1 665c255d 2023-08-04 jrmu (defvar *tolerance* 0.00001)
2 665c255d 2023-08-04 jrmu (defun fixed-point (f first-guess)
4 665c255d 2023-08-04 jrmu (close-enough? (v1 v2)
5 665c255d 2023-08-04 jrmu (< (abs (- v1 v2)) *tolerance*))
7 665c255d 2023-08-04 jrmu (let ((next (funcall f guess)))
8 665c255d 2023-08-04 jrmu (if (close-enough? guess next)
10 665c255d 2023-08-04 jrmu (try next)))))
11 665c255d 2023-08-04 jrmu (try first-guess)))
12 665c255d 2023-08-04 jrmu (defun average (a b)
13 665c255d 2023-08-04 jrmu (/ (+ a b) 2))
15 665c255d 2023-08-04 jrmu (defun dampen-sqrt (x)
16 665c255d 2023-08-04 jrmu (fixed-point
18 665c255d 2023-08-04 jrmu (average y (/ x y)))
21 665c255d 2023-08-04 jrmu (defun dampen-root (x n)
22 665c255d 2023-08-04 jrmu (fixed-point
24 665c255d 2023-08-04 jrmu (average y (/ x (expt y (1- n)))))