Non-linear memory layout transformations and data prefetching ...

CHAPTER3Fast Indexing for Blocked ArrayLayoutsThis chapter proposes a new method to perform blocked array layouts combined with a fastindexing scheme for numerical codes. We use static loop performance analysis to specify theoptimal loop nesting order and legal transformations (including tiling) that give the best recompositionof iterations. Array elements are stored exactly as they are swept by the tiled instructionstream in a blocked layout. We nally apply our ecient indexing to the resulting optimizedcode, to easily translate multi-dimensional indexing of arrays into their blocked memory layoutusing quick and simple binary-mask operations.The remainder of this chapter is organized as follows: Section 3.1 briey discusses the problemof data locality using as example the typical matrix multiplication algorithm. Section 3.2reviews denitions related to Morton ordering. Section 3.3 presents previously proposed nonlineararray layouts, as well as our blocked array layouts along with our ecient array indexing.Finally, concluding remarks are presented in Section 3.4.3.1 The problem: Improving cache locality for array computationsIn this section, we elaborate on the necessity for both control (loop) and data transformations,to fully exploit data locality. We present, stepwise, all optimization phases to improve localityof references with the aid of the typical matrix multiplication kernel.1. unoptimized version