Exercise 1.16

1-2.org

@@ -248,7 +248,31 @@ layout: org
         procedure when `(sine a)' is evaluated?
 
 * 1.2.4: Exponentiation
-  
+
+  #+BEGIN_SRC scheme :tangle yes
+    ;; ===================================================================
+    ;; 1.2.4: Exponentiation
+    ;; ===================================================================
+
+    (define (square x) (* x x))
+
+    (define (expt b n)
+      (expt-iter b n 1))
+
+    (define (expt-iter b counter product)
+      (if (= counter 0)
+          product
+          (expt-iter b
+                     (- counter 1)
+                     (* b product))))
+    (define (fast-expt b n)
+      (cond ((= n 0) 1)
+            ((even? n) (square (fast-expt b (/ n 2))))
+            (else (* b (fast-expt b (- n 1))))))
+
+    (define (even? n)
+      (= (remainder n 2) 0))
+  #+END_SRC
 ** Exercise 1.16
    Design a procedure that evolves an iterative
    exponentiation process that uses successive squaring and uses a
@@ -262,7 +286,22 @@ layout: org
    defining an "invariant quantity" that remains unchanged from state
    to state is a powerful way to think about the design of iterative
    algorithms.)
-  
+
+   ----------------------------------------------------------------------
+
+   #+BEGIN_SRC scheme :tangle yes
+     ;; -------------------------------------------------------------------
+     ;; Exercise 1.16
+     ;; -------------------------------------------------------------------
+
+     (define (1-16 b n)
+       (define (expt-iter b n a)
+         (cond ((= n 0) a)
+               ((even? n) (expt-iter (square b) (/ n 2) a))
+               (else (expt-iter b (- n 1) (* a b)))))
+       (expt-iter b n 1.0))
+   #+END_SRC
+   
 ** Exercise 1.17
    The exponentiation algorithms in this section are
    based on performing exponentiation by means of repeated