Mapping affine loop nests: New results

Dion, Michèle; Robert, Yves

doi:10.1007/bfb0046628

Cited by 31 publications

(10 citation statements)

References 6 publications

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“…An algorithm based on Gaussian elimination was introduced by Feautrier [10], which computes a placement function for the problem of data and code distributions among the processors. When mapping affine loop nests onto distributed memory parallel computers, for the data and computation alignment problem, an access graph to model affine communications more adequately was presented by Dion and Yves [7]. For a program with nested loops, data access pattern analyzing approaches was proposed by Lam et al [24,25] and was used to enable the program to run on a parallel machine in a communication-free manner with certain constraints.…”

Section: Existing Known Methods For Solving the Alignment Problemmentioning

confidence: 99%

Communication-free data alignment for arrays with exponential references in parallelizing compilers for scalable parallel systems

et al. 2009

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In loops, some arrays are referenced with induction variables. To parallelize such kind of loops, those induction variables should be substituted. Thus, those array references that were substituted are formulated as nonlinear expressions. The goal of data alignment is to intelligently map the computations and data onto a set Communication-free data alignment for arrays with exponential references 5 of virtual processors which are organized as a Cartesian grid (or a template in HPF terms), and to provide data locality for parallelizing compilers so that data access communication costs can be minimized. Most data alignment methods are mainly devised to align the referenced arrays using linear subscripts or quadratic subscripts with n loop index variables, and the methods are well developed. Seldom work, however, is researched on the nonlinear expressions of index variables. This paper proposes a new communication-free data alignment technique to align the referenced arrays using exponential subscripts with n loop index variables or other complex nonlinear expressions. The experimental results using SPEC95FP Benchmarks point out that the techniques proposed in the paper can improve the execution time of the subroutines in these benchmarks.

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Section: Existing Known Methods For Solving the Alignment Problemmentioning

confidence: 99%

Communication-free data alignment for arrays with exponential references in parallelizing compilers for scalable parallel systems

et al. 2009

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“…In some cases, however, index spaces and data dependences are incompatible in this sense and can not be considered for the partitioning. To some extent, this corresponds to the requirement for the access graph in the formulation of the affine mapping problem in [8].…”

Section: Stepmentioning

confidence: 99%

A group theoretic approach to data and code partitioning

Besch¹,

Pohl²

1998

Proceedings of the 1998 ACM Symposium on Applied Computing - SAC '98

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We present a new approach to the problem of dependence-free partitioning of structured domains, also known as alignment. The proposed method is based on a unified description of data and dependence structures with the help of abelian groups, and considers alignment as a factorization problem automatically driven by given crossed-and auto-dependences. We develop a mathematical framework and give some empirical results.

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“…Several other techniques have been proposed in [24,25,26] for mapping affine loops on to multiple processors. However, these techniques focus primarily on communication minimization between the processors.…”

Section: Previous Workmentioning

confidence: 99%

A novel approach for partitioning iteration spaces with variable densities

Kejariwal

Nicolau

Banerjee

et al. 2005

Proceedings of the Tenth ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming

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Efficient partitioning of parallel loops plays a critical role in high performance and efficient use of multiprocessor systems. Although a significant amount of work has been done in partitioning and scheduling of loops with rectangular iteration spaces, the problem of partitioning non-rectangular iteration spaces -e.g., triangular, trapezoidal iteration spaces -with variable densities has not been addressed so far to the best of our knowledge. In this paper, we present a mathematical model for partitioning N-dimensional non-rectangular iteration spaces with variable densities. We present a unimodular loop transformation and a geometric approach for partitioning an iteration space along an axis corresponding to the outermost loop across a given number of processors to achieve near-optimal performance, i.e., to achieve nearoptimal load balance across different processors. We present a case study to illustrate the effectiveness of our approach.

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Mapping affine loop nests: New results

Cited by 31 publications

References 6 publications

Communication-free data alignment for arrays with exponential references in parallelizing compilers for scalable parallel systems

Communication-free data alignment for arrays with exponential references in parallelizing compilers for scalable parallel systems

A group theoretic approach to data and code partitioning

A novel approach for partitioning iteration spaces with variable densities

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