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A library for computing with exact real numbers in Haskell.

Prerequisites

  • A generally working development environment (make, gcc)
  • Probably the GMP header files.
  • Haskell version 7.8.4, including Cabal
  • The haskell-mpfr library by Ivo List.

The MPFR Haskell bindings in the haskell-mpfr library rely on low-level implementation details of Haskell. It is likely they will break with newer versions of Haskell.

Installation & Usage

  1. Install the haskell-mpfr library, following the instructions there. Essentially, it is just a cabal install inside the haskell-mpfr source directory.

  2. To install the library, run

     cabal install

    To get a version of the library which allows profiling, use instead

     cabal install --ghc-option=-fprof-auto -p --enable-executable-profiling

  3. Alternatively to the previous step, you can run

     cabal repl

    to get an interactive shell with the library preloaded. This way you can try out the library without installing it.

  4. To create HTML documentation run

     cabal haddock

    The generated HTML files will be placed in dist/doc/html/.

Example

Here is an example session.

Preprocessing library haskell-fast-reals-0.1.0.0...
GHCi, version 7.8.4: http://www.haskell.org/ghc/  :? for help
<... stuff gets loaded ...>
*Data.Reals.Reals> let a = 1.3 :: RealNum
*Data.Reals.Reals> a*(1-a)
[-3.900000000007822e-1,-3.899999999994179e-1]
*Data.Reals.Reals> a / a
[9.999999999972715e-1,1.000000000001819]
*Data.Reals.Reals> let b = 2.7 :: RealNum
*Data.Reals.Reals> a * a - b * b - (a + b) * (a - b)
[-3.128661774106285e-12,4.147295840103611e-12]
*Data.Reals.Reals> a * a
[1.689999999996871,1.690000000004147]
*Data.Reals.Reals> approx (a * a) (precUp 100)
[1.69,1.69]
λ> let int =  (ClosedInterval (appFromInteger 0,appFromInteger 1))
λ> forall int $ \x -> (x * (1 - x)) `less` (0.24 :: RealNum )
False
λ> forall int $ \x -> (x * (1 - x)) `less` (0.26 :: RealNum )
True