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Performance impact of precision reduction in sparse linear systems solvers.

Mawussi Zounon1,2, Nicholas J Higham1, Craig Lucas2

  • 1School of Mathematics, University of Manchester, Manchester, United Kingdom.

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Summary
This summary is machine-generated.

Using single precision arithmetic in parallel sparse linear solvers offers limited speedups. Performance is hampered by subnormal numbers and lack of parallelism, though flushing subnormals to zero helps. Mixed precision requires careful refinement for accuracy.

Keywords:
Iterative refinementLU factorizationMixed precisionReduced precisionSparse linear systemsSubnormal numbers

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Area of Science:

  • Numerical Analysis
  • High-Performance Computing
  • Scientific Computing

Background:

  • Reduced precision arithmetic accelerates dense linear systems but its efficiency in parallel sparse solvers is less understood.
  • Existing research on reduced precision for sparse systems primarily focuses on single-core experiments.

Purpose of the Study:

  • To evaluate the performance benefits of using single precision arithmetic for solving double precision sparse linear systems on multiple cores.
  • To investigate the impact of single precision on both direct and iterative sparse solvers, focusing on LU factorization and matrix-vector products.

Main Methods:

  • Implemented and analyzed the use of single precision arithmetic within key components of LU factorization and matrix-vector product kernels for sparse linear systems.
  • Evaluated performance on multi-core architectures, considering both direct and iterative solver methods.
  • Investigated the role of subnormal numbers and explored strategies like flushing subnormals to zero to mitigate performance degradation.

Main Results:

  • Anticipated speedups for double precision LU factorization using single precision were only achieved for the largest test problems.
  • Performance loss in single precision sparse LU factorization was attributed to subnormal numbers; flushing subnormals to zero mitigated these penalties.
  • Iterative solvers showed modest benefits from single precision incomplete factorization preconditioners, while single precision matrix-vector products yielded an average speedup of 1.5.

Conclusions:

  • The efficiency of reduced precision in parallel sparse solvers is limited by factors including subnormal number intrusion and lack of parallelism in certain solver phases.
  • Strategies like flushing subnormals to zero can improve single precision performance, but accuracy requirements necessitate refinement steps that reduce overall gains.
  • Further research is needed to fully exploit reduced precision for accelerating parallel sparse linear system solvers while maintaining accuracy.