Linear analysis and optimization of stream programs

Abstract

As more complex DSP algorithms are realized in practice, there is an increasing need for high-level stream abstractions that can be compiled without sacrificing efficiency. Toward this end, we present a set of aggressive optimizations that target linear sections of a stream program. Our input language is StreamIt, which represents programs as a hierarchical graph of autonomous filters. A filter is linear if each of its outputs can be represented as an affine combination of its inputs. Linearity is common in DSP components; examples include FIR filters, expanders, compressors, FFTs and DCTs. We demonstrate that several algorithmic transformations, traditionally handtuned by DSP experts, can be completely automated by the compiler. First, we present a linear extraction analysis that automatically detects linear filters from the C-like code in their work function. Then, we give a procedure for combining adjacent linear filters into a single filter, a specialized caching strategy to remove redundant computations, and a method for translating a linear filter to operate in the frequency domain. We also present an optimization selection algorithm, which finds the sequence of combination and frequency transformations that yields the maximal benefit. We have completed a fully-automatic implementation of the above techniques as part of the StreamIt compiler. Using a suite of benchmarks, we show that our optimizations remove, on average, 86% of the floating point instructions required. In addition, we demonstrate an average execution time decrease of 450% and an 800% decrease in the best case.