A Method on Analyzing Performance Sensitivity of Applications Based on Partial Derivatives of Non-linear Regression Equation

Performance sensitivity reflects how sensitive the performance is to the influence factors. Analysis on performance sensitivity of different applications can guide the architects on the architecture design and help programmers on application optimization. In this paper, a performance sensitivity non-linear regression model (PS-NLRM) is set up to quantitatively analyze the performance sensitivity of different applications. In the model, principal components analysis is used to eliminate the linear correlations among influence factors which are quantified with performance events. Non-linear independent variables are introduced by curve fitting in the model. By regression analysis, a non-linear regression model is set up between cycles per instruction (CPI) and performance events. The model is implemented in SPEC CPU2006 integer benchmarks and uses the benchmarks as samples. The model is verified by t test and F test with goodness of fit over 90%. By using the partial derivatives of the non-linear regression equation of the model, performance sensitivity is obtained which is denoted by the quantitative change of CPI with the corresponding changes of the performance events. Based on performance sensitivity, performance of applications can be predicted. The average relative error of predicted performance of SPEC CPU2006 integer benchmarks is about 4.5%, which is half reduced compared with the traditional linear regression models.