1## Copyright 2014-2016 Oliver Heimlich
2##
3## This program is free software; you can redistribute it and/or modify
4## it under the terms of the GNU General Public License as published by
5## the Free Software Foundation; either version 3 of the License, or
6## (at your option) any later version.
7##
8## This program is distributed in the hope that it will be useful,
9## but WITHOUT ANY WARRANTY; without even the implied warranty of
10## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
11## GNU General Public License for more details.
12##
13## You should have received a copy of the GNU General Public License
14## along with this program; if not, see <http://www.gnu.org/licenses/>.
15
16## -*- texinfo -*-
17## @documentencoding UTF-8
18## @defmethod {@@infsup} cos (@var{X})
19##
20## Compute the cosine in radians.
21##
22## Accuracy: The result is a tight enclosure.
23##
24## @example
25## @group
26## cos (infsup (1))
27##   @result{} ans ⊂ [0.5403, 0.54031]
28## @end group
29## @end example
30## @seealso{@@infsup/acos, @@infsup/sec, @@infsup/cosh}
31## @end defmethod
32
33## Author: Oliver Heimlich
34## Keywords: interval
35## Created: 2014-10-05
36
37function x = cos (x)
38
39  if (nargin ~= 1)
40    print_usage ();
41    return
42  endif
43
44  l = u = sinsignl = sinsignu = zeros (size (x.inf));
45
46  ## Check, if wid (x) is certainly greater than 2*pi. This can save the
47  ## computation if some cosine values.
48  width = mpfr_function_d ('minus', -inf, x.sup, x.inf);
49  persistent pi = infsup ("pi");
50  persistent twopi = 2 .* pi;
51  certainlyfullperiod = width >= sup (twopi);
52  l(certainlyfullperiod) = -1;
53  u(certainlyfullperiod) = 1;
54
55  possiblynotfullperiod = not (certainlyfullperiod);
56  if (__check_crlibm__ ())
57    l(possiblynotfullperiod) = min (crlibm_function ('cos', -inf, ...
58                                                     x.inf(possiblynotfullperiod)), ...
59                                    crlibm_function ('cos', -inf, ...
60                                                     x.sup(possiblynotfullperiod)));
61    u(possiblynotfullperiod) = max (crlibm_function ('cos', inf, ...
62                                                     x.inf(possiblynotfullperiod)), ...
63                                    crlibm_function ('cos', inf, ...
64                                                     x.sup(possiblynotfullperiod)));
65
66    ## We use sign (-sin) to know the gradient at the boundaries.
67    sinsignl(possiblynotfullperiod) = sign (-crlibm_function ('sin', .5, ...
68                                                              x.inf(possiblynotfullperiod)));
69    sinsignu(possiblynotfullperiod) = sign (-crlibm_function ('sin', .5, ...
70                                                              x.sup(possiblynotfullperiod)));
71  else
72    l(possiblynotfullperiod) = min (mpfr_function_d ('cos', -inf, ...
73                                                     x.inf(possiblynotfullperiod)), ...
74                                    mpfr_function_d ('cos', -inf, ...
75                                                     x.sup(possiblynotfullperiod)));
76    u(possiblynotfullperiod) = max (mpfr_function_d ('cos', inf, ...
77                                                     x.inf(possiblynotfullperiod)), ...
78                                    mpfr_function_d ('cos', inf, ...
79                                                     x.sup(possiblynotfullperiod)));
80
81    ## We use sign (-sin) to know the gradient at the boundaries.
82    sinsignl(possiblynotfullperiod) = sign (-mpfr_function_d ('sin', .5, ...
83                                                              x.inf(possiblynotfullperiod)));
84    sinsignu(possiblynotfullperiod) = sign (-mpfr_function_d ('sin', .5, ...
85                                                              x.sup(possiblynotfullperiod)));
86  endif
87
88  ## In case of sign (-sin) == 0, we conservatively use sign (-sin) of nextout.
89  sinsignl(sinsignl == 0) = (-1) .* sign (l(sinsignl == 0));
90  sinsignu(sinsignu == 0) = sign (u(sinsignu == 0));
91
92  containsinf = possiblynotfullperiod & ((sinsignl == -1 & sinsignu == 1) | ...
93                                         (sinsignl == sinsignu & ...
94                                          width >= sup (pi))) ...
95                & ne (0, x);
96  l(containsinf) = -1;
97
98  containssup = possiblynotfullperiod & ((sinsignl == 1 & sinsignu == -1) | ...
99                                         (sinsignl == sinsignu & ...
100                                          width >= sup (pi)));
101  u(containssup) = 1;
102
103  emptyresult = isempty (x);
104  l(emptyresult) = inf;
105  u(emptyresult) = -inf;
106
107  l(l == 0) = -0;
108
109  x.inf = l;
110  x.sup = u;
111
112endfunction
113
114%!# from the documentation string
115%!assert (cos (infsup (1)) == "[0x1.14A280FB5068Bp-1, 0x1.14A280FB5068Cp-1]");
116
117%!shared testdata
118%! # Load compiled test data (from src/test/*.itl)
119%! testdata = load (file_in_loadpath ("test/itl.mat"));
120
121%!test
122%! # Scalar evaluation
123%! testcases = testdata.NoSignal.infsup.cos;
124%! for testcase = [testcases]'
125%!   assert (isequaln (...
126%!     cos (testcase.in{1}), ...
127%!     testcase.out));
128%! endfor
129
130%!test
131%! # Vector evaluation
132%! testcases = testdata.NoSignal.infsup.cos;
133%! in1 = vertcat (vertcat (testcases.in){:, 1});
134%! out = vertcat (testcases.out);
135%! assert (isequaln (cos (in1), out));
136
137%!test
138%! # N-dimensional array evaluation
139%! testcases = testdata.NoSignal.infsup.cos;
140%! in1 = vertcat (vertcat (testcases.in){:, 1});
141%! out = vertcat (testcases.out);
142%! # Reshape data
143%! i = -1;
144%! do
145%!   i = i + 1;
146%!   testsize = factor (numel (in1) + i);
147%! until (numel (testsize) > 2)
148%! in1 = reshape ([in1; in1(1:i)], testsize);
149%! out = reshape ([out; out(1:i)], testsize);
150%! assert (isequaln (cos (in1), out));
151