# 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:

• Parametric tiling in the polyhedral model: The Monoparametric Tiling (also called Constant Aspect Ratio Tiling) transformation allows us to stay in the polyhedral domain while tiling parametrically. However, this transformation forces us to have a single tile size parameter, and a fixed ratio for every dimensions.
• Template recognition: Using a library of template (i.e., program whose inputs and parameters are unknown) corresponding to the operations encountered in the BLAS library, we match these template with the tiles of computation extracted from the previous transformation, while managing the semantic properties commonly encountered in linear algebra.

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.

### Publications:

• Conference articles:
• Guillaume Iooss, Christophe Alias, and Sanjay Rajopadhye. On program equivalence with reductions. In 21st International Static Analysis Symposium (SAS'14), Munich, Germany, September 2014.
• Lucas W. Krakow, Louis Rabiet, Yun Zou, Guillaume Iooss, Edwin K. P. Chong, and Sanjay Rajopadhye. Optimizing dynamic resource allocation. In Proceedings of the International Conference on Computational Science, ICCS 2014, Cairns, Queensland, Australia, 10-12 June, 2014, pages 1277--1288, May 2014.
• International workshop:
• Technical report:
• Guillaume Iooss, Sanjay Rajopadhye, Christophe Alias, Yun Zou. Mono-parametric Tiling is a Polyhedral Transformation. Research Report, RR-8802, INRIA, 2015.
• Sanjay Rajopadhye, Guillaume Iooss, Tomofumi Yuki, and Dan Connors. The stencil processing unit: GPGPU done right. Technical report, Colorado State University, March 2013.
• Tomofumi Yuki, Vamshi Basupalli, Gautam Gupta, Guillaume Iooss, DaeGon Kim, Tanveer Pathan, Pradeep Srinivasa, Yun Zou, and Sanjay Rajopadhye. AlphaZ: A system for analysis, transformation, and code generation in the polyhedral equational model. Technical report, Colorado State University, May 2012.

### Old Teaching (TP) at the Ens Lyon:

• (2013-2014) Image (M1 Ens Lyon)
• (2013-2014) LIF3: algorithmique et programmation fonctionnelle et récursive (L1 - Université Lyon 1)
• (2013-2014) Théorie de la programmation (L3 Ens Lyon)
• (2012-2013) Image (M1 Ens Lyon)
• (2012-2013) Compilation (M1 Ens Lyon)

### Contact:

• Email: guillaume.iooss [ - at - ] ens.fr
• Office: S16 (ENS)