sqrt.scala

val tolerance = 0.0001

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

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

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

	iterate( first )
}

def sqrt( x: Double ) = fixedPoint(y => ( y + x/y) / 2 )( 1.0 )

println( sqrt(9876543) )