Understanding memory effects in the automated generation of optimized matrix algebra kernels

Efficient implementation of matrix algebra is important to the performance of many large and complex physical models. Among important tuning techniques is loop fusion which can reduce the amount of data moved between memory and the processor. We have developed the Build to Order (BTO) compiler to automate loop fusion for matrix algebra kernels. In this paper, we present BTO’s analytic memory model which substantially reduces the number of loop fusion options considered by the compiler. We introduce an example that motivates the inclusion of registers in the model. We demonstrate how the model’s modular design facilitates the addition of register allocation to the model’s set of memory components, improving its accuracy