Towards Automatic Synthesis of High-Performance Codes for Electronic Structure Calculations: Data Locality Optimization

Abstract

Abstract. The goal of our project is the development of a program synthesis system to facilitate the development of high-performance parallel programs for a class of computations encountered in computational chemistry and computational physics. These computations are expressible as a set of tensor contractions and arise in electronic structure calculations. This paper provides an overview of a planned synthesis system that will take as input a high-level specification of the computation and generate high-performance parallel code for a number of target architectures. We focus on an approach to performing data locality optimization in this context. Preliminary experimental results on an SGI Origin 2000 are encouraging and demonstrate that the approach is effective.

Efficient synthesis of out-of-core algorithms using a nonlinear optimization solver

“…The optimization presented in this paper has been developed in the context of the Tensor Contraction Engine (TCE) [4,12], a domain-specific compiler for ab initio quantum chemistry calculations. The TCE takes as input a high-level specSadayappan), choppell@iiitmk.ac.in (Venkatesh Choppella).…”

“…ification of a computation expressed as a set of tensor contraction expressions and transforms it into efficient parallel code. Several compile-time optimizations are incorporated into the TCE: algebraic transformations to minimize operation counts [31,32], loop fusion to reduce memory requirements [28,30,29], spacetime trade-off optimization [10], communication minimization [11], and data locality optimization [12,13] of memory-to-cache traffic.…”

“…We have addressed various issues arising in the synthesis context described above focusing primarily on minimizing memory-to-cache data movement [13,12]. In Cociorva et al [13], we developed an integrated approach to fusion and tiling transformations for a restricted class of loops arising in the context of our program synthesis system; these assumed restrictions were subsequently removed [12].…”

“…In Cociorva et al [13], we developed an integrated approach to fusion and tiling transformations for a restricted class of loops arising in the context of our program synthesis system; these assumed restrictions were subsequently removed [12]. We developed a tile size search procedure to estimate the total capacity miss cost for each of a large number of combinations of tile sizes for the various loops of an imperfectly nested loop set.…”

Memory-Constrained Communication Minimization for a Class of Array Computations

“…These include algebraic transformations to minimize the number of arithmetic operations [8,13], loop fusion and array contraction for memory space minimization [13,12], tiling and data locality optimization [1,2], space-time trade-off optimization [3], and data partitioning for communication minimization [9,10]. Since the problem of determining the set of algebraic transformations to minimize operation count was found to be NP-complete, we developed a pruning search procedure [8] that is very efficient in practice.…”