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
|
########################################################################
##
## Copyright (C) 2020-2022 The Octave Project Developers
##
## See the file COPYRIGHT.md in the top-level directory of this
## distribution or <https://octave.org/copyright/>.
##
## This file is part of Octave.
##
## Octave 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.
##
## Octave 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 Octave; see the file COPYING. If not, see
## <https://www.gnu.org/licenses/>.
##
########################################################################
## -*- texinfo -*-
## @deftypefn {} {@var{y} =} sinpi (@var{x})
## Compute sine (@var{x} * pi) for each element of @var{x} accurately.
##
## The ordinary @code{sin} function uses IEEE floating point numbers and may
## produce results that are very close (within a few eps) of the correct
## value, but which are not exact. The @code{sinpi} function is more accurate
## and returns 0 exactly for integer values of @var{x} and +1/-1 for
## half-integer values (e.g., @dots{}, -3/2, -1/2, 1/2, 3/2, @dots{}).
##
## Example @*
## comparison of @code{sin} and @code{sinpi} for integer values of @var{x}
##
## @example
## @group
## sin ([0, 1, 2, 3] * pi)
## @result{}
## 0 1.2246e-16 -2.4493e-16 3.6739e-16
##
## sinpi ([0, 1, 2, 3])
## @result{}
## 0 0 0 0
## @end group
## @end example
##
## @seealso{cospi, sin}
## @end deftypefn
function y = sinpi (x)
if (nargin < 1)
print_usage ();
endif
## Wrap integer multiples so that new domain is [-1, 1)
x = mod (x-1, 2) - 1;
## Integer multiples of pi must be exactly zero
x(x == -1) = 0;
y = sin (x * pi);
endfunction
%!assert (sinpi ([-1, -2, 0, 1, 2]) == 0)
%!assert (sinpi ([-3/2, -1/2, 1/2, 3/2]), [1, -1, 1, -1])
%!assert (sinpi (100 + [0.1:0.1:0.9]), sin ([0.1:0.1:0.9]*pi), 2*eps (100))
%!error <Invalid call> sinpi ()
|
