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

This program is free software: you can redistribute it and/or modify
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 parameters of a series used in a /Spigot/-table to generate /Pi/.
-}

module Factory.Math.Implementations.Pi.Spigot.Series(
-- * Types
-- ** Data-types
Series(..),
-- * Functions
bases
) where

import			Data.Ratio((%))
import qualified	Data.Ratio
import qualified	Factory.Math.Precision	as Math.Precision

{- |
* Defines a series composed from a sum of terms, each one of which is the product of a coefficient and a base.

* The coefficents and bases of the series are described in /Horner form/; @Pi = c1 + (b1 * (c2 + b2 * (c3 + b3 * (...))))@.
-}
data Series i	= MkSeries {
coefficients		:: [i],
baseNumerators		:: [i],
baseDenominators	:: [i],
nTerms			:: Math.Precision.DecimalDigits -> Int	-- ^ The width of the spigot-table, required to accurately generate the requested number of digits.
}

-- | Combines 'baseNumerators' and 'baseDenominators', and as a side-effect, expresses the ratio in lowest terms.
bases :: Integral i => Series i -> [Data.Ratio.Ratio i]
bases MkSeries {
baseNumerators		= n,
baseDenominators	= d
} = zipWith (%) n d

```