Iteration space slicing and its application to communication optimization

Abstract

Program slicing is an analysis that answers questions such as \Which statements might a ect the computation of variable v at statement s?" or \Which statements depend on the value of v computed in statement s?". The answers computed by program slicing are generally a set of statements. We introduce the idea of iteration spacing slicing: we re ne program slicing to ask questions such as \Which iterations of which statements might e ect the computation in iterations I of statement s?" or \Which iterations of which statements depend on the value computed by iterations I of statement s?". One application of this general-purpose technique is optimization of interprocessor communication in data-parallel compilers. For example, we can separate a code fragment into 1) those iterations that must be done before a send, 2) those iterations that don't need to be done before a send and don't depend on non-local data and 3), those iterations that depend on non-local data. We examine applications of iteration space slicing to communication optimizations in parallel executions of programs such as stencil computations and block-cyclic Gaussian elimination with partial pivoting.

Tiling arbitrarily nested loops by means of the transitive

“…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;.…”

“…It applies the transitive closure of a program dependence graph to transform invalid original tiles into valid target ones. From this point of view the program transformation step is rather within the iteration space slicing framework introduced by Pugh and Rosser (1997): Iteration Space Slicing takes dependence information as input to find all statement instances from a given loop nest which must be executed to produce correct values for the specified array elements. The key step in iteration space slicing is calculating the transitive closure of a loop nest dependence graph.…”

TRACO: An Automatic Loop Nest Parallelizer for Numerical Applications

“…It applies the transitive closure of a program dependence graph to specific subspaces of the original loop nest iteration space. At this point of view the program transformation step is rather within the Iteration Space Slicing Framework introduced by Pugh and Rosser [4]: "Iteration Space Slicing takes dependence information as input to find all statement instances from a given loop nest which must be executed to produce correct values for the specified array elements ". The key step in Iteration Space Slicing is calculating the transitive closure of a loop nest dependence graph.…”

“…ISS was introduced by Pugh and Rosser [4]. It takes dependence information as input to find all statement instances that must be executed to produce the correct values for the specified array elements.…”

Optimizing Numerical Code by means of the Transitive Closure of Dependence Graphs

“…However, the tool does not find and use any affine function in the second step to transform the loop nest. TRACO is based on the idea of the Iteration Space Slicing Framework introduced by Pugh and Rosser [10] and applies the transitive closure of a program dependence graph to extract independent subspaces in the original loop nest iteration space.…”