From: Ramakrishnan Muthukrishnan Date: Sat, 27 Mar 2010 19:21:31 +0000 (+0530) Subject: rearranging the procedures and adding the execution examples under (comment ..) X-Git-Url: https://git.rkrishnan.org/%5B/%5D%20/file/URI:LIT:krugkidfnzsc4/%22news.html/index.php?a=commitdiff_plain;h=81eb83eeb81453e01c6aaef20e5523d56391925c;p=sicp.git rearranging the procedures and adding the execution examples under (comment ..) --- diff --git a/chapter1/ch1_1.clj b/chapter1/ch1_1.clj index d5eb731..b96191b 100644 --- a/chapter1/ch1_1.clj +++ b/chapter1/ch1_1.clj @@ -96,21 +96,21 @@ ) ;; 1.1.7 Square root finding using Newton's method -(defn sqrt-iter [guess x] - (if (good-enough? guess x) - guess - (sqrt-iter (improve guess x) - x))) +(defn average [x y] + (/ (+ x y) 2)) (defn improve [guess x] (average guess (/ x guess))) -(defn average [x y] - (/ (+ x y) 2)) - (defn good-enough? [guess x] (< (abs (- (square guess) x)) 0.001)) +(defn sqrt-iter [guess x] + (if (good-enough? guess x) + guess + (sqrt-iter (improve guess x) + x))) + (defn sqrt [x] (sqrt-iter 1.0 x)) @@ -146,49 +146,50 @@ ;; 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. -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 - +(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. @@ -209,7 +210,7 @@ user> (sqrt (square 2000000000000.123)) (defn sqrt [x] (sqrt-iter x 1.0 x)) - +(comment user> (sqrt (square 0.01)) 0.010000000025490743 user> (sqrt (square 0.001)) @@ -234,7 +235,7 @@ user> (sqrt 9) 3.000000001396984 user> (sqrt 81) 9.000000000007091 - +) ;; exercise 1.8: cube root (defn cube [x] (* x x x)) @@ -251,6 +252,7 @@ user> (sqrt 81) (defn cuberoot [x] (cubert-iter x 1.0 x)) +(comment user> (cuberoot (cube 2)) 2.000000000012062 user> (cuberoot (cube 10)) @@ -262,3 +264,23 @@ user> (cuberoot (cube 0.001)) user> (cuberoot (cube 0.0001)) 1.000000000000001E-4 user> +) +;; section 1.1.8 +;; hiding the non-public procedure definitions +(defn- sqrt-iter [guess x] + (if (good-enough? guess x) + guess + (sqrt-iter (improve guess x) + x))) + +(defn- improve [guess x] + (average guess (/ x guess))) + +(defn- average [x y] + (/ (+ x y) 2)) + +(defn- good-enough? [guess x] + (< (abs (- (square guess) x)) 0.001)) + +(defn sqrt [x] + (sqrt-iter 1.0 x))