Fast Arithmetic on Reconfigurable Meshes

We show an O(1) time algorithm for computing the N-point Discrete Fourier Transform (DFT) on an NlogN x NlogN reconfigurable mesh, where each poitn is represented using Theta(logN) bits. Based on the DFT algorithm, we derive O(1) time algorithms for N-bit multiplication, N-bit modular operations, and computing the quotient of two N-bit numbers on an N x N bit model of the reconfigurable mesh. The proposed algorithms lead to AT^2 optimal designs in the bit model of VLSI for 1 leqslant T leqslant sqrt N. All these algorithms run on the MRN, RMESH, and PARBUS models of the reconfigurable mesh, and employ optimal size of the mesh.