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Dependence analysis for supercomputing
Utpal Banerjee
- 01 Jan 1988
671
TL;DR: This chapter discusses one-Dimensional Arrays, Single Loops, and Dependence Tests, which are tests of the theory of Dependence on Vectors and its application to Systems of Equations.
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Abstract: 1. Introduction.- 2. Basic Concepts.- 2.1. Relations and Graphs.- 2.2. Orders on Vectors.- 2.3. Program Model.- 3. Dependence.- 3.1. Dependence Concepts.- 3.2. The Dependence Problem.- 4. Bounds of Linear Functions.- 4.1. Introduction.- 4.2. Bounds in Rectangles.- 4.3. Bounds in Trapezoids.- 5. Linear Diophantine Equations.- 5.1. Introduction.- 5.2. Greatest Common Divisors.- 5.3. Single Equation in Two Variables.- 5.4. Single Equation in Many Variables.- 5.5. Systems of Equations.- Appendix to Chapter 5.- 6. Dependence Tests.- 6.1. Introduction.- 6.2. One-Dimensional Arrays, Single Loops.- 6.3. One-Dimensional Arrays.- 6.4. General Case.- 6.5. Miscellaneous Comments.- References.
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Citations
A data locality optimizing algorithm
Michael Wolf,Monica S. Lam +1 more
- 01 May 1991
TL;DR: An algorithm that improves the locality of a loop nest by transforming the code via interchange, reversal, skewing and tiling is proposed, and is successful in optimizing codes such as matrix multiplication, successive over-relaxation, LU decomposition without pivoting, and Givens QR factorization.
Compiler transformations for high-performance computing
TL;DR: This survey is a comprehensive overview of the important high-level program restructuring techniques for imperative languages, such as C and Fortran, and describes the purpose of each transformation, how to determine if it is legal, and an example of its application.
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Recipes for adjoint code construction
Ralf Giering,Thomas Kaminski +1 more
TL;DR: The described method is based on a few basic principles, which permits the establishment of simple construction rules for adjoint statements and complete adjoint subprograms and is an implementation of the tangent linear and adjoint model compiler (TAMC).
The Omega test: a fast and practical integer programming algorithm for dependence analysis
William Pugh
- 01 Aug 1991
TL;DR: Evidence is presented that suggests conventional wisdom is wrong, and that the Omega test is competitive with approximate algorithms used in practice and suitable for use in production compilers, and has low order polynomial time complexity.
A loop transformation theory and an algorithm to maximize parallelism
Michael Wolf,Monica S. Lam +1 more
TL;DR: The loop transformation theory is applied to the problem of maximizing the degree of coarse- or fine-grain parallelism in a loop nest and it is shown that the maximum degree of parallelism can be achieved by transforming the loops into a nest of coarsest fullypermutable loop nests and wavefronting the fully permutable nests.
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