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Reports (Research Report) Year : 2008

Compensated Horner algorithm in K times the working precision

Nicolas Louvet

Abstract

We introduce an algorithm to evaluate a polynomial with floating point coefficients as accurately as the Horner scheme performed in K times the working precision, for K an arbitrary integer. The principle is to iterate the error-free transformation of the compensated Horner algorithm and to accurately sum the final decomposition. We prove this accuracy property with an apriori error analysis. We illustrate its practical efficiency with numerical experiments on significant environments and IEEE-754 arithmetic. Comparing to existing alternatives we conclude that this K-times compensated algorithm is competitive for K up to 4, i.e. up to 212 mantissa bits.
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Dates and versions

inria-00267077 , version 1 (26-03-2008)

Identifiers

  • HAL Id : inria-00267077 , version 1

Cite

Philippe Langlois, Nicolas Louvet. Compensated Horner algorithm in K times the working precision. [Research Report] 2008. ⟨inria-00267077⟩
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