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Conference Papers Year : 2023

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

Abstract

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 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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