Emulation of Complex Matrix Multiplication based on the Chinese Remainder Theorem

TL;DR

This paper introduces high-performance methods for emulating complex matrix multiplication on low-precision hardware using the Chinese Remainder Theorem, significantly improving speed over native routines.

Contribution

It extends the Ozaki-II scheme to complex matrix multiplication, enabling faster emulation on INT8 engines with adjustable accuracy.

Findings

Achieves 4.4--6.5x speedup over cuBLAS for complex matrix multiplication.

Allows higher speed with lower accuracy or higher accuracy with modest additional time.

Potential to serve as a default algorithm for various applications.

Abstract

Modern computing architectures feature low-precision matrix multiplication units that achieve substantially higher throughput than their high-precision counterparts. Motivated by this architectural trend, the emulation of high-precision matrix multiplication using low-precision hardware has attracted significant interest in the high-performance computing community. Ozaki, Uchino, and Imamura proposed the Ozaki-II scheme as a general framework for emulating matrix multiplication. Building on this framework, Uchino, Ozaki, and Imamura developed high-performance and power-efficient techniques for emulating single- and double-precision real matrix multiplication on INT8 matrix engines. Extending this line of research, the present study proposes high-performance emulation methods for single- and double-precision complex matrix multiplication on INT8 matrix engines, based on the Ozaki-II scheme. On an NVIDIA B200 GPU, the proposed methods achieve 4.4--6.5x and 4.0--5.6x speedups over the native single- and double-precision complex matrix multiplication routines from cuBLAS, respectively, for sufficiently large problem sizes. When lower accuracy than that of the standard routines is acceptable, the proposed methods can operate at even higher speed. Conversely, with only a modest increase in computation time, they can deliver higher accuracy than that of the standard routines. These properties suggest that the proposed approach has the potential to serve as a default algorithm across a wide range of applications.