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CORR
2008
Springer

Optimizing polynomials for floating-point implementation

8 years 10 months ago
Optimizing polynomials for floating-point implementation
The floating-point implementation of a function often reduces to a polynomial approximation on an interval. Remez algorithm provides the polynomial closest to the function, but the evaluation of this polynomial in floating-point may lead to catastrophic cancellations when the approximation interval contains zero and some of the polynomial coefficients are very small in magnitude with respects to others. To obtain cancellation-free polynomials while reducing operation count, an algorithm is presented that forces to zero the smaller coefficients thanks to a modified Remez algorithm targeting an incomplete monomial basis. This algorithm generalizes well-known techniques used for odd or even functions to a wider class of functions, and in a purely numerical way, the function being used as a numerical black box. This algorithm is demonstrated, within a larger polynomial implementation tool, on a range of examples, resulting in polynomials with less coefficients than those obtained the usua...
Florent de Dinechin, Christoph Quirin Lauter
Added 09 Dec 2010
Updated 09 Dec 2010
Type Journal
Year 2008
Where CORR
Authors Florent de Dinechin, Christoph Quirin Lauter
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