PROLOG

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

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  [-π,π]
       radians.

       If y is ±0 and x is < 0, ±π shall be returned.

       If y is ±0 and x is > 0, ±0 shall be returned.

       If y is < 0 and x is ±0, -π/2 shall be returned.

       If y is > 0 and x is ±0, π/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, ±π 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, ±π 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, ±π/2 shall be returned.

       If y is ±Inf and x is -Inf, ±3π/4 shall be returned.

       If y is ±Inf and x is +Inf, ±π/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(3POSIX)