A singular loop transformation framework based on non-singular matrices

Journal Article · Fri Apr 01 04:00:00 UTC 1994 · International Journal of Parallel Programming

DOI:https://doi.org/10.1007/BF02577874· OSTI ID:379411

Li, Wei; Pingali, K ^[1]

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1. Cornell Univ., Ithaca, NY (United States)

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 a transformation called loop scaling. This framework is more general than existing ones; however, it is also more difficult to generate code in our framework. 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 dependences. This completion procedure has applications in parallelization and in the generation of code for NUMA machines.

• Sponsoring Organization: USDOE
• OSTI ID: 379411
• Journal Information: International Journal of Parallel Programming, Journal Name: International Journal of Parallel Programming Journal Issue: 2 Vol. 22; ISSN IJPPE5; ISSN 0885-7458
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ALGORITHMS
ARRAY PROCESSORS
ITERATIVE METHODS
MATRICES
PARALLEL PROCESSING
TRANSFORMATIONS