The research presented in this paper is important and fruitful. However, it is not very accessible due to its length (56 pages) and presentation.

As the increasing complexity of hardware architectures moves them away from the usual programming languages, the importance of the optimizing parts of compilers grows. In order to achieve only a fraction of the peak performance theoretically possible on a recent 64-bit architecture, the compiler must do extremely complicated work. Worse, this work should be tailored to the program to be compiled. This is true for the specific optimizations to be done and for their specific order.

According to the authors, this is because optimizations occur on a syntactic level. They propose a new program representation, called polyhedral, which is claimed to circumvent the limitations of the syntactic representations. They consider the classical loop transformations for automatic parallelization and locality enhancement, and generalize them in their new framework. They show how complex compositions of these optimizations can be necessary in order to achieve the performance possible on the architecture. They also show how these compositions can be easily implemented using their framework.

An application of these ideas on a specific SPEC benchmark leads to very convincing results: compared to the peak performance attainable on the best available compiler, their tool achieves a 32 to 38 percent speedup. Compared to the base SPEC performance numbers, they achieve a 51 to 92 percent speedup for Athlon XP or 64 architectures. However, one should note that these results are obtained using what they call a semi-automatic optimization: in fact, the sequence of transformations is specifically aimed at the chosen benchmark. Thus, although this research already results in distributable GPL software, additional efforts are clearly needed. People interested in this line of work should certainly read this paper.