/usr/share/octave/packages/interval-2.1.0/@infsup/sin.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} sin (@var{X})
##
## Compute the sine in radians.
##
## Accuracy: The result is a tight enclosure.
##
## @example
## @group
## sin (infsup (1))
## @result{} ans ⊂ [0.84147, 0.84148]
## @end group
## @end example
## @seealso{@@infsup/asin, @@infsup/csc, @@infsup/sinh}
## @end defmethod
## Author: Oliver Heimlich
## Keywords: interval
## Created: 2014-10-05
function x = sin (x)
if (nargin ~= 1)
print_usage ();
return
endif
l = u = cossignl = cossignu = zeros (size (x.inf));
## Check, if wid (x) is certainly greater than 2*pi. This can save the
## computation if some sine values.
width = mpfr_function_d ('minus', -inf, x.sup, x.inf);
persistent pi = infsup ("pi");
persistent twopi = 2 .* pi;
certainlyfullperiod = width >= sup (twopi);
l(certainlyfullperiod) = -1;
u(certainlyfullperiod) = 1;
possiblynotfullperiod = not (certainlyfullperiod);
if (__check_crlibm__ ())
l(possiblynotfullperiod) = min (...
crlibm_function ('sin', -inf, x.inf(possiblynotfullperiod)), ...
crlibm_function ('sin', -inf, x.sup(possiblynotfullperiod)));
u(possiblynotfullperiod) = max (...
crlibm_function ('sin', inf, x.inf(possiblynotfullperiod)), ...
crlibm_function ('sin', inf, x.sup(possiblynotfullperiod)));
## We use sign (cos) to know the gradient at the boundaries.
cossignl(possiblynotfullperiod) = sign (...
crlibm_function ('cos', .5, x.inf(possiblynotfullperiod)));
cossignu(possiblynotfullperiod) = sign (...
crlibm_function ('cos', .5, x.sup(possiblynotfullperiod)));
else
l(possiblynotfullperiod) = min (...
mpfr_function_d ('sin', -inf, x.inf(possiblynotfullperiod)), ...
mpfr_function_d ('sin', -inf, x.sup(possiblynotfullperiod)));
u(possiblynotfullperiod) = max (...
mpfr_function_d ('sin', inf, x.inf(possiblynotfullperiod)), ...
mpfr_function_d ('sin', inf, x.sup(possiblynotfullperiod)));
## We use sign (cos) to know the gradient at the boundaries.
cossignl(possiblynotfullperiod) = sign (...
mpfr_function_d ('cos', .5, x.inf(possiblynotfullperiod)));
cossignu(possiblynotfullperiod) = sign (...
mpfr_function_d ('cos', .5, x.sup(possiblynotfullperiod)));
endif
## In case of sign (cos) == 0, we conservatively use sign (cos) of nextout.
cossignl(cossignl == 0) = sign (l(cossignl == 0));
cossignu(cossignu == 0) = (-1) * sign (u(cossignu == 0));
containsinf = possiblynotfullperiod & ((cossignl == -1 & cossignu == 1) | ...
(cossignl == cossignu & ...
width >= sup (pi)));
l(containsinf) = -1;
containssup = possiblynotfullperiod & ((cossignl == 1 & cossignu == -1) | ...
(cossignl == cossignu & ...
width >= sup (pi)));
u(containssup) = 1;
emptyresult = isempty (x);
l(emptyresult) = inf;
u(emptyresult) = -inf;
l(l == 0) = -0;
x.inf = l;
x.sup = u;
endfunction
%!# from the documentation string
%!assert (sin (infsup (1)) == "[0x1.AED548F090CEEp-1, 0x1.AED548F090CEFp-1]");
%!# correct use of signed zeros
%!test
%! x = sin (infsup (0));
%! assert (signbit (inf (x)));
%! assert (not (signbit (sup (x))));
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