{- 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 /Rabinowitz-Wagon/ series; <http://web.comlab.ox.ac.uk/oucl/work/jeremy.gibbons/publications/spigot.pdf> <http://www.mathpropress.com/stan/bibliography/spigot.pdf>. -} module Factory.Math.Implementations.Pi.Spigot.RabinowitzWagon( -- * Constants series ) where import qualified Factory.Math.Implementations.Pi.Spigot.Series as Math.Implementations.Pi.Spigot.Series import qualified Factory.Math.Precision as Math.Precision -- | Defines a series which converges to /Pi/. series :: Integral i => Math.Implementations.Pi.Spigot.Series.Series i series = Math.Implementations.Pi.Spigot.Series.MkSeries { Math.Implementations.Pi.Spigot.Series.baseNumerators = [1 ..], Math.Implementations.Pi.Spigot.Series.baseDenominators = [3, 5 ..], Math.Implementations.Pi.Spigot.Series.coefficients = repeat 2, Math.Implementations.Pi.Spigot.Series.nTerms = Math.Precision.getTermsRequired $ 10 ** negate (3 / 10) {-convergence-rate-} }