## Copyright 2014 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
## @defop Method {@@infsup} times (@var{X}, @var{Y})
## @defopx Operator {@@infsup} {@var{X} .* @var{Y}}
##
## Multiply all numbers of interval @var{X} by all numbers of @var{Y}.
##
## Accuracy: The result is a tight enclosure.
##
## @example
## @group
## x = infsup (2, 3);
## y = infsup (1, 2);
## x .* y
##   @result{} ans = [2, 6]
## @end group
## @end example
## @seealso{@@infsup/rdivide}
## @end defop

## Author: Oliver Heimlich
## Keywords: interval
## Created: 2014-09-30

function x = times (x, y)

  if (nargin ~= 2)
    print_usage ();
    return
  endif
  if (not (isa (x, "infsup")))
    x = infsup (x);
  endif
  if (not (isa (y, "infsup")))
    y = infsup (y);
  elseif (isa (y, "infsupdec"))
    ## Workaround for bug #42735
    result = times (x, y);
    return
  endif

  ## At least one case of interval multiplication is complicated: when zero is an
  ## inner point of both interval factors.  In all other cases it would suffice
  ## to compute a single product for each product boundary.
  ##
  ## It is not significandly faster to do a case by case analysis in order to
  ## save some calls to the times function with directed rounding. Therefore, we
  ## simply compute the product for each pair of boundaries where the min/max
  ## could be located.

  l = min (min (min (...
                      mpfr_function_d ('times', -inf, x.inf, y.inf), ...
                      mpfr_function_d ('times', -inf, x.inf, y.sup)), ...
                mpfr_function_d ('times', -inf, x.sup, y.inf)), ...
           mpfr_function_d ('times', -inf, x.sup, y.sup));
  u = max (max (max (...
                      mpfr_function_d ('times', +inf, x.inf, y.inf), ...
                      mpfr_function_d ('times', +inf, x.inf, y.sup)), ...
                mpfr_function_d ('times', +inf, x.sup, y.inf)), ...
           mpfr_function_d ('times', +inf, x.sup, y.sup));

  ## [0] × anything = [0] × [0]
  ## [Entire] × anything but [0] = [Entire] × [Entire]
  ## This prevents the cases where 0 × inf would produce NaNs.
  entireproduct = isentire (x) | isentire (y);
  l(entireproduct) = -inf;
  u(entireproduct) = inf;
  zeroproduct = (x.inf == 0 & x.sup == 0) | (y.inf == 0 & y.sup == 0);
  l(zeroproduct) = -0;
  u(zeroproduct) = +0;
  emptyresult = isempty (x) | isempty (y);
  l(emptyresult) = inf;
  u(emptyresult) = -inf;

  l(l == 0) = -0;

  x.inf = l;
  x.sup = u;

endfunction

%!# from the documentation string
%!assert (infsup (2, 3) .* infsup (1, 2) == infsup (2, 6));

%!shared testdata
%! # Load compiled test data (from src/test/*.itl)
%! testdata = load (file_in_loadpath ("test/itl.mat"));

%!test
%! # Scalar evaluation
%! testcases = testdata.NoSignal.infsup.mul;
%! for testcase = [testcases]'
%!   assert (isequaln (...
%!     times (testcase.in{1}, testcase.in{2}), ...
%!     testcase.out));
%! endfor

%!test
%! # Vector evaluation
%! testcases = testdata.NoSignal.infsup.mul;
%! in1 = vertcat (vertcat (testcases.in){:, 1});
%! in2 = vertcat (vertcat (testcases.in){:, 2});
%! out = vertcat (testcases.out);
%! assert (isequaln (times (in1, in2), out));

%!test
%! # N-dimensional array evaluation
%! testcases = testdata.NoSignal.infsup.mul;
%! in1 = vertcat (vertcat (testcases.in){:, 1});
%! in2 = vertcat (vertcat (testcases.in){:, 2});
%! out = vertcat (testcases.out);
%! # Reshape data
%! i = -1;
%! do
%!   i = i + 1;
%!   testsize = factor (numel (in1) + i);
%! until (numel (testsize) > 2)
%! in1 = reshape ([in1; in1(1:i)], testsize);
%! in2 = reshape ([in2; in2(1:i)], testsize);
%! out = reshape ([out; out(1:i)], testsize);
%! assert (isequaln (times (in1, in2), out));
