Added recipe for fast inverse square root.

Author: JasonGiedymin

chapters/math/fast-inv-square.md

@@ -0,0 +1,117 @@
+---
+layout: recipe
+title: Fast Inverse Square Root
+chapter: Math
+---
+## Problem
+
+You would like to calculate a the inverse square root[5] of a number quickly.
+
+## Solution
+Appearing in the Quake III Arena source code[1], this strange algorithm uses
+integer operations along with a 'magic number' to calculate floating point
+approximation values of inverse square roots.
+
+In this CoffeeScript variant I supply the original classic, and newer optimal
+32 bit magic numbers found by Chris Lomont[2]. Also supplied is the 64-bit
+sized magic number.
+
+Another feature included is the ability to alter the level of precision.
+This is done by controling the number of iterations for performing Newton's
+method[3].
+
+Depending on the machine and level of percision this algorithm may still
+provide performance increases over the classic.
+
+To run this, compile the script with coffee:
+    coffee -c <this script>.coffee
+
+Then copy & paste the compiled js code in to the JavaSript console of your
+browser.
+
+Note: You will need a browser which supports typed-arrays[4].
+
+References: 
+* [1] [ftp://ftp.idsoftware.com/idstuff/source/quake3-1.32b-source.zip](ftp://ftp.idsoftware.com/idstuff/source/quake3-1.32b-source.zip)
+* [2] [http://www.lomont.org/Math/Papers/2003/InvSqrt.pdf](http://www.lomont.org/Math/Papers/2003/InvSqrt.pdf)
+* [3] [http://en.wikipedia.org/wiki/Newton%27s_method](http://en.wikipedia.org/wiki/Newton%27s_method)
+* [4] [https://developer.mozilla.org/en/JavaScript_typed_arrays](https://developer.mozilla.org/en/JavaScript_typed_arrays)
+* [5] [http://en.wikipedia.org/wiki/Fast_inverse_square_root](http://en.wikipedia.org/wiki/Fast_inverse_square_root)
+
+This code is in gist form here:
+[https://gist.github.com/1036533](https://gist.github.com/1036533)
+
+{% highlight coffeescript %}
+###
+
+Author: Jason Giedymin <jasong _a_t_ apache -dot- org>
+        http://www.jasongiedymin.com
+        https://github.com/JasonGiedymin
+
+Appearing in the Quake III Arena source code[1], this strange algorithm uses
+integer operations along with a 'magic number' to calculate floating point
+approximation values of inverse square roots.
+
+In this CoffeeScript variant I supply the original classic, and newer optimal
+32 bit magic numbers found by Chris Lomont[2]. Also supplied is the 64-bit
+sized magic number.
+
+Another feature included is the ability to alter the level of precision.
+This is done by controling the number of iterations for performing Newton's
+method[3].
+
+Depending on the machine and level of percision this algorithm may still
+provide performance increases over the classic.
+
+To run this, compile the script with coffee:
+    coffee -c <this script>.coffee
+
+Then copy & paste the compiled js code in to the JavaSript console of your
+browser.
+
+Note: You will need a browser which supports typed-arrays[4].
+
+References: 
+[1] ftp://ftp.idsoftware.com/idstuff/source/quake3-1.32b-source.zip
+[2] http://www.lomont.org/Math/Papers/2003/InvSqrt.pdf
+[3] http://en.wikipedia.org/wiki/Newton%27s_method
+[4] https://developer.mozilla.org/en/JavaScript_typed_arrays
+
+###
+
+approx_const_quake_32 = 0x5f3759df # See [1]
+approx_const_32 = 0x5f375a86 # See [2]
+approx_const_64 = 0x5fe6eb50c7aa19f9 # See [2]
+
+fastInvSqrt_typed = (n, precision=1) ->
+	# Using typed arrays. Right now only works in browsers.
+	# Node.JS version coming soon.
+
+    y = new Float32Array(1)
+    i = new Int32Array(y.buffer)
+
+    y[0] = n
+    i[0] = 0x5f375a86 - (i[0] >> 1)
+    
+    for iter in [1...precision]
+        y[0] = y[0] * (1.5 - ((n * 0.5) * y[0] * y[0]))
+    
+    return y[0]
+
+### Sample single runs ###
+testSingle = () ->
+    example_n = 10
+
+    console.log("Fast InvSqrt of 10, precision 1: #{fastInvSqrt_typed(example_n)}")
+    console.log("Fast InvSqrt of 10, precision 5: #{fastInvSqrt_typed(example_n, 5)}")
+    console.log("Fast InvSqrt of 10, precision 10: #{fastInvSqrt_typed(example_n, 10)}")
+    console.log("Fast InvSqrt of 10, precision 20: #{fastInvSqrt_typed(example_n, 20)}")
+    console.log("Classic of 10: #{1.0 / Math.sqrt(example_n)}")
+
+testSingle()
+
+{% endhighlight %}
+
+## Discussion
+
+Questions?