AritPIM: High-Throughput In-Memory Arithmetic

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.

I. Introduction

Emerging processing-in-memory (PIM) systems attempt to overcome the memory-wall bottleneck by rethinking one of the core principles of computing systems: the separation of storage and logic units. This separation has been followed since the introduction of the von Neumann architecture in the 1940 s, when computing systems were primarily utilized for serial program execution. Yet, the recent emergence of data-intensive applications requires parallel high-throughput execution, causing the separation to become a massive bottleneck known as the memory wall [1]. Therefore, PIM integrates logic within the memory to bypass the bandwidth-limited memory interface and enable massive in-memory computational parallelism [2].