object FixedPoint {
   var tolerance = 0.0001
   def abs(x: Double) = if (x >= 0) x else -x
   def isCloseEnough(x: Double, y: Double) = abs((x - y) / x) < tolerance
   def fixedPoint(f: Double => Double)(firstGuess: Double) = {
      def iterate(guess: Double): Double = {
         val next = f(guess)
         println(next)
         if (isCloseEnough(guess, next)) next
         else iterate(next)
      }
      iterate(firstGuess)
   }
   def averageDamp(f: Double => Double)(x: Double) = (x + f(x)) / 2
   def cbrt(x: Double) = fixedPoint(averageDamp(y => x/math.pow(y,2)))(1.0)

   def main(args: Array[String]) {
      println("calculating cube root of 2 : " + cbrt(2))
      println("calculating cube root of 8 : " + cbrt(8))
   }
}