SA_TRSM: A Shape-Aware Auto-Tuning Framework for Small-Scale Irregular-Shaped TRSM

TRSM (Triangular Solve with Matrix) is an algorithm in the BLAS library for efficiently solving systems of linear equations, which is widely used in scientific computing, engineering computing, and machine learning. The traditional TRSM algorithm performs well in solving large-scale converging squareshaped matrices but is inefficient in solving small-scale irregularshaped matrices. In this paper, we propose SATRSM, a Shape-Aware auto-tuning framework that is aware of scale size and irregularity, aiming to improve performance on small-scale irregular-shaped TRSM computations. SA TRSM consists of the install-time stage and the run-time stage. In the install-time stage, we designed five components for generating high-performance kernels. In the run-time stage, we designed the Shape-Aware tiling algorithm and Plan Generator for generating an efficient execution plan. The experimental results show that the average performance of SA TRSM in this paper improves by 29.4,16.1,24.6 times, and 7.8 times on double-precision real, single-precision real, doubleprecision complex, and single-precision complex in turn, relative to the algorithms in MKL.