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

.. _log:

LOG --- Natural logarithm function
**********************************

.. index:: LOG

.. index:: ALOG

.. index:: DLOG

.. index:: CLOG

.. index:: ZLOG

.. index:: CDLOG

.. index:: exponential function, inverse

.. index:: logarithm function

.. index:: natural logarithm function

.. function:: LOG(X)

  ``LOG(X)`` computes the natural logarithm of :samp:`{X}`, i.e. the
  logarithm to the base e.

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

  :return:
    The return value is of type ``REAL`` or ``COMPLEX``.
    The kind type parameter is the same as :samp:`{X}`.
    If :samp:`{X}` is ``COMPLEX``, the imaginary part \omega is in the range
    -\pi < \omega \leq \pi.

  :samp:`{Standard}:`
    Fortran 77 and later, has GNU extensions

  :samp:`{Class}:`
    Elemental function

  :samp:`{Syntax}:`

  .. code-block:: fortran

    RESULT = LOG(X)

  :samp:`{Example}:`

    .. code-block:: fortran

      program test_log
        real(8) :: x = 2.7182818284590451_8
        complex :: z = (1.0, 2.0)
        x = log(x)    ! will yield (approximately) 1
        z = log(z)
      end program test_log

  :samp:`{Specific names}:`
    ============  ================  ==============  ===================
    Name          Argument          Return type     Standard
    ============  ================  ==============  ===================
    ``ALOG(X)``   ``REAL(4) X``     ``REAL(4)``     Fortran 77 or later
    ``DLOG(X)``   ``REAL(8) X``     ``REAL(8)``     Fortran 77 or later
    ``CLOG(X)``   ``COMPLEX(4) X``  ``COMPLEX(4)``  Fortran 77 or later
    ``ZLOG(X)``   ``COMPLEX(8) X``  ``COMPLEX(8)``  GNU extension
    ``CDLOG(X)``  ``COMPLEX(8) X``  ``COMPLEX(8)``  GNU extension
    ============  ================  ==============  ===================