _4_._2_0, _T_r_e_a_t_m_e_n_t _o_f
       _E_r_r_o_r _C_o_n_d_i_t_i_o_n_s _f_o_r _M_a_t_h_e_m_a_t_i_c_a_l _F_u_n_c_t_i_o_n_s, <<mmaatthh..hh>>

CCOOPPYYRRIIGGHHTT
       Portions of this text are reprinted and reproduced in electronic form
       from IEEE Std 1003.1-2017, Standard for Information Technology --
       Portable Operating System Interface (POSIX), The Open Group Base
       Specifications Issue 7, 2018 Edition, Copyright (C) 2018 by the
       Institute of Electrical and Electronics Engineers, Inc and The Open
       Group.  In the event of any discrepancy between this version and the
       original IEEE and The Open Group Standard, the original IEEE and The
       Open Group Standard is the referee document. The original Standard can
       be obtained online at http://www.opengroup.org/unix/online.html .

       Any typographical or formatting errors that appear in this page are
       most likely to have been introduced during the conversion of the source
       files to man page format. To report such errors, see
       https://www.kernel.org/doc/man-pages/reporting_bugs.html .



IEEE/The Open Group                  2017                             ATAN2(3)
