Personal page of Guillaume Iooss

I am currently a Post-Doctorate at ENS (team Parkas), working on synchronous language and the heptagon compiler in the context of the project Assume.

PhD thesis: Detection of linear algebra operations in polyhedral programs

(Dissertation / Slides)

I was a PhD student in cotutelle between ENS Lyon (advisers: Christophe Alias, Alain Darte/ team: Compsys) and Colorado State University (adviser: Sanjay Rajopadhye / team: Melange).

The aim of my PhD thesis was to recognize occurrences linear algebra operations inside polyhedral program. The main challenges are the capability of recognizing sub-computations, the semantic properties management (in particular the summations over a parametric number of elements frequently encountered in linear algebra), while being careful about the scaling of the process. The main intuition is to use a tiling transformation to extract tiles of computation from the program, which are later recognized as being combination of linear algebra operations.

This work is divided into two parts:

Some work was also done on program equivalence modulo associativity and commutativity. In particular, we need to manage reductions, i.e. successive application of an associative and commutative operator on a parametric set of sub-expressions. The main difficulty of proving equivalence is to find a bijection between the two sets of sub-expressions. This problem is linked to the parametric perfect matching problem on a bipartite graph.



Old Teaching (TP) at the Ens Lyon: