1 665c255d 2023-08-04 jrmu (defun iterative-improve (good-enough? improve)
 2 665c255d 2023-08-04 jrmu   (lambda (first-guess)
 3 665c255d 2023-08-04 jrmu     (labels ((improve-iter (guess)
 4 665c255d 2023-08-04 jrmu 	       (let ((improved-guess (funcall improve guess)))
 5 665c255d 2023-08-04 jrmu 		 (if (funcall good-enough? guess improved-guess)
 6 665c255d 2023-08-04 jrmu 		     improved-guess
 7 665c255d 2023-08-04 jrmu 		     (improve-iter improved-guess)))))
 8 665c255d 2023-08-04 jrmu 	     (improve-iter first-guess))))
 9 665c255d 2023-08-04 jrmu (defun improved-sqrt (num)
10 665c255d 2023-08-04 jrmu   (funcall (iterative-improve
11 665c255d 2023-08-04 jrmu 	    (lambda (x y)
12 665c255d 2023-08-04 jrmu 	      (let ((ratio (/ x y)))
13 665c255d 2023-08-04 jrmu 		(and (< ratio 1.001) (> ratio 0.999))))
14 665c255d 2023-08-04 jrmu 	    (lambda (guess)
15 665c255d 2023-08-04 jrmu 	      (average guess (/ num guess))))
16 665c255d 2023-08-04 jrmu 	   1.0))
17 665c255d 2023-08-04 jrmu (defvar *tolerance* 0.00001)
18 665c255d 2023-08-04 jrmu (defun improved-fixed-point (f first-guess)
19 665c255d 2023-08-04 jrmu   (funcall (iterative-improve
20 665c255d 2023-08-04 jrmu 	    (lambda (x y)
21 665c255d 2023-08-04 jrmu 	      (< (abs (- x y)) *tolerance*))
22 665c255d 2023-08-04 jrmu 	    (lambda (guess)
23 665c255d 2023-08-04 jrmu 	      (funcall f guess)))
24 665c255d 2023-08-04 jrmu 	   first-guess))
25 665c255d 2023-08-04 jrmu