Our seminar series is free and available for anyone to attend. Unless otherwise stated, seminars take place on Wednesday afternoons at 2pm in the Kilburn Building during teaching season.

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Concepts for implementing exact real arithmetic

  • Speaker:   Dr  Norbert Muller  (Universitat Trier)
  • Host:   Dave Lester
  • 18th March 2009 at 14:15 in Lecture Theatre 1.4, Kilburn Building
An implementation of exact arithmetic on the real numbers has to fulfill many (antithetic) demands:

On the one hand, its use must be as easy as possible: The handling of exact reals should be similar to ordinary floating point numbers. The implementation has to be very efficient, close to the speed of the hardware. Imperative programming languages are still state of the art for numerical purposes.

On the other hand, computability on real numbers deals with infinite objects and infinite computations. Multi-valued functions are needed to relax continuity constraints, also lazy evaluation can be advantageous. Limits of sequences are the basis for calculus and numerical analysis, which must be reflected in an implementation.

In this talk, we will explain how the iRRAM package for exact real arithmetic tries to match many of these points: For simple applications, it is almost as fast as interval packages based on double precision floating points numbers, but it also covers the cases where fixed precision is not enough and exact reals simplify programming.
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