/usr/share/octave/packages/interval-2.1.0/@infsup/csch.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} csch (@var{X})
##
## Compute the hyperbolic cosecant, that is the reciprocal hyperbolic sine.
##
## Accuracy: The result is a tight enclosure.
##
## @example
## @group
## csch (infsup (1))
## @result{} ans ⊂ [0.85091, 0.85092]
## @end group
## @end example
## @seealso{@@infsup/sinh, @@infsup/sech, @@infsup/coth}
## @end defmethod
## Author: Oliver Heimlich
## Keywords: interval
## Created: 2015-03-15
function x = csch (x)
if (nargin ~= 1)
print_usage ();
return
endif
l = u = zeros (size (x.inf));
select = x.inf >= 0 | x.sup <= 0;
if (any (select(:)))
l(select) = mpfr_function_d ('csch', -inf, x.sup(select));
l(select & x.sup == 0) = -inf;
u(select) = mpfr_function_d ('csch', +inf, x.inf(select));
u(select & x.inf == 0) = inf;
endif
select = x.inf < 0 & x.sup > 0;
if (any (select(:)))
l(select) = -inf;
u(select) = inf;
endif
emptyresult = isempty (x) | (x.inf == 0 & x.sup == 0);
l(emptyresult) = inf;
u(emptyresult) = -inf;
l(l == 0) = -0;
x.inf = l;
x.sup = u;
endfunction
%!# from the documentation string
%!assert (csch (infsup (1)) == "[0x1.B3AB8A78B90Cp-1, 0x1.B3AB8A78B90C1p-1]");
%!# correct use of signed zeros
%!test
%! x = csch (infsup (0, inf));
%! assert (signbit (inf (x)));
%! assert (not (signbit (sup (x))));
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