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