結果

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 2020-12-28 00:13:34
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 18 ms / 9,973 ms
コード長 5,988 bytes
コンパイル時間 2,252 ms
コンパイル使用メモリ 203,008 KB
最終ジャッジ日時 2025-01-17 07:47:50
ジャッジサーバーID
（参考情報） 		judge4 / judge3
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ファイルパターン 結果
other AC * 10
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ソースコード

diff # 

#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;


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;
}

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 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;
}

namespace fastio {
static constexpr int SZ = 1 << 17;
char ibuf[SZ], obuf[SZ];
int pil = 0, pir = 0, por = 0;

struct Pre {
    char num[40000];
    constexpr Pre() : num() {
        for (int i = 0; i < 10000; i++) {
            int n = i;
            for (int j = 3; j >= 0; j--) {
                num[i * 4 + j] = n % 10 + '0';
                n /= 10;
            }
        }
    }
} constexpr pre;

inline void load() {
    memcpy(ibuf, ibuf + pil, pir - pil);
    pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin);
    pil = 0;
}
inline void flush() {
    fwrite(obuf, 1, por, stdout);
    por = 0;
}

inline void rd(char& c) { c = ibuf[pil++]; }
template <typename T>
inline void rd(T& x) {
    if (pil + 32 > pir) load();
    char c;
    do {
        c = ibuf[pil++];
    } while (c < '-');
    bool minus = 0;
    if (c == '-') {
        minus = 1;
        c = ibuf[pil++];
    }
    x = 0;
    while (c >= '0') {
        x = x * 10 + (c & 15);
        c = ibuf[pil++];
    }
    if (minus) x = -x;
}

inline void wt(char c) { obuf[por++] = c; }
template <typename T>
inline void wt(T x) {
    if (por > SZ - 32) flush();
    if (!x) {
        obuf[por++] = '0';
        return;
    }
    if (x < 0) {
        obuf[por++] = '-';
        x = -x;
    }
    int i = 12;
    char buf[16];
    while (x >= 10000) {
        memcpy(buf + i, pre.num + (x % 10000) * 4, 4);
        x /= 10000;
        i -= 4;
    }
    int d = x < 100 ? (x < 10 ? 1 : 2) : (x < 1000 ? 3 : 4);
    memcpy(obuf + por, pre.num + x * 4 + 4 - d, d);
    por += d;
    memcpy(obuf + por, buf + i + 4, 12 - i);
    por += 12 - i;
}

struct Dummy {
    Dummy() { atexit(flush); }
} dummy;

} // namespace fastio
using fastio::rd;
using fastio::wt;
using namespace std;


int main() {

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

    int query; rd(query);
    while (query--) {
        Word64 x; rd(x);
        int ans = solovay_strassen(x);
        wt(x); wt(' '); wt(ans); wt('\n');
    }
    return 0;
}
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