/usr/share/octave/packages/interval-2.1.0/@infsupdec/atan2.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 {@@infsupdec} atan2 (@var{Y}, @var{X})
##
## Compute the inverse tangent with two arguments.
##
## Accuracy: The result is a tight enclosure.
##
## @example
## @group
## atan2 (infsupdec (1), infsupdec (-1))
## @result{} ans ⊂ [2.3561, 2.3562]_com
## @end group
## @end example
## @seealso{@@infsupdec/tan}
## @end defmethod
## Author: Oliver Heimlich
## Keywords: interval
## Created: 2014-10-13
function result = atan2 (y, x)
if (nargin ~= 2)
print_usage ();
return
endif
if (not (isa (y, "infsupdec")))
y = infsupdec (y);
endif
if (not (isa (x, "infsupdec")))
x = infsupdec (x);
endif
result = newdec (atan2 (y.infsup, x.infsup));
## The function is discontinuous for x <= 0 and y == 0
discontinuos = inf (y) < 0 & sup (y) >= 0 & inf (x) < 0;
result.dec(discontinuos) = min (result.dec(discontinuos), _def ());
## For y = [0, y.sup] the function is discontinuous, but its restriction is not
onlyrestrictioncontinuous = inf (y) == 0 & inf (x) < 0;
result.dec(onlyrestrictioncontinuous) = ...
min (result.dec(onlyrestrictioncontinuous), _dac ());
## The only undefined input is <0,0>
result.dec(ismember (0, y) & ismember (0, x)) = _trv ();
result.dec = min (result.dec, min (y.dec, x.dec));
endfunction
%!# from the documentation string
%!assert (isequal (atan2 (infsupdec (1), infsupdec (-1)), infsupdec ("[0x1.2D97C7F3321D2p1, 0x1.2D97C7F3321D3p1]")));
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