square-roots-functional.scala

// a #:: f(a) #:: f(f(a)) #:: f(f(f(a))) #:: ...
def repeat[A](f: A => A)(a: => A): Stream[A] = a #:: repeat(f)(f(a))

def next(n: Double)(x: Double): Double = (x + n/x)/2.0

def within(eps: Double)(s: Stream[Double]): Double = s match {
    case a #:: b #:: rest => if(Math.abs(a-b)<=eps) b else within(eps)(rest)
    case _ => throw new Exception("El stream debería tener por lo menos dos elementos")
}

def sqrt(a0: Double, eps: Double, n: Double): Double = within(eps)(repeat(next(n))(a0))

sqrt(2,0.000001,9) // 3.0

square-roots-imperative.scala

def sqrt(a0: Double, eps: Double, n: Double): Double = {
    var x = a0
    var y = a0 + 2.0 * eps
    while ( Math.abs(x-y) > eps ) {
        y = x
        x = (x + n/x) / 2.0
    }
    x
}

sqrt(2,0.000001,9) // 3.0