NAME
    atanh - inverse hyperbolic tangent

SYNOPSIS
    atanh(x [,eps])

TYPES
    x           real
    eps         0 < real < 1, defaults to epsilon()

    return      real

DESCRIPTION
    Returns the atanh of x to a multiple of eps with error less in
    absolute value than .75 * eps.

    atanh(x) is the real number v for which tanh(v) = x.  It is given by

                atanh(x) = ln((1 + x)/(1 - x))/2

EXAMPLE
    ; print atanh(.5,1e-5), atanh(.5,1e-10), atanh(.5,1e-15), atanh(.5,1e-20)
    0.54931 0.5493061443 0.549306144334055 0.5493061443340548457

LIMITS
    0 < eps < 1

LINK LIBRARY
    NUMBER *qatanh(NUMBER *x, NUMBER *eps)

SEE ALSO
    sinh, cosh, tanh, coth, sech, csch
    asinh, acosh, acoth, asech, acsch
    epsilon

## Copyright (C) 1999,2021,2023  Landon Curt Noll
##
## Calc is open software; you can redistribute it and/or modify it under
## the terms of the version 2.1 of the GNU Lesser General Public License
## as published by the Free Software Foundation.
##
## Calc is distributed in the hope that it will be useful, but WITHOUT
## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
## Public License for more details.
##
## A copy of version 2.1 of the GNU Lesser General Public License is
## distributed with calc under the filename COPYING-LGPL.  You should have
## received a copy with calc; if not, write to Free Software Foundation, Inc.
## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
##
## Under source code control:   1994/03/19 01:40:27
## File existed as early as:    1994
##
## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
