Experimental Results

We present experimental performance data on a Sun Sunfire shared-memory system for the two-index transform computation.

We executed the tiled version of two-index transform for several different tile sizes, first keeping the tile sizes in all dimensions as equal ( The general practice of the programmers writing the quantum chemistry codes is to use equal tile sizes in all the dimensions ). We also used copying of tiles to reduce conflict misses. We have also performed experiments with the tile sizes predicted by our algorithm using the tiled code on different number of processors. The results are shown in Figure  11 and Figure  12 corresponding to two different loop bounds. The optimal tile size obtained by our algorithm for the tiled 2-index transform is (64,16,16,128).The performance obtained using our predicted tile sizes is clearly better than that obtained using other tile sizes.

Figure 11: Comparison of the performance of the Two index transform with tiling with equal tile sizes and our predicted tile size with loop bounds = 1024.

Figure 12: Comparison of the performance of the Two index transform with loop bounds = 2048.

Conclusions In this paper, we have developed an approach for accurate characterization of cache misses for a class of imperfectly nested loops arising in the context of a domain-specific compiler for tensor contraction expressions. An efficient tile size optimization procedure was developed using the approach, and its applicability was demonstrated in optimizing execution of such loops on shared-memory parallel machines.