From: Ramakrishnan Muthukrishnan <vu3rdd@gmail.com>
Date: Fri, 30 Apr 2010 04:15:21 +0000 (+0530)
Subject: Split each exercise into individual files for easier reading. The routines
X-Git-Url: https://git.rkrishnan.org/pf/content/en/seg/about/pf.html?a=commitdiff_plain;h=ba5e14e2b9ba7915a3b63a30f3b2b7d78d408bc4;p=sicp.git

Split each exercise into individual files for easier reading. The routines
described in say, section X.Y is in chX_Y.clj.
---

diff --git a/src/sicp/ch1_1.clj b/src/sicp/ch1_1.clj
index bfe8bdc..4c1c6b7 100644
--- a/src/sicp/ch1_1.clj
+++ b/src/sicp/ch1_1.clj
@@ -11,95 +11,6 @@
   (cond (< x 0) (- x)
 	:else x))
 
-;; exercise 1.1: What is the result printed by the interpreter in response
-;;               to each expression (in order) ?
-
-(def a 3)
-(def b (+ a 1))
-
-(+ a b (* a b))  ; 19
-(= a b) ; false
-
-(if (and (> b a) (< b (* a b)))
-    b
-    a)   ; 4
-
-(cond (= a 4) 6
-      (= b 4) (+ 6 7 a)
-      :else 25)  ; 16
-
-(+ 2 (if (> b a) b a)) ; 6
-
-(* (cond (> a b) a
-	 (< a b) b
-	 :else -1)
-   (+ a 1))      ; 16
-
-;; exercise 1.2: Translate the given expression into prefix form
-(/ (+ 5 4 (- 2 (- 3 (+ 6 (/ 1 5)))))
-   (* 3 (- 6 2) (- 2 7)))  ; -71/300
-
-;; exercise 1.3:  Define a procedure that takes three numbers as
-;;                arguments and returns the sum of the squares of
-;;                the two larger numbers.
-(defn sort3 [a b c]
-  (cond (> b a) (sort3 b a c)
-	(< b c) (sort3 a c b)
-	:else [a b c]))
-
-(defn sum-of-sq-of-two-largest [a b c]
-  (apply sum-of-squares (take 2 (sort3 a b c))))
-
-;; well, I cheated above. Let me use only the constructs introduced
-;; so far in the book. (follows after the sicp meetup #2 on 28/mar/2010.
-(defn sum-of-square-of-two-largest [a b c]
-  (if (> a b)
-    (if (> b c)
-      (sum-of-squares a b) ; a > b > c
-      (sum-of-squares a c))
-    (if (> a c)
-      (sum-of-squares b a)
-      (sum-of-squares b c))))
-
-;; exercise 1.4: Observe that our model of evaluation allows for
-;;               combinations whose operators are compound
-;;               expressions. Use this observation to describe the
-;;               behavior of the following procedure:
-;; (defn a-plus-abs-b [a b]
-;;   ((if (> b 0) + -) a b))
-(comment
-  If b is positive, we do (+ a b) and if it is negative, we do (- a b).
-  This makes use of the fact that the first element in a list is an
-  operand. Here, the operand is chosen based on other operators.
-  )
-
-;; exercise 1.5:  Ben Bitdiddle has invented a test to determine
-;;                whether the interpreter he is faced with is
-;;                using applicative-order evaluation or normal-order
-;;                evaluation. He defines the following two procedures:
-;; (defn p [] (p))
-;; (defn test [x y]
-;;   (if (= x 0)
-;;    0
-;;    y))
-;;
-;; Then he evaluates the expression
-;;
-;; (test 0 (p))
-;;
-;; What behavior will Ben observe with an interpreter that uses
-;; applicative-order evaluation?
-(comment
-  In the case of applicative order evaluation, the test gets into
-  and infinite loop (eventually using all the stack), as the parameters
-  are evaluated before they are actualy used in the function.
-  )
-;; What behavior will he observe with an interpreter that uses
-;; normal-order evaluation? Explain your answer.
-(comment
-  It will print 0, as (p) is not evaluated in this case.
-  )
-
 ;; 1.1.7 Square root finding using Newton's method
 (defn average [x y]
   (/ (+ x y) 2))
@@ -119,82 +30,7 @@
 (defn sqrt [x]
   (sqrt-iter 1.0 x))
 
-;; exercise 1.6
-;; Alyssa P. Hacker doesn't see why if needs to be provided as a special form.
-;; ``Why can't I just define it as an ordinary procedure in terms of cond?''
-(defn new-if [predicate then-clause else-clause]
-  (cond predicate then-clause
-	:else else-clause))
-
-(new-if (= 3 2) 0 5)  ; 5
-(new-if (= 1 1) 0 5)  ; 0
-
-;; Delighted, Alyssa uses new-if to rewrite the square-root program:
-
-(defn sqrt-iter [guess x]
-  (new-if (good-enough? guess x)
-	  guess
-	  (sqrt-iter (improve guess x)
-		     x)))
-
-;; what happens when Alyssa attempts to use this to compute square roots? Explain.
-(comment
-  Since `new-if' is a function, when it is called from sqrt-iter, the parameters
-  are evaluated before it gets called. good-enough? will return a false unless
-  the guess and x are almost the same. guess evaluated to the initial value of
-  guess. sqrt-iter gets evaluated, but gets into an infinite loop. The predicate
-  will have no effect.)
 
-;; Exercise 1.7: The good-enough? test used in computing square roots will not
-;; be very effective for finding the square roots of very small numbers. Also,
-;; in real computers, arithmetic operations are almost always performed with
-;; limited precision. This makes our test inadequate for very large numbers.
-;; Explain these statements, with examples showing how the test fails for small
-;; and large numbers.
-(comment
- user> (sqrt (square 0.001))
- 0.031260655525445276
- user> (sqrt (square 0.2))
- 0.20060990407779591
- user> (sqrt (square 0.01))
- 0.03230844833048122
- user> (sqrt (square 0.02))
- 0.0354008825558513
- user> (sqrt (square 10))
- 10.000000000139897
- user> (sqrt (square 100))
- 100.00000025490743
- user> (sqrt (square 200))
- 200.000000510076
- user> (sqrt (square 2))
- 2.0000000929222947
- user> (sqrt (square 0.1))
- 0.10032578510960607
- user> (sqrt (square 0.01))
- 0.03230844833048122
- user> (sqrt (square 10000))
- 10000.0
- user> (sqrt (square 20000))
- 20000.0
- user> (sqrt (square 200000))
- 200000.0
- user> (sqrt (square 20000000))
- 2.0E7
- user> (sqrt (square 20000000000))
- 2.0E10
- user> (sqrt (square 200000.012))
- 200000.012
- user> (sqrt (square 2000000.123))
- 2000000.123
- user> (sqrt (square 200000000.123))
- 2.00000000123E8
- user> (sqrt (square 2000000000.123))
- 2.000000000123E9
- user> (sqrt (square 20000000000.123))
- 2.0000000000123E10
- user> (sqrt (square 2000000000000.123))
- 2.000000000000123E12
- )
 ;; An alternative strategy for implementing good-enough? is to watch how guess
 ;; changes from one iteration to the next and to stop when the change is a very
 ;; small fraction of the guess.
@@ -241,32 +77,7 @@ user> (sqrt 9)
 user> (sqrt 81)
 9.000000000007091
 )
-;; exercise 1.8: cube root
-(defn improve [guess x]
-  (/ (+ (/ x (square guess)) (* 2 guess)) 3))
-
-(defn cubert-iter [old-guess new-guess x]
-  (if (good-enough? old-guess new-guess x)
-    new-guess
-    (cubert-iter new-guess (improve new-guess x)
-		 x)))
 
-(defn cuberoot [x]
-  (cubert-iter x 1.0 x))
-
-(comment
-user> (cuberoot (cube 2))
-2.000000000012062
-user> (cuberoot (cube 10))
-10.000000000000002
-user> (cuberoot (cube 9))
-9.000000000053902
-user> (cuberoot (cube 0.001))
-0.001000000000000962
-user> (cuberoot (cube 0.0001))
-1.000000000000001E-4
-user>
-)
 ;; section 1.1.8
 ;; hiding the non-public procedure definitions
 (defn- sqrt-iter [guess x]
diff --git a/src/sicp/ch1_2.clj b/src/sicp/ch1_2.clj
index 5e6375d..1021953 100644
--- a/src/sicp/ch1_2.clj
+++ b/src/sicp/ch1_2.clj
@@ -89,84 +89,6 @@
 ;; observation: clojure loop-recur construct is essentially the same as
 ;; the iterative version.
 
-;; exercise 1.9
-(defn ++ [a b]
-  (if (= a 0)
-    b
-    (inc (++ (dec a) b))))
-
-;; (comment
-;;   This version is a recursive process, where the previous call increments
-;;   the sum by 1 and each call decrement the first operand by 1.
-  
-;; user> (dotrace [++] (++ 4 5))
-;; TRACE t3745: (++ 4 5)
-;; TRACE t3746: |    (++ 3 5)
-;; TRACE t3747: |    |    (++ 2 5)
-;; TRACE t3748: |    |    |    (++ 1 5)
-;; TRACE t3749: |    |    |    |    (++ 0 5)
-;; TRACE t3749: |    |    |    |    => 5
-;; TRACE t3748: |    |    |    => 6
-;; TRACE t3747: |    |    => 7
-;; TRACE t3746: |    => 8
-;; TRACE t3745: => 9
-;; 9
-;; )
-
-(defn ++ [a b]
-  (if (= a 0)
-    b
-    (++ (dec a) (inc b))))
-
-;; (comment
-  
-;; user> (dotrace [++] (++ 4 5))
-;; TRACE t3766: (++ 4 5)
-;; TRACE t3767: |    (++ 3 6)
-;; TRACE t3768: |    |    (++ 2 7)
-;; TRACE t3769: |    |    |    (++ 1 8)
-;; TRACE t3770: |    |    |    |    (++ 0 9)
-;; TRACE t3770: |    |    |    |    => 9
-;; TRACE t3769: |    |    |    => 9
-;; TRACE t3768: |    |    => 9
-;; TRACE t3767: |    => 9
-;; TRACE t3766: => 9
-;; 9
-;; )
-
-;; exercise 1.10
-;; ackerman functions
-(defn A [x y]
-  (cond (= y 0) 0
-	(= x 0) (* 2 y)
-	(= y 1) 2
-	:else (A (- x 1)
-		 (A x (- y 1)))))
-
-;; (comment
-;; user> (A 1 10)
-;; 1024
-;; user> (A 2 4)
-;; 65536
-;; user> (A 3 3)
-;; 65536
-;; )
-
-(defn f [n] (A 0 n)) ; f(n) = 2n
-(defn g [n] (A 1 n)) ; g(n) = 2^n
-;; (comment
-;;   g (n) = A (1,n)
-;;         = A (0, A (1, n-1)) = f (A(1,n-1))
-;; 	  = f (f (1,n-2)) 
-;; 	    .....
-;; 	    = f (f (f ... f (1,(n- (n-1)))))
-;; 	      = f (f (f ... 2))
-;; 		= 2 * (2^(n-1))
-;; 		  = 2^n
-;; )
-
-(defn h [n] (A 2 n)) ; h(n) = 2^(n^2)
-
 ;; section 1.2.2: Tree Recursion
 (defn fib [n]
   (cond (= n 0) 0
@@ -206,254 +128,9 @@
 (defn count-change [amount]
   (cc amount 5))
 
-;; exercise 1.11: A function f is defined by the rule that f(n) = n if n < 3
-;;                and f(n) = f(n - 1) + 2f(n  - 2) + 3f(n - 3) if n> 3.
-;;                Write a procedure that computes f by means of a recursive
-;;                process. Write a procedure that computes f by means of an
-;;                iterative process. 
-(defn f [n]
-  (if (< n 3)
-    n
-    (+ (f (- n 1))
-       (* 2 (f (- n 2)))
-       (* 3 (f (- n 3))))))
-
-;; (comment
-;; user> (map f (range 10))
-;; (0 1 2 4 11 25 59 142 335 796)  
-;; )
-
-;; ex 1.11: iterative version
-(defn f-iter [count prev0 prev1 prev2]
-  (if (= count 3)
-    (+ prev0
-       (* 2 prev1)
-       (* 3 prev2))
-    (f-iter (dec count)
-	    (+ prev0
-	       (* 2 prev1)
-	       (* 3 prev2))
-	    prev0
-	    prev1)))
-
-(defn f [n]
-  (if (< n 3)
-    n
-    (f-iter n 2 1 0)))
-
-;; ex 1.11: iterative version with let
-(defn f-iter [count prev0 prev1 prev2]
-  (let [res (+ prev0 (* 2 prev1) (* 3 prev2))]
-    (if (= count 3)
-      res
-      (f-iter (dec count)
-	      res
-	      prev0
-	      prev1))))
-
-;; exercise 1.12.  The following pattern of numbers is called Pascal's triangle.
-;;          1
-;;        1   1
-;;      1   2   1
-;;    1   3   3   1
-;;  1   4   6   4   1
-;; ...................
-;;
-;;                 The numbers at the edge of the triangle are all 1, and each
-;;                 number inside the triangle is the sum of the two numbers above
-;;                 it. Write a procedure that computes elements of Pascal's triangle
-;;                 by means of a recursive process. 
-(defn pascal [row col]
-  (when (<= col row)
-    (if (or (= col 0) (= row col))
-      1
-      (+ (pascal (dec row) col)
-	 (pascal (dec row) (dec col))))))
-
-;; exercise 1.13:
-(comment
-See the pdfs in the directory for the answers.
-)
-
-;; ex 1.13 (contd)
-(defn fib-approx [n]
-  (let [phi (/ (+ 1 (sqrt 5)) 2)]
-    (/ (expt phi n) (sqrt 5))))
-
-;; (comment
-;; user> (map fib-approx (range 10))
-;; (0.4472135954999579 0.7236067977499789 1.1708203932499368 1.8944271909999157 3.065247584249853 4.959674775249769 8.024922359499623 12.984597134749393 21.009519494249016 33.99411662899841)
-;; )
-
-;; exercise 1.14: tree of (count-changes 11)
-(comment
-  See the pdf for the tree representation.
-)
-
-
-;; order of size and computation
-;; see PDF, but below is the trace tree.
-;; (comment
-;; user> (use 'clojure.contrib.trace)
-;; nil
-;; user> (dotrace [count-change cc] (count-change 11))
-;; TRACE t2609: (count-change 11)
-;; TRACE t2610: |    (cc 11 5)
-;; TRACE t2611: |    |    (cc 11 4)
-;; TRACE t2612: |    |    |    (cc 11 3)
-;; TRACE t2613: |    |    |    |    (cc 11 2)
-;; TRACE t2614: |    |    |    |    |    (cc 11 1)
-;; TRACE t2615: |    |    |    |    |    |    (cc 11 0)
-;; TRACE t2615: |    |    |    |    |    |    => 0
-;; TRACE t2616: |    |    |    |    |    |    (cc 10 1)
-;; TRACE t2617: |    |    |    |    |    |    |    (cc 10 0)
-;; TRACE t2617: |    |    |    |    |    |    |    => 0
-;; TRACE t2618: |    |    |    |    |    |    |    (cc 9 1)
-;; TRACE t2619: |    |    |    |    |    |    |    |    (cc 9 0)
-;; TRACE t2619: |    |    |    |    |    |    |    |    => 0
-;; TRACE t2620: |    |    |    |    |    |    |    |    (cc 8 1)
-;; TRACE t2621: |    |    |    |    |    |    |    |    |    (cc 8 0)
-;; TRACE t2621: |    |    |    |    |    |    |    |    |    => 0
-;; TRACE t2622: |    |    |    |    |    |    |    |    |    (cc 7 1)
-;; TRACE t2623: |    |    |    |    |    |    |    |    |    |    (cc 7 0)
-;; TRACE t2623: |    |    |    |    |    |    |    |    |    |    => 0
-;; TRACE t2624: |    |    |    |    |    |    |    |    |    |    (cc 6 1)
-;; TRACE t2625: |    |    |    |    |    |    |    |    |    |    |    (cc 6 0)
-;; TRACE t2625: |    |    |    |    |    |    |    |    |    |    |    => 0
-;; TRACE t2626: |    |    |    |    |    |    |    |    |    |    |    (cc 5 1)
-;; TRACE t2627: |    |    |    |    |    |    |    |    |    |    |    |    (cc 5 0)
-;; TRACE t2627: |    |    |    |    |    |    |    |    |    |    |    |    => 0
-;; TRACE t2628: |    |    |    |    |    |    |    |    |    |    |    |    (cc 4 1)
-;; TRACE t2629: |    |    |    |    |    |    |    |    |    |    |    |    |    (cc 4 0)
-;; TRACE t2629: |    |    |    |    |    |    |    |    |    |    |    |    |    => 0
-;; TRACE t2630: |    |    |    |    |    |    |    |    |    |    |    |    |    (cc 3 1)
-;; TRACE t2631: |    |    |    |    |    |    |    |    |    |    |    |    |    |    (cc 3 0)
-;; TRACE t2631: |    |    |    |    |    |    |    |    |    |    |    |    |    |    => 0
-;; TRACE t2632: |    |    |    |    |    |    |    |    |    |    |    |    |    |    (cc 2 1)
-;; TRACE t2633: |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    (cc 2 0)
-;; TRACE t2633: |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    => 0
-;; TRACE t2634: |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    (cc 1 1)
-;; TRACE t2635: |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    (cc 1 0)
-;; TRACE t2635: |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    => 0
-;; TRACE t2636: |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    (cc 0 1)
-;; TRACE t2636: |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    => 1
-;; TRACE t2634: |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    => 1
-;; TRACE t2632: |    |    |    |    |    |    |    |    |    |    |    |    |    |    => 1
-;; TRACE t2630: |    |    |    |    |    |    |    |    |    |    |    |    |    => 1
-;; TRACE t2628: |    |    |    |    |    |    |    |    |    |    |    |    => 1
-;; TRACE t2626: |    |    |    |    |    |    |    |    |    |    |    => 1
-;; TRACE t2624: |    |    |    |    |    |    |    |    |    |    => 1
-;; TRACE t2622: |    |    |    |    |    |    |    |    |    => 1
-;; TRACE t2620: |    |    |    |    |    |    |    |    => 1
-;; TRACE t2618: |    |    |    |    |    |    |    => 1
-;; TRACE t2616: |    |    |    |    |    |    => 1
-;; TRACE t2614: |    |    |    |    |    => 1
-;; TRACE t2637: |    |    |    |    |    (cc 6 2)
-;; TRACE t2638: |    |    |    |    |    |    (cc 6 1)
-;; TRACE t2639: |    |    |    |    |    |    |    (cc 6 0)
-;; TRACE t2639: |    |    |    |    |    |    |    => 0
-;; TRACE t2640: |    |    |    |    |    |    |    (cc 5 1)
-;; TRACE t2641: |    |    |    |    |    |    |    |    (cc 5 0)
-;; TRACE t2641: |    |    |    |    |    |    |    |    => 0
-;; TRACE t2642: |    |    |    |    |    |    |    |    (cc 4 1)
-;; TRACE t2643: |    |    |    |    |    |    |    |    |    (cc 4 0)
-;; TRACE t2643: |    |    |    |    |    |    |    |    |    => 0
-;; TRACE t2644: |    |    |    |    |    |    |    |    |    (cc 3 1)
-;; TRACE t2645: |    |    |    |    |    |    |    |    |    |    (cc 3 0)
-;; TRACE t2645: |    |    |    |    |    |    |    |    |    |    => 0
-;; TRACE t2646: |    |    |    |    |    |    |    |    |    |    (cc 2 1)
-;; TRACE t2647: |    |    |    |    |    |    |    |    |    |    |    (cc 2 0)
-;; TRACE t2647: |    |    |    |    |    |    |    |    |    |    |    => 0
-;; TRACE t2648: |    |    |    |    |    |    |    |    |    |    |    (cc 1 1)
-;; TRACE t2649: |    |    |    |    |    |    |    |    |    |    |    |    (cc 1 0)
-;; TRACE t2649: |    |    |    |    |    |    |    |    |    |    |    |    => 0
-;; TRACE t2650: |    |    |    |    |    |    |    |    |    |    |    |    (cc 0 1)
-;; TRACE t2650: |    |    |    |    |    |    |    |    |    |    |    |    => 1
-;; TRACE t2648: |    |    |    |    |    |    |    |    |    |    |    => 1
-;; TRACE t2646: |    |    |    |    |    |    |    |    |    |    => 1
-;; TRACE t2644: |    |    |    |    |    |    |    |    |    => 1
-;; TRACE t2642: |    |    |    |    |    |    |    |    => 1
-;; TRACE t2640: |    |    |    |    |    |    |    => 1
-;; TRACE t2638: |    |    |    |    |    |    => 1
-;; TRACE t2651: |    |    |    |    |    |    (cc 1 2)
-;; TRACE t2652: |    |    |    |    |    |    |    (cc 1 1)
-;; TRACE t2653: |    |    |    |    |    |    |    |    (cc 1 0)
-;; TRACE t2653: |    |    |    |    |    |    |    |    => 0
-;; TRACE t2654: |    |    |    |    |    |    |    |    (cc 0 1)
-;; TRACE t2654: |    |    |    |    |    |    |    |    => 1
-;; TRACE t2652: |    |    |    |    |    |    |    => 1
-;; TRACE t2655: |    |    |    |    |    |    |    (cc -4 2)
-;; TRACE t2655: |    |    |    |    |    |    |    => 0
-;; TRACE t2651: |    |    |    |    |    |    => 1
-;; TRACE t2637: |    |    |    |    |    => 2
-;; TRACE t2613: |    |    |    |    => 3
-;; TRACE t2656: |    |    |    |    (cc 1 3)
-;; TRACE t2657: |    |    |    |    |    (cc 1 2)
-;; TRACE t2658: |    |    |    |    |    |    (cc 1 1)
-;; TRACE t2659: |    |    |    |    |    |    |    (cc 1 0)
-;; TRACE t2659: |    |    |    |    |    |    |    => 0
-;; TRACE t2660: |    |    |    |    |    |    |    (cc 0 1)
-;; TRACE t2660: |    |    |    |    |    |    |    => 1
-;; TRACE t2658: |    |    |    |    |    |    => 1
-;; TRACE t2661: |    |    |    |    |    |    (cc -4 2)
-;; TRACE t2661: |    |    |    |    |    |    => 0
-;; TRACE t2657: |    |    |    |    |    => 1
-;; TRACE t2662: |    |    |    |    |    (cc -9 3)
-;; TRACE t2662: |    |    |    |    |    => 0
-;; TRACE t2656: |    |    |    |    => 1
-;; TRACE t2612: |    |    |    => 4
-;; TRACE t2663: |    |    |    (cc -14 4)
-;; TRACE t2663: |    |    |    => 0
-;; TRACE t2611: |    |    => 4
-;; TRACE t2664: |    |    (cc -39 5)
-;; TRACE t2664: |    |    => 0
-;; TRACE t2610: |    => 4
-;; TRACE t2609: => 4
-;; 4  
-;; )
-
-
-;; TODO: orders of growth in space and number of steps.
-
-;; exercise 1.15: sin (x) calculation
-;;    a.  How many times is the procedure p applied when (sine 12.15)
-;;        is evaluated?
-;;    b.  What is the order of growth in space and number of steps (as
-;;        a function of a) used by the process generated by the sine
-;;        procedure when (sine a) is evaluated?
-(defn p [x] (- (* 3 x) (* 4 (cube x))))
-
-(defn sine [angle]
-  (if (not (> (myabs angle) 0.1))
-    angle
-    (p (sine (/ angle 3.0)))))
 
-;; solution to (a) => 5
-;; (comment
-;; user> (dotrace [p] (sine 12.15))
-;; TRACE t2490: (p 0.049999999999999996)
-;; TRACE t2490: => 0.1495
-;; TRACE t2491: (p 0.1495)
-;; TRACE t2491: => 0.4351345505
-;; TRACE t2492: (p 0.4351345505)
-;; TRACE t2492: => 0.9758465331678772
-;; TRACE t2493: (p 0.9758465331678772)
-;; TRACE t2493: => -0.7895631144708228
-;; TRACE t2494: (p -0.7895631144708228)
-;; TRACE t2494: => -0.39980345741334
-;; -0.39980345741334
-;; )
 
-;; solution to b
-;; both space and number of steps grows as log3(a) -> log a to the base 3.
-;;
-;; proof:
-;;   a * (1/3)^n <= 0.1
-;;   => take log to the base 3 on both the sides.
 
-;; Note: Finding the order of space in a recursive process is sort of, equiv
-;;       to finding the number of deferred operations. Which is in-turn the
-;;       same as the depth of the evaluation tree.
 
 ;; 1.2.4: exponentiation
 ;; computing b^n
@@ -480,73 +157,7 @@ See the pdfs in the directory for the answers.
 	(even? n) (square (fast-expt b (/ n 2)))
 	:else (* b (fast-expt b (dec n)))))
 
-;; exercise 1.16:
-(defn myexpt [b n]
-  (expt-iter b n 1))
 
-(defn 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))))
-
-;; exercise 1.17:
-(defn mult [a b]
-  (if (= b 0)
-    0
-    (+ a (mult a (- b 1)))))
-
-;; double
-;; product = 2 * (a * (b/2)) for even b
-;;         = a    + (a * (b - 1)) for odd b
-(defn fast-mult [a b]
-  (cond (= b 0) 0
-	(= b 1) a
-	(even? b) (twice (fast-mult a (half b)))
-	:else (+ a (fast-mult a (- b 1)))))
-
-;; exercise 1.18: iterative multiply thru addition
-;; the idea is to keep a state variable.
-(defn fast-mult-iter [a b k]
-  (cond (= b 0) k
-	(even? b) (fast-mult-iter (twice a) (half b) k)
-	:else (fast-mult-iter a (- b 1) (+ k a))))
-
-(defn fast-mult-new [a b]
-  (fast-mult-iter a b 0))
-
-;; (comment
-;; user> (dotrace [fast-mult-new fast-mult-iter] (fast-mult-new 2 3))
-;; TRACE t2915: (fast-mult-new 2 3)
-;; TRACE t2916: |    (fast-mult-iter 2 3 0)
-;; TRACE t2917: |    |    (fast-mult-iter 2 2 2)
-;; TRACE t2918: |    |    |    (fast-mult-iter 4 1 2)
-;; TRACE t2919: |    |    |    |    (fast-mult-iter 4 0 6)
-;; TRACE t2919: |    |    |    |    => 6
-;; TRACE t2918: |    |    |    => 6
-;; TRACE t2917: |    |    => 6
-;; TRACE t2916: |    => 6
-;; TRACE t2915: => 6
-;; 6
-;; )
-
-;; exercise 1.19: fast fibonacci
-;; see the pdf of the notebook scan for the derivation of p' and q'
-(defn ffib-iter [a b p q count]
-  (cond (= count 0) b
-	(even? count)
-	(ffib-iter a
-		   b
-		   (+ (* p p) (* q q))
-		   (+ (* 2 p q) (* q q))
-		   (/ count 2))
-	:else (ffib-iter (+ (* b q) (* a q) (* a p))
-			 (+ (* b p) (* a q))
-			 p
-			 q
-			 (- count 1))))
-
-(defn ffib [n]
-  (ffib-iter 1 0 0 1 n))
 
 ;;;  Section 1.2.5: GCD
 (defn mygcd [a b]
@@ -554,13 +165,6 @@ See the pdfs in the directory for the answers.
     a
     (mygcd b (rem a b))))
 
-;;; exercise 1.20.
-;;
-;;  normal order - 18, applicative order - 4.
-;;
-;;   too lazy to scan things from the notebook. May be I should instead
-;;   use a wiki.
-
 ;;; section 1.2.6 Primality testing.
 (defn prime? [n]
   (= (smallest-divisor n) n))
@@ -595,225 +199,4 @@ See the pdfs in the directory for the answers.
 	(fermat-test n) (fast-prime? n (dec times))
 	:else false))
 
-;; exercise 1.21
-(comment
-user> (smallest-divisor 199)
-199
-user> (smallest-divisor 1999)
-1999
-user> (smallest-divisor 19999)
-7
-)
-
-;; exercise 1.22
-(defn timed-prime-test [n]
-  (prn)
-  (print n)
-  (start-prime-test n (System/nanoTime)))
-
-(defn start-prime-test [n start-time]
-  (if (prime? n)
-    (report-prime (- (System/nanoTime) start-time))))
-
-(defn report-prime [elapsed-time]
-  (print " *** ")
-  (print elapsed-time))
-
-(defn search-for-primes [a b]
-  (cond (>= a b) nil
-	(even? a) (search-for-primes (+ 1 a) b)
-	(timed-prime-test a) (search-for-primes (+ 2 a) b)
-	:else (search-for-primes (+ 2 a) b)))
-
-;;; three smallest primes greater than 1000
-;;; 1009, 1013, 1019
-(take 3 (filter #(prime? %) (iterate inc 1000)))
-;=> (1009 1013 1019)
-
-;=> 0.9642028750000001
-
-;;; > 10,000: 10007, 10009, 10037
-(take 3 (filter #(prime? %) (iterate inc 10000)))
-;=> (10007 10009 10037)
-
-;=> 1.5897884999999998
-
-;;; > 100,000: 100003, 100019, 100043
-(take 3 (filter #(prime? %) (iterate inc 100000)))
-;=> (100003 100019 100043)
-
-;=> 1.8525091250000003
-
-;;; > 1,000,000: 1000003, 1000033, 1000037
-(take 3 (filter #(prime? %) (iterate inc 1000000)))
-;=> (1000003 1000033 1000037)
-
-;=> 1.908832125
-
-;; time taken seem to increase as the range increases.
-;; but they are totally random on the jvm, so I can't find
-;; the exact relation.
-
-(comment
-user> (microbench 10 (take 3 (filter #(prime? %) (iterate inc 1000))))
-Warming up!
-Benchmarking...
-(1009 1013 1019)
-(1009 1013 1019)
-(1009 1013 1019)
-(1009 1013 1019)
-(1009 1013 1019)
-(1009 1013 1019)
-(1009 1013 1019)
-(1009 1013 1019)
-(1009 1013 1019)
-(1009 1013 1019)
-Total runtime:  0.28404500000000005
-Highest time :  0.083949
-Lowest time  :  0.019416
-Average      :  0.022585000000000008
-(0.083949 0.019416 0.023257 0.020394 0.024165 0.024514 0.024374 0.020813 0.021721 0.021442)
-user> (microbench 10 (take 3 (filter #(prime? %) (iterate inc 10000))))
-Warming up!
-Benchmarking...
-(10007 10009 10037)
-(10007 10009 10037)
-(10007 10009 10037)
-(10007 10009 10037)
-(10007 10009 10037)
-(10007 10009 10037)
-(10007 10009 10037)
-(10007 10009 10037)
-(10007 10009 10037)
-(10007 10009 10037)
-Total runtime:  0.26462800000000003
-Highest time :  0.067118
-Lowest time  :  0.020533
-Average      :  0.022122125000000006
-(0.067118 0.022698 0.024095 0.023537 0.020533 0.020882 0.020603 0.021372 0.020603 0.023187)
-user> (microbench 10 (take 3 (filter #(prime? %) (iterate inc 100000))))
-Warming up!
-Benchmarking...
-(100003 100019 100043)
-(100003 100019 100043)
-(100003 100019 100043)
-(100003 100019 100043)
-(100003 100019 100043)
-(100003 100019 100043)
-(100003 100019 100043)
-(100003 100019 100043)
-(100003 100019 100043)
-(100003 100019 100043)
-Total runtime:  0.265118
-Highest time :  0.073263
-Lowest time  :  0.020254
-Average      :  0.021450125000000004
-(0.073263 0.023048 0.023467 0.021022 0.020394 0.020254 0.021302 0.020812 0.020743 0.020813)  
-)
-
-;;; can't make out any sqrt(10) relation between the numbers. may be because
-;;; jvm compilation is doing some behind the scene tricks.
-
-;;; exercise 1.23
-(defn next-divisor [n]
-  (if (= n 2)
-    3
-    (+ n 2)))
 
-
-(defn find-divisor [n test-divisor]
-  (cond (> (square test-divisor)  n) n
-	(divides? test-divisor n) test-divisor
-	:else (find-divisor n (next-divisor test-divisor))))
-
-(comment
-  I can't see any noticable difference in the speed.
-  )
-
-;;; exercise 1.24
-(comment
-  (microbench 10 (take 3 (filter #(fast-prime? %) (iterate inc 1000))))
-  ...
-  "I did not observe any difference".
-  )
-
-;; exercise 1.25
-(defn expmod [base exp m]
-  (rem (fast-expt base exp) m))
-
-(comment
-  In the case of the original expmod implementation, square and remainder
-  calls are interspersed, so square always deals with a small number, whereas
-  with the above way, we do a series of squaring and then in the end take
-  remainder. Squaring of big numbers are very inefficient as the CPU has to
-  do multi-byte arithmetic which consumes many cycles.
-
-  So the new version is several times slower than the original.
-)
-
-;;; exercise 1.26
-(comment
-  "Instead of calling (square x), Louis now makes does (* x x). In the former,
-   case, x is evaluated only once, where as in the second, x gets evaluated
-   2x, 4x, 8x, 16x and so on (for any x which is recursive). So, if the original
-   computation is considered T(log_n), then the new process T(n). This can also
-   be illustrated with the call tree."
-)
-
-;; exercise 1.27
-(comment
-  "Some notes on Carmichael numbers: Carmichael numbers are those that fail
-   Fermat little test. That is, for any n in the Carmichael set,
-   (prime? n)      => false
-   (fermat-test n) => true."
-  )
-(defn brute-force-fermat-test [n]
-  (try-all 2 n))
-
-(defn try-all [a n]
-  (cond (= a n) true
-	(try-it a n) (try-all (inc a) n)
-	:else false))
-(comment
-  "all the given numbers pass the above test, i.e. for every a < n,
-   a^n mod n === a mod n"
-  user> (brute-force-fermat-test 561)
-  true
-  user> (brute-force-fermat-test 1105)
-  true
-  user> (brute-force-fermat-test 1729)
-  true
-  user> (brute-force-fermat-test 2465)
-  true
-  user> (brute-force-fermat-test 2821)
-  true
-  user> (brute-force-fermat-test 6601)
-  true
-  )
-
-;;; exercise 1.28
-(defn expmod2 [base exp m]
-  (cond (= exp 0) 1
-	(even? exp) (square-test (expmod2 base (/ exp 2) m) m)
-	:else (rem (* base (expmod2 base (dec exp) m))
-		   m)))
-
-(defn square-test [x m]
-  (if (and (not (or (= x 1) (= x (- m 1))))
-	   (= (rem (square x) m) 1))
-    0
-    (rem (square x) m)))
-
-(defn miller-rabin-test [n]
-  (try-it (+ 2 (rand-int (- n 2)))
-	  n))
-
-(defn try-it [a n]
-  (= (expmod2 a (- n 1) n) 1))
-
-(comment
-  "If the random number generated (a) is 1, then this returns false
-   positives. So generate random numbers between 2 and n-1. (is this
-   assumption correct?) "
-  
-  )
\ No newline at end of file
diff --git a/src/sicp/ex1.1.clj b/src/sicp/ex1.1.clj
new file mode 100644
index 0000000..f4792da
--- /dev/null
+++ b/src/sicp/ex1.1.clj
@@ -0,0 +1,27 @@
+(ns sicp.ex1.1
+  (:use [sicp utils]
+	[clojure.contrib trace test-is]))
+
+;; exercise 1.1: What is the result printed by the interpreter in response
+;;               to each expression (in order) ?
+
+(def a 3)
+(def b (+ a 1))
+
+(+ a b (* a b))  ; 19
+(= a b) ; false
+
+(if (and (> b a) (< b (* a b)))
+    b
+    a)   ; 4
+
+(cond (= a 4) 6
+      (= b 4) (+ 6 7 a)
+      :else 25)  ; 16
+
+(+ 2 (if (> b a) b a)) ; 6
+
+(* (cond (> a b) a
+	 (< a b) b
+	 :else -1)
+   (+ a 1))      ; 16
diff --git a/src/sicp/ex1.10.clj b/src/sicp/ex1.10.clj
new file mode 100644
index 0000000..ca35174
--- /dev/null
+++ b/src/sicp/ex1.10.clj
@@ -0,0 +1,36 @@
+(ns sicp.ex1.10
+  (:use [sicp utils]
+	[clojure.contrib trace test-is]))
+
+;; exercise 1.10
+;; ackerman functions
+(defn A [x y]
+  (cond (= y 0) 0
+	(= x 0) (* 2 y)
+	(= y 1) 2
+	:else (A (- x 1)
+		 (A x (- y 1)))))
+
+;; (comment
+;; user> (A 1 10)
+;; 1024
+;; user> (A 2 4)
+;; 65536
+;; user> (A 3 3)
+;; 65536
+;; )
+
+(defn f [n] (A 0 n)) ; f(n) = 2n
+(defn g [n] (A 1 n)) ; g(n) = 2^n
+;; (comment
+;;   g (n) = A (1,n)
+;;         = A (0, A (1, n-1)) = f (A(1,n-1))
+;; 	  = f (f (1,n-2)) 
+;; 	    .....
+;; 	    = f (f (f ... f (1,(n- (n-1)))))
+;; 	      = f (f (f ... 2))
+;; 		= 2 * (2^(n-1))
+;; 		  = 2^n
+;; )
+
+(defn h [n] (A 2 n)) ; h(n) = 2^(n^2)
diff --git a/src/sicp/ex1.11.clj b/src/sicp/ex1.11.clj
new file mode 100644
index 0000000..8e93174
--- /dev/null
+++ b/src/sicp/ex1.11.clj
@@ -0,0 +1,48 @@
+(ns sicp.ex1.11
+  (:use [sicp utils]
+	[clojure.contrib trace test-is]))
+
+;; exercise 1.11: A function f is defined by the rule that f(n) = n if n < 3
+;;                and f(n) = f(n - 1) + 2f(n  - 2) + 3f(n - 3) if n> 3.
+;;                Write a procedure that computes f by means of a recursive
+;;                process. Write a procedure that computes f by means of an
+;;                iterative process. 
+(defn f [n]
+  (if (< n 3)
+    n
+    (+ (f (- n 1))
+       (* 2 (f (- n 2)))
+       (* 3 (f (- n 3))))))
+
+;; (comment
+;; user> (map f (range 10))
+;; (0 1 2 4 11 25 59 142 335 796)  
+;; )
+
+;; ex 1.11: iterative version
+(defn f-iter [count prev0 prev1 prev2]
+  (if (= count 3)
+    (+ prev0
+       (* 2 prev1)
+       (* 3 prev2))
+    (f-iter (dec count)
+	    (+ prev0
+	       (* 2 prev1)
+	       (* 3 prev2))
+	    prev0
+	    prev1)))
+
+(defn f [n]
+  (if (< n 3)
+    n
+    (f-iter n 2 1 0)))
+
+;; ex 1.11: iterative version with let
+(defn f-iter [count prev0 prev1 prev2]
+  (let [res (+ prev0 (* 2 prev1) (* 3 prev2))]
+    (if (= count 3)
+      res
+      (f-iter (dec count)
+	      res
+	      prev0
+	      prev1))))
diff --git a/src/sicp/ex1.12.clj b/src/sicp/ex1.12.clj
new file mode 100644
index 0000000..96fbbe2
--- /dev/null
+++ b/src/sicp/ex1.12.clj
@@ -0,0 +1,22 @@
+(ns sicp.ex1.12
+  (:use [sicp utils]
+	[clojure.contrib trace test-is]))
+
+;; exercise 1.12.  The following pattern of numbers is called Pascal's triangle.
+;;          1
+;;        1   1
+;;      1   2   1
+;;    1   3   3   1
+;;  1   4   6   4   1
+;; ...................
+;;
+;;                 The numbers at the edge of the triangle are all 1, and each
+;;                 number inside the triangle is the sum of the two numbers above
+;;                 it. Write a procedure that computes elements of Pascal's triangle
+;;                 by means of a recursive process. 
+(defn pascal [row col]
+  (when (<= col row)
+    (if (or (= col 0) (= row col))
+      1
+      (+ (pascal (dec row) col)
+	 (pascal (dec row) (dec col))))))
diff --git a/src/sicp/ex1.13.clj b/src/sicp/ex1.13.clj
new file mode 100644
index 0000000..8500e12
--- /dev/null
+++ b/src/sicp/ex1.13.clj
@@ -0,0 +1,18 @@
+(ns sicp.ex1.13
+  (:use [sicp utils]
+	[clojure.contrib trace test-is]))
+
+;; exercise 1.13:
+(comment
+See the pdfs in the directory for the answers.
+)
+
+;; ex 1.13 (contd)
+(defn fib-approx [n]
+  (let [phi (/ (+ 1 (sqrt 5)) 2)]
+    (/ (expt phi n) (sqrt 5))))
+
+;; (comment
+;; user> (map fib-approx (range 10))
+;; (0.4472135954999579 0.7236067977499789 1.1708203932499368 1.8944271909999157 3.065247584249853 4.959674775249769 8.024922359499623 12.984597134749393 21.009519494249016 33.99411662899841)
+;; )
diff --git a/src/sicp/ex1.14.clj b/src/sicp/ex1.14.clj
new file mode 100644
index 0000000..93399ac
--- /dev/null
+++ b/src/sicp/ex1.14.clj
@@ -0,0 +1,133 @@
+(ns sicp.ex1.14
+  (:use [sicp utils]
+	[clojure.contrib trace test-is]))
+
+;; exercise 1.14: tree of (count-changes 11)
+(comment
+  See the notebook (sorry, don't have the time to scan it and put it on the web)
+  for the tree representation.
+)
+
+;; order of size and computation
+;; see PDF, but below is the trace tree.
+;; (comment
+;; user> (use 'clojure.contrib.trace)
+;; nil
+;; user> (dotrace [count-change cc] (count-change 11))
+;; TRACE t2609: (count-change 11)
+;; TRACE t2610: |    (cc 11 5)
+;; TRACE t2611: |    |    (cc 11 4)
+;; TRACE t2612: |    |    |    (cc 11 3)
+;; TRACE t2613: |    |    |    |    (cc 11 2)
+;; TRACE t2614: |    |    |    |    |    (cc 11 1)
+;; TRACE t2615: |    |    |    |    |    |    (cc 11 0)
+;; TRACE t2615: |    |    |    |    |    |    => 0
+;; TRACE t2616: |    |    |    |    |    |    (cc 10 1)
+;; TRACE t2617: |    |    |    |    |    |    |    (cc 10 0)
+;; TRACE t2617: |    |    |    |    |    |    |    => 0
+;; TRACE t2618: |    |    |    |    |    |    |    (cc 9 1)
+;; TRACE t2619: |    |    |    |    |    |    |    |    (cc 9 0)
+;; TRACE t2619: |    |    |    |    |    |    |    |    => 0
+;; TRACE t2620: |    |    |    |    |    |    |    |    (cc 8 1)
+;; TRACE t2621: |    |    |    |    |    |    |    |    |    (cc 8 0)
+;; TRACE t2621: |    |    |    |    |    |    |    |    |    => 0
+;; TRACE t2622: |    |    |    |    |    |    |    |    |    (cc 7 1)
+;; TRACE t2623: |    |    |    |    |    |    |    |    |    |    (cc 7 0)
+;; TRACE t2623: |    |    |    |    |    |    |    |    |    |    => 0
+;; TRACE t2624: |    |    |    |    |    |    |    |    |    |    (cc 6 1)
+;; TRACE t2625: |    |    |    |    |    |    |    |    |    |    |    (cc 6 0)
+;; TRACE t2625: |    |    |    |    |    |    |    |    |    |    |    => 0
+;; TRACE t2626: |    |    |    |    |    |    |    |    |    |    |    (cc 5 1)
+;; TRACE t2627: |    |    |    |    |    |    |    |    |    |    |    |    (cc 5 0)
+;; TRACE t2627: |    |    |    |    |    |    |    |    |    |    |    |    => 0
+;; TRACE t2628: |    |    |    |    |    |    |    |    |    |    |    |    (cc 4 1)
+;; TRACE t2629: |    |    |    |    |    |    |    |    |    |    |    |    |    (cc 4 0)
+;; TRACE t2629: |    |    |    |    |    |    |    |    |    |    |    |    |    => 0
+;; TRACE t2630: |    |    |    |    |    |    |    |    |    |    |    |    |    (cc 3 1)
+;; TRACE t2631: |    |    |    |    |    |    |    |    |    |    |    |    |    |    (cc 3 0)
+;; TRACE t2631: |    |    |    |    |    |    |    |    |    |    |    |    |    |    => 0
+;; TRACE t2632: |    |    |    |    |    |    |    |    |    |    |    |    |    |    (cc 2 1)
+;; TRACE t2633: |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    (cc 2 0)
+;; TRACE t2633: |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    => 0
+;; TRACE t2634: |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    (cc 1 1)
+;; TRACE t2635: |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    (cc 1 0)
+;; TRACE t2635: |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    => 0
+;; TRACE t2636: |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    (cc 0 1)
+;; TRACE t2636: |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    => 1
+;; TRACE t2634: |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    => 1
+;; TRACE t2632: |    |    |    |    |    |    |    |    |    |    |    |    |    |    => 1
+;; TRACE t2630: |    |    |    |    |    |    |    |    |    |    |    |    |    => 1
+;; TRACE t2628: |    |    |    |    |    |    |    |    |    |    |    |    => 1
+;; TRACE t2626: |    |    |    |    |    |    |    |    |    |    |    => 1
+;; TRACE t2624: |    |    |    |    |    |    |    |    |    |    => 1
+;; TRACE t2622: |    |    |    |    |    |    |    |    |    => 1
+;; TRACE t2620: |    |    |    |    |    |    |    |    => 1
+;; TRACE t2618: |    |    |    |    |    |    |    => 1
+;; TRACE t2616: |    |    |    |    |    |    => 1
+;; TRACE t2614: |    |    |    |    |    => 1
+;; TRACE t2637: |    |    |    |    |    (cc 6 2)
+;; TRACE t2638: |    |    |    |    |    |    (cc 6 1)
+;; TRACE t2639: |    |    |    |    |    |    |    (cc 6 0)
+;; TRACE t2639: |    |    |    |    |    |    |    => 0
+;; TRACE t2640: |    |    |    |    |    |    |    (cc 5 1)
+;; TRACE t2641: |    |    |    |    |    |    |    |    (cc 5 0)
+;; TRACE t2641: |    |    |    |    |    |    |    |    => 0
+;; TRACE t2642: |    |    |    |    |    |    |    |    (cc 4 1)
+;; TRACE t2643: |    |    |    |    |    |    |    |    |    (cc 4 0)
+;; TRACE t2643: |    |    |    |    |    |    |    |    |    => 0
+;; TRACE t2644: |    |    |    |    |    |    |    |    |    (cc 3 1)
+;; TRACE t2645: |    |    |    |    |    |    |    |    |    |    (cc 3 0)
+;; TRACE t2645: |    |    |    |    |    |    |    |    |    |    => 0
+;; TRACE t2646: |    |    |    |    |    |    |    |    |    |    (cc 2 1)
+;; TRACE t2647: |    |    |    |    |    |    |    |    |    |    |    (cc 2 0)
+;; TRACE t2647: |    |    |    |    |    |    |    |    |    |    |    => 0
+;; TRACE t2648: |    |    |    |    |    |    |    |    |    |    |    (cc 1 1)
+;; TRACE t2649: |    |    |    |    |    |    |    |    |    |    |    |    (cc 1 0)
+;; TRACE t2649: |    |    |    |    |    |    |    |    |    |    |    |    => 0
+;; TRACE t2650: |    |    |    |    |    |    |    |    |    |    |    |    (cc 0 1)
+;; TRACE t2650: |    |    |    |    |    |    |    |    |    |    |    |    => 1
+;; TRACE t2648: |    |    |    |    |    |    |    |    |    |    |    => 1
+;; TRACE t2646: |    |    |    |    |    |    |    |    |    |    => 1
+;; TRACE t2644: |    |    |    |    |    |    |    |    |    => 1
+;; TRACE t2642: |    |    |    |    |    |    |    |    => 1
+;; TRACE t2640: |    |    |    |    |    |    |    => 1
+;; TRACE t2638: |    |    |    |    |    |    => 1
+;; TRACE t2651: |    |    |    |    |    |    (cc 1 2)
+;; TRACE t2652: |    |    |    |    |    |    |    (cc 1 1)
+;; TRACE t2653: |    |    |    |    |    |    |    |    (cc 1 0)
+;; TRACE t2653: |    |    |    |    |    |    |    |    => 0
+;; TRACE t2654: |    |    |    |    |    |    |    |    (cc 0 1)
+;; TRACE t2654: |    |    |    |    |    |    |    |    => 1
+;; TRACE t2652: |    |    |    |    |    |    |    => 1
+;; TRACE t2655: |    |    |    |    |    |    |    (cc -4 2)
+;; TRACE t2655: |    |    |    |    |    |    |    => 0
+;; TRACE t2651: |    |    |    |    |    |    => 1
+;; TRACE t2637: |    |    |    |    |    => 2
+;; TRACE t2613: |    |    |    |    => 3
+;; TRACE t2656: |    |    |    |    (cc 1 3)
+;; TRACE t2657: |    |    |    |    |    (cc 1 2)
+;; TRACE t2658: |    |    |    |    |    |    (cc 1 1)
+;; TRACE t2659: |    |    |    |    |    |    |    (cc 1 0)
+;; TRACE t2659: |    |    |    |    |    |    |    => 0
+;; TRACE t2660: |    |    |    |    |    |    |    (cc 0 1)
+;; TRACE t2660: |    |    |    |    |    |    |    => 1
+;; TRACE t2658: |    |    |    |    |    |    => 1
+;; TRACE t2661: |    |    |    |    |    |    (cc -4 2)
+;; TRACE t2661: |    |    |    |    |    |    => 0
+;; TRACE t2657: |    |    |    |    |    => 1
+;; TRACE t2662: |    |    |    |    |    (cc -9 3)
+;; TRACE t2662: |    |    |    |    |    => 0
+;; TRACE t2656: |    |    |    |    => 1
+;; TRACE t2612: |    |    |    => 4
+;; TRACE t2663: |    |    |    (cc -14 4)
+;; TRACE t2663: |    |    |    => 0
+;; TRACE t2611: |    |    => 4
+;; TRACE t2664: |    |    (cc -39 5)
+;; TRACE t2664: |    |    => 0
+;; TRACE t2610: |    => 4
+;; TRACE t2609: => 4
+;; 4  
+;; )
+
+
+;; TODO: orders of growth in space and number of steps.
diff --git a/src/sicp/ex1.15.clj b/src/sicp/ex1.15.clj
new file mode 100644
index 0000000..621891d
--- /dev/null
+++ b/src/sicp/ex1.15.clj
@@ -0,0 +1,43 @@
+(ns sicp.ex1.15
+  (:use [sicp utils]
+	[clojure.contrib trace test-is]))
+
+;; exercise 1.15: sin (x) calculation
+;;    a.  How many times is the procedure p applied when (sine 12.15)
+;;        is evaluated?
+;;    b.  What is the order of growth in space and number of steps (as
+;;        a function of a) used by the process generated by the sine
+;;        procedure when (sine a) is evaluated?
+(defn p [x] (- (* 3 x) (* 4 (cube x))))
+
+(defn sine [angle]
+  (if (not (> (myabs angle) 0.1))
+    angle
+    (p (sine (/ angle 3.0)))))
+
+;; solution to (a) => 5
+;; (comment
+;; user> (dotrace [p] (sine 12.15))
+;; TRACE t2490: (p 0.049999999999999996)
+;; TRACE t2490: => 0.1495
+;; TRACE t2491: (p 0.1495)
+;; TRACE t2491: => 0.4351345505
+;; TRACE t2492: (p 0.4351345505)
+;; TRACE t2492: => 0.9758465331678772
+;; TRACE t2493: (p 0.9758465331678772)
+;; TRACE t2493: => -0.7895631144708228
+;; TRACE t2494: (p -0.7895631144708228)
+;; TRACE t2494: => -0.39980345741334
+;; -0.39980345741334
+;; )
+
+;; solution to b
+;; both space and number of steps grows as log3(a) -> log a to the base 3.
+;;
+;; proof:
+;;   a * (1/3)^n <= 0.1
+;;   => take log to the base 3 on both the sides.
+
+;; Note: Finding the order of space in a recursive process is sort of, equiv
+;;       to finding the number of deferred operations. Which is in-turn the
+;;       same as the depth of the evaluation tree.
diff --git a/src/sicp/ex1.16.clj b/src/sicp/ex1.16.clj
new file mode 100644
index 0000000..a38ebe2
--- /dev/null
+++ b/src/sicp/ex1.16.clj
@@ -0,0 +1,12 @@
+(ns sicp.ex1.16
+  (:use [sicp utils]
+	[clojure.contrib trace test-is]))
+
+;; exercise 1.16:
+(defn myexpt [b n]
+  (expt-iter b n 1))
+
+(defn 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))))
diff --git a/src/sicp/ex1.17.clj b/src/sicp/ex1.17.clj
new file mode 100644
index 0000000..a65509d
--- /dev/null
+++ b/src/sicp/ex1.17.clj
@@ -0,0 +1,18 @@
+(ns sicp.ex1.17
+  (:use [sicp utils]
+	[clojure.contrib trace test-is]))
+
+;; exercise 1.17:
+(defn mult [a b]
+  (if (= b 0)
+    0
+    (+ a (mult a (- b 1)))))
+
+;; double
+;; product = 2 * (a * (b/2)) for even b
+;;         = a    + (a * (b - 1)) for odd b
+(defn fast-mult [a b]
+  (cond (= b 0) 0
+	(= b 1) a
+	(even? b) (twice (fast-mult a (half b)))
+	:else (+ a (fast-mult a (- b 1)))))
diff --git a/src/sicp/ex1.18.clj b/src/sicp/ex1.18.clj
new file mode 100644
index 0000000..bf64758
--- /dev/null
+++ b/src/sicp/ex1.18.clj
@@ -0,0 +1,28 @@
+(ns sicp.ex1.18
+  (:use [sicp utils]
+	[clojure.contrib trace test-is]))
+
+;; exercise 1.18: iterative multiply thru addition
+;; the idea is to keep a state variable.
+(defn fast-mult-iter [a b k]
+  (cond (= b 0) k
+	(even? b) (fast-mult-iter (twice a) (half b) k)
+	:else (fast-mult-iter a (- b 1) (+ k a))))
+
+(defn fast-mult-new [a b]
+  (fast-mult-iter a b 0))
+
+;; (comment
+;; user> (dotrace [fast-mult-new fast-mult-iter] (fast-mult-new 2 3))
+;; TRACE t2915: (fast-mult-new 2 3)
+;; TRACE t2916: |    (fast-mult-iter 2 3 0)
+;; TRACE t2917: |    |    (fast-mult-iter 2 2 2)
+;; TRACE t2918: |    |    |    (fast-mult-iter 4 1 2)
+;; TRACE t2919: |    |    |    |    (fast-mult-iter 4 0 6)
+;; TRACE t2919: |    |    |    |    => 6
+;; TRACE t2918: |    |    |    => 6
+;; TRACE t2917: |    |    => 6
+;; TRACE t2916: |    => 6
+;; TRACE t2915: => 6
+;; 6
+;; )
diff --git a/src/sicp/ex1.19.clj b/src/sicp/ex1.19.clj
new file mode 100644
index 0000000..2d83aab
--- /dev/null
+++ b/src/sicp/ex1.19.clj
@@ -0,0 +1,22 @@
+(ns sicp.ex1.19
+  (:use [sicp utils]
+	[clojure.contrib trace test-is]))
+
+;; exercise 1.19: fast fibonacci
+;; see the pdf of the notebook scan for the derivation of p' and q'
+(defn ffib-iter [a b p q count]
+  (cond (= count 0) b
+	(even? count)
+	(ffib-iter a
+		   b
+		   (+ (* p p) (* q q))
+		   (+ (* 2 p q) (* q q))
+		   (/ count 2))
+	:else (ffib-iter (+ (* b q) (* a q) (* a p))
+			 (+ (* b p) (* a q))
+			 p
+			 q
+			 (- count 1))))
+
+(defn ffib [n]
+  (ffib-iter 1 0 0 1 n))
diff --git a/src/sicp/ex1.2.clj b/src/sicp/ex1.2.clj
new file mode 100644
index 0000000..6a1926c
--- /dev/null
+++ b/src/sicp/ex1.2.clj
@@ -0,0 +1,7 @@
+(ns sicp.ex1.2
+  (:use [sicp utils]
+	[clojure.contrib trace test-is]))
+
+;; exercise 1.2: Translate the given expression into prefix form
+(/ (+ 5 4 (- 2 (- 3 (+ 6 (/ 1 5)))))
+   (* 3 (- 6 2) (- 2 7)))  ; -71/300
diff --git a/src/sicp/ex1.20.clj b/src/sicp/ex1.20.clj
new file mode 100644
index 0000000..92512b5
--- /dev/null
+++ b/src/sicp/ex1.20.clj
@@ -0,0 +1,10 @@
+(ns sicp.ex1.20
+  (:use [sicp utils]
+	[clojure.contrib trace test-is]))
+
+;;; exercise 1.20.
+;;
+;;  normal order - 18, applicative order - 4.
+;;
+;;   too lazy to scan things from the notebook. May be I should instead
+;;   use a wiki.
diff --git a/src/sicp/ex1.21.clj b/src/sicp/ex1.21.clj
new file mode 100644
index 0000000..719253f
--- /dev/null
+++ b/src/sicp/ex1.21.clj
@@ -0,0 +1,13 @@
+(ns sicp.ex1.21
+  (:use [sicp utils]
+	[clojure.contrib trace test-is]))
+
+;; exercise 1.21
+(comment
+user> (smallest-divisor 199)
+199
+user> (smallest-divisor 1999)
+1999
+user> (smallest-divisor 19999)
+7
+)
diff --git a/src/sicp/ex1.22.clj b/src/sicp/ex1.22.clj
new file mode 100644
index 0000000..c689f48
--- /dev/null
+++ b/src/sicp/ex1.22.clj
@@ -0,0 +1,112 @@
+(ns sicp.ex1.22
+  (:use [sicp utils]
+	[clojure.contrib trace test-is]))
+
+;; exercise 1.22
+(defn timed-prime-test [n]
+  (prn)
+  (print n)
+  (start-prime-test n (System/nanoTime)))
+
+(defn start-prime-test [n start-time]
+  (if (prime? n)
+    (report-prime (- (System/nanoTime) start-time))))
+
+(defn report-prime [elapsed-time]
+  (print " *** ")
+  (print elapsed-time))
+
+(defn search-for-primes [a b]
+  (cond (>= a b) nil
+	(even? a) (search-for-primes (+ 1 a) b)
+	(timed-prime-test a) (search-for-primes (+ 2 a) b)
+	:else (search-for-primes (+ 2 a) b)))
+
+;;; three smallest primes greater than 1000
+;;; 1009, 1013, 1019
+(take 3 (filter #(prime? %) (iterate inc 1000)))
+;=> (1009 1013 1019)
+
+;=> 0.9642028750000001
+
+;;; > 10,000: 10007, 10009, 10037
+(take 3 (filter #(prime? %) (iterate inc 10000)))
+;=> (10007 10009 10037)
+
+;=> 1.5897884999999998
+
+;;; > 100,000: 100003, 100019, 100043
+(take 3 (filter #(prime? %) (iterate inc 100000)))
+;=> (100003 100019 100043)
+
+;=> 1.8525091250000003
+
+;;; > 1,000,000: 1000003, 1000033, 1000037
+(take 3 (filter #(prime? %) (iterate inc 1000000)))
+;=> (1000003 1000033 1000037)
+
+;=> 1.908832125
+
+;; time taken seem to increase as the range increases.
+;; but they are totally random on the jvm, so I can't find
+;; the exact relation.
+
+(comment
+user> (microbench 10 (take 3 (filter #(prime? %) (iterate inc 1000))))
+Warming up!
+Benchmarking...
+(1009 1013 1019)
+(1009 1013 1019)
+(1009 1013 1019)
+(1009 1013 1019)
+(1009 1013 1019)
+(1009 1013 1019)
+(1009 1013 1019)
+(1009 1013 1019)
+(1009 1013 1019)
+(1009 1013 1019)
+Total runtime:  0.28404500000000005
+Highest time :  0.083949
+Lowest time  :  0.019416
+Average      :  0.022585000000000008
+(0.083949 0.019416 0.023257 0.020394 0.024165 0.024514 0.024374 0.020813 0.021721 0.021442)
+user> (microbench 10 (take 3 (filter #(prime? %) (iterate inc 10000))))
+Warming up!
+Benchmarking...
+(10007 10009 10037)
+(10007 10009 10037)
+(10007 10009 10037)
+(10007 10009 10037)
+(10007 10009 10037)
+(10007 10009 10037)
+(10007 10009 10037)
+(10007 10009 10037)
+(10007 10009 10037)
+(10007 10009 10037)
+Total runtime:  0.26462800000000003
+Highest time :  0.067118
+Lowest time  :  0.020533
+Average      :  0.022122125000000006
+(0.067118 0.022698 0.024095 0.023537 0.020533 0.020882 0.020603 0.021372 0.020603 0.023187)
+user> (microbench 10 (take 3 (filter #(prime? %) (iterate inc 100000))))
+Warming up!
+Benchmarking...
+(100003 100019 100043)
+(100003 100019 100043)
+(100003 100019 100043)
+(100003 100019 100043)
+(100003 100019 100043)
+(100003 100019 100043)
+(100003 100019 100043)
+(100003 100019 100043)
+(100003 100019 100043)
+(100003 100019 100043)
+Total runtime:  0.265118
+Highest time :  0.073263
+Lowest time  :  0.020254
+Average      :  0.021450125000000004
+(0.073263 0.023048 0.023467 0.021022 0.020394 0.020254 0.021302 0.020812 0.020743 0.020813)  
+)
+
+;;; can't make out any sqrt(10) relation between the numbers. may be because
+;;; jvm compilation is doing some behind the scene tricks.
diff --git a/src/sicp/ex1.23.clj b/src/sicp/ex1.23.clj
new file mode 100644
index 0000000..fd55501
--- /dev/null
+++ b/src/sicp/ex1.23.clj
@@ -0,0 +1,19 @@
+(ns sicp.ex1.23
+  (:use [sicp utils]
+	[clojure.contrib trace test-is]))
+
+;;; exercise 1.23
+(defn next-divisor [n]
+  (if (= n 2)
+    3
+    (+ n 2)))
+
+
+(defn find-divisor [n test-divisor]
+  (cond (> (square test-divisor)  n) n
+	(divides? test-divisor n) test-divisor
+	:else (find-divisor n (next-divisor test-divisor))))
+
+(comment
+  I can't see any noticable difference in the speed.
+)
diff --git a/src/sicp/ex1.24.clj b/src/sicp/ex1.24.clj
new file mode 100644
index 0000000..e0c7c56
--- /dev/null
+++ b/src/sicp/ex1.24.clj
@@ -0,0 +1,10 @@
+(ns sicp.ex1.24
+  (:use [sicp utils]
+	[clojure.contrib trace test-is]))
+
+;;; exercise 1.24
+(comment
+  (microbench 10 (take 3 (filter #(fast-prime? %) (iterate inc 1000))))
+  ...
+  "I did not observe any difference".
+)
diff --git a/src/sicp/ex1.25.clj b/src/sicp/ex1.25.clj
new file mode 100644
index 0000000..739cf80
--- /dev/null
+++ b/src/sicp/ex1.25.clj
@@ -0,0 +1,17 @@
+(ns sicp.ex1.25
+  (:use [sicp utils]
+	[clojure.contrib trace test-is]))
+
+;; exercise 1.25
+(defn expmod [base exp m]
+  (rem (fast-expt base exp) m))
+
+(comment
+  In the case of the original expmod implementation, square and remainder
+  calls are interspersed, so square always deals with a small number, whereas
+  with the above way, we do a series of squaring and then in the end take
+  remainder. Squaring of big numbers are very inefficient as the CPU has to
+  do multi-byte arithmetic which consumes many cycles.
+
+  So the new version is several times slower than the original.
+)
diff --git a/src/sicp/ex1.26.clj b/src/sicp/ex1.26.clj
new file mode 100644
index 0000000..be97a62
--- /dev/null
+++ b/src/sicp/ex1.26.clj
@@ -0,0 +1,12 @@
+(ns sicp.ex1.26
+  (:use [sicp utils]
+	[clojure.contrib trace test-is]))
+
+;;; exercise 1.26
+(comment
+  "Instead of calling (square x), Louis now makes does (* x x). In the former,
+   case, x is evaluated only once, where as in the second, x gets evaluated
+   2x, 4x, 8x, 16x and so on (for any x which is recursive). So, if the original
+   computation is considered T(log_n), then the new process T(n). This can also
+   be illustrated with the call tree."
+)
diff --git a/src/sicp/ex1.27.clj b/src/sicp/ex1.27.clj
new file mode 100644
index 0000000..a115dca
--- /dev/null
+++ b/src/sicp/ex1.27.clj
@@ -0,0 +1,34 @@
+(ns sicp.ex1.27
+  (:use [sicp utils]
+	[clojure.contrib trace test-is]))
+
+;; exercise 1.27
+(comment
+  "Some notes on Carmichael numbers: Carmichael numbers are those that fail
+   Fermat little test. That is, for any n in the Carmichael set,
+   (prime? n)      => false
+   (fermat-test n) => true."
+  )
+(defn brute-force-fermat-test [n]
+  (try-all 2 n))
+
+(defn try-all [a n]
+  (cond (= a n) true
+	(try-it a n) (try-all (inc a) n)
+	:else false))
+(comment
+  "all the given numbers pass the above test, i.e. for every a < n,
+   a^n mod n === a mod n"
+  user> (brute-force-fermat-test 561)
+  true
+  user> (brute-force-fermat-test 1105)
+  true
+  user> (brute-force-fermat-test 1729)
+  true
+  user> (brute-force-fermat-test 2465)
+  true
+  user> (brute-force-fermat-test 2821)
+  true
+  user> (brute-force-fermat-test 6601)
+  true
+  )
diff --git a/src/sicp/ex1.28.clj b/src/sicp/ex1.28.clj
new file mode 100644
index 0000000..e9a5923
--- /dev/null
+++ b/src/sicp/ex1.28.clj
@@ -0,0 +1,30 @@
+(ns sicp.ex1.28
+  (:use [sicp utils]
+	[clojure.contrib trace test-is]))
+
+
+;;; exercise 1.28
+(defn expmod2 [base exp m]
+  (cond (= exp 0) 1
+	(even? exp) (square-test (expmod2 base (/ exp 2) m) m)
+	:else (rem (* base (expmod2 base (dec exp) m))
+		   m)))
+
+(defn square-test [x m]
+  (if (and (not (or (= x 1) (= x (- m 1))))
+	   (= (rem (square x) m) 1))
+    0
+    (rem (square x) m)))
+
+(defn miller-rabin-test [n]
+  (try-it (+ 2 (rand-int (- n 2)))
+	  n))
+
+(defn try-it [a n]
+  (= (expmod2 a (- n 1) n) 1))
+
+(comment
+  "If the random number generated (a) is 1, then this returns false
+   positives. So generate random numbers between 2 and n-1. (is this
+   assumption correct?) "
+)
\ No newline at end of file
diff --git a/src/sicp/ex1.3.clj b/src/sicp/ex1.3.clj
new file mode 100644
index 0000000..dea2421
--- /dev/null
+++ b/src/sicp/ex1.3.clj
@@ -0,0 +1,25 @@
+(ns sicp.ex1.3
+  (:use [sicp utils]
+	[clojure.contrib trace test-is]))
+
+;; exercise 1.3:  Define a procedure that takes three numbers as
+;;                arguments and returns the sum of the squares of
+;;                the two larger numbers.
+(defn sort3 [a b c]
+  (cond (> b a) (sort3 b a c)
+	(< b c) (sort3 a c b)
+	:else [a b c]))
+
+(defn sum-of-sq-of-two-largest [a b c]
+  (apply sum-of-squares (take 2 (sort3 a b c))))
+
+;; well, I cheated above. Let me use only the constructs introduced
+;; so far in the book. (follows after the sicp meetup #2 on 28/mar/2010.
+(defn sum-of-square-of-two-largest [a b c]
+  (if (> a b)
+    (if (> b c)
+      (sum-of-squares a b) ; a > b > c
+      (sum-of-squares a c))
+    (if (> a c)
+      (sum-of-squares b a)
+      (sum-of-squares b c))))
diff --git a/src/sicp/ex1.4.clj b/src/sicp/ex1.4.clj
new file mode 100644
index 0000000..2d2db8e
--- /dev/null
+++ b/src/sicp/ex1.4.clj
@@ -0,0 +1,15 @@
+(ns sicp.ex1.4
+  (:use [sicp utils]
+	[clojure.contrib trace test-is]))
+
+;; exercise 1.4: Observe that our model of evaluation allows for
+;;               combinations whose operators are compound
+;;               expressions. Use this observation to describe the
+;;               behavior of the following procedure:
+;; (defn a-plus-abs-b [a b]
+;;   ((if (> b 0) + -) a b))
+(comment
+  If b is positive, we do (+ a b) and if it is negative, we do (- a b).
+  This makes use of the fact that the first element in a list is an
+  operand. Here, the operand is chosen based on other operators.
+  )
diff --git a/src/sicp/ex1.5.clj b/src/sicp/ex1.5.clj
new file mode 100644
index 0000000..0f7c9c0
--- /dev/null
+++ b/src/sicp/ex1.5.clj
@@ -0,0 +1,30 @@
+(ns sicp.ex1.5
+  (:use [sicp utils]
+	[clojure.contrib trace test-is]))
+
+;; exercise 1.5:  Ben Bitdiddle has invented a test to determine
+;;                whether the interpreter he is faced with is
+;;                using applicative-order evaluation or normal-order
+;;                evaluation. He defines the following two procedures:
+;; (defn p [] (p))
+;; (defn test [x y]
+;;   (if (= x 0)
+;;    0
+;;    y))
+;;
+;; Then he evaluates the expression
+;;
+;; (test 0 (p))
+;;
+;; What behavior will Ben observe with an interpreter that uses
+;; applicative-order evaluation?
+(comment
+  In the case of applicative order evaluation, the test gets into
+  and infinite loop (eventually using all the stack), as the parameters
+  are evaluated before they are actualy used in the function.
+  )
+;; What behavior will he observe with an interpreter that uses
+;; normal-order evaluation? Explain your answer.
+(comment
+  It will print 0, as (p) is not evaluated in this case.
+  )
diff --git a/src/sicp/ex1.6.clj b/src/sicp/ex1.6.clj
new file mode 100644
index 0000000..5499c96
--- /dev/null
+++ b/src/sicp/ex1.6.clj
@@ -0,0 +1,29 @@
+(ns sicp.ex1.6
+  (:use [sicp utils]
+	[clojure.contrib trace test-is]))
+
+;; exercise 1.6
+;; Alyssa P. Hacker doesn't see why if needs to be provided as a special form.
+;; ``Why can't I just define it as an ordinary procedure in terms of cond?''
+(defn new-if [predicate then-clause else-clause]
+  (cond predicate then-clause
+	:else else-clause))
+
+(new-if (= 3 2) 0 5)  ; 5
+(new-if (= 1 1) 0 5)  ; 0
+
+;; Delighted, Alyssa uses new-if to rewrite the square-root program:
+
+(defn sqrt-iter [guess x]
+  (new-if (good-enough? guess x)
+	  guess
+	  (sqrt-iter (improve guess x)
+		     x)))
+
+;; what happens when Alyssa attempts to use this to compute square roots? Explain.
+(comment
+  Since `new-if' is a function, when it is called from sqrt-iter, the parameters
+  are evaluated before it gets called. good-enough? will return a false unless
+  the guess and x are almost the same. guess evaluated to the initial value of
+  guess. sqrt-iter gets evaluated, but gets into an infinite loop. The predicate
+  will have no effect.)
diff --git a/src/sicp/ex1.7.clj b/src/sicp/ex1.7.clj
new file mode 100644
index 0000000..8acb861
--- /dev/null
+++ b/src/sicp/ex1.7.clj
@@ -0,0 +1,54 @@
+(ns sicp.ex1.7
+  (:use [sicp utils]
+	[clojure.contrib trace test-is]))
+
+;; Exercise 1.7: The good-enough? test used in computing square roots will not
+;; be very effective for finding the square roots of very small numbers. Also,
+;; in real computers, arithmetic operations are almost always performed with
+;; limited precision. This makes our test inadequate for very large numbers.
+;; Explain these statements, with examples showing how the test fails for small
+;; and large numbers.
+(comment
+ user> (sqrt (square 0.001))
+ 0.031260655525445276
+ user> (sqrt (square 0.2))
+ 0.20060990407779591
+ user> (sqrt (square 0.01))
+ 0.03230844833048122
+ user> (sqrt (square 0.02))
+ 0.0354008825558513
+ user> (sqrt (square 10))
+ 10.000000000139897
+ user> (sqrt (square 100))
+ 100.00000025490743
+ user> (sqrt (square 200))
+ 200.000000510076
+ user> (sqrt (square 2))
+ 2.0000000929222947
+ user> (sqrt (square 0.1))
+ 0.10032578510960607
+ user> (sqrt (square 0.01))
+ 0.03230844833048122
+ user> (sqrt (square 10000))
+ 10000.0
+ user> (sqrt (square 20000))
+ 20000.0
+ user> (sqrt (square 200000))
+ 200000.0
+ user> (sqrt (square 20000000))
+ 2.0E7
+ user> (sqrt (square 20000000000))
+ 2.0E10
+ user> (sqrt (square 200000.012))
+ 200000.012
+ user> (sqrt (square 2000000.123))
+ 2000000.123
+ user> (sqrt (square 200000000.123))
+ 2.00000000123E8
+ user> (sqrt (square 2000000000.123))
+ 2.000000000123E9
+ user> (sqrt (square 20000000000.123))
+ 2.0000000000123E10
+ user> (sqrt (square 2000000000000.123))
+ 2.000000000000123E12
+ )
\ No newline at end of file
diff --git a/src/sicp/ex1.8.clj b/src/sicp/ex1.8.clj
new file mode 100644
index 0000000..b50c5b6
--- /dev/null
+++ b/src/sicp/ex1.8.clj
@@ -0,0 +1,30 @@
+(ns sicp.ex1.8
+  (:use [sicp utils]
+	[clojure.contrib trace test-is]))
+
+;; exercise 1.8: cube root
+(defn improve [guess x]
+  (/ (+ (/ x (square guess)) (* 2 guess)) 3))
+
+(defn cubert-iter [old-guess new-guess x]
+  (if (good-enough? old-guess new-guess x)
+    new-guess
+    (cubert-iter new-guess (improve new-guess x)
+		 x)))
+
+(defn cuberoot [x]
+  (cubert-iter x 1.0 x))
+
+(comment
+user> (cuberoot (cube 2))
+2.000000000012062
+user> (cuberoot (cube 10))
+10.000000000000002
+user> (cuberoot (cube 9))
+9.000000000053902
+user> (cuberoot (cube 0.001))
+0.001000000000000962
+user> (cuberoot (cube 0.0001))
+1.000000000000001E-4
+user>
+)
diff --git a/src/sicp/ex1.9.clj b/src/sicp/ex1.9.clj
new file mode 100644
index 0000000..e81ad1d
--- /dev/null
+++ b/src/sicp/ex1.9.clj
@@ -0,0 +1,48 @@
+(ns sicp.ex1.9
+  (:use [sicp utils]
+	[clojure.contrib trace test-is]))
+
+;; exercise 1.9
+(defn ++ [a b]
+  (if (= a 0)
+    b
+    (inc (++ (dec a) b))))
+
+;; (comment
+;;   This version is a recursive process, where the previous call increments
+;;   the sum by 1 and each call decrement the first operand by 1.
+  
+;; user> (dotrace [++] (++ 4 5))
+;; TRACE t3745: (++ 4 5)
+;; TRACE t3746: |    (++ 3 5)
+;; TRACE t3747: |    |    (++ 2 5)
+;; TRACE t3748: |    |    |    (++ 1 5)
+;; TRACE t3749: |    |    |    |    (++ 0 5)
+;; TRACE t3749: |    |    |    |    => 5
+;; TRACE t3748: |    |    |    => 6
+;; TRACE t3747: |    |    => 7
+;; TRACE t3746: |    => 8
+;; TRACE t3745: => 9
+;; 9
+;; )
+
+(defn ++ [a b]
+  (if (= a 0)
+    b
+    (++ (dec a) (inc b))))
+
+;; (comment
+  
+;; user> (dotrace [++] (++ 4 5))
+;; TRACE t3766: (++ 4 5)
+;; TRACE t3767: |    (++ 3 6)
+;; TRACE t3768: |    |    (++ 2 7)
+;; TRACE t3769: |    |    |    (++ 1 8)
+;; TRACE t3770: |    |    |    |    (++ 0 9)
+;; TRACE t3770: |    |    |    |    => 9
+;; TRACE t3769: |    |    |    => 9
+;; TRACE t3768: |    |    => 9
+;; TRACE t3767: |    => 9
+;; TRACE t3766: => 9
+;; 9
+;; )