Reducing shared memory footprint to leverage high throughput on Tensor Cores and its flexible API extension library

Abstract

Matrix-matrix multiplication is used for various linear algebra algorithms such as matrix decomposition and tensor contraction. NVIDIA Tensor Core is a mixed-precision matrix-matrix multiplication and addition computing unit, where the theoretical peak performance is more than 300 TFlop/s on NVIDIA A100 GPU. NVIDIA provides WMMA API for using Tensor Cores in custom kernel functions. The most common way to use Tensor Core is to supply the input matrices from shared memory, which has higher bandwidth than global memory. However, the Bytes-per-Flops (B/F) ratio of the shared memory and Tensor Cores is small since the performance of Tensor Cores is high. Thus, it is important to reduce the shared memory footprint for efficient Tensor Cores usage. In this paper, we analyze the simple matrix-matrix multiplication on Tensor Cores by the roofline model and figure out that the bandwidth of shared memory might be a limitation of the performance when using WMMA API. To alleviate this issue, we provide a WMMA API extension library to boost the throughput of the computation, which has two components. The first one allows for manipulating the array of registers input to Tensor Cores flexibly. We evaluate the performance improvement of this library. The outcome of our evaluation shows that our library reduces the shared memory footprint and speeds up the computation using Tensor Cores. The second one is an API for the SGEMM emulation on Tensor Cores without additional shared memory usage. We have demonstrated that the single-precision emulating batch SGEMM implementation on Tensor Cores using this library achieves 54.2 TFlop/s on A100 GPU, which outperforms the theoretical peak performance of FP32 SIMT Cores while achieving the same level of accuracy as cuBLAS. The achieved throughput can not be achieved without reducing the shared memory footprint done by our library with the same amount of register usage.