[Haskell-cafe] ANN: interval and polynomial enclosure arithmetics
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.
|-| Dr. Michal Konecny, Computer Science, Aston University
|-| Room MB212D | Tel +44 121 204 3462 | Fax +44 121 204 3681
|-| OpenPGP key http://www.aston.ac.uk/~konecnym/ki.aston
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