High-level semantic optimization of numerical codes

This paper presents a mathematical framework to exploit the semantic properties of matrix operations in loop-based numerical codes. The heart of this framework is an algebraic language called the Abstract Matrix Form which a compiler can use to reason about matrix computations in terms of loop nests, high-level matrix operations, and intermediate forms. We demonstrate how this framework may be used to detect and exploit matrix products in loop-based languages such as FORTRAN and MATLAB, and discuss the resulting performance bene ts.

• Type: Conference
• Year: 1999
• Where: ICS
• Authors: Vijay Menon, Keshav Pingali
• Keywords: Abstract Matrix Form, Distributed And Parallel Computing, ICS 1999, Matrix, Matrix Operations