SHF: Small: Solving the Problems of Scalability and Portability while Maximizing Performance of Multiprecision Scalar and Vector Arithmetic on Clusters of GPUs

该项目将 PI 之前的研究扩展到利用商用图形处理器 (GPU) 实现多精度算术的高性能。当计算需要比标准计算机系统支持更高的数值精度时，多精度 (MP) 算术在科学、工程和数学中具有重要的应用。它也是安全互联网通信中使用的密码学的重要组成部分。 GPU 可以将 MP 运算加速两个数量级以上。然而，实现这种性能需要新颖的算法和软件工具。在先前的资助下实现的求幂世界纪录性能将扩展到包括浮点向量运算。新的代码生成模型将能够在新一代图形处理器上处理更广泛的精度。正在开发对 GPU 集群协同工作解决更大问题的支持，以及 MP 库有效性的实际演示，例如展示一个 GPU 如何从一百多个服务器上卸载解密工作，其安全级别比目前常用的更高。每一代 GPU 架构都需要对多精度代码进行大量实验和重新设计，以获得新的最佳值。然而，便携式和可扩展包的潜在好处可能会在某些应用领域带来变革。这项工作扩展了 PI 之前的工作，将浮点和向量纳入其中，并开始向 GPU 集群过渡。其结果将是一个公开可用的多精度算术包和实现工具集，使科学界能够轻松地充分利用 GPU 扩展，在相同的技术步骤中，每美元性能和每瓦性能比 CPU 至少提高一个数量级。该方法依赖于一组新颖的 GPU 存储模型，这些模型提供了更高级别的抽象，代码生成工具可以在该抽象级别上针对给定的精度大小和 GPU 架构生成搜索算法、寄存器/内存布局和内核启动几何的最佳组合，以实现最大的资源利用率。

This project extends the PI's prior research into achieving high performance for multiprecision arithmetic utilizing commodity graphics processors (GPUs). Multiprecision (MP) arithmetic has important applications in science, engineering, and mathematics when computations require greater numerical precision than standard computer systems support. It is also an important part of cryptography used in secure internet communication. GPUs can accelerate MP arithmetic by more than two orders of magnitude. However, achieving this performance requires novel algorithms and software tools. The world-record performance for exponentiation achieved under the prior grant will be extended to include floating point vector arithmetic. A new code generation model will enable handling a wider range of precisions across newer generations of graphics processors. Support for clusters of GPUs to work together on larger problems, and practical demonstrations of the effectiveness of MP library such as showing how one GPU can offload decryption work from more than a hundred servers, with higher levels of security than are currently in common use, is being developed. Each generation of GPU architecture requires extensive experimentation and reworking of multiprecision code to obtain a new optimum. Yet the potential benefits of a portable and scalable package could be transformational in certain application areas. This effort extends PI's prior work to include floating point and vectors, and begin the transition to GPU clusters. The result will be a publicly available multi-precision arithmetic package and implementation toolset that enables the scientific community to easily take full advantage of GPU scaling to obtain at least an order of magnitude improvement in performance per dollar and performance per watt over CPUs at the same technology step. The approach relies on a novel set of models for GPU storage that provide a higher level of abstraction over which the code generation tools can search for optimal combinations of algorithm, register/memory layout, and kernel launch geometry for a given precision size and GPU architectural generation to achieve maximum resource utilization.