Emulating round-to-nearest-ties-to-zero "augmented" floating-point operations using round-to-nearest-ties-to-even arithmetic

The 2019 version of the IEEE 754 Standard for Floating-Point Arithmetic recommends that new “augmented” operations should be provided for the binary formats. These operations use a new “rounding direction”: round to nearest ties-to-zero. We show how they can be implemented using the currently available operations, using round-to-nearest ties-to-even with a partial formal proof of correctness

On the robustness of the 2Sum and Fast2Sum algorithms

International audienceThe 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