結果

問題 No.3030 ミラー・ラビン素数判定法のテスト
ユーザー 👑 MizarMizar
提出日時 2022-08-27 20:20:42
言語 C++17
(gcc 13.2.0 + boost 1.83.0)
結果
AC  
実行時間 32 ms / 9,973 ms
コード長 5,733 bytes
コンパイル時間 187 ms
コンパイル使用メモリ 33,104 KB
実行使用メモリ 4,380 KB
最終ジャッジ日時 2023-08-10 16:39:34
合計ジャッジ時間 953 ms
ジャッジサーバーID
（参考情報） 		judge13 / judge12
このコードへのチャレンジ（β）

テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 1 ms
4,376 KB
testcase_01 AC 2 ms
4,380 KB
testcase_02 AC 1 ms
4,376 KB
testcase_03 AC 1 ms
4,380 KB
testcase_04 AC 20 ms
4,380 KB
testcase_05 AC 19 ms
4,380 KB
testcase_06 AC 12 ms
4,376 KB
testcase_07 AC 11 ms
4,380 KB
testcase_08 AC 11 ms
4,380 KB
testcase_09 AC 32 ms
4,380 KB
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ソースコード

diff # 

#include <cstdbool>
#include <cstdint>
#include <cstdio>
class U64Mont {
private:
    static uint64_t _ni(uint64_t n) { // n * ni == 1 (mod 2**64)
        // // n is odd number, n = 2*k+1, n >= 1, n < 2**64, k is non-negative integer, k >= 0, k < 2**63
        // ni0 := n; // = 2*k+1 = (1+(2**2)*((k*(k+1))**1))/(2*k+1)
        uint64_t ni = n;
        // ni1 := ni0 * (2 - (n * ni0)); // = (1-(2**4)*((k*(k+1))**2))/(2*k+1)
        // ni2 := ni1 * (2 - (n * ni1)); // = (1-(2**8)*((k*(k+1))**4))/(2*k+1)
        // ni3 := ni2 * (2 - (n * ni2)); // = (1-(2**16)*((k*(k+1))**8))/(2*k+1)
        // ni4 := ni3 * (2 - (n * ni3)); // = (1-(2**32)*((k*(k+1))**16))/(2*k+1)
        // ni5 := ni4 * (2 - (n * ni4)); // = (1-(2**64)*((k*(k+1))**32))/(2*k+1)
        // // (n * ni5) mod 2**64 = ((2*k+1) * ni5) mod 2**64 = 1 mod 2**64
        for (int i = 0; i < 5; ++i) {
            ni = ni * (2 - n * ni);
        }
        return ni;
    }
    static uint64_t _n1(uint64_t n) { // == n - 1
        return n - 1;
    }
    static uint64_t _nh(uint64_t n) { // == (n + 1) / 2
        return (n >> 1) + 1;
    }
    static uint64_t _r(uint64_t n) { // == 2**64 (mod n)
        return (-n) % n;
    }
    static uint64_t _rn(uint64_t n) { // == -(2**64) (mod n)
        return n - _r(n);
    }
    static uint64_t _r2(uint64_t n) { // == 2**128 (mod n)
        return (uint64_t)((-((__uint128_t)n)) % ((__uint128_t)n));
    }
    static uint32_t _k(uint64_t n) { // == trailing_zeros(n1)
        // https://gcc.gnu.org/onlinedocs/gcc/Other-Builtins.html#Other-Builtins
        return __builtin_ctzll(n - 1);
    }
    static uint64_t _d(uint64_t n) { // == n1 >> k // n == 2**k * d + 1
        return (n - 1) >> _k(n);
    }
public:
    const uint64_t n; // == n
    const uint64_t ni; // n * ni == 1 (mod 2**64)
    const uint64_t n1; // == n - 1
    const uint64_t nh; // == (n + 1) / 2
    const uint64_t r; // == 2**64 (mod n)
    const uint64_t rn; // == -(2**64) (mod n)
    const uint64_t r2; // == 2**128 (mod n)
    const uint64_t d; // == n1 >> k // n == 2**k * d + 1
    const uint32_t k; // == trailing_zeros(n1)
    U64Mont(uint64_t n)
        : n(n), ni(_ni(n)), n1(_n1(n)), nh(_nh(n)), r(_r(n)), rn(_rn(n)), r2(_r2(n)), d(_d(n)), k(_k(n)) {}
    uint64_t add(uint64_t a, uint64_t b) {
        // add(a, b) == a + b (mod n)
        unsigned long long t, u;
        // https://gcc.gnu.org/onlinedocs/gcc/Integer-Overflow-Builtins.html#Integer-Overflow-Builtins
        bool f1 = __builtin_uaddll_overflow(a, b, &t);
        bool f2 = __builtin_usubll_overflow(t, f1 ? n : 0, &u);
        return f2 ? t : u;
    }
    uint64_t sub(uint64_t a, uint64_t b) {
        // sub(a, b) == a - b (mod n)
        unsigned long long t;
        // https://gcc.gnu.org/onlinedocs/gcc/Integer-Overflow-Builtins.html#Integer-Overflow-Builtins
        bool f = __builtin_usubll_overflow(a, b, &t);
        return t + (f ? n : 0);
    }
    uint64_t div2(uint64_t ar) {
        // div2(ar) == ar / 2 (mod n)
        if ((ar & 1) == 0) {
            return (ar >> 1);
        } else {
            return (ar >> 1) + nh;
        }
    }
    uint64_t mrmul(uint64_t ar, uint64_t br) {
        // mrmul(ar, br) == (ar * br) / r (mod n)
        // R == 2**64
        // gcd(N, R) == 1
        // N * ni mod R == 1
        // 0 <= ar < N < R
        // 0 <= br < N < R
        // T := ar * br
        // t := floor(T / R) - floor(((T * ni mod R) * N) / R)
        // if t < 0 then return t + N else return t
        __uint128_t t = ((__uint128_t)ar) * ((__uint128_t)br);
        uint64_t u = (uint64_t)(t >> 64);
        uint64_t v = (uint64_t)((((__uint128_t)(((uint64_t)t) * ni)) * ((__uint128_t)n)) >> 64);
        unsigned long long w;
        // https://gcc.gnu.org/onlinedocs/gcc/Integer-Overflow-Builtins.html#Integer-Overflow-Builtins
        bool f = __builtin_usubll_overflow(u, v, &w);
        return w + (f ? n : 0);
    }
    uint64_t mr(uint64_t ar) {
        // mr(ar) == ar / r (mod n)
        // R == 2**64
        // gcd(N, R) == 1
        // N * ni mod R == 1
        // 0 <= ar < N < R
        // t := floor(ar / R) - floor(((ar * ni mod R) * N) / R)
        // if t < 0 then return t + N else return t
        uint64_t v = (uint64_t)((((__uint128_t)(ar * ni)) * ((__uint128_t)n)) >> 64);
        return v == 0 ? 0 : n - v;
    }
    uint64_t ar(uint64_t a) {
        // ar(a) == a * r (mod n)
        return mrmul(a, r2);
    }
    uint64_t pow(uint64_t ar, uint64_t b) {
        // pow(ar, b) == ((ar / r) ** b) * r (mod n)
        uint64_t t = ((b & 1) == 0) ? r : ar;
        b >>= 1;
        while (b != 0) {
            ar = mrmul(ar, ar);
            if ((b & 1) != 0) { t = mrmul(t, ar); }
            b >>= 1;
        }
        return t;
    }
};
const uint64_t bases[] = {2,325,9375,28178,450775,9780504,1795265022};
bool miller_rabin(uint64_t n) {
    // Deterministic variants of the Miller-Rabin primality test
    // http://miller-rabin.appspot.com/
    if (n == 2) { return true; }
    if (n < 2 || (n & 1) == 0) { return false; }
    U64Mont mont(n);
    for (int i = 0; i < 7; ++i) {
        uint64_t a = bases[i];
        if (a >= n) { a %= n; if (a == 0) { continue; } }
        uint64_t ar = mont.ar(a);
        uint64_t tr = mont.pow(ar, mont.d);
        if (tr == mont.r || tr == mont.rn) { continue; }
        for (int j = 1; j < mont.k; ++j) { tr = mont.mrmul(tr, tr); if (tr == mont.rn) { goto cont; } }
        return false;
        cont: continue;
    }
    return true;
}
int main(int argc, char *argv[]) {
    int n;
    scanf("%d", &n);
    for(int i = 0; i < n; ++i) {
        unsigned long long x;
        scanf("%llu", &x);
        printf("%llu %d\n", x, miller_rabin((uint64_t)x) ? 1 : 0);
    }
}
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