Automatic Tools for Deriving, Analyzing, and Implementing Linear Algebra Libraries

货车de Geijin，RobertCCF-0342369建议的项目将开发原型工具，用于高性能顺序和并行线性代数库的自动推导、自动实现、自动性能建模和自动稳定性分析。作为建议的项目的一部分，将创建一套工具，将合并上述原型（半）自动化系统的功能。 该功能将扩展到包括针对不同语言的API自动生成代码，具有多级存储器（包括分布式存储器）的架构的自动成本分析以及自动稳定性分析。 系统的输入将是线性代数表达式形式的矩阵运算。 输出将是给定操作的整个算法家族、顺序和并行架构的高性能实现、实现的成本分析以及算法的稳定性分析。该系统的演示将是自动创建下一代高性能库，其功能包括LAPACK等，它是一种简化的知识系统，是开发高性能计算机的基础，性能线性代数库，它代表了这个项目对科学的主要贡献。对已经达到的理解水平的最终证明。所提出的工作的成功将通过以下几个方面来衡量：（1）自动化工具的广泛适用性;（2）适应新的体系结构特征所需的工作量;以及（3）新功能能够被工具容纳的难易程度。换句话说，成功的衡量将在很大程度上取决于生产力，维护和适用性。

Van de Geijin, RobertCCF-0342369The proposed project will develop prototype tools for the automaticderivation, automatic implementation, automatic performance modeling,and automatic stability analysis of high-performance sequential andparallel linear algebra libraries.As part of the proposed project, a set of tools will be created thatwill merge the capabilities of the above described prototypem (semi-) automated systems. The functionality will be extended to encompass automated generation of code targeting APIs for different languages, automated cost analysis for architectures with multi-level memories (including distributed memory) as well as automated stability analysis. The input to the system will be matrix operations in form of linear algebraic expression. The output will be entire families of algorithms for the given operations, high-performance implementations for sequential and parallel architectures, cost analyses of the implementations, and stability analyses of the algorithms. A demonstration of the system will be the automatic creation of a next-generation high-performance library with functionality that encompasses LAPACK and more, parameterized for a broad range of sequential and parallel architectures.It is the reduction to a system of the knowledge that underlies thedevelopment of high-performance linear algebra libraries thatrepresents the primary contribution to science of this project.Automation of the kind that is targeted is the ultimate demonstrationof the level of understanding that has been achieved.The success of the proposed work will then measured by: (1) thebroadness of applicability of the automated tools; (2) the amount ofeffort required to accommodate new architectural features; and (3) theease with which new functionality can be accommodated by the tools.In other words, the measurement of success will largely be withrespect to productivity, maintenance, and applicability.