# Ultimately Fast Accurate Summation

@article{Rump2009UltimatelyFA, title={Ultimately Fast Accurate Summation}, author={Siegfried M. Rump}, journal={SIAM J. Sci. Comput.}, year={2009}, volume={31}, pages={3466-3502} }

We present two new algorithms FastAccSum and FastPrecSum, one to compute a faithful rounding of the sum of floating-point numbers and the other for a result “as if” computed in $K$-fold precision. Faithful rounding means the computed result either is one of the immediate floating-point neighbors of the exact result or is equal to the exact sum if this is a floating-point number. The algorithms are based on our previous algorithms AccSum and PrecSum and improve them by up to 25%. The first…

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