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Converting Linear to Logarithmic Iteration

Recall an example of linear iteration: 
     (define power   ; compute be  iteratively
       (lambda (b e)
         (power-product 1 b e)))

     (define power-product
       (lambda (a b e)    ; returns a times be
         (if (= e 0)
             a
             (power-product (* a b) b (- e 1)))))
Linear iteration can be converted to logarithmic iteration by recognizing that if e is even, then

a × be = a × (b2)e/2 
    (define power-product
      (lambda (a b e)
        (if (= e 0)
            a
            (if (even? e)
                (power-product a (* b b) (/ e 2))
                (power-product (* a b) b (- e 1))))))
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