Performance of the extended precision VRP processor on various Krylov subspace solvers - CEA - Commissariat à l’énergie atomique et aux énergies alternatives
Poster De Conférence Année : 2024

Performance of the extended precision VRP processor on various Krylov subspace solvers

Résumé

Numerical stability is a central aspect of high performance scientific computation, since the growing scale of modern problems has led researchers to complex numerical techniques which are vulnerable to round-off and quantization errors. This is particularly true for iterative Krylov subspace projective solvers, which are the workhorse the modern scientific applications. Here, higher precision, e.g. larger significand size, can mitigate these numerical instabilities and allow for simpler and more memory efficient computations. The VRP Processor [1] is designed to accelerate extended precision arithmetics in hardware. It supports 1/ a fast arithmetic unit for up to 512 bits of mantissa and 2/ support in memory for unaligned floating-point (FP) arrays. The objective of this study is to assess the performance impact of using the VRP with extended precision on common solver algorithms, e.g. conjugate gradient (CG), its preconditionned variant (PCG) and biconjugate gradient (BiCG). We consider two metrics: 1/ convergence speed, which refers to the number of iterations necessary for reaching that objective and 2/ execution time, including memory access time, measured in clock cycles. Execution time depends from the actual implementation of both hardware and low-level software, and from the input matrix structure and values. Our sample matrices principally come from the Florida sparse Matrix Collection [2]. We restrict ourselves to real matrices, which may be symmetric (for CG and PCG) or asymmetric (for BiCG).We compare execution time between different precisions (including standard double format) on the same VRP platform Our results confirm the benefits of extended precision for Krylov subspace solvers. For the CG solver, extending precision around 128 mantissa bits appears optimal in terms of iteration count and mostly beneficial for cycle count. The benefit for the BiCG solver is even greater. When using precisions above 256 bits, BiCG convergence becomes predictable.
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Dates et versions

cea-04799487 , version 1 (23-11-2024)

Identifiants

  • HAL Id : cea-04799487 , version 1

Citer

Yves Durand, Alexandre Hoffmann, Jérome Fereyre. Performance of the extended precision VRP processor on various Krylov subspace solvers. LACIRM24 - Numerical Linear Algebra, Sep 2024, Marseille, France. , 2024. ⟨cea-04799487⟩
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