Exercise 5.3: Design a machine to compute square
roots using Newton’s method, as described in 1.1.7:


(define (sqrt x)
  (define (good-enough? guess)
    (< (abs (- (square guess) x)) 0.001))
  (define (improve guess)
    (average guess (/ x guess)))
  (define (sqrt-iter guess)
    (if (good-enough? guess)
        guess
        (sqrt-iter (improve guess))))
  (sqrt-iter 1.0))

Begin by assuming that good-enough? and improve operations are
available as primitives.  Then show how to expand these in terms of arithmetic
operations.  Describe each version of the sqrt machine design by drawing
a data-path diagram and writing a controller definition in the register-machine
language.