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

Mioara Joldes 1 Jean-Michel Muller 1 Valentina Popescu 1
1 ARIC - Arithmetic and Computing
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
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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ACM Transactions on Mathematical Software, Association for Computing Machinery, 2017, 44 (2), pp.1 - 27. 〈10.1145/3121432〉
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Soumis le : mercredi 18 octobre 2017 - 10:01:04
Dernière modification le : jeudi 19 octobre 2017 - 15:03:33

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Mioara 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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