module Factory.Math.Implementations.Pi.Borwein.Implementation(
openR
) where
import qualified Control.Arrow
import qualified Control.Parallel.Strategies
import qualified Factory.Math.Implementations.Pi.Borwein.Series as Math.Implementations.Pi.Borwein.Series
import qualified Factory.Math.Precision as Math.Precision
openR
:: Math.Implementations.Pi.Borwein.Series.Series squareRootAlgorithm factorialAlgorithm
-> squareRootAlgorithm
-> factorialAlgorithm
-> Math.Precision.DecimalDigits
-> Rational
openR :: Series squareRootAlgorithm factorialAlgorithm
-> squareRootAlgorithm
-> factorialAlgorithm
-> DecimalDigits
-> Rational
openR Math.Implementations.Pi.Borwein.Series.MkSeries {
terms :: forall squareRootAlgorithm factorialAlgorithm.
Series squareRootAlgorithm factorialAlgorithm
-> squareRootAlgorithm
-> factorialAlgorithm
-> DecimalDigits
-> (Rational, [Rational])
Math.Implementations.Pi.Borwein.Series.terms = squareRootAlgorithm
-> factorialAlgorithm -> DecimalDigits -> (Rational, [Rational])
terms,
convergenceRate :: forall squareRootAlgorithm factorialAlgorithm.
Series squareRootAlgorithm factorialAlgorithm -> ConvergenceRate
Math.Implementations.Pi.Borwein.Series.convergenceRate = ConvergenceRate
convergenceRate
} squareRootAlgorithm
squareRootAlgorithm factorialAlgorithm
factorialAlgorithm DecimalDigits
decimalDigits = (Rational -> Rational -> Rational)
-> (Rational, Rational) -> Rational
forall a b c. (a -> b -> c) -> (a, b) -> c
uncurry Rational -> Rational -> Rational
forall a. Fractional a => a -> a -> a
(/) ((Rational, Rational) -> Rational)
-> ((Rational, [Rational]) -> (Rational, Rational))
-> (Rational, [Rational])
-> Rational
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Strategy (Rational, Rational)
-> (Rational, Rational) -> (Rational, Rational)
forall a. Strategy a -> a -> a
Control.Parallel.Strategies.withStrategy (
Strategy Rational
-> Strategy Rational -> Strategy (Rational, Rational)
forall a b. Strategy a -> Strategy b -> Strategy (a, b)
Control.Parallel.Strategies.parTuple2 Strategy Rational
forall a. NFData a => Strategy a
Control.Parallel.Strategies.rdeepseq Strategy Rational
forall a. NFData a => Strategy a
Control.Parallel.Strategies.rdeepseq
) ((Rational, Rational) -> (Rational, Rational))
-> ((Rational, [Rational]) -> (Rational, Rational))
-> (Rational, [Rational])
-> (Rational, Rational)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. ([Rational] -> Rational)
-> (Rational, [Rational]) -> (Rational, Rational)
forall (a :: * -> * -> *) b c d.
Arrow a =>
a b c -> a (d, b) (d, c)
Control.Arrow.second (
[Rational] -> Rational
forall (t :: * -> *) a. (Foldable t, Num a) => t a -> a
sum ([Rational] -> Rational)
-> ([Rational] -> [Rational]) -> [Rational] -> Rational
forall b c a. (b -> c) -> (a -> b) -> a -> c
. DecimalDigits -> [Rational] -> [Rational]
forall a. DecimalDigits -> [a] -> [a]
take (
ConvergenceRate -> DecimalDigits -> DecimalDigits
forall i. Integral i => ConvergenceRate -> DecimalDigits -> i
Math.Precision.getTermsRequired ConvergenceRate
convergenceRate DecimalDigits
decimalDigits
)
) ((Rational, [Rational]) -> Rational)
-> (Rational, [Rational]) -> Rational
forall a b. (a -> b) -> a -> b
$ squareRootAlgorithm
-> factorialAlgorithm -> DecimalDigits -> (Rational, [Rational])
terms squareRootAlgorithm
squareRootAlgorithm factorialAlgorithm
factorialAlgorithm DecimalDigits
decimalDigits