Comprehensive Optimization of Parametric Kernels for Graphics Processing Units

This work deals with the optimization of computer programs targeting Graphics Processing Units (GPUs). The goal is to lift, from programmers to optimizing compilers, the heavy burden of determining program details that are dependent on the hardware characteristics. The expected benefit is to improve robustness, portability and efficiency of the generated computer programs. We address these requirements by: (1) treating machine and program parameters as unknown symbols during code generation, and (2) generating optimized programs in the form of a case discussion, based on the possible values of the machine and program parameters. By taking advantage of recent advances in the area of computer algebra, preliminary experimentation yield promising results.