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 much more general than those previously known in the literature (i.e., it applies to a wider operand domain).

翻译：本文提出了在所有忠实舍入模式下应用FastTwoSum作为无误差变换的充分且更通用的条件。此外，还专门针对舍入至奇数模式给出了确保FastTwoSum作为无误差变换的保证条件。本文还描述了一种专为舍入至奇数设计的浮点数分解方法，该方法是一种可配置比特分布的无误差变换（即针对舍入至奇数的ExtractScalar）。我们提出的充分条件比文献中已知的条件更为通用（即适用于更广的操作数域）。