Static Analysis of Parameterized Loop Nests for Energy Efficient Use of Data Caches

D'Alberto, Paolo; Nicolau, Alexandru; Veidenbaum, Alexander V.; Gupta, Rajesh K.

doi:10.1007/978-1-4419-9292-5_11

Cited by 8 publications

(13 citation statements)

References 13 publications

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“…It must be noted that a lot of research involving parametric polytopes has been done in the compiler community like, for instance, affine loop nest analysis and transformation [26], [27], the improvement of data locality of nested loops [28], counting lattice points, their images, their projections [29], computing the number of distinct memory locations accessed by a loop nest [30], parametrized integer programming [31]. Many specifications of multimedia algorithms are often parametrized for reason of generality.…”

Section: Memory Size Computation Problemmentioning

confidence: 99%

Computation of Storage Requirements for Multi-Dimensional Signal Processing Applications

Balasa

Zhu

Luican

2007

IEEE Trans. VLSI Syst.

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Abstract-Many integrated circuit systems, particularly in the multimedia and telecom domains, are inherently data dominant. For this class of systems, a large part of the power consumption is due to the data storage and data transfer. Moreover, a significant part of the chip area is occupied by memory. The computation of the memory size is an important step in the system-level exploration, in the early stage of designing an optimized (for area and/or power) memory architecture for this class of systems. This paper presents a novel nonscalar approach for computing exactly the minimum size of the data memory for high-level procedural specifications of multidimensional signal processing applications. In contrast with all the previous works which are estimation methods, this approach can perform exact memory computations even for applications with numerous and complex array references, and also with large numbers of scalars.

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Section: Memory Size Computation Problemmentioning

confidence: 99%

Computation of Storage Requirements for Multi-Dimensional Signal Processing Applications

Balasa

Zhu

Luican

2007

IEEE Trans. VLSI Syst.

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“…The class of "affine programs" (affine access functions to arrays in affine bounded loop nests) has been tackled in the past by many researchers, since they occur frequently and are resource-consuming, in applications like digital audio/video, imaging, graphics, compression/decompression, etc. In this context, array linearization [28], cache access optimization [11,5,15], and memory size computation [32,33] reduce to the problem of counting the number of images of integer points in a polytope (or a Zpolytope 1 ) by an affine function, or equivalently counting the solutions to a Presburger formula. If the considered programs contain unknown variables at compile-time, this problem has to be solved analytically, and the solution has to be expressed as a function of these parameters.…”

Section: Introductionmentioning

confidence: 99%

Memory optimization by counting points in integer transformations of parametric polytopes

Seghir

Loechner

2006

Proceedings of the 2006 International Conference on Compilers, Architecture and Synthesis for Embedded Systems

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Memory size reduction and memory accesses optimization are crucial issues for embedded systems. In the context of affine programs, these two challenges are classically tackled by array linearization, cache access optimization and memory size computation. Their formalization in the polyhedral model reduce to solving the following problem: count the number of solutions of a Presburger formula.In this paper we propose a novel algorithm that answers this question. We solve the Presburger formula whose solution is a union of parametric Z-polytopes and we propose an algorithm to count points in such a union of parametric Z-polytopes. These algorithms were implemented and we compare them to other existing methods.

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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%

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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Static Analysis of Parameterized Loop Nests for Energy Efficient Use of Data Caches

Cited by 8 publications

References 13 publications

Computation of Storage Requirements for Multi-Dimensional Signal Processing Applications

Computation of Storage Requirements for Multi-Dimensional Signal Processing Applications

Memory optimization by counting points in integer transformations of parametric polytopes

Experiences with Enumeration of Integer Projections of Parametric Polytopes

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