# A note on Dekker’s FastTwoSum algorithm

@article{Lange2020ANO, title={A note on Dekker’s FastTwoSum algorithm}, author={Marko Lange and Shin'ichi Oishi}, journal={Numerische Mathematik}, year={2020}, volume={145}, pages={383-403} }

More than 45 years ago, Dekker proved that it is possible to evaluate the exact error of a floating-point sum with only two additional floating-point operations, provided certain conditions are met. Today the respective algorithm for transforming a sum into its floating-point approximation and the corresponding error is widely referred to as $${{\,\mathrm{FastTwoSum}\,}}$$ FastTwoSum . Besides some assumptions on the floating-point system itself—all of which are satisfied by any binary IEEE…

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Computing the exact sign of sums of products with floating point arithmetic

- Computer ScienceArXiv
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The algorithm is efficient and uses only of floating point arithmetic, which is much faster than exact arithmetic, and it is proved that the algorithm is correct and the efficient and tested C++ code for it is correct.

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