Algorithmic Truncation of MiniMax Polynomial Coefficients
Sara Tawfik, Hossam A. H. Fahmy · 2006
Elementary and high-level functions can be computed in hardware using polynomial approximation techniques. There are many techniques in the literature to calculate the coefficients of such polynomials. Remez algorithm as presented by Veidinger (1960) provides the optimal polynomial in the Chebyshev sense that is minimizing the maximum error (minimax approximation). This paper presents an algorithm for truncating the coefficients of the minimax polynomials obtained from Remez algorithm using an algorithmic method. A gain of 3 and 4 bits of accuracy over the direct rounding is reported. Muller addressed the same problem but his algorithm is applicable for the second order polynomials only. This paper presents an algorithm that is applicable for any order