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Pré-Publication, Document De Travail Année : 2016

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

Résumé

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 et versions

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

Identifiants

  • HAL Id : hal-01351529 , version 1

Citer

Mioara Joldes, Valentina Popescu, Jean-Michel Muller. Tight and rigourous error bounds for basic building blocks of double-word arithmetic. 2016. ⟨hal-01351529v1⟩

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