{-
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 .
-}
{- |
[@AUTHOR@] Dr. Alistair Ward
[@DESCRIPTION@] Implements a /Ramanujan/-type series for /Pi/; .
-}
module Factory.Math.Implementations.Pi.Ramanujan.Implementation(
-- * Functions
openR
) where
import qualified Control.Parallel.Strategies
import qualified Factory.Math.Implementations.Pi.Ramanujan.Series as Math.Implementations.Pi.Ramanujan.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.Ramanujan.Series.Series squareRootAlgorithm factorialAlgorithm -- ^ This /Pi/-algorithm is parameterised by the type of other algorithms to use.
-> squareRootAlgorithm -- ^ The specific /square-root/ algorithm to apply to the above series.
-> factorialAlgorithm -- ^ The specific /factorial/-algorithm to apply to the above series.
-> Math.Precision.DecimalDigits -- ^ The number of decimal digits required.
-> Rational
openR Math.Implementations.Pi.Ramanujan.Series.MkSeries {
Math.Implementations.Pi.Ramanujan.Series.terms = terms,
Math.Implementations.Pi.Ramanujan.Series.getSeriesScalingFactor = getSeriesScalingFactor,
Math.Implementations.Pi.Ramanujan.Series.convergenceRate = convergenceRate
} squareRootAlgorithm factorialAlgorithm decimalDigits = uncurry (/) $ Control.Parallel.Strategies.withStrategy (
Control.Parallel.Strategies.parTuple2 Control.Parallel.Strategies.rdeepseq Control.Parallel.Strategies.rdeepseq
) (
getSeriesScalingFactor squareRootAlgorithm decimalDigits,
Math.Summation.sumR 64 . take (
Math.Precision.getTermsRequired convergenceRate decimalDigits
) $ terms factorialAlgorithm
) -- Pair.