PROLOG | NAME | SYNOPSIS | DESCRIPTION | RETURN VALUE | ERRORS | EXAMPLES | APPLICATION USAGE | RATIONALE | FUTURE DIRECTIONS | SEE ALSO | COPYRIGHT

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

PROLOG         top

       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         top

       atan2, atan2f, atan2l — arc tangent functions

SYNOPSIS         top

       #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         top

       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         top

       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         top

       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         top

   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         top

       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         top

       None.

FUTURE DIRECTIONS         top

       None.

SEE ALSO         top

       acos(3p), asin(3p), atan(3p), feclearexcept(3p), fetestexcept(3p),
       hypot(3p), isnan(3p), sqrt(3p), tan(3p)

       The Base Definitions volume of POSIX.1‐2008, Section 4.19, Treatment
       of Error Conditions for Mathematical Functions, math.h(0p)

COPYRIGHT         top

       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 .

IEEE/The Open Group                 2013                           ATAN2(3P)