Odd but Error-Free FastTwoSum: More General Conditions for FastTwoSum as an Error-Free Transformation for Faithful Rounding Modes

TL;DR

This paper broadens the applicability of FastTwoSum as an error-free transformation under various faithful rounding modes, including round-to-odd, by establishing more general conditions and tailored floating-point splitting methods.

Contribution

It introduces more general conditions for FastTwoSum as an EFT across all faithful rounding modes and develops a tailored floating-point splitting for round-to-odd modes.

Findings

More general conditions for FastTwoSum as EFT under faithful rounding modes

Guarantees established for round-to-odd modes

A configurable floating-point splitting tailored for round-to-odd modes

Abstract

This paper proposes sufficient, yet more general conditions for applying FastTwoSum as an error-free transformation (EFT) under all faithful rounding modes. Additionally, it also identifies guarantees tailored to round-to-odd for establishing FastTwoSum as an EFT. This paper also describes a floating-point splitting tailored for round-to-odd that is an EFT where the distribution of bits is configurable (i.e., ExtractScalar for round-to-odd). Our sufficient conditions are more general than those previously known in the literature (i.e., it applies to a wider operand domain).