From 8839af0454b86a84af00b782bf22de82c67525e3 Mon Sep 17 00:00:00 2001
From: rsiddharth <s@ricketyspace.net>
Date: Sat, 3 Mar 2018 18:09:53 +0000
Subject: net: Add (net ricketyspace sicp one forty).

* net/ricketyspace/sicp/one/forty.scm: New file.
---
 net/ricketyspace/sicp/one/forty.scm | 37 +++++++++++++++++++++++++++++++++++++
 1 file changed, 37 insertions(+)
 create mode 100644 net/ricketyspace/sicp/one/forty.scm

diff --git a/net/ricketyspace/sicp/one/forty.scm b/net/ricketyspace/sicp/one/forty.scm
new file mode 100644
index 0000000..34d0a26
--- /dev/null
+++ b/net/ricketyspace/sicp/one/forty.scm
@@ -0,0 +1,37 @@
+;;;; Under Creative Commons Attribution-ShareAlike 4.0
+;;;; International. See
+;;;; <https://creativecommons.org/licenses/by-sa/4.0/>.
+
+(define-module (net ricketyspace sicp one forty)
+  #:export (forty cubic))
+
+(define tolerance 0.000000000001)
+(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 dx 0.00001)
+(define (deriv g)
+  (lambda (x)
+    (/ (- (g (+ x dx)) (g x))
+       dx)))
+
+(define (newton-transform g)
+  (lambda (x)
+    (- x (/ (g x) ((deriv g) x)))))
+
+(define (newtons-method g guess)
+  (fixed-point (newton-transform g) guess))
+
+(define (cubic a b c)
+  (lambda (x)
+    (+ (expt x 3) (* a (expt x 2)) (* b x) c)))
+
+(define (forty a b c)
+  (newtons-method (cubic a b c) 1))
-- 
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