..
  Copyright 1988-2021 Free Software Foundation, Inc.
  This is part of the GCC manual.
  For copying conditions, see the GPL license file

.. _atan2:

ATAN2 --- Arctangent function 
******************************

.. index:: ATAN2

.. index:: DATAN2

.. index:: trigonometric function, tangent, inverse

.. index:: tangent, inverse

.. function:: ATAN2(Y, X)

  ``ATAN2(Y, X)`` computes the principal value of the argument
  function of the complex number X + i Y.  This function can
  be used to transform from Cartesian into polar coordinates and
  allows to determine the angle in the correct quadrant.

  :param Y:
    The type shall be ``REAL``.

  :param X:
    The type and kind type parameter shall be the same as :samp:`{Y}`.
    If :samp:`{Y}` is zero, then :samp:`{X}` must be nonzero.

  :return:
    The return value has the same type and kind type parameter as :samp:`{Y}`. It
    is the principal value of the complex number X + i Y.  If :samp:`{X}`
    is nonzero, then it lies in the range -\pi \le \atan (x) \leq \pi.
    The sign is positive if :samp:`{Y}` is positive.  If :samp:`{Y}` is zero, then
    the return value is zero if :samp:`{X}` is strictly positive, \pi if
    :samp:`{X}` is negative and :samp:`{Y}` is positive zero (or the processor does
    not handle signed zeros), and -\pi if :samp:`{X}` is negative and
    :samp:`{Y}` is negative zero.  Finally, if :samp:`{X}` is zero, then the
    magnitude of the result is \pi/2.

  :samp:`{Standard}:`
    Fortran 77 and later

  :samp:`{Class}:`
    Elemental function

  :samp:`{Syntax}:`

  .. code-block:: fortran

    RESULT = ATAN2(Y, X)

  :samp:`{Example}:`

    .. code-block:: fortran

      program test_atan2
        real(4) :: x = 1.e0_4, y = 0.5e0_4
        x = atan2(y,x)
      end program test_atan2

  :samp:`{Specific names}:`
    ================  ================  ===========  ====================
    Name              Argument          Return type  Standard
    ================  ================  ===========  ====================
    ``ATAN2(X, Y)``   ``REAL(4) X, Y``  ``REAL(4)``  Fortran 77 and later
    ``DATAN2(X, Y)``  ``REAL(8) X, Y``  ``REAL(8)``  Fortran 77 and later
    ================  ================  ===========  ====================

  :samp:`{See also}:`
    Alias: 
    ATAN 
    Degrees function: 
    ATAN2D