New number representation and conversion techniques on reconfigurable mesh

Several new number representations based on the residue number system are presented which use the smallest prime numbers as moduli and are suited for parallel computations on a reconfigurable mesh architecture. It is shown how to convert in O(1) time any integer ranging between 0 and n-1, from any commonly used representation to any new representation proposed in the paper (and vice versa) using an n×O(log²n/log log n) reconfigurable mesh. In particular, some of the previously known conversion techniques are improved. Moreover, as a by product, it is shown how to compute in O(1) time the prefix sums of n bits improving previously known results. Applications to the summation and prefix sums of N h-bit integers are also considered. The summation and the prefix sums can be computed in O(1) time using O(h log N+log²N/log log N)×Nh and O(h ²+log² N/log(h+log N))×O(N(h+log N)) reconfigurable meshes, respectively, improving all previously known results for most values of h including, for instance, h=O(log N)