Abstract

In this paper, we propose a generic method of automatic parallelization for sparse matrix computation. This method is based on both a refinement of the data-dependence test proposed by Bernstein and an inspector–executor scheme which is specialized to each input program of the compiler. This analysis mixes compilation process and run-time process.

The sparsity of underlying data-structure determines a specific parallelism which increases the degree of parallelism of an algorithm. Such a source of parallelism had already been applied to many numerical algorithms such as the usual Cholesky factorization or LU-decomposition algorithms considered as the gold standards of parallelization based on sparsity. The standard automatic parallelization method cannot tackle such source of parallelism because it is based on the value of cells arrays and not merely on the memory addressing function.

Addressing the automatization of this parallelism requires to develop a mixed compile-time and runtime approach integrated in a inspector–executor process. The compilation step provides a dedicated inspector devoted to the analyzed program. The inspector computes the dependence graph at runtime which allows a dynamic parallelization of the execution.

As expressed just before, the generic scheme developed in this paper follows the design principles which have been applied, but at each time in an ad hoc way, to many sparse parallelization of numerical algorithms such as Cholesky algorithm. As far as we know, no general formal framework has been proposed to automate such a method of sparse parallelization. In this paper, we propose a generic framework of sparse parallelization (i.e. numerical program independent) which can be applied to any numerical programs satisfying the usual syntactic constraints of parallelization.

Keywords: Parallelization; Dependence analysis; Sparse matrix compiler