New number representation and conversion techniques on reconfigurable mesh

• Published in: Proceedings. Fifth International Conference on High Performance Computing (Cat. No. 98EX238) pp. 2 - 10
• Main Authors: Bertossi, A.A., Mei, A.
• Format: Conference Proceeding
• Language: English
• Published: IEEE 1998
• Subjects: Arithmetic; Broadcasting; Data structures; Image processing; Joining processes; Logic; Mathematics; Parallel algorithms; Read only memory; Switches
• ISBN: 9780818691942; 0818691948
• DOI: 10.1109/HIPC.1998.737964

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/spl times/O(log/sup 2/n/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+log/sup 2/N/log log N)/spl times/Nh and O(h/sup 2/+log/sup 2/ N/log(h+log N))/spl times/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).