[Haskell-cafe] ANN: interval and polynomial enclosure arithmetics

Michal Konecny mik at konecny.aow.cz
Fri Aug 8 08:38:56 EDT 2008


I have recently released the following two Haskell packages, which 
model and reasonably efficiently implement exact real arithmetic:

  implements arbitrary-precision interval arithmetic 
  for approximating real numbers

  implements arbitrary-precision arithmetic 
  of bounded-degree piecewise-polynomial enclosures
  for approximating functions of type R^n -> R^m

The libraries are fairly stable and complete (AERN-Real more so than 
AERN-RnToRm) and members of the KEG research group at Aston 
University have used  it for reliably solving differential equations 
and numerical constraint satisfaction problems.

Also, the libraries are designed in multiple levels of abstraction 
that are clearly separated by type classes.  Thanks to this it is 
very easy to switch between different implementations of the 
lower-levels, eg using a different floating point type or different
representation of polynomials.

There are many similarities between AERN-Real and Augustsson's numbers 
package.  The main difference is in how the bit-size of arbitrary 
precision floating point numbers is determined.  In numbers, the bit 
size is determined statically via types using a type-level encoding 
of natural numbers.  In AERN-Real, the bit-size is part of the 
floating-point number, which slows the arithmetic down a bit but one 
can change precision dynamically.

Best regards,
|-| Dr. Michal Konecny, Computer Science, Aston University 
|-| Room MB212D | Tel +44 121 204 3462 | Fax +44 121 204 3681
|-| http://www.aston.ac.uk/~konecnym
|-| OpenPGP key http://www.aston.ac.uk/~konecnym/ki.aston
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