Optimizing sparse matrix computations through compiler-assisted programming

Abstract

Existing high-performance implementations of sparse matrix codes are intricate and result in large code bases. In fact, a single floating-point operation requires 400 to 600 lines of additional code to "prepare" this operation. This imbalance severely obscures code development, thereby complicating maintenance and portability. In this paper, we propose a drastically different approach in order to continue to effectively handle these codes. We propose to only specify the essence of the computation on the level of individual matrix elements. All additional source code to embed these computations are then generated and optimized automatically by the compiler. This approach is far superior to existing library approaches and allows code to perform scatter/gather operations, matrix reordering, matrix data structure handling, handling of fill-in, etc., to be generated automatically. Experiments show that very efficient data structures can be generated and the resulting codes can be very competitive.