Repeating values for pcg64_k32_fast

[BJTor]

After quite a bit of testing I've found that the "fast" versions of the extended pcg generators give enough of a performance boost to be worthwhile. However I am finding that I see repeated value sequences well below the stated period of the generator. I suspect this is my ignorance and I'm setting something up wrong, but for pcg64_k32_fast, advancing the state by 2^126 seems to get us back to an identical state and corresponding identical samples. Example code is below and produces the following output:

% ./pcg64ext_test
Expected period = 2^2174
Advance RNG2 by 8.50706e+37 (2^126) steps.
Sample from RNG1 = 16965488128385771295
Sample from RNG2 = 16965488128385771295

Am I missing something here?

---

pcg64ext_test.cpp:

#include "pcg_random.hpp"

typedef pcg64_k32_fast RngType; // 2174-bit state, 64-bit samples

int main() {
    // Create two copies of the same generator
    std::cout << "Expected period = 2^" << RngType::period_pow2() << std::endl;
    RngType rng1;
    RngType rng2 = rng1;

    // Tell the second generator to advance by 2^126 steps. This should be well
    // within the expected period (2^2174) so should not repeat.
    RngType::state_type numSteps(1);
    numSteps = numSteps << 126;
    std::cout << "Advance RNG2 by " << double(numSteps) << " (2^126) steps." << std::endl;
    rng2.advance(numSteps);

    std::cout << "Sample from RNG1 = " << rng1() << std::endl;
    std::cout << "Sample from RNG2 = " << rng2() << std::endl;
}

[bhaller]

That shows one identical sample; but does it continue to repeat the same sequence thereafter?

[BJTor]

Yes, the samples then seem to repeat (I checked the next 10 or so). Also, displaying the generator state seems to show that the state is identical.

Stepping through the code I had expected that when the standard state was exhausted (i.e. advance or sampling overflows the uint128) then the extended state would be updated. That doesn't seem to happen. It looks like both "can_tick" and "can_tock" are defined false and so "update_table" is never called. (I'm assuming that is the thing that would update the extended state, but I'm still trying to learn the code so could be way off the mark.)

[BJTor]

I also verified that if I skip RNG2 forward just less than 2^126 samples then start sampling, the repetition starts at exactly 2^126 samples. This corresponds to exhausting the state since as an MCG it has two unusable bits of state.