Squares RNG is a counter-based version of Middle Square Weyl Sequence RNG.  Counter-based RNGs have no state and are well suited to parallel processing.  There is no need to maintain or initialize a state.  Squares is faster than Middle Square Weyl Sequence on an Intel Core i7-9700.  Processing speed is, of course, processor dependent and may vary on other processors.  If you are currently using Middle Square Weyl Sequence, you might consider Squares.  It produces data of equivalent quality and is easier to use since there is no state.

This generator passes BigCrush and PractRand.