The first algorithm is to make use of the central limit theorem. While the method described above is quite simple to program, it does a poor job of generating random deviates in the tails of the distribution. There are far better ways to do accomplish this task. If the inverse is an accurate one, then that number will be a pseudo-random normal deviate. This method will be as fast and as good as is the approximation you choose for the inverse of the cumulative normal.
Lets start with a simple case, just a bivariate normal.
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