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...

• Type: Journal
• Year: 2008
• Where: CORR
• Authors: Florent de Dinechin, Christoph Quirin Lauter
• Keywords: Algorithm, CORR 2008, Education, Polynomials, Remez Algorithm