/usr/share/octave/packages/interval-2.1.0/@infsup/atanh.m is in octave-interval 2.1.0-2.
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##
## This program is free software; you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 3 of the License, or
## (at your option) any later version.
##
## This program 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 General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with this program; if not, see <http://www.gnu.org/licenses/>.
## -*- texinfo -*-
## @documentencoding UTF-8
## @defmethod {@@infsup} atanh (@var{X})
##
## Compute the inverse hyperbolic tangent.
##
## Accuracy: The result is a tight enclosure.
##
## @example
## @group
## atanh (infsup (.5))
## @result{} ans ⊂ [0.5493, 0.54931]
## @end group
## @end example
## @seealso{@@infsup/tanh}
## @end defmethod
## Author: Oliver Heimlich
## Keywords: interval
## Created: 2014-10-07
function x = atanh (x)
if (nargin ~= 1)
print_usage ();
return
endif
x = intersect (x, infsup (-1, 1));
## atanh is monotonically increasing between (-1, -inf) and (1, inf)
l = mpfr_function_d ('atanh', -inf, x.inf);
u = mpfr_function_d ('atanh', +inf, x.sup);
emptyresult = isempty (x) | x.sup <= -1 | x.inf >= 1;
l(emptyresult) = inf;
u(emptyresult) = -inf;
l(l == 0) = -0;
x.inf = l;
x.sup = u;
endfunction
%!# from the documentation string
%!assert (atanh (infsup (.5)) == "[0x1.193EA7AAD030Ap-1, 0x1.193EA7AAD030Bp-1]");
%!# correct use of signed zeros
%!test
%! x = atanh (infsup (0));
%! assert (signbit (inf (x)));
%! assert (not (signbit (sup (x))));
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