Application of Statistical Models to Select Tile Size Minimizing the Execution Time of Parallelized Tiled Loop Nests

The reduction of software development time is an important practical problem to be dealt with by contemporary computer science. Resolving this problem is an object of research carried out both in scientific and industrial centres. One of the main areas of this research is compilation. Within compilation, a computer program written in a programming language comprehensible for a man is converted into an executable form comprehensible for a computer. Applying appropriately selected transformations (tiling also known as blocking) during compilation, one can transform a program, written in a given programming language and for a given hardware platform, to various yet semantically equivalent executables which however differ in execution times. The paper presents a statistical model which allows for selecting from semantically equivalent, tiled source code variants of a given program the variants with best anticipated execution times. The paper also demonstrates how the elaborated model can be applied in iterative compilation for shortening software development time