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Communication Dans Un Congrès Année : 2023

Towards a correctly-rounded and fast power function in binary64 arithmetic

Résumé

We design algorithms for the correct rounding of the power function xy 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 in an extended version of this paper, 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.
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hal-04326201 , version 1 (06-12-2023)

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  • HAL Id : hal-04326201 , version 1

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Tom Hubrecht, Claude-Pierre Jeannerod, Paul Zimmermann. Towards a correctly-rounded and fast power function in binary64 arithmetic. 2023 IEEE 30th Symposium on Computer Arithmetic (ARITH 2023), Sep 2023, Portland, Oregon (USA), United States. ⟨hal-04326201⟩
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