Enhancement of Incremental Performance Parameter Estimation on ppOpen-AT

We propose an efficient implementation of discretized spline function (d-Spline) based incremental performance parameter estimation (IPPE) on 2D parameter space. IPPE generates a data fitting function based on d-Splines for a few sampling points, inserting each new sampling point successively until the optimal parameter among chosen parameter values stops changing. This method updates a data fitting function according to a new sampling parameter value for every iteration. D-Splines can be calculated by solving the least-squares problem, in which the number of unknowns is equal to the number of combinations of performance parameter values. In this study, we propose an efficient implementation method based on the iterative solver such as a conjugate gradient method. In a prior work, the least-square problem was solved using QR decomposition. It can efficiently update d-Spline functions according to new sampling parameter values but requires substantial memory usage. Through numerical tests, our proposed method can reduce the memory usage significantly, and its performance is comparable with QR decomposition. Moreover, we implement this method in ppOpen-AT, a framework that adds auto-tuning functionality to user code by inserting a few lines of tuning directives. In addition, to test the effectiveness of our method, it is applied to the algebraic multigrid method that has many performance parameters and is used repeatedly in one simulation, e.g., a fluid simulation. Finally, our method found near-optimal parameters with a little cost for searching parameters. It used only 25 combinations among the 160 parameter combinations for the test. Its performance difference from the optimal parameter was only 5%. Our method turned out to be twice as fast as the brute-force search method.