Abstract

The problem of choosing fast implementations for a class of recursive algorithms such as the fast Fourier transforms can be formulated as an optimization problem over the language generated by a suitably defined grammar. We propose a novel algorithm that solves this problem by reducing it to maximizing an objective function over the sinks of a directed acyclic graph. This algorithm valuates nodes using Monte-Carlo and grows a subgraph in the most promising directions by considering local maximum k-armed bandits. When used inside an adaptive linear transform library, it cuts down the search time by an order of magnitude compared to the existing algorithm. In some cases, the performance of the implementations found is also increased by up to 10% which is of considerable practical importance since it consequently improves the performance of all applications using the library.

Abstract. We present the Operator Language (OL), a framework to automatically generate fast numerical kernels. OL provides the structure to extend the program generation system Spiral beyond the transform domain. Using OL, we show how to automatically generate library functionality for the fast Fourier transform and multiple non-transform kernels, including matrix-matrix multiplication, synthetic aperture radar (SAR), circular convolution, sorting networks, and Viterbi decoding. The control flow of the kernels is data-independent, which allows us to cast their algorithms as operator expressions. Using rewriting systems, a structural architecture model and empirical search, we automatically generate very fast C implementations for state-of-the-art multicore CPUs that rival hand-tuned implementations.

Abstract-Automatic tuning has emerged as a solution to provide high-performance libraries for fast changing, increasingly complex computer architectures. We distinguish offline adaptation (e.g., in ATLAS) that is performed during installation without the full problem description from online adaptation (e.g., in FFTW) that is performed at runtime. Offline adaptive libraries are simpler to use, but, unfortunately, writing the adaptation heuristics that power them is a daunting task. The overhead of online adaptive libraries, on the other hand, makes them unsuitable for a number of applications. In this paper, we propose to automatically generate heuristics in the form of decision trees using a statistical classifier, effectively converting an online adaptive library into an offline one. As testbed we use Spiral-generated adaptive transform libraries for current multicores with vector extensions. We show that replacing the online search with generated decision trees maintains a performance competitive with vendor libraries while allowing for a simpler interface and reduced computation overhead.

Abstract. This paper presents a program generator for fast software Viterbi decoders for arbitrary convolutional codes. The input to the generator is a specification of the code and a single-instruction multiple-data (SIMD) vector length. The output is an optimized C implementation of the decoder that uses explicit Intel SSE vector instructions. At the heart of the generator is a small domain-specific language called VL to express the structure of the forward pass. Vectorization is done by rewriting VL expressions, which a compiler then translates into actual code in addition to performing further optimizations specific to the vector instruction set. Benchmarks show that the generated decoders match the performance of available expert hand-tuned implementations, while spanning the entire space of convolutional codes. An online interface to the generator is provided at www.spiral.net.