Linear algebra

Programming language

Geometry

Vectorization (mathematics)

Mathematics

Digital signal processor

Computation

Computer hardware

Operating system

Code generation

Compiler

Parallel computing

Computer science

Digital signal processing

Implementation

Computer engineering

Key (lock)

SIMD

Speedup

Applications targeting digital signal processors (DSPs) benefit from fast implementations of small linear algebra kernels. While existing auto-vectorizing compilers are effective at extracting performance from large kernels, they struggle to invent the complex data movements necessary to optimize small kernels. To get the best performance, DSP engineers must hand-write and tune specialized small kernels for a wide spectrum of applications and architectures. We present Diospyros, a search-based compiler that automatically finds efficient vectorizations and data layouts for small linear algebra kernels. Diospyros combines symbolic evaluation and equality saturation to vectorize computations with irregular structure. We show that a collection of Diospyros-compiled kernels outperform implementations from existing DSP libraries by 3.1× on average, that Diospyros can generate kernels that are competitive with expert-tuned code, and that optimizing these small kernels offers end-to-end speedup for a DSP application.

Vectorization for digital signal processors via equality saturation