Many applications require fast implementations of signal processing algorithms to analyze data in real time or to effectively process many large data sets. Fast implementations of a signal transform need to take advantage of structure in the transformation matrix to factor the transform into a product of structured matrices. These factorizations compute the transform with fewer operations than the naive implementation of matrix multiplication. Signal transforms can have a vast number of factorizations, with each factorization of a single transform represented by a unique but mathematically equivalent formula. Interestingly, when implemented in code, these formulas can have significantly different runtimes on the same processor, sometimes differing by an order of magnitude. Further, the optimal implementations differ significantly between processors. Therefore, determining which formula is the most efficient for a particular processor is of great interest.
This thesis contributes methods for automating the modeling and optimization of performance across a variety of signal processing algorithms. Modeling and understanding performance can greatly aid in intelligently pruning the huge search space when optimizing performance. Automation is vital considering the size of the search space, the variety of signal processing algorithms, and the constantly changing computer platform market.
To automate the optimization of signal transforms, we have developed and implemented a number of different search methods in the SPIRAL system. These search methods are capable of optimizing a variety of different signal transforms, including new user-specified transforms. We have developed a new search method for this domain, STEER, which uses an evolutionary stochastic algorithm to find fast implementations.
To enable computer modeling of signal processing performance, we have developed and analyzed a number of feature sets to describe formulas representing specific transforms. We have developed several different models of formula performance, including models that predict runtimes of formulas and models that predict the number of cache misses formulas incur.
Further, we have developed a method that uses these learned models to generate fast implementations. This method is able to construct fast formulas, allowing us to intelligently search through only the most promising formulas. While the learned model is trained on data from one transform size, our method is able to produce fast formulas across many transform sizes, including larger sizes, even though it has never timed a formula of those other sizes.