Fast Multidimensional Performance Parameter Estimation with Multiple One-Dimensional d-Spline Parameter Search

One approach of software automatic tuning is the incremental performance parameter estimation (IPPE) method, which is based on discrete spline function (d-Spline). We have applied IPPE to multidimensional performance parameter estimation. IPPE starts with the minimum number of the sampling points. It adds other sampling points by updating d-Spline at every iteration. For multidimensional performance parameter estimation, IPPE method using multidimensional d-Spline was studied in our previous work. However, the parameter estimation cost increases significantly as the number of performance parameters increases, because the calculation cost of multidimensional d-Spline is much higher than one-dimensional d-Spline. Computational cost for one-dimensional d-Spline is negligible. In this study, we propose a method for estimating the optimum value of multidimensional performance parameters by repeating one-dimensional d-Spline parameter search. We demonstrated that our method is able to identify optimal parameters with little cost. In case of three dimensional performance parameter estimation, our proposed method required only 104.8 combinations out of 1440 possible parameter combinations. We experimentally showed that multiple one-dimensional d-Spline parameter search is efficient for multidimensional performance parameter estimation.