Auto-tuning stencil computations on multicore and accelerators

The recent transformation from an environment where gains in computational performance came from increasing clock frequency and other hardware engineering innovations, to an environment where gains are realized through the deployment of ever increasing numbers of modest performance cores has profoundly changed the landscape of scientific application programming. This exponential increase in core count represents both an opportunity and a challenge: access to petascale simulation capabilities and beyond will require that this concurrency be efficiently exploited. The problem for application programmers is further compounded by the diversity of multicore architectures that are now emerging [4]. From relatively complex out-of-order CPUs with complex cache structures, to relatively simple cores that support hardware multithreading, to chips that require explicit use of software controlled memory, designing optimal code for these different platforms represents a serious impediment. An emerging solution to this problem is auto-tuning: the automatic generation of many versions of a code kernel that incorporate various tuning strategies, and the benchmarking of these to select the highest performing version. Typical tuning strategies might include: maximizing incore performance with loop unrolling and restructuring; maximizing memory bandwidth by exploiting non-uniform memory access (NUMA), engaging prefetch by directives; and minimizing memory traffic by cache blocking or array padding. Often a key parameter is associated with each tuning strategy (e.g., the amount of loop unrolling or the cache blocking factor), and these parameters must be explored in addition to the layering of the basic strategies themselves