Modern compilers are responsible for translating the idealistic operational semantics of the source program into a form that makes efficient use of a highly complex heterogeneous machine. Since optimization problems are associated with huge and unstructured search spaces, this combinational task is poorly achieved in general, resulting in weak scalability and disappointing sustained performance. We address this challenge by working on the program representation itself, using a semi-automatic optimization approach to demonstrate that current compilers offen suffer from unnecessary constraints and intricacies that can be avoided in a semantically richer transformation framework. Technically, the purpose of this paper is threefold: (1) to show that syntactic code representations close to the operational semantics lead to rigid phase ordering and cumbersome expression of architecture-aware loop transformations, (2) to illustrate how complex transformation sequences may be needed to achieve significant performance benefits, (3) to facilitate the automatic search for program transformation sequences, improving on classical polyhedral representations to better support operation research strategies in a simpler, structured search space. The proposed framework relies on a unified polyhedral representation of loops and statements, using normalization rules to allow flexible and expressive transformation sequencing. This 262 Girbal et al.representation allows to extend the scalability of polyhedral dependence analysis, and to delay the (automatic) legality checks until the end of a transformation sequence. Our work leverages on algorithmic advances in polyhedral code generation and has been implemented in a modern research compiler.

Static compiler optimizations can hardly cope with the complex run-time behavior and hardware components interplay of modern processor architectures. Multiple architectural phenomena occur and interact simultaneously, which requires the optimizer to combine multiple program transformations. Whether these transformations are selected through static analysis and models, runtime feedback, or both, the underlying infrastructure must have the ability to perform long and complex compositions of program transformations in a flexible manner. Existing compilers are ill-equipped to perform that task because of rigid phase ordering, fragile selection rules using pattern matching, and cumbersome expression of loop transformations on syntax trees. Moreover, iterative optimization emerges as a pragmatic and general means to select an optimization strategy via machine learning and operations research. Searching for the composition of dozens of complex, dependent, parameterized transformations is a challenge for iterative approaches.The purpose of this article is threefold: (1) to facilitate the automatic search for compositions of program transformations, introducing a richer framework which improves on classical polyhedral representations, suitable for iterative optimization on a simpler, structured search space, (2) to illustrate, using several examples, that syntactic code representations close to the operational semantics hamper the composition of transformations, and (3) that complex compositions of transformations can be necessary to achieve significant performance benefits. The proposed framework relies on a unified polyhedral representation of loops and statements. The key is to clearly separate four types of actions associated with program transformations: iteration domain, schedule, data layout and memory access functions modifications. The framework is implemented within the Open64/ORC compiler, aiming for native IA64, AMD64 and IA32 code generation, along with source-to-source optimization of Fortran90, C and C++.

Abstract. We seek to extend the scope and efficiency of iterative compilation techniques by searching not only for program transformation parameters but for the most appropriate transformations themselves. For that purpose, we need to find a generic way to express program transformations and compositions of transformations. In this article, we introduce a framework for the polyhedral representation of a wide range of program transformations in a unified way. We also show that it is possible to generate efficient code after the application of polyhedral program transformations. Finally, we demonstrate an implementation of the polyhedral representation and code generation techniques in the Open64/ORC compiler.