Autotuning Divide-and-Conquer Matrix-Vector Multiplication

Divide and conquer is an important concept in computer science. It is used ubiquitously to simplify and speed up programs. However, it needs to be optimized, with respect to parameter settings for example, in order to achieve the best performance. The problem boils down to searching for the best implementation choice on a given set of requirements, such as which machine the program is running on. The goal of this thesis is to apply and evaluate the Ztune approach [14] on serial divide-and-conquer matrix-vector multiplication. We implemented Ztune to autotune serial divide-and-conquer matrix-vector multiplication on machines with different hardware configurations, and found that Ztuneoptimized codes ran 1%-5% faster than the hand-optimized counterparts. We also compared Ztune-optimized results with other matrix-vector multiplication libraries including the Intel Math Kernel Library and OpenBLAS. Since the matrix-vector multiplication problem is a level 2 BLAS, it is not as computationally intensive as level 3 BLAS problems such as matrix-matrix multiplication and stencil computation. As a result, the measurement in matrix-vector multiplication is more prone to error from factors such as noise, cache alignment of the matrix, and cache states, which lead to wrong decision choices for Ztune. We explored multiple options to get more accurate measurements and demonstrated the techniques that remedied these issues. Lastly, we applied the Ztune approach to matrix-matrix multiplication, and we were able to achieve 2%-85% speedup compared to the hand-tuned code. This thesis represents joint work with Ekanathan Palamadai Natarajan. Thesis Supervisor: Professor Charles E. Leiserson Title: Edwin Sibley Webster Professor in Electrical Engineering and Computer Science 1This research was supported in part by NSF Grants 1314547 and 1533644.