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，利用商品图形处理器（GPU）实现多精度算法的高性能。多精度（MP）算法在科学、工程和数学中有重要的应用，当计算需要比标准计算机系统支持更高的数值精度时。它也是用于安全互联网通信的密码学的重要组成部分。GPU可以将MP算法加速两个数量级以上。然而，实现这种性能需要新的算法和软件工具。在先前的授权下实现的幂运算的世界纪录性能将扩展到包括浮点向量运算。一个新的代码生成模型将使处理更广泛的精度在新一代的图形处理器。支持GPU集群在更大的问题上协同工作，以及MP库有效性的实际演示，例如展示一个GPU如何从100多个服务器卸载解密工作，其安全级别比目前常用的更高，正在开发中。每一代GPU架构都需要大量的实验和多精度代码的返工，以获得新的最佳效果。然而，便携式和可扩展的软件包的潜在好处在某些应用领域可能是变革性的。这项工作扩展了PI之前的工作，包括浮点和向量，并开始过渡到GPU集群。其结果将是一个公开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，与CPU相比，每美元的性能和每瓦的性能至少有一个数量级的提高。该方法依赖于一组新的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上搜索算法、寄存器/内存布局和内核启动几何结构的最佳组合，以实现给定精度大小和GPU架构生成的最大资源利用率。

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.