Swift tail-recursion experimentation: Recursive non-mutating implementation of Gregory-Leibnitz pi approximation.

FunctionalLeibnizPiApprox

// Recursive implementation
func LeibnizPiApproximationFunc(#afterIterations: Int) -> Double
{
   // See http://stackoverflow.com/questions/24270693/nested-recursive-function-in-swift
   var ApproxPi: (Double, Double, Double, Int) -> Double = { _ in return 0.0 }
   
   ApproxPi =
   {
      (denom : Double, factor : Double, piAccum: Double, iteration: Int) -> Double in
      
      if (iteration == 0)
      {
         return piAccum
      }
      
      return ApproxPi(denom + 2.0,
         factor * -1.0,
         piAccum + (factor * (4.0 / denom)),
         iteration - 1)
   }
   return ApproxPi(3.0, -1.0, 4.0, afterIterations)
}

let i = 6000
println(LeibnizPiApproximationFunc(afterIterations: i))