Look left, look right, look left again: an application of fractal symbolic analysis to linear algebra code restructuring

Authors:
Vijay Menon;Keshav Pingali
Affiliations:
Microprocessor Technology Lab, Intel Corporation, Santa Clara, CA;Department of Computer Science, Cornell University, Ithaca, NY
Venue:
International Journal of Parallel Programming
Year:
2004

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Abstract

Fractal symbolic analysis is a symbolic analysis technique for verifying the legality of program transformations. It is strictly more powerful than dependence analysis; for example, it can be used to verify the legality of blocking LU factorization with pivoting, a task for which dependence analysis is inadequate. In this paper, we show how fractal symbolic analysis can be used to convert between left- and right-looking versions of three kernels of central importance in computational science: triangular solve, Cholesky factorization, and LU factorization with pivoting.