Exercise 1.17

src/sicp/chapter_1/ex_1_17.clj

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+(ns sicp.chapter-1.ex-1-17)
+
+; Exercise 1.17
+; The exponentiation algorithms in this section are based on performing exponentiation by means of repeated
+; multiplication.
+;
+; In a similar way, one can perform integer multiplication by means of repeated addition.
+; The following multiplication procedure (in which it is assumed that our language can only add, not multiply)
+; is analogous to the expt procedure:
+;
+
+(defn multi
+  [a b]
+  (if (= b 0)
+    0
+    (+ a (* a (- b 1)))))
+
+; This algorithm takes a number of steps that is linear in b. Now suppose we include, together with addition,
+; operations double, which doubles an integer, and halve, which divides an (even) integer by 2.
+; Using these, design a multiplication procedure analogous to fast-expt that uses a logarithmic number of steps.
+
+(defn multi-fast
+  [a b]
+  (cond (= b 0) 0
+        (even? b) (* 2 (multi-fast a (/ b 2)))
+        :else (+ a (multi-fast a (- b 1)))))

test/sicp/chapter_1/ex_1_17_test.clj

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+(ns sicp.chapter-1.ex-1-17-test
+  (:require [clojure.test :refer :all]
+            [sicp.chapter-1.ex-1-17 :refer [multi multi-fast]]))
+
+(deftest multi-test
+  (time (is (= 2 (multi 1 2))))                             ; "Elapsed time: 2.383128 msecs"
+  (time (is (= 50 (multi 10 5))))                           ; "Elapsed time: 1.087389 msecs"
+  (time (is (= 6703582689499996764
+               (multi 12345340404 543005091))))             ; "Elapsed time: 0.852849 msecs"
+)
+
+(deftest multi-fast-test
+  (time (is (= 2 (multi-fast 1 2))))                        ; "Elapsed time: 1.258788 msecs"
+  (time (is (= 50 (multi-fast 10 5))))                      ; "Elapsed time: 1.582771 msecs"
+  (time (is (= 6703582689499996764
+               (multi-fast 12345340404 543005091))))        ; "Elapsed time: 1.01612 msecs"
+)