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

该项目扩展了PI先前的研究，以利用商用图形处理器(GPU)实现高性能的多精度运算。当计算需要比标准计算机系统支持的更高的数值精度时，多精度(MP)算法在科学、工程和数学中有重要的应用。它也是用于安全互联网通信的密码学的重要组成部分。图形处理器可以将MP算法加速两个数量级以上。然而，实现这一性能需要新颖的算法和软件工具。在之前的授权下实现的乘法运算的世界纪录性能将扩大到包括浮点向量算术。新的代码生成模型将支持在新一代图形处理器上处理更广泛的精度。正在开发对多个图形处理器集群共同处理更大问题的支持，并正在开发MP库的有效性的实际演示，例如展示一个图形处理器如何以高于目前普遍使用的安全级别从一百多台服务器上卸载解密工作。每一代GPU架构都需要对多精度代码进行广泛的实验和重新编写，以获得新的最佳性能。然而，在某些应用程序领域，可移植和可扩展包的潜在好处可能是变革性的。这项工作扩展了PI之前的工作，包括浮点和向量，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，在相同技术步骤的情况下，在每美元性能和每瓦性能方面比CPU至少提高一个数量级。该方法依赖于一组新的用于GPU存储的模型，这些模型提供了更高级别的抽象，在此基础上，代码生成工具可以搜索给定精度大小和GPU架构生成的算法、寄存器/存储器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.