Memory-Constrained Data Locality Optimizations for Tensor Contractions

Abstract. The accurate modeling of the electronic structure of atoms and molecules involves computationally intensive tensor contractions over large multidimensional arrays. Efficient computation of these contractions usually requires the generation of temporary intermediate arrays. These intermediates could be extremely large, requiring their storage on disk. However, the intermediates can often be generated and used in batches through appropriate loop fusion transformations. To optimize the performance of such computations a combination of loop fusion and loop tiling is required, so that the cost of disk I/O is minimized. In this paper, we address the memory-constrained data-locality optimization problem in the context of this class of computations. We develop an optimization framework to search among a space of fusion and tiling choices to minimize the data movement overhead. The effectiveness of the developed optimization approach is demonstrated on a computation representative of a component used in quantum chemistry suites.

Synthesis of High-Performance Parallel Programs for a Class of Ab Initio Quantum Chemistry Models

Invited Paper This paper provides an overview of a program synthesis system for a class of quantum chemistry computations. These computations are expressible as a set of tensor contractions and arise in electronic structure modeling. The input to the system is a a high-level specification of the computation, from which the system can synthesize high-performance parallel code tailored to the characteristics of th

Automatic code generation for many-body electronic structure methods: The Tensor Contraction Engine

As both electronic structure methods and the computers on which they are run become increasingly complex, the task of producing robust, reliable, high-performance implementations of methods at a rapid pace becomes increasingly daunting. In this paper we present an overview of the Tensor Contraction Engine (TCE), a unique effort to address issues of both productivity and performance through automatic code generation. The TCE is designed to take equations for many-body methods in a convenient high-level form and acts like an optimizing compiler, producing an implementation tuned to the target computer system and even to the specific chemical problem of interest. We provide examples to illustrate the TCE approach, including the ability to target different parallel programming models, and the effects of particular optimizations. This paper is dedicated to Prof. Rodney J. Bartlett on the occasion of his 60 th birthday