A Modified Staggered Correction Arithmetic with Enhanced Accuracy and Very Wide Exponent Range

  • Authors:

  • Frithjof Blomquist;Werner Hofschuster;Walter Krämer

  • Affiliations:

  • Scientific Computing/Software Engineering, Bergische Universität Wuppertal, Wuppertal, Germany D-42097;Scientific Computing/Software Engineering, Bergische Universität Wuppertal, Wuppertal, Germany D-42097;Scientific Computing/Software Engineering, Bergische Universität Wuppertal, Wuppertal, Germany D-42097

  • Venue:
  • Numerical Validation in Current Hardware Architectures
  • Year:
  • 2009

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Abstract

A so called staggered precision arithmetic is a special kind of a multiple precision arithmetic based on the underlying floating point data format (typically IEEE double format) and fast floating point operations as well as exact dot product computations. Due to floating point limitations it is not an arbitrary precision arithmetic. However, it typically allows computations using several hundred mantissa digits. A set of new modified staggered arithmetics for real and complex data as well as for real interval and complex interval data with very wide exponent range is presented. Some applications will show the increased accuracy of computed results compared to ordinary staggered interval computations. The very wide exponent range of the new arithmetic operations allows computations far beyond the IEEE data formats. The new modified staggered arithmetics would be extremely fast if an exact dot product was available in hardware (the fused accumulate and add instruction is only one step in this direction). This paper describes work in progress. Updates of the software as well as additional documentation may be downloaded from our web site http://www. math.uni-wuppertal.de/~xsc