{-
	Copyright (C) 2011-2015 Dr. Alistair Ward

	This program is free software: you can redistribute it and/or modify
	it under the terms of the GNU General Public License as published by
	the Free Software Foundation, either version 3 of the License, or
	(at your option) any later version.

	This program is distributed in the hope that it will be useful,
	but WITHOUT ANY WARRANTY; without even the implied warranty of
	MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
	GNU General Public License for more details.

	You should have received a copy of the GNU General Public License
	along with this program.  If not, see <http://www.gnu.org/licenses/>.
-}
{- |
 [@AUTHOR@]	Dr. Alistair Ward

 [@DESCRIPTION@]	Defines the set of /Borwein/-type algorithms (currently only one) which have been implemented; <http://www.pi314.net/eng/borwein.php>.
-}

module Factory.Math.Implementations.Pi.Borwein.Algorithm(
-- * Types
-- ** Data-types
        Algorithm(..)
) where

import qualified        Data.Default
import qualified        Factory.Math.Factorial                                  as Math.Factorial
import qualified        Factory.Math.Implementations.Pi.Borwein.Borwein1993     as Math.Implementations.Pi.Borwein.Borwein1993
import qualified        Factory.Math.Implementations.Pi.Borwein.Implementation  as Math.Implementations.Pi.Borwein.Implementation
import qualified        Factory.Math.Pi                                         as Math.Pi
import qualified        Factory.Math.SquareRoot                                 as Math.SquareRoot

{- |
	* Define those /Borwein/-series which have been implemented.

	* Though currently there's only one, provision has been made for the addition of more.
-}
data Algorithm squareRootAlgorithm factorialAlgorithm   =
        Borwein1993 squareRootAlgorithm factorialAlgorithm      -- ^ <https://en.wikipedia.org/wiki/Borwein%27s_algorithm>.
        deriving (Eq, Read, Show)

instance (
        Data.Default.Default    squareRootAlgorithm,
        Data.Default.Default    factorialAlgorithm
 ) => Data.Default.Default (Algorithm squareRootAlgorithm factorialAlgorithm)   where
        def     = Borwein1993 Data.Default.def Data.Default.def

instance (
        Math.SquareRoot.Algorithmic     squareRootAlgorithm,
        Math.Factorial.Algorithmic      factorialAlgorithm
 ) => Math.Pi.Algorithmic (Algorithm squareRootAlgorithm factorialAlgorithm)    where
        openR (Borwein1993 squareRootAlgorithm factorialAlgorithm)      = Math.Implementations.Pi.Borwein.Implementation.openR Math.Implementations.Pi.Borwein.Borwein1993.series squareRootAlgorithm factorialAlgorithm