TCE-OpMin

Revision as of 07:52, 7 January 2008

Introduction

The first step in the TCE’s code synthesis process is the transformation of input equations into an equivalent form with minimal operation count. Equations typically range from around ten to over a hundred terms, each involving the contraction of two or more tensors, and most quantum chemical methods involve two or more coupled equations of this type. One of our operation minimization algorithms focuses on the use of single-term optimization (strength reduction or parenthesization), which decomposes multi-tensor contraction operations into a sequence of binary contractions, coupled with a global search of the composite single-term solution space for factorization opportunities. Exhaustive search (for small cases) and a number of heuristics were shown to be effective in minimizing the operation count.

Common subexpression elimination (CSE) is a classical optimization technique used in traditional optimizing compilers to reduce the number of operations, where intermediates are identified that can be computed once and stored for use multiple times later. CSE is routinely used in the manual formulation of quantum chemical methods, but because of the complexity of the equations, it is extremely difficult to explore all possible formulations manually. CSE is a powerful technique that allows the exploration of the much larger algorithmic space than our previous approaches to operation minimization. However, the cost of the search itself grows explosively. We have developed an approach to CSE identification in the context of operation minimization for tensor contraction expressions. The developed approach is shown to be very effective, in that it automatically finds efficient computational forms for challenging tensor equations.

Quantum chemists have proposed domain-specific heuristics for strength reduction and factorization for specific forms of tensor contraction expressions. However, their work does not consider the general form of arbitrary tensor contraction expressions. Approaches to single-term optimizations and factorization of tensor contraction expressions were presented in ^[1]. Common subexpression identification to enhance single-term optimization is discussed in ^[2].

Contact Info

Please contact Albert Hartono (hartonoa@cse.ohio-state.edu) for questions.

References

1. ↑ Automated Operation Minimization of Tensor Contraction Expressions in Electronic Structure Calculations. Albert Hartono, Alexander Sibiryakov, Marcel Nooijen, Gerald Baumgartner, David E. Bernholdt, So Hirata, Chi-Chung Lam, Russell M. Pitzer, J. Ramanujam, and P. Sadayappan. International Conference on Computational Science (ICCS'05) pages 155-164, May 2005
2. ↑ Identifying Cost-Effective Common Subexpressions to Reduce Operation Count in Tensor Contraction Evaluations. Albert Hartono, Qingda Lu, Xiaoyang Gao, Sriram Krishnamoorthy, Marcel Nooijen, Gerald Baumgartner, Venkatesh Choppella, David Bernholdt, Russell Pitzer, J. Ramanujam, Atanas Rountev, and P. Sadayappan. International Conference on Computational Science (ICCS'06) LNCS 3991, pages 267-275, May 2006