Accurate Sum and Dot Product

@article{Ogita2005AccurateSA,
  title={Accurate Sum and Dot Product},
  author={Takeshi Ogita and Siegfried M. Rump and Shin'ichi Oishi},
  journal={SIAM J. Sci. Comput.},
  year={2005},
  volume={26},
  pages={1955-1988}
}
Algorithms for summation and dot product of floating-point numbers are presented which are fast in terms of measured computing time. We show that the computed results are as accurate as if computed in twice or K-fold working precision, $K\ge 3$. For twice the working precision our algorithms for summation and dot product are some 40% faster than the corresponding XBLAS routines while sharing similar error estimates. Our algorithms are widely applicable because they require only addition… 
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