Bienvenue !

Our overall objective is to advance the fields of computer arithmetic and computer algebra, their interaction with formal verification, and their applications, in order to achieve unprecedented performance, accuracy, and reliability of numerical calculations. We work on arithmetic algorithms and their implementation, approximation methods, Euclidean lattices, certified computing, computer algebra and formal verification.

We address the following four broad challenges:

• Reliability of numerical evaluations
  Rounding, quantification and truncation errors make calculations unreliable, particularly in critical systems.
• Function approximation
  Finding fast and accurate approximations remains difficult, especially in floating-point precision.
• High-dimensional computations
  With the increase in data, numerical stability is put to the test, particularly for fast transformations such as the FFT and neural networks.
• Building trust with a wide audience
  Mistrust of numerical calculations, especially in mathematics and engineering, requires better documented, reliable and certified tools.

Main collaborations: LIP6 (Sorbonne Université), LMF (Université Paris-Saclay), LORIA (Université de Lorraine), University of Waterloo (Canada), Bosch, Mitsubishi Electric R & D Centre Europe.