New Loop Transformation Techniques for Massive Parallelism

Lu, Lee-Chung; Chen, Marina

doi:10.21236/ada249325

Cited by 7 publications

(5 citation statements)

References 12 publications

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“…There has been much work addressing the problem of rewriting in a systematic way a loop nest according to a nonsingular transformation [6], [18], [21], [22]. All these works assume that the source iteration space to which the transformation is applied is a convex space.…”

Section: Loop Permutation Phasementioning

confidence: 99%

“…Conventional techniques, however, compute the loop bounds in the final code from the outermost to the innermost loop. 6 Therefore, redundant bounds in the innermost loops cannot be eliminated until the multilevel tiling process has been finished.…”

Section: Generating Fewer Redundant Boundsmentioning

confidence: 99%

“…T ILING is a loop transformation that a compiler can use to automatically create block algorithms [1], [2], so that locality is achieved [3], [4], [5] and/or parallelism is exploited [6], [7]. It partitions the iteration space defined by the loop structures into tiles of the same size and shape.…”

Section: Introductionmentioning

confidence: 99%

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A cost-effective implementation of multilevel tiling

Jimenez

Llaberia

Fernandez

2003

IEEE Trans. Parallel Distrib. Syst.

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This paper presents a new cost-effective algorithm to compute exact loop bounds when multilevel tiling is applied to a loop nest having affine functions as bounds (nonrectangular loop nest). Traditionally, exact loop bounds computation has not been performed because its complexity is doubly exponential on the number of loops in the multilevel tiled code and, therefore, for certain classes of loops (i.e., nonrectangular loop nests), can be extremely time consuming. Although computation of exact loop bounds is not very important when tiling only for cache levels, it is critical when tiling includes the register level. This paper presents an efficient implementation of multilevel tiling that computes exact loop bounds and has a much lower complexity than conventional techniques. To achieve this lower complexity, our technique deals simultaneously with all levels to be tiled, rather than applying tiling level by level as is usually done. For loop nests having very simple affine functions as bounds, results show that our method is between 1.5 and 2.8 times faster than conventional techniques. For loop nests having not so simple bounds, we have measured speedups as high as 2,300. Additionally, our technique allows eliminating redundant bounds efficiently. Results show that eliminating redundant bounds in our method is between 2.2 and 11 times faster than in conventional techniques for typical linear algebra programs.

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Section: Loop Permutation Phasementioning

confidence: 99%

Section: Generating Fewer Redundant Boundsmentioning

confidence: 99%

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A cost-effective implementation of multilevel tiling

Jimenez

Llaberia

Fernandez

2003

IEEE Trans. Parallel Distrib. Syst.

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“…Some previous works [8,9] have addressed the problem of code generation when unimodular matrices are used to transform the original IS. [22] includes conditional statements in order to deal with the sparseness that is introduced in the target IS when a non-unimodular matrix is used. Other authors [12,13,14] have made proposals to avoid these conditionals and, as a consequence, reduce the overhead introduced by them.…”

Section: Code Generationmentioning

confidence: 99%

Align and distribute-based linear loop transformations

Torres

Ayguadé

Labarta

et al. 1994

Languages and Compilers for Parallel Computing

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In this paper we generalize the framework of linear loop transformations in the sense that loop alignment is considered as a new component in the transformation process. The aim is to match the structure of loop nests with the data distribution and alignment in order to eliminate non-local references whenever possible when compiling a sequential program for a distributed memory machine. The alignment and distribution functions are assumed to be user specified or automatically generated by the compiler. The transformation process is modelled with nonsingular matrices and we use the ideas recently proposed in this field to find part of the transformation matrix and generate an efficient transformed code. However, additional aspects have to be studied when the alignment and distribution functions are considered, both in the obtaining of the transformation matrix and in the generation of code.

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“…Parutrun has not produced effective speed-up. Lu [15], and Lu and Chen [16], describe run-time methods for parallelizing loops with indirect array accesses (in Fortran and C) and (restricted) pointer accesses (in C). Their methods pre-execute a loop nest at run time to find data dependences between program statements in the loop.…”

Section: Related Workmentioning

confidence: 99%

Dynamic parallelization of modifications to directed acyclic graphs

Huelsbergen

Proceedings of the 1996 Conference on Parallel Architectures and Compilation Technique

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W e describe a higher-order interprocedural technique, called dynamic resolution, for the automatic parallelization of procedures that destructively manipulate dynamic DAGs. Dynamic resolution detects shared data and correctly coordinates access to thzs data at run time. I n pointer-unsafe languages such as C, dynamic resolution requires programmer identification of acyclic data structures and use of dynamic resolution's macros for pointer manipulations. I n pointer-safe languages such as ML, cyclicity can often be inferred by the compiler and parallelization via dynamic resolution can be completely automatic.This paper empirically studies the performance of dynamic resolution. Our study reveals that dynamic resolution applied to statically unparallelizable programs can outperform the optimized sequential versions on fast shared-memory multiprocessors. I n particular, dynamic-resolution implementations of two problems ( D A G rewrite and in-place list quicksort) using three processors already outperform their sequential counterparts. For both problems, the absolute performance of dynamic resolution steadily improves as processors are added. W e also observe that dynamic resolution can offset its runtime overheads in the presence of some shared structure. Dynamic resolution is the first technique that can automatically and eflectively parallelize D A G rewrite and destructive list quicksort.

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New Loop Transformation Techniques for Massive Parallelism

Cited by 7 publications

References 12 publications

A cost-effective implementation of multilevel tiling

A cost-effective implementation of multilevel tiling

Align and distribute-based linear loop transformations

Dynamic parallelization of modifications to directed acyclic graphs

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