Parameterizing loop fusion for automated empirical tuning

Traditional compilers are limited in their ability to optimize applications for different architectures because statically modeling the effect of specific optimizations on different hardware implementations is difficult. Recent research has been addressing this issue through the use of empirical tuning, which uses trial executions to determine the optimization parameters that are most effective on a particular hardware platform. In this paper, we investigate empirical tuning of loop fusion, an important transformation for optimizing a significant class of real-world applications. In spite of its usefulness, fusion has attracted little attention from previous empirical tuning research, partially because it is much harder to configure than transformations like loop blocking and unrolling. This paper presents novel compiler techniques that extend conventional fusion algorithms to parameterize their output when optimizing a computation, thus allowing the compiler to formulate the entire configuration space for loop fusion using a sequence of integer parameters. The compiler can then employ an external empirical search engine to find the optimal operating point within the space of legal fusion configurations and generate the final optimized code using a simple code transformation system. We have implemented our approach within our compiler infrastructure and conducted preliminary experiments using a simple empirical search strategy. Our results convey new insights on the interaction of loop fusion with limited hardware resources, such as available registers, while confirming conventional wisdom about the effectiveness of loop fusion in improving application performance