An Active Linear Algebra Library Using Delayed Evaluation and Runtime Code Generation

Active libraries can be defined as libraries which play an active part in the compilation (in particular, the optimisation) of their client code. This paper explores the idea of delaying evaluation of expressions built using library calls, then generating code at runtime for the particular compositions that occur. We explore this idea with a dense linear algebra library for C++. The key optimisations in this context are loop fusion and array contraction. Our library automatically fuses loops, identifies unnecessary intermediate temporaries, and contracts temporary arrays to scalars. Performance is evaluated using a benchmark suite of linear solvers from ITL (the Iterative Template Library), and is compared with MTL (the Matrix Template Library). Excluding runtime compilation overheads (caching means they occur only on the first iteration), for larger matrix sizes, performance matches or exceeds MTL – and in some cases is more than 60% faster.