Sqrt by Newton's method.

sqrt_demo.lisp

;; Oh yeah.
;;
;;; Code:

(defun (sqrt-iter guess x)
  (if (good-enough? guess x)
      guess
    (sqrt-iter (improve guess x)
	       x)))
(defun (improve guess x)
  (average guess (/ x guess)))

(defun (average x y)
  (/ (+ x y) 2))

(defun (good-enough? guess x)
  (< (abs (- (square guess) x)) 0.001))

(defun (sqrt x)
  (sqrt-iter 1.0 x))

;; Running Baby!
(sqrt 9)

(sqrt (+ 100 37))

(sqrt (+ (sqrt 2) (sqrt 3)))

(square (sqrt 1000))

SqrtDemo.java

import static java.lang.Math.*;
import static java.lang.System.out;

public class SqrtDemo {
	
    public static void main(String... args) {
	out.printf("%.15f\n", sqrt (9));
        out.printf("%.15f\n", sqrt (100 + 37));
        out.printf("%.15f\n", sqrt (sqrt (2) + sqrt (3)));
        out.printf("%.15f\n", pow  (sqrt (1000), 2));
    }

    private static double sqrt_iter(double guess, double x) {
	if (good_enough (guess, x)) return guess;
        return sqrt_iter (improve (guess, x), x);
    }

    private static double improve(double guess, double x) {
	return average(guess, (x / guess));
    }

    private static double average(double x, double y) {
	return (x + y) / 2;
    }

    private static boolean good_enough(double guess, double x) {
	return (abs (pow (guess, 2.0) - x) < 0.001) ? true : false;
    }

    private static double sqrt(double x) {
    	return sqrt_iter(1.0, x);
    }
}