High-order Taylor series approximation for efficient computation of elementary functions


A replacement piecewise polynomial methodology is proposed to compute elementary functions by using high-order Taylor approximation. The high-order power terms of the series are proposed to be approximated by using easy and quick table lookup. Furthermore, the similarity and regularity among the Taylor coefficients will make attainable the sharing of the lookup tables. The authors have developed a mistake analysis method to estimate the utmost error of the proposed approximation approach, and formulated the procedure for determining the hardware parameters in the approximation unit. Finally, the authors have designed one-precision approximation unit for computing six common elementary functions. The coefficient sharing approach will result in a minimum of 30.fivep.c reduction in the coefficient lookup tables. Compared with a previous work by Piñeiro et al., the authors will save twenty seven.91p.c of the lookup tables with some extra cost in computation hardware. Compared with the work by Alimohammad et al., 34.eighty five% of the lookup tables will be saved with the same computation hardware value. The authors conclude that the proposed approaches will effectively scale back the lookup tables needed within the piecewise polynomial approximation for efficient elementary function computation.

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