Symbolic Polynomial Maximization Over Convex Sets and Its Application to Memory Requirement Estimation

Clauss, Philippe; Fernandez, F.J.; Garbervetsky, Diego; Verdoolaege, Sven

doi:10.1109/tvlsi.2008.2002049

Cited by 23 publications

(20 citation statements)

References 42 publications

(76 reference statements)

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“…There are techniques [Braberman et al 2008;Clauss et al 2009] that can compute the memory requirements of object-oriented programs with region-based garbage collection. These systems infer invariants and use external tools that count the number of integer points in the corresponding polytopes to obtain bounds.…”

Section: Other Workmentioning

confidence: 99%

Multivariate amortized resource analysis

Hoffmann

Aehlig

Hofmann

2012

ACM Trans. Program. Lang. Syst.

115

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We study the problem of automatically analyzing the worst-case resource usage of procedures with several arguments. Existing automatic analyses based on amortization or sized types bound the resource usage or result size of such a procedure by a sum of unary functions of the sizes of the arguments.In this article we generalize this to arbitrary multivariate polynomial functions thus allowing bounds of the form mn which had to be grossly overestimated by m 2 + n 2 before. Our framework even encompasses bounds like i, j≤n m i m j where the m i are the sizes of the entries of a list of length n.This allows us for the first time to derive useful resource bounds for operations on matrices that are represented as lists of lists and to considerably improve bounds on other superlinear operations on lists such as longest common subsequence and removal of duplicates from lists of lists. Furthermore, resource bounds are now closed under composition which improves accuracy of the analysis of composed programs when some or all of the components exhibit superlinear resource or size behavior.The analysis is based on a novel multivariate amortized resource analysis. We present it in form of a type system for a simple first-order functional language with lists and trees, prove soundness, and describe automatic type inference based on linear programming.We have experimentally validated the automatic analysis on a wide range of examples from functional programming with lists and trees. The obtained bounds were compared with actual resource consumption. All bounds were asymptotically tight, and the constants were close or even identical to the optimal ones.

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Section: Other Workmentioning

confidence: 99%

Multivariate amortized resource analysis

Hoffmann

Aehlig

Hofmann

2012

ACM Trans. Program. Lang. Syst.

115

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“…Later, in 2009, this approach was improved to consider polynomials defined over a parametrized polytope. The related paper also shows applications on estimating the memory requirements of programs [3].…”

Section: Extensions and Perspectivesmentioning

confidence: 99%

Author retrospective for counting solutions to linear and nonlinear constraints through ehrhart polynomials

Clauss¹

2014

25th Anniversary International Conference on Supercomputing Anniversary Volume -

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“…To find some sufficient conditions on the parameter values ensuring that (1) is satisfied, we use a method based on symbolic Bernstein expansion of polynomials defined over parametrized convex polytopes, described in Clauss and Tchoupaeva [2004] and Clauss et al [2009] and implemented in the ISL library [Verdoolaege 2010]. This method allows us to compute the maximum value that can be reached by a polynomial.…”

Section: Extension To Polynomial Codesmentioning

confidence: 99%

Polyhedral parallelization of binary code

Pradelle

Ketterlin

Clauss

2012

ACM Trans. Archit. Code Optim.

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International audienceMany automatic software parallelization systems have been proposed in the past decades, but most of them are dedicated to source-to-source transformations. This paper shows that parallelizing executable programs is feasible, even if they require complex transformations, and in effect decouples parallelization from compilation, for example, for closed-source or legacy software, where binary code is the only available representation. We propose an automatic parallelizer, which is able to perform advanced parallelization on binary code. It first parses the binary code and extracts high-level information. From this information, a C program is generated. This program captures only a subset of the program semantics, namely, loops and memory accesses. This C program is then parallelized using existing, state-of-the-art parallelizers, including advanced polyhedral parallelizers. The original program semantics is then re-injected, and the transformed parallel loop nests are recompiled by a standard C compiler. We show on the PolyBench benchmark suite that our system successfully detects and parallelizes almost all the loop nests from the binary code, using a recent polyhedral loop parallelizer as a backend. The paper ends by elaborating a strategy to parallelize more complex programs, such as those containing non-linear accesses to memory, and provides a few example case-studies

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Symbolic Polynomial Maximization Over Convex Sets and Its Application to Memory Requirement Estimation

Cited by 23 publications

References 42 publications

Multivariate amortized resource analysis

Multivariate amortized resource analysis

Author retrospective for counting solutions to linear and nonlinear constraints through ehrhart polynomials

Polyhedral parallelization of binary code

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