Aravind Sukumaran-Rajam
Abstract
Runtime code optimization and speculative execution are becoming increasingly prominent to leverage performance in the current multi- and many-core era. However, a wider and more efficient use of such techniques is mainly hampered by the prohibitive time overhead induced by centralized data race detection, dynamic code behavior modeling, and code generation. Most of the existing Thread Level Speculation (TLS) systems rely on naively slicing the target loops into chunks and trying to execute the chunks in parallel with the help of a centralized performance-penalizing verification module that takes care of data races. Due to the lack of a data dependence model, these speculative systems are not capable of doing advanced transformations, and, more importantly, the chances of rollback are high. The polyhedral model is a well-known mathematical model to analyze and optimize loop nests. The current state-of-art tools limit the application of the polyhedral model to static control codes. Thus, none of these tools can generally handle codes with while loops, indirect memory accesses, or pointers. Apollo (Automatic POLyhedral Loop Optimizer) is a framework that goes one step beyond and applies the polyhedral model dynamically by using TLS. Apollo can predict, at runtime, whether the codes are behaving linearly or not, and it applies polyhedral transformations on-the-fly. This article presents a novel system that enables Apollo to handle codes whose memory accesses and loop bounds are not necessarily linear. More generally, this approach expands the applicability of the polyhedral model at runtime to a wider class of codes. Plugging together both linear and nonlinear accesses to the dependence prediction model enables the application of polyhedral loop optimizing transformations even for nonlinear code kernels while also allowing a low-cost speculation verification.
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Index Terms
- The Polyhedral Model of Nonlinear Loops
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Reviews
William M. Waite
The polyhedral model is a technique for optimizing loop nests in a program. Each calculated value is modeled by a point, and the dependencies among the values from one iteration to the next are modeled by vectors connecting the points. The result is an object called a polytope that lies in an n -dimensional space, where n is the number of loops. Each point of the polytope has the values of the loop indexes as its coordinates in that space. Performance improvements can be made by applying certain kinds of geometrical transformations to the polytope and then converting the result back to code. Analysis is carried out at compile time, based on static properties of the program, and must therefore make conservative assumptions. Previous papers proposed a framework to support dynamic analysis and speculative execution of the model. Here, Sukumaran-Rajam and Clauss show how to remove some of the constraints that the model places on the behavior of loop variables and the form of index expressions. After introducing the problem, the authors discuss the polyhedral model and its limitations. They then provide the architecture of Apollo, the system discussed in earlier papers, and explain how they extend it to remove its constraints. The paper concludes with a review of related work and some results obtained by applying the extended framework to programs selected from several standard benchmark suites. The paper is well written but quite dense; I would not recommend it to a novice in the optimization area. A reader is expected to understand multicore optimization techniques in general and the polyhedral model in particular. There is a good set of references to help access this material, and the examples are well chosen. A person familiar with the area should have little difficulty understanding and evaluating the authors' contribution. Online Computing Reviews Service
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