Mercurial > octave
view scripts/ode/private/kahan.m @ 22323:bac0d6f07a3e
maint: Update copyright notices for 2016.
author | John W. Eaton <jwe@octave.org> |
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date | Wed, 17 Aug 2016 01:05:19 -0400 |
parents | f7f97d7e9294 |
children | 869c02fde46c |
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## Copyright (C) 2013-2016 Roberto Porcu' <roberto.porcu@polimi.it> ## ## 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 ## <http://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} and ## @code{integrate_const} to better catch equality comparisons. ## ## The first input argument is the variable that will contain the summation, ## so that is also returned as first output argument in order to reuse it in ## next calls to @code{kahan} function. ## ## The second input argument contains the compensation term and it 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