LCG? Really? Mersenne Twister originally became the cool kid because LCG's are so bad. Well, at least your standard issue `rand(3)` implementations tend(ed) to be.
Yes, 128-bit LCGs with well-chosen constant(s) are fast as hell and pass all statistical tests (you don't even need the addition factor, a good multiplier works too ("MCG")):
I'm less sure about the terminology, but shouldn't we distinguish truncated LCGs from untruncated (plain) LCGs? It is clear that untruncated LCGs have very predictable lower bits by the definition and don't have "perfectly good statistical properties" by its own (it would have been fine if untruncated LCGs weren't wildly popular though). One of PCG's biggest contributions to me is a distinct name given to LCG plus tampering so that we can avoid the ambiguous "LCG" label.
Yeah, I’d think if I had to sit down and write a definition for LCG, it would just be X_(n+1) = (a X_n + c) mod m. Since we’ve discovered “high bits good, low bits bad”, we can create generators that are based on LCGs but either throw away the low bits or mix them in. I don’t know if I’d call them LCGs, though.
