/usr/share/octave/packages/interval-3.1.0/@infsup/sin.m is in octave-interval 3.1.0-5.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 | ## Copyright 2014-2016 Oliver Heimlich
## Copyright 2017 Joel Dahne
##
## 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;
u(u == 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))));
%!# test fix for bug #51283
%!test
%! x = sin (infsup ([0, 0]));
%! assert (signbit (inf (x)));
%! assert (not (signbit (sup (x))));
%!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.sin;
%! for testcase = [testcases]'
%! assert (isequaln (...
%! sin (testcase.in{1}), ...
%! testcase.out));
%! endfor
%!test
%! # Vector evaluation
%! testcases = testdata.NoSignal.infsup.sin;
%! in1 = vertcat (vertcat (testcases.in){:, 1});
%! out = vertcat (testcases.out);
%! assert (isequaln (sin (in1), out));
%!test
%! # N-dimensional array evaluation
%! testcases = testdata.NoSignal.infsup.sin;
%! in1 = vertcat (vertcat (testcases.in){:, 1});
%! 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);
%! out = reshape ([out; out(1:i)], testsize);
%! assert (isequaln (sin (in1), out));
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