From 70afc89a72a21e3dc41a1072d6ba79bc5380e3ec Mon Sep 17 00:00:00 2001
From: rsiddharth <s@ricketyspace.net>
Date: Sun, 8 Apr 2018 01:28:32 +0000
Subject: net: Add (net ricketyspace sicp one fortyfive).

* net/ricketyspace/sicp/one/fortyfive.scm: New file.
---
 net/ricketyspace/sicp/one/fortyfive.scm | 58 +++++++++++++++++++++++++++++++++
 1 file changed, 58 insertions(+)
 create mode 100644 net/ricketyspace/sicp/one/fortyfive.scm

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
+;;;
-- 
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