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ATAN2(3P)                  POSIX Programmer's Manual                 ATAN2(3P)
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 tan-
       gent of y/x in the range [-n,n] radians.
       If y is +-0 and x is < 0, +-n shall be returned.
       If y is +-0 and x is > 0, +-0 shall be returned.
       If y is < 0 and x is +-0, -n/2 shall be returned.
       If y is > 0 and x is +-0, n/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, +-n 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, +-n 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, +-n/2 shall be returned.
       If y is +-Inf and x is -Inf, +-3n/4 shall be returned.
       If y is +-Inf and x is +Inf, +-n/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 bet-
       ter 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 Electri-
       cal 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.ker-
       nel.org/doc/man-pages/reporting_bugs.html .
IEEE/The Open Group                  2013                            ATAN2(3P)