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 binary formats. These use a “rounding direction”: round-to-nearest ties-to-zero . We show how they can implemented using currently available operations, xmlns:xlink="http://www.w3.org/1999/xlink">ties-to-even with partial formal proof correctness.