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

该项目将开发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的原型工具。作为提议项目的一部分，将创建一组工具，这些工具将合并上述原型（半）自动化系统的功能。该功能将被扩展到包括针对不同语言的api的自动代码生成，具有多级内存（包括分布式内存）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，参数化适用于广泛的顺序和并行体系结构。这是对知识系统的简化，是高性能线性代数库开发的基础，代表了该项目对科学的主要贡献。所针对的那种自动化是对已达到的理解水平的最终展示。拟议工作的成功将通过以下方式来衡量：(1)自动化工具的适用性范围；(2)容纳新建筑特征所需的工作量；(3)工具能够容纳新功能的难易程度。换句话说，成功的度量将在很大程度上与生产力、维护和适用性有关。

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.