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## -*- 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
