src/math/prime.hpp

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• Last update: 2020-05-08 21:35:33+09:00
• Include: #include "src/math/prime.hpp"

Code

bool is_prime(ll n) {
    if (n <= 1) return false;
    if (n == 2) return true;
    if (n % 2 == 0) return false;
    ll d = n - 1;
    while (d % 2 == 0) d /= 2;
    for (ll a : {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}) {
        if (n <= a) break;
        ll t = d;
        ll y = pow_mod<__int128_t>(a, t, n);  // over
        while (t != n - 1 && y != 1 && y != n - 1) {
            y = __int128_t(y) * y % n;  // flow
            t <<= 1;
        }
        if (y != n - 1 && t % 2 == 0) {
            return false;
        }
    }
    return true;
}

ll pollard_single(ll n) {
    auto f = [&](ll x) { return (__int128_t(x) * x + 1) % n; };
    if (is_prime(n)) return n;
    if (n % 2 == 0) return 2;
    ll st = 0;
    while (true) {
        st++;
        ll x = st, y = f(x);
        while (true) {
            ll p = gcd((y - x + n), n);
            if (p == 0 || p == n) break;
            if (p != 1) return p;
            x = f(x);
            y = f(f(y));
        }
    }
}

V<ll> pollard(ll n) {
    if (n == 1) return {};
    ll x = pollard_single(n);
    if (x == n) return {x};
    V<ll> le = pollard(x);
    V<ll> ri = pollard(n / x);
    le.insert(le.end(), ri.begin(), ri.end());
    return le;
}

ll primitive_root(ll p) {
    auto v = pollard(p - 1);
    while (true) {
        ll g = global_gen.uniform(1LL, p - 1);  //[1, p-1]
        bool ok = true;
        for (auto d : v) {
            ll f = (p - 1) / d;
            if (pow_mod<__int128_t>(g, f, p) == 1) {
                ok = false;
                break;
            }
        }
        if (ok) return g;
    }
}

#line 1 "src/math/prime.hpp"
bool is_prime(ll n) {
    if (n <= 1) return false;
    if (n == 2) return true;
    if (n % 2 == 0) return false;
    ll d = n - 1;
    while (d % 2 == 0) d /= 2;
    for (ll a : {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}) {
        if (n <= a) break;
        ll t = d;
        ll y = pow_mod<__int128_t>(a, t, n);  // over
        while (t != n - 1 && y != 1 && y != n - 1) {
            y = __int128_t(y) * y % n;  // flow
            t <<= 1;
        }
        if (y != n - 1 && t % 2 == 0) {
            return false;
        }
    }
    return true;
}

ll pollard_single(ll n) {
    auto f = [&](ll x) { return (__int128_t(x) * x + 1) % n; };
    if (is_prime(n)) return n;
    if (n % 2 == 0) return 2;
    ll st = 0;
    while (true) {
        st++;
        ll x = st, y = f(x);
        while (true) {
            ll p = gcd((y - x + n), n);
            if (p == 0 || p == n) break;
            if (p != 1) return p;
            x = f(x);
            y = f(f(y));
        }
    }
}

V<ll> pollard(ll n) {
    if (n == 1) return {};
    ll x = pollard_single(n);
    if (x == n) return {x};
    V<ll> le = pollard(x);
    V<ll> ri = pollard(n / x);
    le.insert(le.end(), ri.begin(), ri.end());
    return le;
}

ll primitive_root(ll p) {
    auto v = pollard(p - 1);
    while (true) {
        ll g = global_gen.uniform(1LL, p - 1);  //[1, p-1]
        bool ok = true;
        for (auto d : v) {
            ll f = (p - 1) / d;
            if (pow_mod<__int128_t>(g, f, p) == 1) {
                ok = false;
                break;
            }
        }
        if (ok) return g;
    }
}

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