Static analysis by abstract interpretation of the functional correctness of matrix manipulating programs

Abstract

We present new abstract domains to prove automatically the functional correctness of algorithms implementing matrix operations, such as matrix addition, multiplication, GEMM (general matrix multi- plication), or more generally BLAS (Basic Linear Algebra Subprograms). In order to do so, we introduce a family of abstract domains parameter- ized by a set of matrix predicates and by a numeric domain. We show that our analysis is robust enough to prove the functional correctness of several versions of matrix addition and multiplication codes result- ing from loop reordering, loop tiling, inverting the iteration order, line swapping, and expression decomposition. Finally, we extend our method to enable modular analysis on code fragments manipulating matrices by reference, and show that it results in a significant analysis speedup.