Mixed precision LU factorization on GPU tensor cores: reducing data movement and memory footprint
Mixed precision LU factorization on GPU tensor cores: reducing data movement and memory footprint
复制标题
GPU 张量核心上的混合精度 LU 分解：减少数据移动和内存占用
DOI：
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发表时间：
2023
期刊：
影响因子：
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通讯作者：
Théo Mary
中科院分区：
文献类型：
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作者：
Florent Lopez;Théo Mary
配备混合精度张量核心单元的现代GPU在加速密集线性代数运算（如LU分解）方面具有巨大潜力。然而，最先进的混合半/单精度LU分解算法都需要以单精度存储矩阵，导致昂贵的数据移动和存储成本。这可以通过以下事实来解释：简单地将存储精度从单精度切换到半精度会导致精度的显著损失，从而丧失使用张量核心技术带来的所有精度优势。在这篇文章中，我们提出了一个新的因式分解算法，它能够以半精度存储矩阵，而不会导致任何显着的准确性损失。我们的方法是基于一个左看方案，采用单精度缓冲区的控制大小和一个混合精度双分区算法，利用张量核心的面板分解。我们的数值结果表明，与现有技术相比，所提出的方法具有相似的精度，但只有一半的数据移动和内存占用，因此可能更快：它在V100和A100 GPU上分别实现了高达2倍和3.5倍的加速比。
Modern GPUs equipped with mixed precision tensor core units present great potential to accelerate dense linear algebra operations such as LU factorization. However, state-of-the-art mixed half/single precision LU factorization algorithms all require the matrix to be stored in single precision, leading to expensive data movement and storage costs. This is explained by the fact that simply switching the storage precision from single to half leads to significant loss of accuracy, forfeiting all accuracy benefits from using tensor core technology. In this article, we propose a new factorization algorithm that is able to store the matrix in half precision without incurring any significant loss of accuracy. Our approach is based on a left-looking scheme employing single precision buffers of controlled size and a mixed precision doubly partitioned algorithm exploiting tensor cores in the panel factorizations. Our numerical results show that compared with the state of the art, the proposed approach is of similar accuracy but with only half the data movement and memory footprint, and hence potentially much faster: it achieves up to 2× and 3.5× speedups on V100 and A100 GPUs, respectively.