// Square root, second version (Chapter 4, Scala by Example)
//
// some defs are nested inside "sqrt"
//
// simplified nested defs: no local x parameter


def abs(x: Double) = if (x > 0.0) x else -x

def square(x: Double) = x * x


def sqrt(x: Double) = {

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

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

  def sqrtIter(guess: Double): Double = { 
    println( guess );
    if ( isGoodEnough(guess)) guess
    else sqrtIter(improve(guess))
  }

  if (x < 0.0) error("cannot compute sqrt for negative values " + x)
  sqrtIter(1.0)
}