HIGH-SPEED FUNCTION APPROXIMATION

Methods and apparatuses are presented for determining coefficients for a polynomial-based approximation of a function, by iteratively estimating a first coefficient, reducing the first coefficient to a lower precision to obtain a first limited-precision coefficient, analytically calculating a second coefficient by taking into account the first limited-precision coefficient, reducing the second coefficient to a lower precision to obtain a second limited-precision coefficient, iteratively estimating a third coefficient by taking into account at least one of the first limited-precision coefficient and the second limited-precision coefficient, and reducing the third coefficient to a lower precision to obtain a third limited-precision coefficient. In one embodiment of the invention, the polynomial-based approximation relates to a minimax approximation of the function approximated, and at least one of the steps for iteratively estimating the first coefficient and iteratively estimating the third coefficient involves use of a Remez exchange algorithm.