Odd but Error-Free FastTwoSum: More General Conditions for FastTwoSum as an Error-Free Transformation for Faithful Rounding Modes
This work offers a theoretical extension for numerical analysis, enabling error-free summation in a broader range of rounding modes, which is incremental for the field of floating-point arithmetic.
The paper provides more general sufficient conditions for FastTwoSum to be an error-free transformation under all faithful rounding modes, and introduces a configurable floating-point splitting method for round-to-odd. The conditions apply to a wider operand domain than previously known.
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).