Not only that, but if you were to write this in (say) Java, which uses a linear congruential random number generator, doing it this way would probably be even f

Not only that, but if you were to write this in (say) Java, which uses a linear congruential random number generator, doing it this way would probably be even faster due to the higher quality random numbers. The least significant bits on a linear congruential generator aren't terribly random.