An auto-tuning technique is devised for fast pre/postprocessing for the singular value decomposition of dense square matrices with the Dongarra or the Bischof-Murata algorithms. The computation speed of these two algorithms varies depending on a parameter and specification of computers. By dividing these algorithms into several parts and by modeling each of them, we can estimate their computation times accurately. This enables us to choose an optimal parameter and the faster algorithm prior to execution. Consequently the pre/postprocessing is done faster and the singular value decomposition is applied faster to dense square matrices. Numerical experiments show the effectiveness of the proposed auto-tuning function. The I-SVD library, which incorporates this auto-tuning function, has been published.