Automatic Generation of Efficient Linear Algebra Programs

The level of abstraction at which application experts reason about linear algebra computations and the level of abstraction used by developers of high-performance numerical linear algebra libraries do not match. The former is conveniently captured by high-level languages and libraries such as Matlab and Eigen, while the latter expresses the kernels included in the BLAS and LAPACK libraries. Unfortunately, the translation from a high-level computation to an efficient sequence of kernels is a task, far from trivial, that requires extensive knowledge of both linear algebra and high-performance computing. Internally, almost all high-level languages and libraries use efficient kernels; however, the translation algorithms are too simplistic and thus lead to a suboptimal use of said kernels, with significant performance losses. In order to both achieve the productivity that comes with high-level languages, and make use of the efficiency of low level kernels, we are developing Linnea, a code generator for linear algebra problems. As input, Linnea takes a high-level description of a linear algebra problem and produces as output an efficient sequence of calls to high-performance kernels. In 25 application problems, the code generated by Linnea always outperforms Matlab, Julia, Eigen and Armadillo, with speedups up to and exceeding 10×.