Linear Loop Transformations in Optimising Compilers for Parallel Machines

We present the linear loop transformation framework which is the formal basis for state of the art optimization techniques in restructuring compilers for parallel machines. The framework uniies most existing transformations and provides a systematic set of code generation techniques for arbitrary compound loop transformations. The algebraic representation of the loop structure and its transformation give way to quantitative techniques for optimizing performance on parallel machines. We discuss in detail the techniques for generating the transformed loop and deriving the desired linear transformation.