Easy Multi-Precision Acceleration via Vectorization

Abstract

High level programming languages and accelerators are powerful enablers for a wide range of applications. Accelerators offer significant performance via diverse numeric precision and increased memory bandwidth and capacity. These enable new algorithms to be explored. Construction of these algorithms can be enabled by the ready accessibility of these performance features in high-level languages. Achieving scalable vertical (within a compute node), precision (over various numeric precisions), and temporal (over different generations of hardware) performance while retaining productivity requires effective abstractions. Vectorized coding that expresses operations as high-level matrix mathematics has historically been an important method for achieving portable performance. This paper examines the performance availability across a wide range of precisions and hardware using simple vectorized coding techniques applied to several example programs that highlight bandwidth, real and complex matrix multiplication, and 2D convolution. The systems evaluated span nearly a decade of computing hardware, enabling direct comparison of performance gains over this period. This work demonstrates that near hardware peak performance is readily accessible from high-level programming environments. In particular for memory bandwidth, real and complex matrix multiplication in double/single/half precision, and 2D convolutions using the Fast Fourier Transform (FFT). Furthermore, algorithms that trade decreased compute intensity for increased memory intensity have significant potential.