This paper proposes the parallel numerical library called ILIB which realises auto-tuning facilities with selectable calculation kernels, communication methods between processors, and various number of unrolling for loop expansion. This auto-tuning methodology has advantage not only in usability of library but also in performance of library. In fact, results of the performance evaluation show that the auto-tuning or auto-correction feature for the parameters is a crucial technique to attain high performance. A set of parameters which are auto-selected by this auto-tuning methodology gives us several kinds of important knowledge for highly efficient program production. These kinds of knowledge will help us to develop some other high-performance programs, in general.