atan2(3p) — Linux manual page


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.1‐2017 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         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

       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>

           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.

RATIONALE         top




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.1‐2017, Section 4.20,
       Treatment of Error Conditions for Mathematical Functions,

COPYRIGHT         top

       Portions of this text are reprinted and reproduced in electronic
       form from IEEE Std 1003.1-2017, Standard for Information
       Technology -- Portable Operating System Interface (POSIX), The
       Open Group Base Specifications Issue 7, 2018 Edition, Copyright
       (C) 2018 by the Institute of Electrical and Electronics
       Engineers, Inc and The Open Group.  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 .

IEEE/The Open Group               2017                         ATAN2(3P)

Pages that refer to this page: math.h(0p)atan(3p)hypot(3p)