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



PROLOG
       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.

NAME
       atan2, atan2f, atan2l -- arc tangent functions

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 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 errno
       to zero and call feclearexcept(FE_ALL_EXCEPT) before calling these
       functions. On return, if errno is non-zero or fetestexcept(FE_INVALID |
       FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW) is non-zero, an error has
       occurred.

RETURN VALUE
       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 atan(), atan2f(), and atan2l() 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.

ERRORS
       These functions may fail if:

       Range Error The result underflows.

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

       The following sections are informative.

EXAMPLES
   Converting Cartesian to Polar Coordinates System
       The function below uses atan2() to convert a 2d vector expressed in
       cartesian coordinates (_x,_y) to the polar coordinates (rho,theta).
       There are other ways to compute the angle theta, using asin() acos(),
       or atan().  However, atan2() presents here two advantages:

        *  The angle's quadrant is automatically determined.

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

       Finally, this example uses hypot() rather than sqrt() since it is
       better for special cases; see hypot() 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);
           }

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

RATIONALE
       None.

FUTURE DIRECTIONS
       None.

SEE ALSO
       acos(), asin(), atan(), feclearexcept(), fetestexcept(), hypot(),
       isnan(), sqrt(), tan()

       The Base Definitions volume of POSIX.1-2017, Section 4.20, Treatment of
       Error Conditions for Mathematical Functions, <math.h>

COPYRIGHT
       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)
