Communication pre-evaluation in HPF

Boulet, Pierre; Redon, Xavier

doi:10.1007/bfb0057861

Cited by 7 publications

(21 citation statements)

References 7 publications

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“…Parametric Linear Inequalities with Existential Variables. Boulet [9] proposes to compute the enumerator of a set of parametric linear inequalities with existential variables in two steps. First, parametric integer programming (PIP) [20] is used to eliminate the existential variables, after which Clauss's [15] method is used to enumerate the resulting set of linear inequalities.…”

Section: Examplementioning

confidence: 99%

“…This combination can handle the parametric counting problems with existential variables reported in [2,6,9,12] that were previously considered difficult or even unsolvable. Since PIP is worst-case exponential, we also investigate an alternative method that uses a number of simple polynomial rewriting rules to eliminate existential quantifiers.…”

Section: Examplementioning

confidence: 99%

“…These counts are used to drive optimizations such as increasing parallelism [38], minimizing memory size [1,2,27,38,42], estimating worst case execution time [28], increasing cache effectiveness [6,16], high-level transformations for DSP applications [23], converting software loops into parallel hardware implementations [5,18,22,25,38] and minimizing communication overhead in distributed applications [9,26,37]. In many of these optimizations, the objects or events to be counted are modeled as the integer solutions to systems of linear inequalities, i.e., as the elements of a set S = { x ∈ Z d | Ax + c ≥ 0 }, with A ∈ Z n×d and c ∈ Z n .…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Experiences with Enumeration of Integer Projections of Parametric Polytopes

Verdoolaege

Beyls

Bruynooghe

et al. 2005

Lecture Notes in Computer Science

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Abstract. Many compiler optimization techniques depend on the ability to calculate the number of integer values that satisfy a given set of linear constraints. This count (the enumerator of a parametric polytope) is a function of the symbolic parameters that may appear in the constraints. In an extended problem (the "integer projection" of a parametric polytope), some of the variables that appear in the constraints may be existentially quantified and then the enumerated set corresponds to the projection of the integer points in a parametric polytope. This paper shows how to reduce the enumeration of the integer projection of parametric polytopes to the enumeration of parametric polytopes. Two approaches are described and experimentally compared. Both can solve problems that were considered very difficult to solve analytically.

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Section: Examplementioning

confidence: 99%

Section: Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Experiences with Enumeration of Integer Projections of Parametric Polytopes

Verdoolaege

Beyls

Bruynooghe

et al. 2005

Lecture Notes in Computer Science

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“…Examples include counting the number of calculations, accessed memory locations or statement executions in a loop nest or parts thereof [6,21,23,28,29,38]; calculating the number of cache misses in a loop [12,16,24]; computing the number of dynamically allocated bytes [11]; enumerating the number of live array elements at a given iteration (i, j) [27,42]; counting how many parallel processing elements can be used when executing a loop on an FPGA [5,22,25] and computing the amount of communication for a given schedule of parallel tasks on a distributed computing system [9,26,37].…”

Section: Introductionmentioning

confidence: 99%

“…Computing the number of elements in such a set is, amongst others, needed in the program analyses described in [1,2,5,6,9,12,16,25,26,37,42]. Practical examples are discussed in an extended version of this paper, see [39].…”

Section: Introductionmentioning

confidence: 99%

Compiler Construction

2005

Lecture Notes in Computer Science

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Counting Integer Points in Parametric Polytopes Using Barvinok's Rational Functions

et al. 2007

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Many compiler optimization techniques depend on the ability to calculate the number of elements that satisfy certain conditions. If these conditions can be represented by linear constraints, then such problems are equivalent to counting the number of integer points in (possibly) parametric polytopes.It is well known that the enumerator of such a set can be represented by an explicit function consisting of a set of quasi-polynomials, each associated with a chamber in the parameter space. Previously, interpolation was used to obtain these quasi-polynomials, but this technique has several disadvantages. Its worst-case computation time for a single quasi-polynomial is exponential in the input size, even for fixed dimensions. The worst-case size of such a quasi-polynomial (measured in bits needed to represent the quasi-polynomial) is also exponential in the input size. Under certain conditions this technique even fails to produce a solution.Our main contribution is a novel method for calculating the required quasi-polynomials analytically. It extends an existing method, based on Barvinok's decomposition, for counting the number of integer points in a non-parametric polytope. Our technique always produces a solution and computes polynomially-sized enumerators in polynomial time (for fixed dimensions).

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Communication pre-evaluation in HPF

Cited by 7 publications

References 7 publications

Experiences with Enumeration of Integer Projections of Parametric Polytopes

Experiences with Enumeration of Integer Projections of Parametric Polytopes

Compiler Construction

Counting Integer Points in Parametric Polytopes Using Barvinok's Rational Functions

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