Implementation and performance evaluation of an extended precision floating-point arithmetic library for high-accuracy semidefinite programming

Mioara Joldes 1 Jean-Michel Muller 2, 3 Valentina Popescu 4, 3
1 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
LAAS - Laboratoire d'analyse et d'architecture des systèmes [Toulouse]
2 ARIC - Arithmetic and Computing
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : Semidefinite programming (SDP) is widely used in optimization problems with many applications, however , certain SDP instances are ill-posed and need more precision than the standard double-precision available. Moreover, these problems are large-scale and could benefit from parallelization on specialized architectures such as GPUs. In this article, we implement and evaluate the performance of a floating-point expansion-based arithmetic library (newFPLib) in the context of such numerically highly accurate SDP solvers. We plugged-in the newFPLib with the state-of-the-art SDPA solver for both CPU and GPU-tuned implementations. We compare and contrast both the numerical accuracy and performance of SDPA-GMP,-QD and-DD, which employ other multiple-precision arithmetic libraries against SDPA-newFPLib. We show that our newFPLib is a very good trade-off for accuracy and speed when solving ill-conditioned SDP problems.
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Mioara Joldes, Jean-Michel Muller, Valentina Popescu. Implementation and performance evaluation of an extended precision floating-point arithmetic library for high-accuracy semidefinite programming. IEEE Symposium on Computer Arithmetic (Arith24), Jul 2017, London, United Kingdom. ⟨hal-01491255v2⟩

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