TL; DR: #include <ext/random> and use __gnu_cxx::sfmt19937 just as std::mt19937.

Hi all,

I'm here to share a thing that seems not that well-known in the whole community.

There is a SIMD-oriented Fast Mersenne Twister (SFMT) implementation in GCC's library.
As its name suggested, it's a faster MT-like PRNG implementation based on SIMD.
SFMT is not exactly MT, but it shares some similarities and is much faster than the traditional MT.
If you are interested in more details about it, you could check this paper.

I test the two codes below in the Codeforces' custom test using GNU G++20 11.2.0 (64 bit, winlibs).
The result looks good.

#include <bits/stdc++.h>
#include <ext/random>
using namespace std;

using RNG = __gnu_cxx::sfmt19937;
decltype(RNG()()) x;

int n = 1'000'000'000;

int main() {
    cin.tie(nullptr)->sync_with_stdio(false);
    RNG rnd(1234);
    for (int i = 0; i < n; ++i)
        x = rnd();
    cout << rnd() << '\n';
    return 0;
}

#include <bits/stdc++.h>
using namespace std;

using RNG = mt19937;
decltype(RNG()()) x;

int n = 1'000'000'000;

int main() {
    cin.tie(nullptr)->sync_with_stdio(false);
    RNG rnd(1234);
    for (int i = 0; i < n; ++i)
        x = rnd();
    cout << rnd() << '\n';
    return 0;
}

p.s. there's also __gnu_cxx::sfmt19937_64 if you want a 64-bit PRNG.