This function uses the Newton method to estimate a square root function. The iterator starts off with a guess of 1.0. This guess is then squared to see if the difference is small enough to call it 'good.' For really large/small values this estimate is normalized before comparing it to an epsilon. The results are gradually improved by taking the …

sqrt.scala

  def sqrt(x: Double): Double = {
    def isGoodEnough(guess: Double): Boolean =
      abs(square(guess) - x) / x < 0.001

    def improve(guess: Double): Double =
      (guess + x / guess) / 2

    def sqrtIter(guess: Double): Double =
      if (isGoodEnough(guess)) guess
      else sqrtIter(improve(guess))

    sqrtIter(1.0)
  }