NAME
    asech - inverse hyperbolic secant

SYNOPSIS
    asech(x [,eps])

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

    return      real

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

    asech(x) is the real number v for which sech(v) = x.  It is given by

                asech(x) = ln((1 + sqrt(1 - x^2))/x)

EXAMPLE
    ; print asech(.5,1e-5), asech(.5,1e-10), asech(.5,1e-15), asech(.5,1e-20)
    1.31696 1.3169578969 1.316957896924817 1.31695789692481670862

LIMITS
    0 < eps < 1

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

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

## Copyright (C) 1999,2023  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
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## Calc is distributed in the hope that it will be useful, but WITHOUT
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## Public License for more details.
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## A copy of version 2.1 of the GNU Lesser General Public License is
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## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
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## Under source code control:   1995/11/13 03:49:00
## File existed as early as:    1995
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## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
