Section: New Results

Constant Aspect-Ratio Parametric Tiling

Participants : Guillaume Iooss [PhD student] , Sanjay Rajopadhye [Colorado State University] , Christophe Alias, Yun Zou [PhD student, Colorado State University] .

Parametric tiling is a well-known transformation that is widely used to improve locality, parallelism, and granularity. However, parametric tiling is also a non-linear transformation and this prevents polyhedral analysis or further polyhedral transformation after parametric tiling. It is therefore generally applied during the code generation phase.

This result consists on a method to stay polyhedral in a special case of parametric tiling, where all the dimensions are tiled and all the tile sizes are constant multiples of a single tile size parameter. We call this Constant Aspect Ratio Tiling. We show how to mathematically transform a polyhedron and an affine function into their tiled counterpart and show how to obtain good generated code.

This work has been accepted for publication at IMPACT'14 [8] .