/usr/share/octave/packages/interval-2.1.0/@infsup/acosh.m is in octave-interval 2.1.0-2.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 | ## Copyright 2014-2016 Oliver Heimlich
##
## 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} acosh (@var{X})
##
## Compute the inverse hyperbolic cosine.
##
## Accuracy: The result is a tight enclosure.
##
## @example
## @group
## acosh (infsup (2))
## @result{} ans ⊂ [1.3169, 1.317]
## @end group
## @end example
## @seealso{@@infsup/cosh}
## @end defmethod
## Author: Oliver Heimlich
## Keywords: interval
## Created: 2014-10-07
function x = acosh (x)
if (nargin ~= 1)
print_usage ();
return
endif
persistent domain = infsup (1, inf);
x = intersect (x, domain);
## acosh is monotonically increasing from (1, 0) to (inf, inf)
l = mpfr_function_d ('acosh', -inf, x.inf);
u = mpfr_function_d ('acosh', +inf, x.sup);
l(l == 0) = -0;
emptyresult = isempty (x);
l(emptyresult) = inf;
u(emptyresult) = -inf;
x.inf = l;
x.sup = u;
endfunction
%!# Empty interval
%!assert (acosh (infsup ()) == infsup ());
%!# Singleton intervals
%!assert (acosh (infsup (0)) == infsup ());
%!assert (acosh (infsup (1)) == infsup (0));
%!test
%! x = infsup (1 : 3 : 100);
%! assert (min (subset (acosh (x), log (x + sqrt (x + 1) .* sqrt (x - 1)))));
%!# Bounded intervals
%!assert (acosh (infsup (0, 1)) == infsup (0));
%!# Unbounded intervals
%!assert (acosh (infsup (-inf, 0)) == infsup ());
%!assert (acosh (infsup (-inf, 1)) == infsup (0));
%!assert (acosh (infsup (0, inf)) == infsup (0, inf));
%!assert (acosh (infsup (1, inf)) == infsup (0, inf));
%!assert (subset (acosh (infsup (2, inf)), infsup (1, inf)));
%!# from the documentation string
%!assert (acosh (infsup (2)) == "[0x1.5124271980434, 0x1.5124271980435]");
%!# correct use of signed zeros
%!test
%! x = acosh (infsup (1));
%! assert (signbit (inf (x)));
%! assert (not (signbit (sup (x))));
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