A Linear Algebra Framework for Static High Performance Fortran Code Distribution

Abstract

High Performance Fortran (HPF) was developed to support data parallel programming for single-instruction multiple-data (SIMD) and multiple-instruction multiple-data (MIMD) machines with distributed memory. The programmer is provided a familiar uniform logical address space and specifies the data distribution by directives. The compiler then exploits these directives to allocate arrays in the local memories, to assign computations to elementary processors, and to migrate data between processors when required. We show here that linear algebra is a powerful framework to encode HPF directives and to synthesize distributed code with space-efficient array allocation, tight loop bounds, and vectorized communications forINDEPENDENTloops. The generated code includes traditional optimizations such as guard elimination, message vectorization and aggregation, and overlap analysis. The systematic use of an affine framework makes it possible to prove the compilation scheme correct.

Static Compilation Analysis for Host-Accelerator Communication Optimization

“…The automatic transformation process in Par4All is heavily based on pips compiler framework phases [17,1]. The latter uses a linear algebra library [2] to analyze, transform and parallelize programs using polyhedral representations [11]. Parallel loop nests are outlined (i.e.…”

Compilation et optimisation statique des communications hôte-accélérateur

“…Le processus de transformation automatisée dans PAR4ALL repose fortement sur les capacités des passes de PIPS. Ce dernier utilise une librairie d'algèbre linéaire [1] pour manipuler une représenta-tion polyédrique des abstractions d'un programme [8] et détecter les nids de boucles parallèles. Ces boucles sont ensuite extraites dans des fonctions marquées exécutables sur le GPU, ce qu'on appelle des noyaux dans la terminologie de programmation hybride.…”

PARADIGM (version 2.0): a new HPF compilation system

“…In addition, the arrays are assumed to have the most general data alignments and data distributions. Ancourt et al have shown in [2] how systems of inequalities could be used to conveniently express alignment and distribution information, in addition to synthesizing distributed code for loops qualified by the INDEPENDENT directive. We have applied their representations in our framework, extending the scheme to handle general DO loops.…”

“…Consider the following code excerpt in HPF: t =ĈP c +Ĉ p +l (2) c =0 (3) wherẽ lA ã ũA (4) 0 t ũT ,l T (5) 0 p P1 (6) 0 l Ĉ1 (7) For the given example, the corresponding matrices and vectors are: The solution set forã in the above system directly gives us the ownership set, which is a function of the processor identity vectorp, amongst other parameters such as the template cell vectort.…”