Variable Point: A Number Format for Area- and Energy-Efficient Multiplication of High-Dynamic-Range Numbers

2025-11-28

AI Summary

To address the trade-off between limited dynamic range in fixed-point arithmetic and high hardware overhead in floating-point representations for high-dynamic-range signals in digital VLSI design, this paper proposes a novel Variable-Point (VP) numeric format. VP dynamically adjusts the binary point position, thereby significantly extending representable value ranges while maintaining bit-width and hardware complexity comparable to fixed-point implementations. Building upon this format, we design a low-overhead matrix-vector multiplication engine and apply it to the VLSI implementation of a multi-antenna wireless communication spatial equalizer. Post-layout synthesis results demonstrate that, compared to a fully optimized fixed-point baseline, the VP-based design achieves a 20% reduction in area and a 10% reduction in power consumption—without any loss in numerical accuracy or computational performance. This work thus enables joint optimization of area efficiency, energy consumption, and dynamic range in high-throughput signal processing accelerators.

Technology Category

• Machine Learning: Hardware-aware ML
• Search and Optimization: Mixed Discrete/Continuous Search
• Computer Vision: Learning & Optimization for CV

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Virtualization and resource management in Web systems and infrastructures
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

Fixed-point number representation is commonly employed in digital VLSI designs that have stringent hardware efficiency constraints. However, fixed-point numbers cover a relatively small dynamic range for a given bitwidth. In contrast, floating-point numbers offer a larger dynamic range at the cost of increased hardware complexity. In this paper, we propose a novel number format called variable-point (VP). VP numbers cover a larger dynamic range than fixed-point numbers with similar bitwidth, without notably increasing hardware complexity -- this allows for a more efficient representation of signals with high dynamic range. To demonstrate the efficacy of the proposed VP number format, we consider a matrix-vector multiplication engine for spatial equalization in multi-antenna wireless communication systems involving high-dynamic-range signals. Through post-layout VLSI implementation results, we demonstrate that the proposed VP-based design achieves 20% and 10% area and power savings, respectively, compared to a fully optimized fixed-point design, without incurring any noticeable performance degradation.

Problem

• Proposes a novel variable-point number format for efficient multiplication
• Addresses limited dynamic range of fixed-point numbers in VLSI designs
• Enables area and power savings in high-dynamic-range signal processing

Innovation

• Variable-point format for high-dynamic-range multiplication
• Efficient hardware without complexity of floating-point
• Area and power savings in VLSI implementation