Extracting Data Parallelism in Non-Stencil Kernel Computing by Optimally Coloring Folded Memory Conflict Graph

Abstract

Irregular memory access pattern in non-stencil kernel computing renders the well-known hyperplane- [1], lattice- [2], or tessellation-based [3] HLS techniques ineffective. We develop an elegant yet effective technique that synthesizes memory-optimal architecture from high level software code in order to maximize application-specific data parallelism. Our basic idea is to exploit graph structures embedded in data access pattern and computation structure in order to perform the memory banking that maximizes parallel memory accesses while conserving both hardware and energy consumption. Specifically, we priority color a weighted conflict graph generated from folding the fundamental conflict graph to maximize memory conflict reduction. Most interestingly, our graph-based methodology enables a straightforward tradeoff between the number of memory banks and minimizing memory conflicts.We empirically test our methodology with Vivado HLx 2015.4 on a standard Kintex-7 device for six benchmark computing kernels by measuring conflict reduction. In particular, our approach only require 9.56% LUT, 3.2% FF, 2.5% BRAM, and 11.33% DSP of the total available hardware resource to obtain a mapping function that achieves a 90% conflict reduction on a modified forward Gaussian elimination Kernel with 4 simultaneous memory accesses.