SPIRAL: Code Generation for DSP Transforms

Abstract

Abstract-Fast changing, increasingly complex, and diverse computing platforms pose central problems in scientific computing: How to achieve, with reasonable effort, portable optimal performance? We present SPIRAL that considers this problem for the performance-critical domain of linear digital signal processing (DSP) transforms. For a specified transform, SPIRAL automatically generates high performance code that is tuned to the given platform. SPIRAL formulates the tuning as an optimization problem, and exploits the domain-specific mathematical structure of transform algorithms to implement a feedback-driven optimizer. Similar to a human expert, for a specified transform, SPIRAL "intelligently" generates and explores algorithmic and implementation choices to find the best match to the computer's microarchitecture. The "intelligence" is provided by search and learning techniques that exploit the structure of the algorithm and implementation space to guide the exploration and optimization. SPIRAL generates high performance code for a broad set of DSP transforms including the discrete Fourier transform, other trigonometric transforms, filter transforms, and discrete wavelet transforms. Experimental results show that the code generated by SPIRAL competes with, and sometimes outperforms, the best available human tuned transform library code.

Parallelization of Wavelet Filters Using Simd Extensions

“…This is important because each parallelization presented in this work is one of many possible solutions and it is not at all clear that the shown solutions could not be improved. Since in practice it would be an almost unaccomplishable amount of work to hand-code a variety of solutions to find the best, automatic optimization techniques as in [12] are required.…”

Multi-stage Programming with Functors and Monads: Eliminating Abstraction Overhead from Generic Code

“…MetaOCaml gives us assurance that these errors, and more subtle type errors, shall never occur in the generated code. SPIRAL [23] is another even more ambitious project. But SPIRAL does intentional code analysis, relying on a set of code transformation "rules" which make sense, but which are not proven to be either complete or confluent.…”

“…This approach gives a stronger equational theory [22], and avoids the danger of creating unsoundness [21]. Furthermore, intensional code analysis essentially requires one to insert both an optimizing compiler and an automated theorem proving system into the code generating system [23,5,24,6]. While this is potentially extremely powerful and an exciting area of research, it is also extremely complex, which means that it is currently more error-prone and difficult to ascertain the correctness of the resulting code.…”

Automatic Generation of the HPC Challenge’s Global FFT Benchmark for BlueGene/P

“…FFT algorithms reduce the runtime to O(n log(n)) and can be written in the form of structured sparse matrix factorization using the Kronecker product formalism [6,12]. The twopoint FFT is given by the butterfly matrix,…”