{- Copyright (C) 2011 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 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