Generating High-Performance General Size Linear Transform Libraries Using Spiral

Developing numerical libraries that achieve highest performance on modern computer architectures became an extremely difficult task due to the increasingly complicated microarchitectures, deep cache hierarchies, and different forms of onchip parallelism, such as multiple processor cores and SIMD short vector instruction sets. The difficulty of library development led to interest in automated tools that simplify the development of high-performance libraries, without sacrificing performance. Program generator Spiral [2] is an example of such tool for the domain of linear transforms, such as the discrete Fourier transform (DFT), FIR filters, and others. Spiral automatically generates the optimized and platform-adapted implementation given only the transforms specification (e.g. DFT1024) and a high-level description of the recursive divide-and-conquer algorithm in the domain-specific language called SPL (Signal Processing Language). Spiral performs optimizations such as vectorization and parallelization using rewriting on the high-level of abstraction provided by SPL, and also lower-level representations. To exploit the potential offered by the development automation tools, Intel Integrated Performance Primitives (IPP) library, which provides a wide number of optimized linear transform functions, starting with version 6.0, will include a special domain for the functions automatically generated by Spiral. To date Spiral was restricted to generating code for transforms of fixed size, known at generation time. In this paper we overview our latest research results [3] that enable generating full general size libraries, for which the transform size is only known at runtime.