A Paradigm for Generalized Multi-Level Priority Encoders
Maxwell Phillips, Firas Hassan, Ahmed Ammar
TL;DR
The paper addresses the high hardware cost of priority encoders at large input widths by introducing a generalized multi level PE paradigm built via composition and cascading. It systematically analyzes and compares standard, recursive, tree, two level, and multi level PE architectures on FPGA and ASIC, revealing a clear complexity delay tradeoff and the notable efficiency of two level encoders for reducing complexity. The main contributions are the multi level design framework, formalized construction methods, and a comprehensive complexity and delay analysis that yields practical recommendations and a hardware designer toolkit. This work enables informed architecture selection for high precision computing tasks and memory applications by providing cross technology guidance and a quantified understanding of the tradeoffs involved.
Abstract
Priority encoders are typically considered expensive hardware components in terms of complexity, especially at high bit precisions or input lengths (e.g., above 512 bits). However, if the complexity can be reduced, priority encoders can feasibly accelerate a variety of key applications, such as high-precision integer arithmetic and content-addressable memory. We propose a new paradigm for constructing priority encoders by generalizing the previously proposed two-level priority encoder structure. We extend this concept to three and four levels using two techniques -- cascading and composition -- and discuss further generalization. We then analyze the complexity and delay of new and existing priority encoder designs as a function of input length, for both FPGA and ASIC implementation technologies. In particular, we compare the multi-level structure to the traditional single-level priority encoder structure, a tree-based design, a recursive design, and the two-level structure. We find that the two-level architecture provides balanced performance -- reducing complexity by around half, but at the cost of a corresponding increase in delay. Additional levels have diminishing returns, highlighting a tradeoff between complexity and delay. Meanwhile, the tree and recursive designs are generally faster, but are more complex than the two-level and multi-level structures. We explore several characteristics and patterns of the designs across a wide range of input lengths. We then provide recommendations on which architecture to use for a given input length and implementation technology, based on which design factors -- such as complexity or delay -- are most important to the hardware designer. With this overview and analysis of various priority encoder architectures, we provide a priority encoder toolkit to assist hardware designers in creating the most optimal design.