Exercise 1.16.  Design a procedure that evolves an iterative exponentiation 
process that uses successive squaring and uses a logarithmic number of steps, 
as does fast-expt.

(Hint: Using the observation that (b^(n/2))^2 = (b^2)^(n/2), keep, along with 
the exponent n and the base b, an additional state variable a, and define the 
state transformation in such a way that the product a b^n is unchanged from 
state to state. At the beginning of the process a is taken to be 1, and the 
answer is given by the value of a at the end of the process. In general, the 
technique of defining an invariant quantity that remains unchanged from state 
to state is a powerful way to think about the design of iterative algorithms.)


(define (fast-expt b n)
  (fast-expt-iter b n 1))

(define (fast-expt-iter b n a)
  (cond ((= n 0)    a)
        ((even? n) (fast-expt-iter (* b b) (/ n 2) a))
        (else      (fast-expt-iter b (- n 1) (* a b)))))