NAME
    sech - hyperbolic secant

SYNOPSIS
    sech(x [,eps])

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

    return	real

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

    sech(x) = 2/(exp(x) + exp(-x))

EXAMPLE
    ; print sech(1, 1e-5), sech(1, 1e-10), sech(1, 1e-15), sech(1, 1e-20)
    0.64805 0.6480542737 0.648054273663885 0.64805427366388539958

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

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

SEE ALSO
    sinh, cosh, tanh, csch, coth, 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:	1995/11/13 03:49:00
## File existed as early as:	1995
##
## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/