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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

Universidade de A Coruña Ministerio de
		      Educación y Ciencia

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.

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