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Fri Mar 15 20:56:46 EDT 2013

Normalization: Fast inverse square root

Some nice bit twiddling tricks[1].

Made me wonder if I should use N-R for the normalization problem..

To compute 1 / sqrt(q) where r^2 = c^2 + s^2 ~= 1, it might be good
enough to just use the N-R update for f(x) = 1/x^2 - r^2
 
   u(x) = 1/2 x * (3 - r^2 x^2)

Since x will be close to one, this gives the series of estimates:

x0 = 1
x1 = (3 - r^2) / 2    

Here x1 is actally the same as 1st order Taylor approx of 
1 / (1 + x)^1/2  with  1 + x = r^2 from [2].



[1] http://en.wikipedia.org/wiki/Fast_inverse_square_root
[2] entry://20130309-182723




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