Applying Automated Memory Analysis to Improve Iterative Algorithms

Historically, iterative solvers have been designed so as to minimize the number of floating-point operations. We propose instead that iterative solvers should be designed to minimize the amount of data that must be loaded from the memory hierarchy to the CPU. In this paper, we describe automated memory analysis, a technique to improve the memory efficiency of a sparse linear iterative solver. Our automated memory analysis uses a language processor to predict the data movement required for an iterative algorithm based upon a Matlab implementation. We demonstrate how automated memory analysis is used to reduce the execution time of a component of a global parallel ocean model. In particular, code modifications identified or evaluated through automated memory analysis enables a 46% reduction in execution time for the conjugate gradient solver on a small serial problem. Further, we achieve a 9% reduction in total execution time for the full model on 64 processors. The predictive capabilities of our automated memory analysis can be used to simplify the development of memory efficient numerical algorithms or software.