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2017 IEEE 24th Symposium on Computer Arithmetic (ARITH)

DOI: 10.1109/arith.2017.18



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

Proceedings article published in 2017 by Mioara Joldes, Jean-Michel Muller ORCID, Valentina Popescu
This paper is available in a repository.
This paper is available in a repository.

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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.