..
  Copyright 1988-2022 Free Software Foundation, Inc.
  This is part of the GCC manual.
  For copying conditions, see the copyright.rst file.

.. _atanh:

.. index:: ATANH

.. index:: DATANH

.. index:: area hyperbolic tangent

.. index:: inverse hyperbolic tangent

.. index:: hyperbolic function, tangent, inverse

.. index:: tangent, hyperbolic, inverse

ATANH --- Inverse hyperbolic tangent function
*********************************************

.. function:: ATANH(X)

  ``ATANH(X)`` computes the inverse hyperbolic tangent of :samp:`{X}`.

  :param X:
    The type shall be ``REAL`` or ``COMPLEX``.

  :return:
    The return value has same type and kind as :samp:`{X}`. If :samp:`{X}` is
    complex, the imaginary part of the result is in radians and lies between
    -\pi/2 \leq \Im \atanh(x) \leq \pi/2.

  Standard:
    Fortran 2008 and later

  Class:
    Elemental function

  Syntax:
    .. code-block:: fortran

      RESULT = ATANH(X)

  Example:
    .. code-block:: fortran

      PROGRAM test_atanh
        REAL, DIMENSION(3) :: x = (/ -1.0, 0.0, 1.0 /)
        WRITE (*,*) ATANH(x)
      END PROGRAM

  Specific names:
    .. list-table::
       :header-rows: 1

       * - Name
         - Argument
         - Return type
         - Standard

       * - ``DATANH(X)``
         - ``REAL(8) X``
         - ``REAL(8)``
         - GNU extension

  See also:
    Inverse function: 
    :ref:`TANH`