the alignment problem by brian christian

The algorithms that implement the transformations can then be precisely described in terms of certain abstract mathematical algorithms. The transformations are developed in a consistent mathematical framework using objects like directed graphs, matrices and linear equations.

Loop Transformations for Restructuring Compilers: The Foundations provides a rigorous theory of loop transformations. Many loop transformations have been designed over the years, and several of them can be found in any parallelizing compiler currently in use in industry or at a university research facility.

This is where one expects to find major chunks of computation that need to be performed repeatedly for different values of the index variable. Much attention in this field of research has been focused on the Fortran do loop. The job of a restructuring compiler is to discover the dependence structure of a given program and transform the program in a way that is consistent with both that dependence structure and the characteristics of the given machine. There is a tremendous investment in existing sequential programs, and scientists and engineers continue to write their application programs in sequential languages (primarily in Fortran),but the demand for increasing speed is constant. A heuristic algorithm is devised and shown to both be efficient and provide excellent results.Īutomatic transformation of a sequential program into a parallel form is a subject that presents a great intellectual challenge and promises great practical rewards. The problem as formulated is shown to be NP-complete. The cost function and the machine model used are abstractions of the current generation of SIMD and MIMD distributed-memory machines. The problem of index domain alignment is formulated as finding a set of suitable alignment functions that embed the index domains of the arrays into a common index domain so as to minimize the cost of data movement. It also simplifies, both conceptually and in practice, the task of data partition and communication generation in the context of a parallelizing compiler for distributed-memory machines. The alignment technique presented here focuses on minimizing the data movement between processors due to cross-references between multiple distributed arrays. How this distribution is done affects the amount of data movement required and, therefore, the program performance. Programming distributed-memory machines requires that the data associated with a given computation be partitioned and distributed to the local storage of each individual processor.

The alignment problem by brian christian