  Tuning numerical libraries has become more difficult over time, as systems
get more sophisticated. In particular, modern multicore machines make the
behaviour of algorithms hard to forecast and model. In this paper, we tackle
the issue of tuning a dense QR factorization on multicore architectures. We
show that it is hard to rely on a model, which motivates us to design a fully
empirical approach. We exhibit few strong empirical properties that enable us
to efficiently prune the search space. Our method is automatic, fast and
reliable. The tuning process is indeed fully performed at install time in less
than one and ten minutes on five out of seven platforms. We achieve an average
performance varying from 97% to 100% of the optimum performance depending on
the platform. This work is a basis for autotuning the PLASMA library and
enabling easy performance portability across hardware systems.
