Understanding the most efficient design and utilization of emerging multicore systems is one of the most challenging questions faced by the mainstream and scientific computing industries in several decades. Our work explores multicore stencil (nearest-neighbor) computations — a class of algorithms at the heart of many structured grid codes, including PDE solvers. We develop a number of effective optimization strategies, and build an auto-tuning environment that searches over our optimizations and their parameters to minimize runtime, while maximizing performance portability. To evaluate the effectiveness of these strategies we explore the broadest set of multicore architectures in the current HPC literature, including the

We present the design and implementation of an automatic polyhedral source-to-source transformation framework that can optimize regular programs (sequences of possibly imperfectly nested loops) for parallelism and locality simultaneously. Through this work, we show the practicality of analytical model-driven automatic transformation in the polyhedral model.Unlike previous polyhedral frameworks, our approach is an end-to-end fully automatic one driven by an integer linear optimization framework that takes an explicit view of finding good ways of tiling for parallelism and locality using affine transformations. The framework has been implemented into a tool to automatically generate OpenMP parallel code from C program sections. Experimental results from the tool show very high performance for local and parallel execution on multi-cores, when compared with state-of-the-art compiler frameworks from the research community as well as the best native production compilers. The system also enables the easy use of powerful empirical/iterative optimization for general arbitrarily nested loop sequences.

We present an auto-tuning approach to optimize application performance on emerging multicore architectures. The methodology extends the idea of searchbased performance optimizations, popular in linear algebra and FFT libraries, to application-specific computational kernels. Our work applies this strategy to a lattice Boltzmann application (LBMHD) that historically has made poor use of scalar microprocessors due to its complex data structures and memory access patterns. We explore one of the broadest sets of multicore architectures in the HPC literature, including the Intel Clovertown, AMD Opteron X2, Sun Niagara2, STI Cell, as well as the single core Intel Itanium2. Rather than hand-tuning LBMHD for each system, we develop a code generator that allows us identify a highly optimized version for each platform, while amortizing the human programming effort. Results show that our autotuned LBMHD application achieves up to a 14 × improvement compared with the original code. Additionally, we present detailed analysis of each optimization, which reveal surprising hardware bottlenecks and software challenges for future multicore systems and applications. 1

Performance of stencil computations can be significantly improved through smart implementations that improve memory locality, computation reuse, or parallelize the computation. Unfortunately, efficient implementations are hard to obtain because they often involve non-traditional transformations, which means that they cannot be produced by optimizing the reference stencil with a compiler. In fact, many stencils are produced by code generators that were tediously handcrafted. In this paper, we show how stencil implementations can be produced with sketching. Sketching is a software synthesis approach where the programmer develops a partial implementation— a sketch—and a separate specification of the desired functionality given by a reference (unoptimized) stencil. The synthesizer then completes the sketch to behave like the specification, filling in code fragments that are difficult to develop manually. Existing sketching systems work only for small finite programs, i.e., programs that can be represented as small Boolean circuits. In this paper, we develop a sketching synthesizer that works for stencil computations, a large class of programs that, unlike circuits, have unbounded inputs and outputs, as well as an unbounded number of computations. The key contribution is a reduction algorithm that turns a stencil into a circuit, allowing us to synthesize stencils using an existing sketching synthesizer.

Stencil-based kernels constitute the core of many important scientific applications on block-structured grids. Unfortunately, these codes achieve a low fraction of peak performance, due primarily to the disparity between processor and main memory speeds. In this paper, we explore the impact of trends in memory subsystems on a variety of stencil optimization techniques and develop performance models to analytically guide our optimizations. Our work targets cache reuse methodologies across single and multiple stencil sweeps, examining cache-aware algorithms as well as cache-oblivious techniques on the Intel Itanium2, AMD Opteron, and IBM Power5. Additionally, we consider stencil computations on the heterogeneous multi-core design of the Cell processor, a machine with an explicitly-managed memory hierarchy. Overall our work represents one of the most extensive analyses of stencil optimizations and performance modeling to date. Results demonstrate that recent trends in memory system organization have reduced the efficacy of traditional cacheblocking optimizations. We also show that a cache-aware implementation is significantly faster than a cache-oblivious approach, while the explicitly managed memory on Cell enables the highest overall efficiency: Cell attains 88 % of algorithmic peak while the best competing cache-based processor only achieves 54 % of algorithmic peak performance.

We present the design and implementation of a fully automatic polyhedral source-to-source transformation framework that can optimize regular programs (sequences of possibly imperfectly nested loops) for parallelism and locality simultaneously. Through this work, we show the practicality of analytical model-driven automatic transformation in the polyhedral model – far beyond what is possible by current production compilers. Unlike previous works, our approach is an end-to-end fully automatic one driven by an integer linear optimization framework that takes an explicit view of finding good ways of tiling for parallelism and locality using affine transformations. We also address generation of tiled code for multiple statement domains of arbitrary dimensionalities under (statement-wise) affine transformations – an issue that has not been addressed previously. Experimental results from the implemented system show very high speedups for local and parallel execution on multi-cores over state-of-the-art compiler frameworks from the research community as well as the best native compilers. The system also enables the easy use of powerful empirical/iterative optimization for general arbitrarily nested loop sequences.

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ABSTRACT: This work introduces a generalized framework for automatically tuning stencil computations to achieve superior performance on a broad range of multicore architectures. Stencil (nearest-neighbor) based kernels constitute the core of many important scientific applications involving block-structured grids. Auto-tuning systems search over optimization strategies to find the combination of tunable parameters that maximizes computational efficiency for a given algorithmic kernel. Although the auto-tuning strategy has been successfully applied to libraries, generalized stencil kernels are not amenable to packaging as libraries. Studied kernels in this work include both memory-bound kernels as well as a computation-bound bilateral filtering kernel. We introduce a generalized stencil auto-tuning framework that takes a straightforward Fortran expression of a stencil kernel and automatically generates tuned implementations of the kernel in C or Fortran to achieve performance portability across diverse computer architectures. KEYWORDS: Multicore, XT4, Auto-tuning, Auto-parallelization 1

We present a new cache oblivious scheme for iterative stencil computations that performs beyond system bandwidth limitations as though gigabytes of data could reside in an enormous on-chip cache. We compare execution times for 2D and 3D spatial domains with up to 128 million double precision elements for constant and variable stencils against hand-optimized naive code and the automatic polyhedral parallelizer and locality optimizer PluTo and demonstrate the clear superiority of our results. The performance benefits stem from a tiling structure that caters for data locality, parallelism and vectorization simultaneously. Rather than tiling the iteration space from inside, we take an exterior approach with a predefined hierarchy, simple regular parallelogram tiles and a locality preserving parallelization. These advantages come at the cost of an irregular work-load distribution but a tightly integrated loadbalancer ensures a high utilization of all resources.

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