A Paradigm for Generalized Multi-Level Priority Encoders

TL;DR

This paper introduces a generalized multi-level priority encoder paradigm that reduces complexity and analyzes tradeoffs between complexity and delay across various architectures for high-precision applications.

Contribution

It extends the two-level priority encoder concept to multiple levels using cascading and composition, providing a comprehensive analysis and a toolkit for optimal hardware design.

Findings

Two-level architecture halves complexity with increased delay

Additional levels offer diminishing complexity benefits

Tree and recursive designs are faster but more complex

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.