Which C++ random number engines have a O(1) discard function?

Question

Since C++11 there are a number of std random number engines. One of the member functions they implement is void discard(int long long z) which skips over z randomly

Answer 1

Well, if you use precomputed jump points, O(1) will work for each and every RNG in existence. Please, remember, that there are algorithm which might have better than O(z), but not O(1) - say, O(log₂ z).

If we're talking about jump to arbitrary point, things get interesting. For example, for linear congruential generator there is known O(log₂ z) jump ahead algorithm, based upon paper by F. Brown, "Random Number Generation with Arbitrary Stride," Trans. Am. Nucl. Soc. (Nov. 1994). Code example is here.

There is LCG RNG in the C++11 standard, not sure how fast jump ahead is done in particular implementation (http://en.cppreference.com/w/cpp/numeric/random/linear_congruential_engine)

PCG family of RNGs share the same property, I believe