Stanford 50: State of the Art and Future Directions of Computational Mathematics and Numerical Computing


  • March 31, 2007
  • 9:25 am - 9:50 am

The challenge of multicore and specialized accelerators for mathematical software

Jack Dongarra (University of Tennessee)

Recent versions of microprocessors exhibit performance characteristics for 32-bit floating-point arithmetic (single precision) that are substantially higher than for 64-bit floating-point (double precision). Examples include Intel's Pentium IV and M processors, AMD's Opteron architectures, IBM's Cell processor, and various GPUs. Single precision operations can be performed up to two times faster on the Pentium and up to ten times faster on the Cell compared to double precision.

Our motivation is to exploit single precision whenever possible and resort to double precision at critical stages while attempting to provide full double precision results. The results described are fairly general and can be applied to various problems in linear algebra, such as solving large sparse systems using direct or iterative methods, and some eigenvalue problems. There are limitations, such as when the problem condition exceeds the reciprocal of single precision accuracy. In that case the double precision algorithm should be used.

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