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Pré-Publication, Document De Travail Année : 2023

Accurate Horner Methods in Real and Complex Floating-Point Arithmetic

Résumé

In this article, we derive accurate Horner methods in real and complex floating-point arithmetic. In particular, we show that these methods are as accurate as if computed in k-fold precision, where k ≥ 2, and then rounded into the working precision. When k = 2, our methods are comparable or faster than the existing compensated Horner routines. When compared to multi-precision software, such as MPFR and MPC, our methods are significantly faster for k ≤ 8, that is, up to 489 bits in the significand.
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Dates et versions

hal-04030542 , version 1 (15-03-2023)

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  • HAL Id : hal-04030542 , version 1

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Thomas R Cameron, Stef Graillat. Accurate Horner Methods in Real and Complex Floating-Point Arithmetic. 2023. ⟨hal-04030542⟩
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