Automatic implementation and platform adaptation of discrete filtering and wavelet algorithms

Moore's law, with the doubling of the transistor count every 18 months, poses serious challenges to high-performance numerical software designers: how to stay close to the maximum achievable performance on ever-changing and ever-faster hardware technologies? Up-to-date numerical libraries are usually maintained by large teams of expert programmers who hand-tune the code to a specific class of computer platforms, sacrificing portability for performance. Every new generation of processors reopens the cycle of implementing, tuning, and debugging. The SPIRAL system addresses this problem by automatically generating and implementing algorithms for DSP numerical kernels and searching for the best solution on the platform of interest. Using search, SPIRAL adapts code to take optimal advantage of the available platform features, such as the architecture of the memory hierarchy and register banks. As a result, SPIRAL generates high-performance implementations for DSP transforms that are competitive with the best hand-coded numerical libraries provided by hardware vendors. In this thesis, we focus on automatic implementation and platform adaptation of filtering and wavelet kernels, which are at the core of many performance-critical DSP applications. We formulate many well-known algorithms for FIR filters and discrete wavelet transforms (DWT) using a concise and flexible symbolic mathematical language and integrate it in the SPIRAL system. This enables automatic generation and search over the comprehensive space of competitive algorithms, often leading to complex solutions that are hardly ever considered by a human programmer. Experimental results show that our automatically generated and tuned code for FIR filters and DWTs is competitive and sometimes even outperforms hand-coded numerical libraries provided by hardware vendors. This implies that the richness and the extent of the automatically generated search space can match human ingenuity in achieving high performance. Our system generates high-quality code for digital filtering and wavelet kernels across most current and compatible future computer platforms and frees software developers from tedious and time-consuming coding at the machine level.