NAME
    tanh - hyperbolic tangent

SYNOPSIS
    tanh(x [,eps])

TYPES
    x		real
    eps		0 < real < 1, 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)
    0.76159 0.761594156 0.761594155955765 0.76159415595576488812

LIMITS
    unlike sin and cos, x must be real
    0 < eps < 1

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

SEE ALSO
    sinh, cosh, coth, sech, csch
    asinh, acosh, atanh, 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 01:40:30
## 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/