A data locality optimizing algorithm

Abstract

This paper proposes an algorithm that improves the locality of a loop nest by transforming the code via interchange, reversal, skewing and tiling. The loop transformation rrlgorithm is based on two concepts: a mathematical formulation of reuse and locality, and a loop transformation theory that unifies the various transforms as unimodular matrix tmnsfonnations. The algorithm haa been implemented in the SUIF (Stanford University Intermediate Format) compiler, and is successful in optimizing codes such as matrix multiplication, successive over-relaxation (SOR), LU decomposition without pivoting, and Givens QR factorization. Performance evaluation indicates that locatity optimization is especially crucial for scaling up the performance of parallel code. Programming Language Design and Implementation.

Tiling arbitrarily nested loops by means of the transitive

“…This is why we restrict related work only to techniques aimed at automatic generation of tiled code. There has been a considerable amount of research into tiling, demonstrating how to aggregate a set of loop nest iterations into tiles with each tile as an atomic macro statement, from pioneer papers (Irigoin and Triolet, 1988;Wolf and Lam, 1991;Ramanujam and Sadayappan, 1992) to those presenting advanced techniques (Bondhugula et al, 2008a;Griebl, 2004;Lim et al, 1999;Wonnacott and Strout, 2013). Several popular frameworks are used to produce tiled code automatically: the classic polyhedral model (Feautrier, 1992a;1992b;Lim and Lam, 1994;Bondhugula et al, 2008a), the sparse polyhedral model (Strout et al, 2004), the non-polyhedral model (Kim and Rajopadhye, 2009), and iteration space slicing (Pugh and Rosser, 1997;.…”

“…Tiling (Irigoin and Triolet, 1988;Wolf and Lam, 1991;Ramanujam and Sadayappan, 1992;Xue, 1996;Bondhugula et al, 2008a;Griebl, 2004;Lim et al, 1999) is a very important iteration reordering transformation for both improving data locality and coarsening the granularity of parallelism.…”

Programming for Locality and Parallelism with Hierarchically Tiled Arrays

“…The same approach has been studied as a compiler optimization technique where loops are automatically restructured so that arrays are accessed by tiles rather than in the more natural but less efficient row or column order [AbKL81, WoLa91,McCT96]. Although in some cases these algorithms require that the arrays to be manipulated be stored by tiles, in many cases this is not necessary and the reorganization of the computation usually suffices to significantly improve the memory hierarchy performance of the algorithms.…”

Towards Automatic Synthesis of High-Performance Codes for Electronic Structure Calculations: Data Locality Optimization

“…Although considerable research on loop transformations for locality has been reported in the literature [22,24,33], issues concerning the need to use loop fusion and loop tiling in an integrated manner for locality and memory usage optimization have not been considered. Wolf et al [34] consider the integrated treatment of fusion and tiling only from the point of view of enhancing locality and do not consider the impact of the amount of required memory; the memory requirement is a key issue for the problems considered in this paper.…”

“…Wolf et al [34] consider the integrated treatment of fusion and tiling only from the point of view of enhancing locality and do not consider the impact of the amount of required memory; the memory requirement is a key issue for the problems considered in this paper. Loop tiling for enhancing data locality has been studied extensively [27,33,30], and analytic models of the impact of tiling on locality have been developed [7,20,25]. Recently, a data-centric version of tiling called data shackling has been developed [12,13] (together with more recent work by Ahmed et al [1]) which allows a cleaner treatment of locality enhancement in imperfectly nested loops.…”