bionic (3) atan2.3posix.gz

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.1‐2008 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.1‐2008, Section 4.19, 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, 2013 Edition,
       Standard  for  Information Technology -- Portable Operating System Interface (POSIX), The Open Group Base
       Specifications Issue 7, Copyright (C) 2013 by the Institute of Electrical and Electronics Engineers,  Inc
       and  The  Open Group.  (This is POSIX.1-2008 with the 2013 Technical Corrigendum 1 applied.) 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.unix.org/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 .