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 the target architecture. Several components of the synthesis system are described, focusing on performance optimization issues that they address.

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.

Abstract. This paper describes an approach to synthesis of efficient out-of-core code for a class of imperfectly nested loops that represent tensor contraction computations. Tensor contraction expressions arise in many accurate computational models of electronic structure. The developed approach combines loop fusion with loop tiling and uses a performance-model driven approach to loop tiling for the generation of out-of-core code. Experimental measurements are provided that show a good match with model-based predictions and demonstrate the effectiveness of the proposed algorithm.

Abstract.Complex tensor contraction expressions arise in accurate electronic structure models in quantum chemistry, such as the coupled cluster method. Transformations using algebraic properties of commutativity and associativity can be used to significantly decrease the number of arithmetic operations required for evaluation of these expressions. Operation minimization is an important optimization step for the Tensor Contraction Engine, a tool being developed for the automatic transformation of high-level tensor contraction expressions into efficient programs. The identification of common subexpressions among a set of tensor contraction expressions can result in a reduction of the total number of operations required to evaluate the tensor contractions. In this paper, we develop an effective algorithm for common subexpression identification and demonstrate its effectiveness on tensor contraction expressions for coupled cluster equations.

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