Preprint Number 08–53 TOWARDS DENSE LINEAR ALGEBRA FOR HYBRID GPU ACCELERATED MANYCORE SYSTEMS

Abstract: If multicore is a disruptive technology, try to imagine hybrid multicore systems enhanced with accelerators! This is happening today as accelerators, in particular Graphical Processing Units (GPUs), are steadily making their way into the high performance computing (HPC) world. We highlight the trends leading to the idea of hybrid manycore/GPU systems, and we present a set of techniques that can be used to efficiently program them. The presentation is in the context of Dense Linear Algebra (DLA), a major building block for many scientific com-puting applications. We motivate the need for new algorithms that would split the computation in a way that would fully exploit the power that each of the hybrid components offers. As the area of hybrid multicore/GPU computing is still in its infancy, we also argue for its importance in view of what future architectures may look like. We therefore envision the need for a DLA library similar to LAPACK but for hybrid manycore/GPU systems. We illustrate the main ideas with an LU-factorization algorithm where particular techniques are used to reduce the amount of pivoting, resulting in an algorithm achieving up to 388 GFlop/s for single and up to 99.4 GFlop/s for double precision factorization on a hybrid Intel Xeon (2x4 cores @ 2.33 GHz) – NVIDIA GeForce GTX 280 ∗ (240 cores @ 1.30 GHz) system