Abstract. In this paper, we describe transformation recipes, which provide a high-level interface to the code transformation and code generation capability of a compiler. These recipes can be generated by compiler decision algorithms or savvy software developers. This interface is part of an auto-tuning framework that explores a set of different implementations of the same computation and automatically selects the best-performing implementation. Along with the original computation, a transformation recipe specifies a range of implementations of the computation resulting from composing a set of high-level code transformations. In our system, an underlying polyhedral framework coupled with transformation algorithms takes this set of transformations, composes them and automatically generates correct code. We first describe an abstract interface for transformation recipes, which we propose to facilitate interoperability with other transformation frameworks. We then focus on the specific transformation recipe interface used in our compiler and present performance results on its application to kernel and library tuning and tuning of key computations in high-end applications. We also show how this framework can be used to generate and auto-tune parallel OpenMP or CUDA code from a high-level specification. 1

Multicore processors have become mainstream and the number of cores in a chip will continue to increase every year. Programming these architectures to effectively exploit their very high computation power is a non trivial task. First, an application program needs to be explicitly restructured using a set of code transformation techniques to optimize for specific architectural features, especially for parallelism and data locality. Then a significant amount of time is spent on tuning the optimized code to find the best optimization parameter values. However, high performance often means lower productivity as the optimized codes become difficult to understand, maintain and modify. In this dissertation, we present techniques to address these issues by automatic generation of efficient parallel programs, and by the use of empirical search for tuning. The research from this dissertation has been implemented and made publicly available as two useful software tools: one for parameterized tiled loop generation, and one for empirical performance tuning using annotations. Tiling is a critical loop transformation that optimizes both for data locality enhancement

Abstract. Numerical solutions of nonlinear partial differential equations frequently rely on iterative Newton-Krylov methods, which linearize a finite-difference stencil-based discretization of a problem, producing a sparse matrix with regular structure. Knowledge of this structure can be used to exploit parallelism and locality of reference on modern cache-based multi- and manycore architectures, achieving high performance for computations underlying commonly used iterative linear solvers. In this paper we describe our approach to sparse matrix data structure design and our implementation of the kernels underlying iterative linear solvers in PETSc. We also describe autotuning of CUDA implementations based on high-level descriptions of the stencil-based matrix and vector operations. Key words.

Abstract—Finite-difference, stencil-based discretization approaches are widely used in the solution of partial differential equations describing physical phenomena. Newton-Krylov iterative methods commonly used in stencil-based solutions generate matrices that exhibit diagonal sparsity patterns.To exploit these structures on modern GPUs, we extend the standard diagonal sparse matrix representation and define new matrix and vector data types in the PETSc parallel numerical toolkit. We create tunable CUDA implementations of the operations associated with these types after identifying a number of GPU-specific optimizations and tuning parameters for these operations. We discuss our implementation of GPU autotuning capabilities in the Orio framework and present performance results for several kernels, comparing them with vendor-tuned library implementations. Index Terms—autotuning, stencil, CUDA, GPU I.