Transitive Closure of a Union of Dependence Relations for Parameterized Perfectly-Nested Loops

Bielecki, Wlodzimierz; Kraska, K.; Klimek, Tomasz

doi:10.1007/978-3-642-39958-9_4

Cited by 3 publications

(2 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In Sect. 3.3, we suggest calculating R * kk using a finite integral linear combination of basis dependence distance vectors Bielecki et al (2013).…”

mentioning

confidence: 99%

Using basis dependence distance vectors in the modified Floyd–Warshall algorithm

2014

Self Cite

View full text Add to dashboard Cite

In this paper, we present a modified Floyd-Warshall algorithm, where the most time-consuming part-calculating transitive closure describing self-dependences for each loop statement-is computed applying basis dependence distance vectors derived from all vectors describing self-dependences. We demonstrate that the presented approach reduces the transitive closure calculation time for parameterized graphs representing all dependences in the loop in comparison with that yielded by means of techniques implemented in the Omega and ISL libraries. This increases the applicability scope of techniques based on transitive closure of dependence graphs and being aimed at building optimizing compilers. Experimental results for NASA Parallel Benchmarks are discussed.

show abstract

“…In Sect. 3.3, we suggest calculating R * kk using a finite integral linear combination of basis dependence distance vectors Bielecki et al (2013).…”

mentioning

confidence: 99%

Using basis dependence distance vectors in the modified Floyd–Warshall algorithm

2014

Self Cite

View full text Add to dashboard Cite

show abstract

“…In the presented algorithm, we propose to calculate D * kk using a finite linear combination of basis dependence distance vectors [5].…”

mentioning

confidence: 99%

Using Basis Dependence Distance Vectors to Calculate the Transitive Closure of Dependence Relations by Means of the Floyd-Warshall Algorithm

Bielecki

Kraska

Klimek

2013

Combinatorial Optimization and Applications

Self Cite

View full text Add to dashboard Cite

In this paper, we present a modified Floyd-Warshall algorithm, where the most time-consuming part -calculating transitive closure describing self-dependences for each loop statement -is computed by means of basis dependence distance vectors derived from all vectors describing self-dependences. We demonstrate that the presented approach reduces the transitive closure calculation time for parameterized graphs representing all dependences in the loop in comparison with techniques implemented in the Omega and ISL libraries. This increases the applicability scope of techniques based on transitive closure of dependence graphs. Experimental results for NASA Parallel Benchmarks are discussed.

show abstract

Computing Invariants with Transformers: Experimental Scalability and Accuracy

Maisonneuve

Hermant

Irigoin

2014

Electronic Notes in Theoretical Computer Science

View full text Add to dashboard Cite

International audienceUsing abstract interpretation, invariants are usually obtained by solving iteratively a system of equations linking preconditions according to program statements. However, it is also possible to abstract first the statements as transformers, and then propagate the preconditions using the transformers. The second approach is modular because procedures and loops can be abstracted once and for all, avoiding an iterative resolution over the call graph and all the control flow graphs. However, the transformer approach based on polyhedral abstract domains encurs two penalties: some invariant accuracy may be lost when computing transformers, and the execution time may increase exponentially because the dimension of a transformer is twice the dimension of a precondition. The purposes of this article are 1) to measure the benefits of the modular approach and its drawbacks in terms of execution time and accuracy using significant examples and a newly developed benchmark for loop invariant analysis, ALICe, 2) to present a new technique designed to reduce the accuracy loss when computing transformers, 3) to evaluate experimentally the accuracy gains this new technique and other previously discussed ones provide with ALICe test cases and 4) to compare the executions times and accuracies of different tools, ASPIC, ISL, PAGAI and PIPS. Our results suggest that the transformer-based approach used in PIPS, once improved with transformer lists, is as accurate as the other tools when dealing with the ALICe benchmark. Its modularity nevertheless leads to shorter execution times when dealing with nested loops and procedure calls found in real applications

show abstract

Transitive Closure of a Union of Dependence Relations for Parameterized Perfectly-Nested Loops

Cited by 3 publications

References 16 publications

Using basis dependence distance vectors in the modified Floyd–Warshall algorithm

Using basis dependence distance vectors in the modified Floyd–Warshall algorithm

Using Basis Dependence Distance Vectors to Calculate the Transitive Closure of Dependence Relations by Means of the Floyd-Warshall Algorithm

Computing Invariants with Transformers: Experimental Scalability and Accuracy

Contact Info

Product

Resources

About