Merge pull request coffeescript-cookbook#19 from JasonGiedymin/master

Added section on a faster Fibonacci routine.

Author: peterhellberg

chapters/math/fast-fibonacci.textile

@@ -0,0 +1,103 @@
+---
+layout: recipe
+title: Converting Radians and Degrees
+chapter: Math
+---
+
+h2. Problem
+
+You would like to calculate a number N in the Fibonacci sequence but want
+to do it quickly.
+
+h2. Solution
+
+The following solution (which can still be improved on) was originally
+talked about on Robin Houston's blog.
+
+Here are a few links talking about the algorithm and ways to improve it:
+# <a href="http://bosker.wordpress.com/2011/04/29/the-worst-algorithm-in-the-world/">http://bosker.wordpress.com/2011/04/29/the-worst-algorithm-in-the-world/</a>
+# <a href="http://www.math.rutgers.edu/~erowland/fibonacci.html">http://www.math.rutgers.edu/~erowland/fibonacci.html</a>
+# <a href="http://jsfromhell.com/classes/bignumber">http://jsfromhell.com/classes/bignumber</a>
+# <a href="http://www.math.rutgers.edu/~erowland/fibonacci.html">http://www.math.rutgers.edu/~erowland/fibonacci.html</a>
+# <a href="http://bigintegers.blogspot.com/2010/11/square-division-power-square-root.html">http://bigintegers.blogspot.com/2010/11/square-division-power-square-root.html</a>
+# <a href="http://bugs.python.org/issue3451">http://bugs.python.org/issue3451</a>
+
+This code is in gist form here:
+<a href="https://gist.github.com/1032685">https://gist.github.com/1032685</a>
+
+{% highlight coffeescript %}
+### 
+Author: Jason Giedymin <jasong _a_t_ apache -dot- org>
+        http://www.jasongiedymin.com
+        https://github.com/JasonGiedymin
+
+This CoffeeScript Javascript Fast Fibonacci code is 
+based on the python code from Robin Houston's blog.
+See below links.
+
+A few things I want to introduce in time are implementions of 
+Newtonian, Burnikel / Ziegler, and Binet's algorithms on top
+of a Big Number framework.
+
+Todo: 
+- https://github.com/substack/node-bigint
+- BZ and Newton mods.
+- Timing
+
+
+###
+
+MAXIMUM_JS_FIB_N = 1476
+
+fib_bits = (n) ->
+	#Represent an integer as an array of binary digits.
+
+	bits = []
+	while n > 0
+    	[n, bit] = divmodBasic(n, 2)
+    	bits.push(bit)
+
+  	bits.reverse()
+  	return bits
+
+fibFast = (n) ->
+	#Fast Fibonacci
+
+	if n < 0
+		console.log "Choose an number >= 0"
+		return
+
+	[a, b, c] = [1, 0, 1]
+
+	for bit in fib_bits(n)
+	    if bit
+	    	[a, b] = [(a+c)*b, b*b + c*c]
+	    else
+	    	[a, b] = [a*a + b*b, (a+c)*b]
+
+	    c = a + b
+	  	return b
+
+divmodNewton = (x, y) ->
+	throw new Error "Method not yet implemented yet."
+
+divmodBZ = () ->
+	throw new Error "Method not yet implemented yet."
+
+divmodBasic = (x, y) ->
+	###
+	Absolutely nothing special here. Maybe later versions will be Newtonian or
+	Burnikel / Ziegler _if_ possible...
+	###
+
+	return [(q = Math.floor(x/y)), (r = if x < y then x else x % y)]
+
+start = (new Date).getTime();
+calc_value = fibFast(MAXIMUM_JS_FIB_N)
+diff = (new Date).getTime() - start;
+console.log("[#{calc_value}] took #{diff} ms.")
+{% endhighlight %}
+
+h2. Discussion
+
+Questions?