Auto-tuning a Matrix Routine for High Performance

Well-written scientific simulations typically get tremendous performance gains by using highly optimized library routines. Some of the most fundamental of these routines perform matrix-matrix multiplications and related routines, known as BLAS (Basic Linear Algebra Subprograms). Optimizing these library routines for efficiency is therefore of tremendous importance for many scientific simulations. In fact, some of them are often hand-optimized in assembly language for a given processor, in order to get the best possible performance. In this paper, we present a new tuning approach, combining a small snippet of assembly code with an auto-tuner. For our preliminary test-case, the symmetric rank-2 update, the resulting routine outperforms the best auto-tuner and vendor supplied code on our target machine, an Intel quad-core processor. It also performs less than 1.2% slower than the best hand coded library. Our novel approach shows a lot of promise for further performance gains on modern multi-core and many-core processors.