Shapes and flattening

Nesl is a first-order functional language with an apply-to-each construct and other parallel primitives that enables the expression of irregular nested data-parallel (NDP) algorithms. To compile Nesl, Blelloch and others developed a global flattening transformation that maps irregular NDP code into regular flat data parallel (FDP) code suitable for executing on SIMD or SIMT architectures, such as GPUs. While flattening solves the problem of mapping irregular parallelism into a regular model, it requires significant additional optimizations to produce performant code. Nessie is a compiler for Nesl that generates CUDA code for running on Nvidia GPUs. The Nessie compiler relies on a fairly complicated shape analysis that is performed on the FDP code produced by the flattening transformation. Shape analysis plays a key rôle in the compiler as it is the enabler of fusion optimizations, smart kernel scheduling, and other optimizations. In this paper, we present a new approach to the shape analysis problem for Nesl that is both simpler to implement and provides better quality shape information. The key idea is to analyze the NDP representation of the program and then preserve shape information through the flattening transformation.