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

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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.