1 (defvar tolerance 0.00001)
2 (defun fixed-point (f first-guess)
3   (labels (
4 	   (close-enough? (v1 v2)
5 			  (< (abs (- v1 v2)) tolerance))
6 	   (try (guess)
7 		(let ((next (funcall f guess)))
8 		  (if (close-enough? guess next)
9 		      next
10 		    (try next)))))
11 	  (try first-guess)))
12 (defun average (a b)
13   (/ (+ a b) 2))
14 (defun dampen-sqrt (x)
15   (fixed-point
16    (lambda (y)
17      (average y (/ x y)))
18    1.0))
19 
20 (fixed-point (lambda (x) (1+ (/1 x))) 1.0)
21 
22 (defvar tolerance 0.00001)
23 (defun fixed-point (f first-guess)
24   (labels (
25 	   (close-enough? (v1 v2)
26 			  (< (abs (- v1 v2)) tolerance))
27 	   (try (guess)
28 		(format t "Trying ~F~%" guess)
29 		(let ((next (funcall f guess)))
30 		  (if (close-enough? guess next)
31 		      next
32 		    (try next)))))
33 	  (try first-guess)))
34 (defun average (a b)
35   (/ (+ a b) 2))
36 (defun xx (x)
37   (/ (log 1000) (log x)))
38 (defun dampen-xx (x)
39   (average x (xx x)))
40 (print (fixed-point #'xx 2.0))
41 (print (fixed-point #'dampen-xx 2.0))
42