miller_rabin
(src/math/miller_rabin.hpp)

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• Last update: 2024-11-09 02:03:28+09:00
• Include: #include "src/math/miller_rabin.hpp"

miller_rabin

bool miller_rabin(ll n)

整数 $n$ が素数であるか判定します．
$n$ が非正の場合は false を返します．

計算量

• $O(\log n)$

Depends on

• template (src/template/template.hpp)

Verified with

• verify/library_checker/number_theory/primality_test.test.cpp
• verify/unit_test/math/lucas.test.cpp

Code

#pragma once
#include "../template/template.hpp"
constexpr __int128_t pow_mod_128(__int128_t x, __int128_t n, const __int128_t mod) {
    assert(n >= 0 and mod >= 1);
    x %= mod;
    if(x < 0) x += mod;
    __int128_t res = 1;
    while(n > 0) {
        if(n & 1) res = res * x % mod;
        x = x * x % mod;
        n >>= 1;
    }
    return res;
}
constexpr bool miller_rabin(const long long n) {
    if(n <= 2) return n == 2;
    if(n % 2 == 0) return false;
    constexpr long long bases[7] = {2, 325, 9375, 28178, 450775, 9780504, 1795265022};
    long long d = n - 1;
    while(d % 2 == 0) d /= 2;
    for(const long long base : bases) {
        if(base % n == 0) continue;
        long long t = d;
        long long y = pow_mod_128(base, t, n);
        while(t != n - 1 and y != 1 and y != n - 1) {
            y = (__int128_t)y * y % n;
            t *= 2;
        }
        if(y != n - 1 and t % 2 == 0) return false;
    }
    return true;
}

#line 2 "src/template/template.hpp"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using P = pair<long long, long long>;
#define rep(i, a, b) for(long long i = (a); i < (b); ++i)
#define rrep(i, a, b) for(long long i = (a); i >= (b); --i)
constexpr long long inf = 4e18;
struct SetupIO {
    SetupIO() {
        ios::sync_with_stdio(0);
        cin.tie(0);
        cout << fixed << setprecision(30);
    }
} setup_io;
#line 3 "src/math/miller_rabin.hpp"
constexpr __int128_t pow_mod_128(__int128_t x, __int128_t n, const __int128_t mod) {
    assert(n >= 0 and mod >= 1);
    x %= mod;
    if(x < 0) x += mod;
    __int128_t res = 1;
    while(n > 0) {
        if(n & 1) res = res * x % mod;
        x = x * x % mod;
        n >>= 1;
    }
    return res;
}
constexpr bool miller_rabin(const long long n) {
    if(n <= 2) return n == 2;
    if(n % 2 == 0) return false;
    constexpr long long bases[7] = {2, 325, 9375, 28178, 450775, 9780504, 1795265022};
    long long d = n - 1;
    while(d % 2 == 0) d /= 2;
    for(const long long base : bases) {
        if(base % n == 0) continue;
        long long t = d;
        long long y = pow_mod_128(base, t, n);
        while(t != n - 1 and y != 1 and y != n - 1) {
            y = (__int128_t)y * y % n;
            t *= 2;
        }
        if(y != n - 1 and t % 2 == 0) return false;
    }
    return true;
}

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