#597869 (C++17) No.8030 ミラー・ラビン素数判定法のテスト

• 問題: No.8030 ミラー・ラビン素数判定法のテスト
• ユーザー: pyranine
• 提出日時: 2020-12-27 23:59:12
• 言語: C++17 (gcc 13.3.0 + boost 1.89.0)
• 結果: AC
• 実行時間: 17 ms / 9,973 ms
• コード長: 4,219 bytes
• コンパイル時間: 1,800 ms
• コンパイル使用メモリ: 196,084 KB
• 最終ジャッジ日時: 2025-01-17 07:47:35
• ジャッジサーバーID （参考情報）: judge2 / judge4

ファイルパターン	結果
other	AC * 10

ソースコード

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

using Int8 = int8_t;
using Int16 = int16_t;
using Int32 = int32_t;
using Int64 = int64_t;
using Int128 = __int128_t;

using Word8 = uint8_t;
using Word16 = uint16_t;
using Word32 = uint32_t;
using Word64 = uint64_t;
using Word128 = __uint128_t;

using Int = int_fast64_t;
using Word = uint_fast64_t;

using F32 = float;
using F64 = double;
using F80 = long double;

int jacobi(Int a, Word n) {
    Word t;
    int j = 1;
    while(a) {
        if (a < 0) {
            a = -a ;
            if ((n & 3) == 3) j = -j;
        }
        int ba = __builtin_ctzll(a);
        a >>= ba;
        if (((n & 7) == 3 || (n & 7) == 5) && (ba & 1)) j = -j;
        if ((a & n & 3) == 3) j = -j;
        t = a;
        a = n;
        n = t;
        a %= n;
        if (a > n / 2) a -= n;
    }
    return n == 1 ? j : 0;
}

static inline Word addmod64(Word x, Word y, Word n) { return x + y >= n ? x + y - n : x + y; }
static inline Word submod64(Word x, Word y, Word n) { return x >= y  ? x - y : x - y + n; }
static inline Word ex_gcd(Word y) {
    Word u = 1, v = 0;
    Word x = 1ULL << 63;
    for (int i = 0; i < 64; i++) {
        if (u & 1){
            u = (u + y) / 2;
            v = v / 2 + x;
        }
        else {
            u >>= 1;
            v >>= 1;
        }
    }
    return -v;
}
static inline Word64 MR(Word128 x, Word64 m, Word64 n) {
    Int64 z = (x >> 64) - ((((Word64)x * m) * (Word128)n) >> 64);
    return z < 0 ? z + n : z;
}
static inline Word64 RM(Word64 x, Word64 r2, Word64 m, Word64 n) { return MR((Word128)r2 * x, m, n); }
static inline Word64 mulmod64(Word64 x, Word64 y, Word64 m, Word64 n) { return MR((Word128)x * y, m, n); }

int solovay_strassen(const Word64 n) {
    if(n <= 1) return 0;
    if(n <= 3) return 1;
    if(!(n & 1)) return 0;
    const Word64 one = -1ULL % n + 1;
    const Word64 r2 = (Word128) (Int128) -1 % n + 1;
    const Word64 m = ex_gcd(n);

    {
        Word64 d = (n - 1) << __builtin_clzll(n-1);
        Word64 t = one << 1;
        if (t >= n) t -= n;
        for (d <<= 1; d; d <<= 1) {
            t = mulmod64(t, t, m, n);
            if (d >> 63) {
                t <<= 1;
                if (t >= n) t -= n;
            }
        }
        if(t != one){
            Word64 x = (n - 1) & -(n - 1);
            Word64 mone = n - one;
            for (x >>= 2; t != mone; x >>= 1) {
                if (x == 0) return 0;
                t = mulmod64(t, t, m, n);
            }
        }
    }


    {
        Int64 D = 5;
        for(int i = 0; jacobi(D, n) != -1 && i < 64; i++) {
            if(i == 32){
                Word32 k = round(sqrtl(n));
                if (k * k == n) return 0;
            }
            if (i & 1) D -= 2;
            else D += 2;
            D = -D;
        }
        Word64 Q = RM(D < 0 ? (1 - D) / 4 % n : n - (D - 1) / 4 % n, r2, m, n);
        Word64 u, v, Qn;
        Word64 k = (n + 1) << __builtin_clzll(n + 1);
        u = one;
        v = one;
        Qn = Q;
        D %= (Int64)n;
        D = RM(D < 0 ? n + D : D, r2, m, n);
        for (k <<= 1; k; k <<= 1) {
            u = mulmod64(u,v,m,n);
            v = submod64(mulmod64(v,v,m,n), addmod64(Qn, Qn, n), n);
            Qn = mulmod64(Qn, Qn, m, n);
            if (k >> 63) {
                Word64 uu = addmod64(u, v, n);
                if (uu & 1) uu += n;
                uu >>= 1;
                v = addmod64(mulmod64(D,u,m,n), v, n);
                if (v & 1) v += n;
                v >>= 1;
                u = uu;
                Qn = mulmod64(Qn, Q, m, n);
            }
        }

        if (u == 0 || v == 0) return 1;
        Word64 x = (n + 1) & ~n;
        for (x >>= 2; x; x >>= 1) {
            u = mulmod64(u,v,m,n);
            v = submod64(mulmod64(v,v,m,n), addmod64(Qn, Qn, n), n);
            if (v == 0) return 1;
            Qn = mulmod64(Qn, Qn, m, n);
        }
    }

    return 0;
}

int main() {

    cin.tie(nullptr);
    cout.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(15);

    int query; cin >> query;
    while (query--) {
        Word64 x; cin >> x;
        cout << x << ' ' << solovay_strassen(x) << '\n';
    }
    return 0;
}