Odd but Error-Free FastTwoSum: More General Conditions for FastTwoSum as an Error-Free Transformation for Faithful Rounding Modes
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866916015025160192 |
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| author | Park, Sehyeok Lim, Jay P. Nagarakatte, Santosh |
| author_facet | Park, Sehyeok Lim, Jay P. Nagarakatte, Santosh |
| contents | 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). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_17198 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Odd but Error-Free FastTwoSum: More General Conditions for FastTwoSum as an Error-Free Transformation for Faithful Rounding Modes Park, Sehyeok Lim, Jay P. Nagarakatte, Santosh Mathematical Software 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). |
| title | Odd but Error-Free FastTwoSum: More General Conditions for FastTwoSum as an Error-Free Transformation for Faithful Rounding Modes |
| topic | Mathematical Software |
| url | https://arxiv.org/abs/2601.17198 |