AritPIM: High-Throughput In-Memory Arithmetic

TL;DR

This paper introduces novel in-memory algorithms for fundamental arithmetic operations, leveraging PIM architectures to achieve high throughput and energy efficiency, including the first digital PIM algorithms for floating-point addition.

Contribution

It develops new algorithmic techniques for digital PIM that enable all four basic arithmetic operations on fixed-point and floating-point numbers, surpassing previous limitations.

Findings

First digital PIM algorithms for floating-point addition

Significant throughput improvements over GPU implementations

Enhanced energy efficiency in memristive PIM systems

Abstract

Digital processing-in-memory (PIM) architectures are rapidly emerging to overcome the memory-wall bottleneck by integrating logic within memory elements. Such architectures provide vast computational power within the memory itself in the form of parallel bitwise logic operations. We develop novel algorithmic techniques for PIM that, combined with new perspectives on computer arithmetic, extend this bitwise parallelism to the four fundamental arithmetic operations (addition, subtraction, multiplication, and division), for both fixed-point and floating-point numbers, and using both bit-serial and bit-parallel approaches. We propose a state-of-the-art suite of arithmetic algorithms, demonstrating the first algorithm in the literature of digital PIM for a majority of cases - including cases previously considered impossible for digital PIM, such as floating-point addition. Through a case study on memristive PIM, we compare the proposed algorithms to an NVIDIA RTX 3070 GPU and demonstrate significant throughput and energy improvements.