Build to order linear algebra kernels

The performance bottleneck for many scientific applications is the cost of memory access inside linear algebra kernels. Tuning such kernels for memory efficiency is a complex task that reduces the productivity of computational scientists. Software libraries such as the Basic Linear Algebra Subprograms (BLAS) ameliorate this problem by providing a standard interface for which computer scientists and hardware vendors have created highly-tuned implementations. Scientific applications often require a sequence of BLAS operations, which presents further opportunities for memory optimization. However, because BLAS are tuned in isolation they do not take advantage of these opportunities. This phenomenon motivated the recent addition to the BLAS of several routines that perform sequences of operations. Unfortunately, the exact sequence of operations needed in a given situation is highly application dependent, so many more routines are needed. In this paper we present preliminary work on a domain- specific compiler that generates implementations for arbitrary sequences of basic linear algebra operations and tunes them for memory efficiency. We report experimental results for dense kernels and show speedups of 25 % to 120 % relative to sequences of calls to GotoBLAS and vendor-tuned BLAS on Intel Xeon and IBM PowerPC platforms.