Section: New Results

Parametric Loop Tiling with Constant Aspect Ratio

Participants : Guillaume Iooss, Christophe Alias, Sanjay Rajopadhye [Colorado State University, USA] .

Parametric tiling is a well-known transformation which is widely used to improve locality, parallelism, and granularity (see also the next section for more details). 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.

To address this issue, we presented a method to remain in a polyhedral representation, in a special case of parametric tiling where all the dimensions are tiled and all tile sizes are constant multiples of a single tile size parameter. We call this Constant Aspect Ratio Tiling. We showed how to mathematically transform a polyhedron and an affine function into their tiled counterpart, which are the two main operations needed in such a transformation.

The approach is now implemented, and has been tested successfully on several kernels commonly used in the community (matrix multiply, jacobi 1D, jacobi 2D). A corresponding paper was published at the IMPACT 2014 workshop [8] .