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Title: A Singular Loop Transformation Framework Based on Non-singular Matrices
Authors: Li, Wei
Pingali, Keshav
Keywords: theory center
Issue Date: Jul-1992
Publisher: Cornell University
Abstract: In this paper, we discuss a loop transformation framework that is based on integer non-singular matrices. The transformations included in this framework are called A-transformations and include permutation, skewing and reversal, as well as transformation called loop scaling. This framework i s more general than existing ones; however, it is also more difficult to generate code in our frame- work. This paper shows how integer lattice theory can be used to generate efficient code. An added advantage of our framework over existing ones is that there is a simple completion algorithm which, given a partial transformation matrix, produces a full transformation matrix that satisfies all dependencies. This completion procedure has applications in parallelization and in the generation of code for NUMA machines.
Appears in Collections:Cornell Theory Center Technical Reports

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