Introduction of the Residue Number Arithmetic Logic Unit With Brief Computational Complexity Analysis

TL;DR

This paper introduces a novel residue number arithmetic logic unit capable of performing fractional arithmetic operations efficiently without carry, significantly reducing computation time for complex operations in digital systems.

Contribution

It presents a new residue-based fractional arithmetic method and hardware design that enables fast, carry-free fractional computations in a single clock cycle regardless of word size.

Findings

Fractional addition, subtraction, multiplication occur in one clock cycle.

Complex operations like sum of products are performed efficiently in extended format.

Normalization operation has an execution time of order O(p).

Abstract

Digital System Research has pioneered the mathematics and design for a new class of computing machine using residue numbers. Unlike prior art, the new breakthrough provides methods and apparatus for general purpose computation using several new residue based fractional representations. The result is that fractional arithmetic may be performed without carry. Additionally, fractional operations such as addition, subtraction and multiplication of a fraction by an integer occur in a single clock period, regardless of word size. Fractional multiplication is of the order O(p), where p equals the number of residues. More significantly, complex operations, such as sum of products, may be performed in an extended format, where fractional products are performed and summed using single clock instructions, regardless of word width, and where a normalization operation with an execution time of the order O(p) is performed as a final step.