The fast Walsh Hadamard transform (WHT) is done using patterns of addition and subtractions.
That means it is extremely fast and also the central limit theorem applies. If you transform an array of random numbers the output numbers will have a Gaussian distribution (aka the Normal distribution).
The O'Connor transform is a series of WHT's and random permutations (with optional random sign flipping) that converts arbitrary numerical data into data with a Gaussian distribution. It has a lot of uses for Compressive Sensing, Genetic algorithms, Neural Nets and Random projections.
I have extremely fast code here:Interesting Source Code
There are also some other projects there that are very interesting.