### From Wikimization

CSUM in Digital Signal Processing terms

function s=csum(x)
% CSUM Sum of elements using a compensated summation algorithm
%
% For large vectors, the native sum command in Matlab does
% not appear to use a compensated summation algorithm which
% can cause significant roundoff errors.
%
% This code implements a variant of Kahan's compensated
% summation algorithm which often takes about twice as long,
% but produces more accurate sums when the number of
% elements is large.
%
% See also SUM
%
% Example:
% v=rand(1e7,1);
% sum1 = sum(v);
% sum2 = csum(v);
% fprintf('sum1 = %18.16e\nsum2 = %18.16e\n', sum1, sum2);
% David Gleich, Stanford University, 2008
s_hat=0; y=0; e=0;
for i=1:numel(x)
s_hat_old = s_hat;
y = x(i) + e;
s_hat = s_hat_old + y;
e = (s_hat_old - s_hat) + y;
end