{- 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@] * Implements a /Bailey-Borwein-Plouffe/ formula; <http://mathworld.wolfram.com/PiFormulas.html> * Surprisingly, because of the huge size of the 'Rational' quantities, it is a /single/ call to @Factory.Math.Summation.sum'@, rather than the calculation of the many terms in the series, which is the performance-bottleneck. -} module Factory.Math.Implementations.Pi.BBP.Implementation( -- * Functions openR ) where import Data.Ratio((%)) import qualified Factory.Math.Implementations.Pi.BBP.Series as Math.Implementations.Pi.BBP.Series import qualified Factory.Math.Precision as Math.Precision import qualified Factory.Math.Summation as Math.Summation -- | Returns /Pi/, accurate to the specified number of decimal digits. openR :: Math.Implementations.Pi.BBP.Series.Series -- ^ This /Pi/-algorithm is parameterised by the type of other algorithms to use. -> Math.Precision.DecimalDigits -- ^ The number of decimal digits required. -> Rational openR Math.Implementations.Pi.BBP.Series.MkSeries { Math.Implementations.Pi.BBP.Series.numerators = numerators, Math.Implementations.Pi.BBP.Series.getDenominators = getDenominators, Math.Implementations.Pi.BBP.Series.seriesScalingFactor = seriesScalingFactor, Math.Implementations.Pi.BBP.Series.base = base } decimalDigits = (seriesScalingFactor *) . Math.Summation.sum' 8 . take ( Math.Precision.getTermsRequired ( recip . fromIntegral $ abs {-potentially negative-} base -- The convergence-rate. ) decimalDigits ) . zipWith (*) ( iterate (/ fromIntegral base) 1 -- Generate the scaling-ratio, between successive terms. ) $ map ( sum . zipWith (%) numerators . getDenominators ) [0 ..]