diff options
| -rw-r--r-- | net/ricketyspace/sicp/one/fortyfive.scm | 58 |
1 files changed, 58 insertions, 0 deletions
diff --git a/net/ricketyspace/sicp/one/fortyfive.scm b/net/ricketyspace/sicp/one/fortyfive.scm new file mode 100644 index 0000000..4e6f9dd --- /dev/null +++ b/net/ricketyspace/sicp/one/fortyfive.scm @@ -0,0 +1,58 @@ +;;;; Under Creative Commons Attribution-ShareAlike 4.0 +;;;; International. See +;;;; <https://creativecommons.org/licenses/by-sa/4.0/>. +;;;; + +(define-module (net ricketyspace sicp one fortyfive) + #:use-module (net ricketyspace sicp one fortythree) + #:export (nth-root)) + +(define tolerance 0.00001) +(define (fixed-point f first-guess) + (define (close-enough? v1 v2) + (< (abs (- v1 v2)) tolerance)) + (define (try guess) + (let ((next (f guess))) + (if (close-enough? guess next) + next + (try next)))) + (try first-guess)) + +(define (average a b) (/ (+ a b) 2.0)) + +(define (average-damp f) + (lambda (x) (average x (f x)))) + +(define (log2 x) (/ (log x) (log 2.0))) + +(define (nth-root n x) + (let ((avg-dmp (repeated average-damp (floor (log2 n)))) + (func (lambda (y) (/ x (expt y (1- n)))))) + (fixed-point (avg-dmp func) 1.0))) + +;;; GNU Guile REPL +;;; +;;; scheme@(guile-user)> ,use (net ricketyspace sicp one fortyfive) +;;; scheme@(guile-user)> (nth-root 4 (expt 9 4)) +;;; $68 = 9.0 +;;; scheme@(guile-user)> (nth-root 10 (expt 9 10)) +;;; $69 = 9.000001442413728 +;;; scheme@(guile-user)> (nth-root 15 (expt 9 15)) +;;; $70 = 8.999995679416626 +;;; scheme@(guile-user)> (nth-root 16 (expt 9 16)) +;;; $71 = 9.00000000000018 +;;; scheme@(guile-user)> (nth-root 31 (expt 9 31)) +;;; $72 = 9.000004691148337 +;;; scheme@(guile-user)> (nth-root 32 (expt 9 32)) +;;; $73 = 9.0 +;;; scheme@(guile-user)> (nth-root 63 (expt 9 63)) +;;; $74 = 8.999995131856686 +;;; scheme@(guile-user)> (nth-root 64 (expt 9 64)) +;;; $75 = 9.000000000000114 +;;; scheme@(guile-user)> (nth-root 128 (expt 9 128)) +;;; $76 = 9.000000000000083 +;;; scheme@(guile-user)> (nth-root 255 (expt 9 255)) +;;; $77 = 9.00000496391279 +;;; scheme@(guile-user)> (nth-root 256 (expt 9 256)) +;;; $78 = 9.000000000000018 +;;; |