Scala stuff

sqrt.scala

import scala.annotation.tailrec
import math.abs

//Fixed point algorithm
object fpalgorithm {
  val tolerance = 0.0001

  def fixedPoint(f: Double => Double)(firstGuess: Double) = {

    def isCloseEnough(x: Double, y: Double) =
    abs((x - y) / x) / x < tolerance

    @tailrec
    def iterate(guess: Double): Double = {
      val next = f(guess)
      if (isCloseEnough(guess, next)) next
      else iterate(next)
    }
    iterate(firstGuess)
  }

  def averageDamp(f: Double => Double)(x: Double) = (x + f(x)) / 2

  //With averageDamp
  def sqrt(x: Double) = {
    fixedPoint(averageDamp(y => x / y))(1.0)
  }

  //Without averageDamp
  def sqrt2(x: Double) = fixedPoint(y => (y + (x / y)) / 2)(1.0)

  sqrt(512) * sqrt(512)
  sqrt2(512) * sqrt2(512)
}