Copyright (C) 2011 Dr. Alistair Ward

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{- |
 [@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
) where

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
import qualified	ToolShed.Defaultable

{- |
	* 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	-- ^ <http://en.wikipedia.org/wiki/Borwein%27s_algorithm>.
	deriving (Eq, Read, Show)

instance (
	ToolShed.Defaultable.Defaultable	squareRootAlgorithm,
	ToolShed.Defaultable.Defaultable	factorialAlgorithm
 ) => ToolShed.Defaultable.Defaultable (Algorithm squareRootAlgorithm factorialAlgorithm)	where
	defaultValue	= Borwein1993 ToolShed.Defaultable.defaultValue ToolShed.Defaultable.defaultValue

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