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ATAN2(3P)		   POSIX Programmer's Manual		     ATAN2(3P)

       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.

       atan2, atan2f, atan2l — arc tangent functions

       #include <math.h>

       double atan2(double y, double x);
       float atan2f(float y, float x);
       long double atan2l(long double y, long double x);

       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

       Upon  successful	 completion, these functions shall return the arc tan‐
       gent 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

       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.

       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.

   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>

	   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);

       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.



       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>

       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 .

       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‐ .

IEEE/The Open Group		     2013			     ATAN2(3P)

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