NAME
    tanh - hyperbolic tangent

SYNOPSIS
    tanh(x [,eps])

TYPES
    x		real
    eps		nonzero real, defaults to epsilon()

    return	real

DESCRIPTION
    Calculate the tanh of x to the nearest or next to nearest multiple of
    epsilon, with absolute error less than .75 * abs(eps).

    tanh(x) = (exp(2*x) - 1)/(exp(2*x) + 1)

EXAMPLE
    ; print tanh(1, 1e-5), tanh(1, 1e-10), tanh(1, 1e-15), tanh(1, 1e-20)
    .76159 .761594156 .761594155955765 .76159415595576488812

LIMITS
    unlike sin and cos, x must be real
    eps > 0

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

SEE ALSO
    sinh, cosh, sech, csch, coth, epsilon

## Copyright (C) 1999  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.
##
## @(#) $Revision: 30.1 $
## @(#) $Id: tanh,v 30.1 2007/03/16 11:10:42 chongo Exp $
## @(#) $Source: /usr/local/src/bin/calc/help/RCS/tanh,v $
##
## Under source code control:	1994/03/19 01:40:30
## 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/
