Solving Sparse Triangular Linear Systems in Modern GPUs: A Synchronization-Free Algorithm

Sparse triangular linear systems are ubiquitous in a wide range of science and engineering fields, and represent one of the most important building blocks of Sparse Numerical Lineal Algebra methods. For this reason, their parallel solution has been subject of exhaustive study, and efficient implementations of this kernel can be found for almost every hardware platform. However, the strong data dependencies that serialize a great deal of the execution and the load imbalance inherent to the triangular structure poses serious difficulties for its parallel performance, specially in the context of massively- parallel processors such as GPUs. To this day, the most widespread GPU implementation of this kernel is the one distributed in NVIDIA CUSPARSE library, which relies on a preprocessing stage to determine the parallel execution schedule. Although the solution phase is highly efficient, this strategy pays the cost of constant synchronizations with the CPU. In this work, we present a synchronization-free GPU al- gorithm to solve sparse triangular linear systems for the CSR format. The experimental evaluation shows performance improvements over CUSPARSE and a recently proposed synchronization-free method for the CSC matrix format.