No abstract

We present optimization techniques for high level equational programs that are generalizations of affine control loops (ACLs). Significant parts of the SpecFP and PerfectClub benchmarks are ACLs. They often contain reductions: associative and commutative operators applied to a collection of values. They also often exhibit reuse: intermediate values computed or used at different index points being identical. We develop various techniques to automatically exploit reuse to simplify the computational complexity of evaluating reductions. Finally, we present an algorithm for the optimal application of such simplifications resulting in an equivalent specification with minimum complexity.

Abstract. Many bioinformatics studies require the analysis of RNA or DNA structures. More specifically, extensive work is done to elaborate efficient algorithms able to predict the 2-D folding structures of RNA or DNA sequences. However, the high computational complexity of the algorithms, combined with the rapid increase of genomic data, triggers the need of faster methods. Current approaches focus on parallelizing these algorithms on multiprocessor systems or on clusters, yielding to good performance but at a relatively high cost. Here, we explore the use of computer graphics hardware to speed up these algorithms which, theoretically, provide both high performance and low cost. We use the CUDA programming language to harness the power of NVIDIA graphic cards for general computation with a C-like environment. Performances on recent graphic cards achieve a ×17 speed-up.

The polyhedral model provides a single unified foundation for systolic array synthesis and automatic parallelization of loop programs. We investigate the problem of memory reuse when compiling Alpha (a functional language based on this model). Direct compilation would require unacceptably large memory (for example O(n 3 ) for matrix multiplication). Researchers have previously addressed the problem of memory reuse, and the analysis that this entails for projective memory allocations. This paper addresses, for a given schedule, the choice of the projections so as to minimize the volume of the residual memory. We prove tight bounds on the number of linearly independent projection vectors. Our method is constructive, yielding an optimal memory allocation. We extend the method to modular functions, and deal with the subsequent problems of code generation. Our ideas are illustrated on a number of examples generated by the current version of the Alpha compiler.

Parameterized tiled loops-where the tile sizes are not fixed at compile time, but remain symbolic parameters until later-are quite useful for iterative compilers and "auto-tuners" that produce highly optimized libraries and codes. Tile size parameterization could also enable optimizations such as register tiling to become dynamic optimizations. Although it is easy to generate such loops for (hyper) rectangular iteration spaces tiled with (hyper) rectangular tiles, many important computations do not fall into this restricted domain. Parameterized tile code generation for the general case of convex iteration spaces being tiled by (hyper) rectangular tiles has in the past been solved with bounding box approaches or symbolic Fourier Motzkin approaches. However, both approaches have less than ideal code generation efficiency and resulting code quality. We present the theoretical foundations, implementation, and experimental validation of a simple, unified technique for generating parameterized tiled code. Our code generation efficiency is comparable to all existing code generation techniques including those for fixed tile sizes, and the resulting code is as efficient as, if not more than, all previous techniques. Thus the technique provides parameterized tiled loops for free! Our "one-size-fits-all" solution, which is available as open source software can be adapted for use in production compilers.