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 .