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.
Domaines
Informatique [cs]Origine | Fichiers produits par l'(les) auteur(s) |
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