Provably correct vectorization of nested-parallel programs

The work/step framework provides a high-level cost model for nested data-parallel programming languages, allowing programmers to understand the efficiency of their codes without concern for the eventual mapping of tasks to processors. Vectorization, or flattening, is the key technique for compiling nested-parallel languages. This paper presents a formal study of vectorization, considering three low-level targets: the EREW, bounded-contention CREW, and CREW variants of the VRAM. For each, we describe a variant of the cost model and prove the correctness of vectorization for that model. The models impose different constraints on the set of programs and implementations that can be considered; we discuss these in detail.