## Copyright (C) 2013-2018 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
## <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