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Funded by the Vicerreitoría de Investigación of the University of A Coruña and the Ministry of Education and Science of Spain 
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Efficient Search-Space Pruning for Integrated Fusion and Tiling Transformations
Xiaoyang Gao1, Sriram
Krishnamoorthy1, Swarup
Kumar Sahoo1, Chi-Chung
Lam1, Gerald
Baumgartner2,
J. Ramanujam3 and P. Sadayappan1
1 Department of Computer Science and
Engineering, The Ohio State
University, USA
2 Department of Computer Science, Louisiana State University, USA
3 Department of Electrical and Computer Engineering, Louisiana State University, USA
Compile-time optimizations involve a number of transformations such as loop permutation, fusion, tiling, array contraction, etc. Determination of the choice of these transformations that minimizes the execution time is a challenging task. We address this problem in the context of tensor contraction expressions involving arrays too large to fit in main memory. Domain-specific features of the computation are exploited to develop an integrated framework that facilitates the exploration of a large search space of optimizations. In this paper, we discuss the exploration of the space of loop fusion, permutation and tiling transformations in order to minimize the disk I/O cost. These transformations are integrated and pruning strategies are presented that significantly reduce the number of loop structures to be evaluated. In addition, we consider data layout optimization in the context of tensor contractions. Evaluation of the framework using representative contraction expressions from quantum chemistry shows a dramatic reduction in the size of the search space using the strategies presented.
