#793825 (C++17) No.3030 ミラー・ラビン素数判定法のテスト

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問題	No.3030 ミラー・ラビン素数判定法のテスト
ユーザー	👑 Mizar
提出日時	2022-08-29 04:08:29
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	33 ms / 9,973 ms
コード長	7,345 bytes
コンパイル時間	427 ms
コンパイル使用メモリ	36,224 KB
実行使用メモリ	5,248 KB
最終ジャッジ日時	2024-11-16 23:59:59
合計ジャッジ時間	1,071 ms
ジャッジサーバーID （参考情報）	judge2 / judge1

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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	2 ms 5,248 KB
testcase_01	AC	1 ms 5,248 KB
testcase_02	AC	2 ms 5,248 KB
testcase_03	AC	2 ms 5,248 KB
testcase_04	AC	21 ms 5,248 KB
testcase_05	AC	22 ms 5,248 KB
testcase_06	AC	12 ms 5,248 KB
testcase_07	AC	12 ms 5,248 KB
testcase_08	AC	12 ms 5,248 KB
testcase_09	AC	33 ms 5,248 KB

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ソースコード

raw source code

#pragma GCC target ("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,avx2,bmi2,lzcnt,tune=native")
//#pragma GCC target ("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#pragma GCC optimize("O3")
//#pragma GCC optimize("unroll-loops")
#ifndef NDEBUG
#define NDEBUG
#endif
#include <cassert>
#include <ctime>
#include <cstdio>
#include <cstdbool>
#include <cstdint>
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);
        }
        assert(n * ni == 1); // n * ni == 1 (mod 2**64)
        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) { // == -1 * (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(n - 1)
        // https://gcc.gnu.org/onlinedocs/gcc/Other-Builtins.html#Other-Builtins
        return __builtin_ctzll(_n1(n));
    }
    static uint64_t _d(uint64_t n) { // == (n - 1) >> trailing_zeros(n - 1) // n == 2**k * d + 1
        return _n1(n) >> _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; // == -1 * (2**64) (mod n)
    const uint64_t r2; // == 2**128 (mod n)
    const uint64_t d; // == (n - 1) >> trailing_zeros(n - 1) // n == 2**k * d + 1
    const uint32_t k; // == trailing_zeros(n - 1)
    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))
        { assert((n & 1) == 1); }
    uint64_t add(uint64_t a, uint64_t b) {
        // add(a, b) == a + b (mod n)
        assert(a < n);
        assert(b < 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)
        assert(a < n);
        assert(b < 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)
        assert(ar < n);
        return (ar >> 1) + ((ar & 1) == 0 ? 0 : 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
        assert(ar < n);
        assert(br < n);
        __uint128_t t = ((__uint128_t)ar) * ((__uint128_t)br);
        unsigned long long w;
        // https://gcc.gnu.org/onlinedocs/gcc/Integer-Overflow-Builtins.html#Integer-Overflow-Builtins
        bool f = __builtin_usubll_overflow((unsigned long long)(t >> 64), (unsigned long long)((((__uint128_t)(((uint64_t)t) * ni)) * ((__uint128_t)n)) >> 64), &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
        assert(ar < n);
        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)
        assert(a < n);
        return mrmul(a, r2);
    }
    uint64_t pow(uint64_t ar, uint64_t b) {
        // pow(ar, b) == ((ar / r) ** b) * r (mod n)
        assert(ar < n);
        if (b == 0) { return r; }
        for (; (b & 1) == 0; b >>= 1) { ar = mrmul(ar, ar); }
        uint64_t tr = ar;
        for (b >>= 1; b != 0; b >>= 1) {
            ar = mrmul(ar, ar);
            if ((b & 1) != 0) { tr = mrmul(tr, ar); }
        }
        return tr;
    }
};

U64Mont u64mont_new(uint64_t n) { return U64Mont(n); }
uint64_t u64mont_add(U64Mont *mont, uint64_t ar, uint64_t br) { return mont->add(ar, br); }
uint64_t u64mont_sub(U64Mont *mont, uint64_t ar, uint64_t br) { return mont->sub(ar, br); }
uint64_t u64mont_div2(U64Mont *mont, uint64_t ar) { return mont->div2(ar); }
uint64_t u64mont_mrmul(U64Mont *mont, uint64_t ar, uint64_t br) { return mont->mrmul(ar, br); }
uint64_t u64mont_mr(U64Mont *mont, uint64_t a) { return mont->mr(a); }
uint64_t u64mont_ar(U64Mont *mont, uint64_t a) { return mont->ar(a); }
uint64_t u64mont_pow(U64Mont *mont, uint64_t ar, uint64_t b) { return mont->pow(ar, b); }

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 (const auto& base : bases) {
        uint64_t a = base;
        if (a >= n) { a %= n; if (a == 0) { continue; } }
        uint64_t tr = mont.pow(mont.ar(a), mont.d);
        if (tr == mont.r) { continue; }
        for (uint32_t j = 1; tr != mont.rn; ++j) {
            if (j >= mont.k) { return false; }
            tr = mont.mrmul(tr, tr);
        }
    }
    return true;
}

int main(int argc, char *argv[]) {
    struct timespec start_time, end_time;
    clock_gettime(CLOCK_PROCESS_CPUTIME_ID, &start_time);
    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);
    }
    clock_gettime(CLOCK_PROCESS_CPUTIME_ID, &end_time);
    double d_sec =
        (double)(end_time.tv_sec - start_time.tv_sec) +
        (double)(end_time.tv_nsec - start_time.tv_nsec) / (1000 * 1000 * 1000);
    fprintf(stderr, "time:%f\n", d_sec);
}

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