Efficient synthesis of out-of-core algorithms using a nonlinear optimization solver

We address the problem of efficient out-of-core code generation for a special class of imperfectly nested loops encoding tensor contractions arising in quantum chemistry computations. These loops operate on arrays too large to fit in physical memory. The problem involves determining optimal tiling of loops and placement of disk I/O statements. This entails a search in an explosively large parameter space. We formulate the problem as a nonlinear optimization problem and use a discrete constraint solver to generate optimized out-of-core code. The solution generated using the discrete constraint solver consistently outperforms other approaches by up to a factor of four. Measurements on sequential and parallel versions of the generated code demonstrate the effectiveness of the approach.