Section: New Results

Solving AAA constraints analytically

Participants : Emilien Kofman, Dumitru Potop Butucaru, Thomas Carle, Raul Gorcitz, Robert de Simone, Mohamed Bergach, Amine Oueslati.

Given two abstract modeling descriptions, one of a dataflow process network for the application, one of a block diagram structure for the computing platform and its interconnects, together with cost functions for the elementary compuations and communications, one is bound to seek optimal mappings pairing the two. Amongst all the possible techniques, an obvious one consists in solving constraint using general solvers (real, integer, or boolean constraint programming, SMT solvers, etc). Given the NP-hard nature of the problem, the issue here is to scale to the dimensions of realistic problems. We conducted extensive experiments on several case studies, with as extra objective the concern of studying how the formulation of constraints, or the exploiation of additional information (in concurency or exclusion of tasks, structural symmetries,...) could impact favorably or negatively the process. Results were compiled in a publication [57] .

In the framework of the PhD thesis of Mohamed Bergach, under CIFRE funding with Kontron Toulon, we studied how to adjust a radar application, that typically computes extensively FFT convolutions, on an hybrid CPU/GPU architecture such as IntelCore IvyBridge and Haswell processors. This approach works in two stages: first we considered how to implement a FFT redex as large as possible in exactly one core (either a CPU core or a GPU Execution Unit), so as to make full use of the local register memories and SIMD/vectorial instructions. Not by accident certainly FFT blocks of size exactly 8 and 16 respectively can so be fitted on a GPU (resp. CPU) block. This provides a new "compound" instruction, on which to build modularly and optimization the allocation of larger aplications based on such basic block. This is fully described in Mohamed Bergach PhD document [16] .