Frédéric de Mesmay (PhD. thesis, Electrical and Computer Engineering, Carnegie Mellon University, 2010)
On the Computer Generation of Adaptive Numerical Libraries
Preprint (3.2 MB)

Very fast runtime is crucial in many applications in scientific computing, multimedia processing, communication, and control. Most of these applications spend the bulk of the computation in well known mathematical functions which are provided by highly optimized libraries. The development and maintenance of these libraries has become extraordinarily difficult. Optimal performance requires multiple-core balancing, careful use of vector instruction sets, and locality optimization. These optimizations require highly-skilled programmers and are often platform-specific, which means maintenance is a considerable effort given the short processor release cycles.

The Spiral system has successfully addressed these issues by automatically generating high performance libraries given only a high-level mathematical algorithm description in a language called SPL. Spiral produced high performance code using a number of techniques including SPL rewriting systems and a form iterative compilation. However, to date Spiral has been limited in two key aspects. First, Spiral could only generate libraries for the domain of linear transforms; second, all optimizations for a specific target platform are performed during the source code generation, that is, the produced libraries themselves had no dynamic platform-adaptation mechanism.

In this thesis we make progress on both fronts. We present a framework and its implementation for the computer generation of functionalities that are not transforms, specifically matrix multiplication and convolutional decoding. The framework builds on the operator language (OL) that we introduce and that extends SPL. Similar to prior work on transforms, we then develop OL rewriting system to explore algorithm choice, to vectorize and parallelize, and to derive the basic library structure called recursion step closure. The actual code is obtained through a backend that supports different target languages. The generated libraries exhibit a performance comparable to libraries that are hand-written for commodity workstations.

Further, we enable the generation of platform-adaptive libraries, through adaptation modules that can be inserted into our libraries, which are generated to support different ways to compute the same function. We distinguish between online adaptation and offline adaptation and provide mechanism for both. Online adaptation happens during the actual user function call when the input size is provided. Given this size, the library searches for the best computation strategy inside the library, which can then be used for subsequent computations of this size. We provide the dynamic programming strategy used in prior work and introduce a novel kind of Monte-Carlo search on graphs. Finally, we present a machine learning approach that performs offline (during installation time) adaptation with an online adaptive library. First a search is run to produce solutions for a set of sizes. Based on the result, a learning algorithm derives solutions for all sizes in the form of a set of decision trees that are then inserted into the library to render it deterministic. Experiments show the viability of both approaches.

Learn the current Spiral system, Discrete/fast Fourier transform, Search/Learning for optimization, Numerical kernels we consider, General size libraries, Beyond transforms, Linear algebra