Compilers: principles, techniques, and tools
Compilers: principles, techniques, and tools
Selected papers of the second workshop on Languages and compilers for parallel computing
A data locality optimizing algorithm
PLDI '91 Proceedings of the ACM SIGPLAN 1991 conference on Programming language design and implementation
LAPACK's user's guide
A practical algorithm for exact array dependence analysis
Communications of the ACM
Some efficient solutions to the affine scheduling problem: I. One-dimensional time
International Journal of Parallel Programming
A singular loop transformation framework based on non-singular matrices
International Journal of Parallel Programming
Enhancing array dataflow dependence analysis with on-demand global value propagation
ICS '95 Proceedings of the 9th international conference on Supercomputing
Symbolic analysis for parallelizing compilers
ACM Transactions on Programming Languages and Systems (TOPLAS)
Commutativity analysis: a new analysis technique for parallelizing compilers
ACM Transactions on Programming Languages and Systems (TOPLAS)
Compiler blockability of dense matrix factorizations
ACM Transactions on Mathematical Software (TOMS)
IEEE Transactions on Parallel and Distributed Systems
High Performance Compilers for Parallel Computing
High Performance Compilers for Parallel Computing
Compiler techniques for MATLAB programs
Compiler techniques for MATLAB programs
The maple symbolic computation system
ACM SIGSAM Bulletin
Synthesizing Transformations for Locality Enhancement of Imperfectly-Nested Loop Nests
International Journal of Parallel Programming
A unified framework for nonlinear dependence testing and symbolic analysis
Proceedings of the 18th annual international conference on Supercomputing
Equivalence Checking of Static Affine Programs Using Widening to Handle Recurrences
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Equivalence checking of static affine programs using widening to handle recurrences
ACM Transactions on Programming Languages and Systems (TOPLAS)
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Modern compilers perform wholesale restructuring of programs to improve their efficiency. Dependence analysis is the most widely used technique for proving the correctness of such transformations, but it suffers from the limitation that it considers only the memory locations read and written by a statement, and does not assume any particular interpretation for the operations in that statement. Exploiting the semantics of these operations permits more transformations to be proved correct, and is critical for automatic restructuring of codes such as LU with partial pivoting.One approach to exploiting the semantics of program operations is symbolic analysis and comparison of programs. In principle, this technique is very powerful, but in practice, it is intractable for all but the simplest programs.In this paper, we propose a new form of symbolic analysis and comparison of programs which is appropriate for use in restructuring compilers. Fractal symbolic analysis compares a program and its transformed version by repeatedly simplifying these programs until symbolic analysis becomes tractable while ensuring that equality of the simplified programs is sufficient to guarantee equality of the original programs.Fractal symbolic analysis combines some of the power of symbolic analysis with the tractability of dependence analysis. We discuss a prototype implementation of fractal symbolic analysis, and show how it can be used to solve the long-open problem of verifying the correctness of transformations required to improve the cache performance of LU factorization with partial pivoting.