# atan2

## 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.
    


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