High-speed coprocessors for computing nonlinear functions are important for advanced scientific computing as well as real-time image processing. In this paper we develop an efficient interpolative approach to such coprocessors. Performed on suitable subintervals of the range of interest, our interpolation which uses third degree polynomial is adequate for many elementary functions of interest with double precision mantissas. Our method requires only one major multiplication, two minor multiplications and a few additions. The minor multiplications are for the second and third degree terms, and their significant bits are much fewer than those of the first degree term. This leads to a very fast and efficient VLSI architecture for such coprocessors. It appears that polynomial based interpolation can yield considerable benefits over previously used approaches, when execution time and silicon area are considered. Further, it is possible to combine the computation of multiple functions on a single chip, with most of the resources on the chip shared for several functions.