Towards a correctly-rounded and fast power function in binary64 arithmetic (original) (raw)

Pré-Publication, Document De Travail Année : 2023

Résumé

We design algorithms for the correct rounding of the power function x y in the binary64 IEEE 754 format, for all rounding modes, modulo the knowledge of hardest-to-round cases. Our implementation of these algorithms largely outperforms previous correctly-rounded implementations and is not far from the efficiency of current mathematical libraries, which are not correctly-rounded. Still, we expect our algorithms can be further improved for speed. The proofs of correctness are fully detailed, with the goal to enable a formal proof of these algorithms. We hope this work will motivate the next IEEE 754 revision committee to require correct rounding for mathematical functions.

Mots clés

• IEEE 754 double precision binary64 format power function correct rounding efficiency
• IEEE 754
• double precision
• binary64 format
• power function
• correct rounding
• efficiency

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https://inria.hal.science/hal-04159652

Soumis le : mercredi 12 juillet 2023-08:37:35

Dernière modification le : vendredi 24 octobre 2025-17:40:11

Archivage à long terme le : vendredi 13 octobre 2023-18:08:39

Dates et versions

hal-04159652 , version 1 (12-07-2023)

hal-04159652 , version 2 (08-02-2024)

Licence

Identifiants

• HAL Id : hal-04159652 , version 1

Citer

Tom Hubrecht, Claude-Pierre Jeannerod, Paul Zimmermann. Towards a correctly-rounded and fast power function in binary64 arithmetic. 2023. ⟨hal-04159652v1⟩

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