A Rewriting System for the Vectorization of Signal Transforms
Franz Franchetti (Carnegie Mellon University)Yevgen Voronenko (Carnegie Mellon University)
Markus Püschel (Carnegie Mellon University)
Abstract:
We present a rewriting system that automatically vectorizes signal
transform algorithms at a high level of abstraction. The input to the
system is a transform algorithm given as a formula in the well-known
Kronecker product formalism. The output is a "vectorized" formula,
which means it consists exclusively of constructs that can be directly mapped into short vector code. This approach obviates compiler vectorization, which is known to be limited in this domain. We included the formula vectorization into the Spiral program generator for signal transforms, which enables us to generate vectorized code and optimize through search over alternative algorithms. Benchmarks for the discrete Fourier transform (DFT) show that our generated floating-point code is competitive with and that our fixed-point code clearly outperforms
the best available libraries.
Keywords:
Numerical Methods (Linear algebra), Parallel and Distributed Computing
