Efficient function approximation using truncated multipliers and squarers

This paper presents a technique for designing linear and quadratic interpolators for function approximation using truncated multipliers and squarers. Initial coefficient values are found using a Chebyshev series approximation, and then adjusted through exhaustive simulation to minimize the maximum absolute error of the interpolator output. This technique is suitable for any function and any precision up to 24-bits (IEEE single precision). Designs for linear and quadratic interpolators that implement the reciprocal function, f(x) = 1/x, are presented and analyzed as an example. We show that a 24-bit truncated reciprocal quadratic interpolator with a design specification of ± 1 ulp error requires 24.1 % fewer partial products to implement than a comparable standard interpolator with the same error specification.