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Tight and rigourous error bounds for basic building blocks of double-word arithmetic

Abstract : We analyze several classical basic building blocks of double-word arithmetic (frequently called " double-double arithmetic " in the literature): the addition of a double-word number and a floating-point number, the addition of two double-word numbers, the multiplication of a double-word number by a floating-point number, the multiplication of two double-word numbers, the division of a double-word number by a floating-point number , and the division of two double-word numbers. For multiplication and division we get better relative error bounds than the ones previously published. For addition of two double-word numbers, we show that the previously published bound was wrong, and we provide a relative error bound. We introduce new algorithms for division. We also give examples that illustrate the tightness of our bounds.
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https://hal.archives-ouvertes.fr/hal-01351529
Contributor : Jean-Michel Muller Connect in order to contact the contributor
Submitted on : Wednesday, October 18, 2017 - 10:01:04 AM
Last modification on : Monday, May 16, 2022 - 4:58:02 PM
Long-term archiving on: : Friday, January 19, 2018 - 12:23:24 PM

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Mioara Maria Joldes, Jean-Michel Muller, Valentina Popescu. Tight and rigourous error bounds for basic building blocks of double-word arithmetic. ACM Transactions on Mathematical Software, Association for Computing Machinery, 2017, 44 (2), pp.1 - 27. ⟨10.1145/3121432⟩. ⟨hal-01351529v3⟩

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