The I test: an improved dependence test for automatic parallelization and vectorization

Kong, Xiangyun; Klappholz, David; Psarris, Kleanthis

doi:10.1109/71.86109

Cited by 82 publications

(36 citation statements)

References 6 publications

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“…This aids in both bounds analysis and in the filtering of self-output dependences. These enhancements can also be useful to other more powerful dependence tests such as the I-test [18,22] Analysis of CR-forms for loops MJ and MI determine both forms to be monotonically increasing. What are not known are the upperbounds of the CR forms for any of the loops or the monotonicity of the CR-form for loop MRS. Based on what is known, the CR-enhanced Banerjee test is able to reduce the direction vector ( * , * , * ) to {(<>,*,=),(=,<>,=)}, thus filtering a loop-carried dependence (loop MJ) for a non-linear dependence equation.…”

Section: Discussionmentioning

confidence: 99%

An empirical evaluation of chains of recurrences for array dependence testing

Birch

Engelen

Gallivan

et al. 2006

Proceedings of the 15th International Conference on Parallel Architectures and Compilation Techniques

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Code restructuring compilers rely heavily on program analysis techniques to automatically detect data dependences between program statements. Dependences between statement instances in the iteration space of a loop nest impose ordering constraints that must be preserved in order to produce valid optimized, vectorized, and parallelized loop nests. This paper evaluates a new approach for fast and accurate nonlinear array dependence testing using Chains of Recurrences (CRs). A flow-sensitive loop analysis algorithm is presented for constructing the CR forms of array index expressions. Unlike other approaches, the CR forms are directly integrated into a standard dependence test to solve nonlinear CR-based dependence equations. To study the coverage and performance of the proposed CR-based enhancements of a standard test, we chose the inexact Banerjee test. We implemented a new CR-based Banerjee test in the Polaris compiler and compared the results to the Omega test and Range test on a set of SPEC and LAPACK Benchmark programs. The experimental results suggest that a CR enhancement can dramatically increase the effectiveness of a dependence test without a significant cost increase. More surprisingly, the findings indicate that the enhanced test exceeds the capabilities of the Omega and Range tests for many nonlinear dependence relations detected in the PERFECT Club and LAPACK Benchmark programs.

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Section: Discussionmentioning

confidence: 99%

An empirical evaluation of chains of recurrences for array dependence testing

Birch

Engelen

Gallivan

et al. 2006

Proceedings of the 15th International Conference on Parallel Architectures and Compilation Techniques

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show abstract

“…Though the two tests produce exact yes/no answers, they have worst-case exponential time complexity. The I-test [7] is a polynomial time test. Generally speaking, the I-test is a linear time exact test in most cases for single dimensional array references, but cannot precisely handle multidimensional array references involving coupled subscripts and rely on information known at compile time [8] .…”

Section: Introductionmentioning

confidence: 99%

A general data dependence analysis to nested loop using integer interval theory

Zhou¹,

Zeng²

2006

Proceedings 20th IEEE International Parallel &Amp; Distributed Processing Symposium

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Many dependence tests have been proposed for loop parallelization in the case of arrays with linear subscripts, but little work has been done on the arrays with non-linear subscripts, which sometimes occur in parallel benchmarks and scientific and engineering applications. This paper focuses on array subscripts coupled integer power index variables. We attempt to use the integer interval theory to solve the above difficult dependence test problem. Some "interval solution" rules for polynomial equations have been proposed in this paper. Furthermore, based on the proposed rules, we present a novel approach to loop dependence analysis, which is termed the Polynomial Variable Interval test or PVI-test, and also develop a related algorithm. Some case studies show that the PVI-test is effective and efficient. Compared to the VI test, the PVI-test makes significant improvement, and is therefore a more general scheme of dependence test.

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“…So the data dependence analysis is the foundation of the whole parallelization process. However, it is not an easy problem to determine whether any two statement instances are dependent because it involves to the problem of integer program, so the mainstream approaches usually obtain the approximation solutions by testing [7][8][9][10][11][12][13][14][15][16][17][18].…”

Section: Data Dependence Analysismentioning

confidence: 99%

“…λ-test [8] extends Banerjee test for coupled dimensions. I-test [9] converts the constraints into equation system of integer adjacent intervals and each time solves one of interval equation.…”

Section: Data Dependence Analysismentioning

confidence: 99%

A Survey of Loop Parallelization: Models, Approaches, and Recent Developments

Ye¹,

Deng²,

Zou³

2016

IJGDC

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In cloud computing era, automatic parallelization is still significant for virtualization platform. However, after several decades of development, the overall effect is still to be improved. Summary of the mainstream technology developments will be beneficial to reveal the future direction and trend. This paper reviews the technology of loop parallelization, which is the key issue in automatic parallelization. After introducing the basic models and approaches, we focus on the recent developments, on which we obtain the trend of this field and the conclusions about future.

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The I test: an improved dependence test for automatic parallelization and vectorization

Cited by 82 publications

References 6 publications

An empirical evaluation of chains of recurrences for array dependence testing

An empirical evaluation of chains of recurrences for array dependence testing

A general data dependence analysis to nested loop using integer interval theory

A Survey of Loop Parallelization: Models, Approaches, and Recent Developments

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