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On the Robustness of the 2Sum and Fast2Sum Algorithms

The 2Sum and Fast2Sum algorithms are important building blocks in numerical computing. They are used (implicitely or explicitely) in many compensated algorithms (such as compensated summation or compensated polynomial evaluation). They are also used for manipulating floating-point expansions. We show that these algorithms are much more robust than it is usually believed: The returned result makes sense even when the rounding function is not round-to-nearest, and they are almost immune to overflow.