Yet Another Way of Building Exact Polyhedral Model for Weakly Dynamic Affine Programs

TL;DR

This paper introduces a novel method for constructing an exact polyhedral model for weakly dynamic affine programs, enabling precise dataflow analysis even with complex control structures like arbitrary ifs.

Contribution

It extends the exact polyhedral model to handle data-dependent conditions, allowing transformation of programs into dataflow computation models.

Findings

Exact polyhedral model built for programs with arbitrary ifs.

Model can be converted into equivalent dataflow programs.

Supports transformation to dataflow computation semantics.

Abstract

Exact polyhedral model (PM) can be built in the general case if the only control structures are {\tt do}-loops and structured {\tt if}s, and if loop counter bounds, array subscripts and {\tt if}-conditions are affine expressions of enclosing loop counters and possibly some integer constants. In more general dynamic control programs, where arbitrary {\tt if}s and {\tt while}s are allowed, in the general case the usual dataflow analysis can be only fuzzy. This is not a problem when PM is used just for guiding the parallelizing transformations, but is insufficient for transforming source programs to other computation models (CM) relying on the PM, such as our version of dataflow CM or the well-known KPN. The paper presents a novel way of building the exact polyhedral model and an extension of the concept of the exact PM, which allowed us to add in a natural way all the processing related to the data dependent conditions. Currently, in our system, only arbirary {\tt if}s (not {\tt while}s) are allowed in input programs. The resulting polyhedral model can be easily put out as an equivalent program with the dataflow computation semantics.