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Article Dans Une Revue IEEE Transactions on Computers Année : 2005

High-Speed Function Approximation using a Minimax Quadratic Interpolator

Résumé

A table-based method for high-speed function approximation in single-precision floating-point format is presented in this paper. Our focus is the approximation of reciprocal, square root, square root reciprocal, exponentials, logarithms, trigonometric functions, powering (with a fixed exponent p), or special functions. The algorithm presented here combines table look-up, an enhanced minimax quadratic approximation, and an efficient evaluation of the second-degree polynomial (using a specialized squaring unit, redundant arithmetic, and multioperand addition). The execution times and area costs of an architecture implementing our method are estimated, showing the achievement of the fast execution times of linear approximation methods and the reduced area requirements of other second-degree interpolation algorithms. Moreover, the use of an enhanced minimax approximation which, through an iterative process, takes into account the effect of rounding the polynomial coefficients to a finite size allows for a further reduction in the size of the look-up tables to be used, making our method very suitable for the implementation of an elementary function generator in state-of-the-art DSPs or graphics processing units (GPUs).
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Dates et versions

ensl-00000002 , version 1 (27-03-2006)

Identifiants

Citer

Jean-Michel Muller, Stuart Oberman, Jose-Alejandro Pineiro, Javier Bruguera. High-Speed Function Approximation using a Minimax Quadratic Interpolator. IEEE Transactions on Computers, 2005, 54 (3), pp.304-318. ⟨10.1109/TC.2005.52⟩. ⟨ensl-00000002⟩
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