Productively Expressing High-performance Spatial Designs of Givens Rotation-based QR Decomposition Algorithm

TL;DR

This paper demonstrates how to express and optimize the Givens-rotation-based QR decomposition algorithm on spatial architectures using T2S, addressing unique challenges and providing a tutorial for non-expert programmers.

Contribution

It introduces a method to effectively implement high-performance QR decomposition on spatial architectures with T2S, clarifying complex spatial programming principles.

Findings

Successfully expressed QR decomposition in T2S for spatial architectures

Provided a tutorial approach for non-experts in spatial programming

Addressed non-rectangular loop iteration challenges in spatial design

Abstract

QR decomposition is used prevalently in wireless communication. In this paper, we express the Givens-rotation-based QR decomposition algorithm on a spatial architecture using T2S (Temporal To Spatial), a high-productivity spatial programming methodology for expressing high-performance spatial designs. There are interesting challenges: the loop iteration space is not rectangular, and it is not obvious how the imperative algorithm can be expressed in a functional notation, the starting point of T2S. Using QR decomposition as an example, this paper elucidates some general principle, and de-mystifies high-performance spatial programming. The paper also serves as a tutorial of spatial programming for programmers who are not mathematicians, not expert programmers, and not experts on spatial architectures, but still hope to intuitively identify a high-performance design and map to spatial architectures efficiently.