Basic Linear Algebra Subprograms (BLAS) are the building blocks for various numerical algorithms and are widely used in scientific computations. However, some linear algebra applications need more precision than the standard double precision available in most existing BLAS libraries. In this paper, we implement and evaluate multiple-precision scalar and vector BLAS functions on graphics processing units (GPUs). We use the residue number system (RNS) to represent arbitrary length floating-point numbers. The non-positional nature of RNS enables parallelism in multiple-precision arithmetic and makes RNS a good tool for high-performance computing applications. We first present new data-parallel algorithms for multiplying and adding RNS-based floating-point representations. Next, we suggest algorithms for multiple-precision vectors specially designed for parallel computations on GPUs. Using these algorithms, we develop and evaluate four GPU-accelerated multiple-precision BLAS functions, ASUM, DOT, SCAL, and AXPY. It is shown through experiments that in many cases, the implemented functions achieve significantly better performance compared to existing multiple-precision software for CPU and GPU.

基本线性代数子程序（BLAS）是各种数值算法的基础，并广泛用于科学计算中。但是，某些线性代数应用需要比大多数现有BLAS库中提供的标准双精度更高的精度。在本文中，我们在图形处理单元（GPU）上实现并评估了多精度标量和矢量BLAS函数。我们使用残数系统（RNS）表示任意长度的浮点数。RNS的非位置性质可实现多精度算术中的并行性，并使RNS成为高性能计算应用程序的良好工具。我们首先提出新的数据并行算法，用于乘以和添加基于RNS的浮点表示。下一个，我们建议为GPU上的并行计算特别设计的多精度向量算法。使用这些算法，我们开发并评估了四个GPU加速的高精度BLAS函数ASUM，DOT，SCAL和AXPY。通过实验表明，在许多情况下，与用于CPU和GPU的现有多精度软件相比，已实现的功能可实现明显更好的性能。