SICP 1.1.7 "Squre Roots by Newton's Method"

square-roots-by-newtons-method.clj

;; SICP 1.1.7 "Squre Roots by Newton's Method"
;;
;;  user=>  (load-file "sicp/square-roots-by-newtons-method.clj")
;;  #'user/sqrt
;;  user=> sqrt
;;  #<user$sqrt user$sqrt@1b0c6cfc>
;;  user=> (sqrt 9)
;;  3.00009155413138
;;  user=> (sqrt (+ 100 37))
;;  11.704699917758145
;;  user=> (sqrt (+ (sqrt 2) (sqrt 3)))
;;  1.7739279023207892
;;  user=> (square (sqrt 1000))
;;  1000.000369924366

(defn square [x] (* x x))

(defn abs
 "The absolute-value procedure"
 [x]
 (cond (> x 0) x
       (= x 0) 0
       (< x 0) (- x)))

(defn good-enough?
 [guess, x]
 (< (abs (- (square guess) x)) 0.001))

(defn average [x y]
 (/ (+ x y) 2))

(defn improve [guess x]
 (average guess (/ x guess)))


(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))