/usr/share/octave/packages/interval-2.1.0/@infsup/cot.m is in octave-interval 2.1.0-2.
This file is owned by root:root, with mode 0o644.
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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} cot (@var{X})
##
## Compute the cotangent in radians, that is the reciprocal tangent.
##
## Accuracy: The result is a tight enclosure.
##
## @example
## @group
## cot (infsup (1))
## @result{} ans ⊂ [0.64209, 0.6421]
## @end group
## @end example
## @seealso{@@infsup/tan, @@infsup/csc, @@infsup/sec}
## @end defmethod
## Author: Oliver Heimlich
## Keywords: interval
## Created: 2015-03-15
function x = cot (x)
if (nargin ~= 1)
print_usage ();
return
endif
l = u = zeros (size (x));
## Check, if wid (x) is certainly greater than pi. This may save computation of
## some cotangent values.
width = mpfr_function_d ('minus', -inf, x.sup, x.inf);
persistent pi = infsup ("pi");
certainlyfullperiod = width >= sup (pi);
possiblynotfullperiod = not (certainlyfullperiod);
l(possiblynotfullperiod) = ...
mpfr_function_d ('cot', -inf, x.sup(possiblynotfullperiod));
u(possiblynotfullperiod) = ...
mpfr_function_d ('cot', +inf, x.inf(possiblynotfullperiod));
l(x.sup == 0) = -inf;
u(x.inf == 0) = +inf;
singularity = certainlyfullperiod | ...
l > u | (...
width > 2 & (...
sign (l) == sign (u) | ...
max (abs (l), abs (u)) < 1));
l(singularity) = -inf;
u(singularity) = inf;
emptyresult = isempty (x) | (x.inf == 0 & x.sup == 0);
l(emptyresult) = inf;
u(emptyresult) = -inf;
x.inf = l;
x.sup = u;
endfunction
%!# from the documentation string
%!assert (cot (infsup (1)) == "[0x1.48C05D04E1CFDp-1, 0x1.48C05D04E1CFEp-1]");
|