A GPU Method for the Analysis Stage of the SPTRSV Kernel

The solution of sparse triangular linear systems of equations (SPTRSV) is often the main computational bottleneck of many numerical methods in science and engineering. In GPUs, this operation is solved using mainly two approaches. Level-set strategies perform a costly pre-processing (called analysis stage) to examine the dependencies between rows of the matrix and derive a static schedule for the subsequent solution stage. On the other hand, synchronization-free methods discover this scheduling dynamically and avoid the analysis stage, although some hybrid synchronization-free methods can leverage the level-set analysis to improve the performance. In this work, we present an efficient GPU routine to compute the analysis stage and then apply some of these ideas to accelerate a synchronization-free solver that does not require analysis. The experimental comparison with the well-known cusparse library shows up to 40 × speedups in the solution of triangular linear systems, and up to 262 × concerning the level-set analysis phase.