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
|
########################################################################
##
## Copyright (C) 2013-2024 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{sum} =} kahan (@var{sum}, @var{comp}, @var{term})
## @deftypefnx {} {[@var{sum}, @var{comp}] =} kahan (@var{sum}, @var{comp}, @var{term})
##
## This function implements the Kahan summation algorithm, also known as
## compensated summation.
##
## The algorithm significantly reduces the numerical error in the total
## obtained by adding a sequence of finite precision floating point numbers,
## compared to the straightforward approach. For more details
## see @url{http://en.wikipedia.org/wiki/Kahan_summation_algorithm}.
## This function is called by @code{integrate_adaptive} to better catch
## equality comparisons.
##
## The first input argument is the variable that will contain the summation.
## This variable is also returned as the first output argument in order to
## reuse it in subsequent calls to @code{kahan} function.
##
## The second input argument contains the compensation term and is returned
## as the second output argument so that it can be reused in future calls of
## the same summation.
##
## The third input argument @var{term} is the variable to be added to
## @var{sum}.
## @end deftypefn
function [sum, comp] = kahan (sum, comp, term)
y = term - comp;
t = sum + y;
comp = (t - sum) - y;
sum = t;
endfunction
|
