Loop interchange

Abstract: Supercompilers must reschedule computations defined by nested DO-loops in order to make an efficient use of supercomputer features (vector units, multiple elementary processors, cache memory, etc…). Many rescheduling techniques like loop interchange, loop strip-mining or rectangular partitioning have been described to speedup program execution. We present here a class of partitionings that encompasses previous techniques and provides enough flexibility to adapt code to multiprocessors with two levels of parallelism and two levels of memory.

Abstract: In the past decade, processor speed has become significantly faster than memory speed. Small, fast cache memories are designed to overcome this discrepancy, but they are only effective when programs exhibit data locality. In the this article, we present compiler optimizations to improve data locality based on a simple yet accurate cost model. The model computes both temporal and spatial reuse of cache lines to find desirable loop organizations. The cost model drives the application of compound transformations consisting of loop permutation, loop fusion, loop distribution, and loop reversal. To validate our optimization strategy, we implemented our algorithms and ran experiments on a large collection of scientific programs and kernels. Experiments illustrate that for kernels our model and algorithm can select and achieve the best loop structure for a nest. For over 30 complete applications, we executed the original and transformed versions and simulated cache hit rates. We collected statistics about the inherent characteristics of these programs and our ability to improve their data locality. To our knowledge, these studies are the first of such breadth and depth. We found performance improvements were difficult to achieve bacause benchmark programs typically have high hit rates even for small data caches; however, our optimizations significanty improved several programs.

Abstract: Tiling is a well-known loop transformation to improve temporal locality of nested loops. Current compiler algorithms for tiling are limited to loops which are perfectly nested or can be transformed, in trivial ways, into a perfect nest. This paper presents a number of program transformations to enable tiling for a class of nontrivial imperfectly-nested loops such that cache locality is improved. We define a program model for such loops and develop compiler algorithms for their tiling. We propose to adopt odd-even variable duplication to break anti- and output dependences without unduly increasing the working-set size, and to adopt speculative execution to enable tiling of loops which may terminate prematurely due to, e.g. convergence tests in iterative algorithms. We have implemented these techniques in a research compiler, Panorama. Initial experiments with several benchmark programs are performed on SGI workstations based on MIPS R5K and R10K processors. Overall, the transformed programs run faster by 9% to 164%.

Abstract: Vectorization has been an important method of using data-level parallelism to accelerate scientific workloads on vector machines such as Cray for the past three decades. In the last decade it has also proven useful for accelerating multimedia and embedded applications on short SIMD architectures such as MMX, SSE and AltiVec. Most of the focus has been directed at innermost loops, effectively executing their iterations concurrently as much as possible. Outer loop vectorization refers to vectorizing a level of a loop nest other than the innermost, which can be beneficial if the outer loop exhibits greater data-level parallelism and locality than the innermost loop. Outer loop vectorization has traditionally been performed by interchanging an outer-loop with the innermost loop, followed by vectorizing it at the innermost position. A more direct unroll-and-jam approach can be used to vectorize an outer-loop without involving loop interchange, which can be especially suitable for short SIMD architectures. In this paper we revisit the method of outer loop vectorization, paying special attention to properties of modern short SIMD architectures. We show that even though current optimizing compilers for such targets do not apply outer-loop vectorization in general, it can provide significant performance improvements over innermost loop vectorization. Our implementation of direct outer-loop vectorization, available in GCC 4.3, achieves speedup factors of 3.13 and 2.77 on average across a set of benchmarks, compared to 1.53 and 1.39 achieved by innermost loop vectorization, when running on a Cell BE SPU and PowerPC970 processors respectively. Moreover, outer-loop vectorization provides new reuse opportunities that can be vital for such short SIMD architectures, including efficient handling of alignment. We present an optimization tapping such opportunities, capable of further boosting the performance obtained by outer-loop vectorization to achieve average speedup factors of 5.26 and 3.64.