Digit systolic algorithms for fine-grain architectures

In this paper, the authors present a novel scheme for performing arithmetic efficiently on fine-grain programmable architectures and FPGA-based systems. They achieve an O(n) speedup over the bit-serial methods of existing fine-grain systems such as the DAP, the MPP and the CM2, within the constraints of regular, near neighbor communication and only a small amount of on-chip memory. This is possible by means of digit systolic algorithms which avoid broadcast and operate in a fully systolic manner at the digit level. They use digit online techniques coupled with a base 4, signed-digit number system to limit carry propagation. Although the algorithms are bit-serial, the authors are able to match the performance of the bit-parallel methods, while retaining low communication complexity. Efficient O(n) time algorithms for multiplication and division of fixed-point, variable precision numbers are given. By using the organization of logic blocks suggested in this paper, problems of placement and routing that exist in systems built using FPGAs can be avoided. Since the algorithms are amenable to pipelining, very high throughput can be obtained