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Journal Articles ACM Transactions on Mathematical Software Year : 2017

Tight and rigorous 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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Dates and versions

hal-01351529 , version 1 (03-08-2016)
hal-01351529 , version 2 (29-03-2017)
hal-01351529 , version 3 (18-10-2017)

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