NAME
    asinh - inverse hyperbolic sine

SYNOPSIS
    asinh(x [,eps])

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

    return      real

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

    asinh(x) is the real number v for which sinh(v) = x.  It is given by

                asinh(x) = ln(x + sqrt(1 + x^2))

EXAMPLE
    ; print asinh(2, 1e-5), asinh(2, 1e-10), asinh(2, 1e-15), asinh(2, 1e-20)
    1.44363 1.4436354752 1.44363547517881 1.44363547517881034249

LIMITS
    0 < eps < 1

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

SEE ALSO
    sinh, cosh, tanh, coth, sech, csch
    acosh, atanh, acoth, asech, 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
## as published by the Free Software Foundation.
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## 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
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## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
##
## Under source code control:   1994/03/19 01:40:25
## 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/