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Accumulation of double precision vector

5 years ago • updated by 5 years ago • 1

Quadruple precision floating-point accumulation of a double precision vector p is emulated numerically in Matlab:

function t = orosumvec(p, recurs)
   x = cumsum(p);
   z = x - p;
   u = (z - x) + p;
   v = [0
        x(1:end-1)] - z;
   if ~recurs
      t = sum([u
               v
               x(end)]);
   else
      t = orosumvec([u
                     v
                     x(end)], 0);
   end
end

This is verified by Advanpix Multiprecision Toolbox.

Matlab's built-in variable precision arithmetic, vpa() from Mathworks Symbolic Math Toolbox,

produces erroneous results in 2018. One recursive call is necessary and sufficient.

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