Scala By Example Chapter 5 Solutions - Exercise 5.3.1

Exercise 5.3.1 Write a function for cube roots using fixedPoint and averageDamp.

Both fixedPoint and averageDamp functions remain the same. Instead of sqrt, now theres a cbrt function which calculates the cube root. The math library is used to avail of the exponential function.

	object FixedPoint {
	var tolerance = 0.0001
	def abs(x: Double) = if (x >= 0) x else -x
	def isCloseEnough(x: Double, y: Double) = abs((x - y) / x) < tolerance
	def fixedPoint(f: Double => Double)(firstGuess: Double) = {
	def iterate(guess: Double): Double = {
	val next = f(guess)
	println(next)
	if (isCloseEnough(guess, next)) next
	else iterate(next)
	}
	iterate(firstGuess)
	}
	def averageDamp(f: Double => Double)(x: Double) = (x + f(x)) / 2
	def cbrt(x: Double) = fixedPoint(averageDamp(y => x/math.pow(y,2)))(1.0)
	def main(args: Array[String]) {
	println("calculating cube root of 2 : " + cbrt(2))
	println("calculating cube root of 8 : " + cbrt(8))
	}
	}

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