Formal loop merging for signal transforms

A critical optimization in the domain of linear signal transforms, such as the discrete Fourier transform (DFT), is loop merging, which increases data locality and reuse and thus performance. In particular, this includes the conversion of shuffle operations into array reindexings. To date, loop merging is well understood only for the DFT, and only for Cooley-Tukey FFT based algorithms, which excludes DFT sizes divisible by large primes. In this paper, we present a formal loop merging framework for general signal transforms and its implementation within the SPIRAL code generator. The framework consists of Σ-SPL, a mathematical language to express loops and index mappings; a rewriting system to merge loops in Σ-SPL; and a compiler that translates Σ-SPL into code. We apply the framework to DFT sizes that cannot be handled using only the Cooley-Tukey FFT and compare our method to FFTW

• Type: Conference
• Year: 2005
• Where: PLDI
• Authors: Franz Franchetti, Yevgen Voronenko, Markus Püschel
• Keywords: Cooley-Tukey FFT, Loop Merging Framework, PLDI 2005, Programming Languages, Signal Transforms