tests/math/miller-rabin/libchecker.test.cpp

• View this file on GitHub
• Last update: 2025-06-26 16:44:42+09:00
• Problem: https://judge.yosupo.jp/problem/primality_test

Depends on

• FastIO (library/fastio.hpp)
• ミラー・ラビン素数判定法 (library/math/miller-rabin.hpp)

Code

#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < (n); ++i)
using ll = long long;
using ull = unsigned long long;

#include "../../../library/fastio.hpp"
#include "../../../library/math/miller-rabin.hpp"
#define PROBLEM "https://judge.yosupo.jp/problem/primality_test"

int main() {
  int q;
  asalib::FastIO >> q;
  while (q--) {
    ull n;
    asalib::FastIO >> n;
    asalib::FastIO << (asalib::math::miller_rabin_test(n) ? "Yes" : "No") << '\n';
  }
  return 0;
}

#line 1 "tests/math/miller-rabin/libchecker.test.cpp"
#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < (n); ++i)
using ll = long long;
using ull = unsigned long long;

#line 2 "library/fastio.hpp"

#line 5 "library/fastio.hpp"
#include <concepts>
#line 11 "library/fastio.hpp"
#include <type_traits>
using namespace std;

// TODO: 何も入力がない場合にも対応する？

namespace asalib {
  namespace _internal {
    class FastIO {
      private:
      using uint = unsigned int;
      static constexpr uint BUFFER_SIZE = 1 << 20;
      static constexpr uint MAX_TOKEN_SIZE = 64;

      // ===== Read ===== //

      private:
      array<char, BUFFER_SIZE> read_buffer;
      array<char, BUFFER_SIZE>::iterator read_ptr;
      uint read_size = 0;

      inline void load() {
        // まだ読んでないデータを前に持ってくる
        memcpy(read_buffer.begin(), read_ptr, read_size - (read_ptr - read_buffer.begin()));
        read_size -= read_ptr - read_buffer.begin();
        read_ptr = read_buffer.begin();
        // stdin から読み込み
        read_size += fread(read_buffer.begin() + read_size, 1, BUFFER_SIZE - read_size, stdin);
      }

      inline void skip_space() {
        // 制御文字 + space
        // DEL (127 = 0x7F) がコーナーケースだがまあ使わんやろ
        while (*read_ptr <= ' ') ++read_ptr;
      }

      template<typename T>
        requires(integral<T> || is_same_v<T, __int128_t> || is_same_v<T, __uint128_t>)
      inline void _read_uint(T& x) {
        x = 0;
        while (true) {
          uint64_t v;
          memcpy(&v, read_ptr, 8);
          // '0' -> 0 処理
          // こっちを先にやることで制御文字系もはじく
          v -= 0x30'30'30'30'30'30'30'30;
          // ASCII 範囲外
          if (v & 0x80'80'80'80'80'80'80'80) break;
          // 桁ごとの数字から数値に
          v = (v * 10 + (v >> 8)) & 0x00ff00ff00ff00ff;
          v = (v * 100 + (v >> 16)) & 0x0000ffff0000ffff;
          v = (v * 10000 + (v >> 32)) & 0x00000000ffffffff;
          x = 1'0000'0000 * x + v;
          read_ptr += 8;
        }
        while (true) {
          uint32_t v;
          memcpy(&v, read_ptr, 4);
          v -= 0x30'30'30'30;
          if (v & 0x80'80'80'80) break;
          v = (v * 10 + (v >> 8)) & 0x00ff00ff;
          v = (v * 100 + (v >> 16)) & 0x0000ffff;
          x = 1'0000 * x + v;
          read_ptr += 4;
        }
        while (true) {
          uint16_t v;
          memcpy(&v, read_ptr, 2);
          v -= 0x3030;
          if (v & 0x8080) break;
          v = (v * 10 + (v >> 8)) & 0x00ff;
          x = 100 * x + v;
          read_ptr += 2;
        }
        if (*read_ptr > ' ') x = 10 * x + (*read_ptr++ & 0x0f);
      }

      inline void read_commonop() {
        // そろそろ限界なら読み込み
        if ((read_ptr - read_buffer.begin()) + MAX_TOKEN_SIZE >= BUFFER_SIZE) load();
        skip_space();
      }

      public:
      FastIO& operator>>(char& x) {
        read_commonop();
        x = *read_ptr++;
        return *this;
      }

      FastIO& operator>>(string& x) {
        read_commonop();
        x.clear();
        while (*read_ptr > ' ') {
          x += *read_ptr++;
          if (read_ptr == read_buffer.end()) load();
        }
        return *this;
      }

      template<typename T>
        requires(integral<T> || is_same_v<T, __int128_t> || is_same_v<T, __uint128_t>)
      FastIO& operator>>(T& x) {
        read_commonop();
        constexpr bool is_signed = is_signed_v<T> || is_same_v<T, __int128_t>;
        if constexpr (is_signed) {
          if (*read_ptr == '-') {
            ++read_ptr;
            _read_uint(x);
            x = -x;
            return *this;
          }
        }
        _read_uint(x);
        return *this;
      }

      // ===== Write ===== //

      private:
      array<char, BUFFER_SIZE> write_buffer;
      array<char, BUFFER_SIZE>::iterator write_ptr;
      static constexpr uint MAX_PRECOMPUTE_NUM = 1'0000;
      static constexpr uint MAX_PRECOMPUTE_NUM_DIGIT = 4;

      static constexpr array<char, MAX_PRECOMPUTE_NUM * MAX_PRECOMPUTE_NUM_DIGIT> digits = [] {
        array<char, MAX_PRECOMPUTE_NUM * MAX_PRECOMPUTE_NUM_DIGIT> digits {};
        for (uint i = 0; i < MAX_PRECOMPUTE_NUM; ++i) {
          uint x = i;
          for (int j = MAX_PRECOMPUTE_NUM_DIGIT - 1; j >= 0; --j) {
            digits[i * MAX_PRECOMPUTE_NUM_DIGIT + j] = '0' + (x % 10);
            x /= 10;
          }
        }
        return digits;
      }();

      template<typename T>
        requires(integral<T> || is_same_v<T, __int128_t> || is_same_v<T, __uint128_t>)
      static constexpr array<T, numeric_limits<T>::digits10 + 1> Pow10 = [] {
        array<T, numeric_limits<T>::digits10 + 1> pow10 {};
        pow10[0] = 1;
        for (uint i = 1; i < pow10.size(); ++i) pow10[i] = pow10[i - 1] * 10;
        return pow10;
      }();

      inline void write_commonop() {
        // そろそろ限界なら書き込む
        if ((write_ptr - write_buffer.begin()) + MAX_TOKEN_SIZE >= BUFFER_SIZE) flush();
      }

      inline void putchar(const char& x) { *write_ptr++ = x; }

      template<typename T, int NumDig>
        requires(integral<T> || is_same_v<T, __int128_t> || is_same_v<T, __uint128_t>)
      inline void _write_uint_top(const T& x) {
        // leading-zero を書き込まないようにする
        if constexpr (NumDig > 1) {
          if (x < Pow10<T>[NumDig - 1]) {
            _write_uint_top<T, NumDig - 1>(x);
            return;
          }
        }
        copy_n(digits.begin() + (x + 1) * MAX_PRECOMPUTE_NUM_DIGIT - NumDig, NumDig, write_ptr);
        write_ptr += NumDig;
      }

      template<typename T, int NumDig>
        requires(integral<T> || is_same_v<T, __int128_t> || is_same_v<T, __uint128_t>)
      inline void _write_uint(const T& x) {
        if constexpr (NumDig >= 0) {
          if constexpr (NumDig > MAX_PRECOMPUTE_NUM_DIGIT) _write_uint<T, NumDig - MAX_PRECOMPUTE_NUM_DIGIT>(x / MAX_PRECOMPUTE_NUM);
          copy_n(digits.begin() + x % MAX_PRECOMPUTE_NUM * MAX_PRECOMPUTE_NUM_DIGIT, MAX_PRECOMPUTE_NUM_DIGIT, write_ptr);
          write_ptr += MAX_PRECOMPUTE_NUM_DIGIT;
        }
      }

      template<typename T, int NumDig>
        requires(integral<T> || is_same_v<T, __int128_t> || is_same_v<T, __uint128_t>)
      inline void _write_uint_root(const T& x) {
        if constexpr (is_same_v<T, __int128_t> || is_same_v<T, __uint128_t>) {
          // 128bit 除算はおそいので 64bit 除算を使う
          if (x < Pow10<T>[16]) {
            _write_uint_root<uint64_t, NumDig>(x);
          }
          else if (x < Pow10<T>[32]) {
            _write_uint_root<uint64_t, NumDig>(x / Pow10<T>[16]);
            _write_uint<uint64_t, 16>(x % Pow10<T>[16]);
          }
          else {
            _write_uint_root<uint64_t, NumDig>(x / Pow10<T>[32]);
            _write_uint<uint64_t, 16>(x % Pow10<T>[32] / Pow10<T>[16]);
            _write_uint<uint64_t, 16>(x % Pow10<T>[16]);
          }
          return;
        }

        if constexpr (NumDig < numeric_limits<T>::digits10) {
          if (x >= Pow10<T>[NumDig]) {
            _write_uint_root<T, NumDig + MAX_PRECOMPUTE_NUM_DIGIT>(x);
            return;
          }
        }
        _write_uint_top<T, MAX_PRECOMPUTE_NUM_DIGIT>(x / Pow10<T>[NumDig - MAX_PRECOMPUTE_NUM_DIGIT]);
        if constexpr (NumDig > MAX_PRECOMPUTE_NUM_DIGIT) _write_uint<T, NumDig - MAX_PRECOMPUTE_NUM_DIGIT>(x % Pow10<T>[NumDig - MAX_PRECOMPUTE_NUM_DIGIT]);
      }

      public:
      inline void flush() {
        fwrite(write_buffer.begin(), 1, write_ptr - write_buffer.begin(), stdout);
        write_ptr = write_buffer.begin();
      }

      FastIO& operator<<(const char& x) {
        write_commonop();
        putchar(x);
        return *this;
      }

      FastIO& operator<<(const string& x) {
        write_commonop();
        uint idx = 0;
        while (idx < x.size()) {
          const uint siz = min(BUFFER_SIZE - (uint) (write_ptr - write_buffer.begin()), (uint) x.size() - idx);
          copy_n(x.begin() + idx, siz, write_ptr);
          write_ptr += siz;
          idx += siz;
          if (write_ptr == write_buffer.end()) flush();
        }
        return *this;
      }

      template<typename T>
        requires(integral<T> || is_same_v<T, __int128_t> || is_same_v<T, __uint128_t>)
      FastIO& operator<<(const T& x) {
        write_commonop();
        constexpr bool is_signed = is_signed_v<T> || is_same_v<T, __int128_t>;
        if constexpr (is_signed) {
          if (x < 0) {
            putchar('-');
            _write_uint_root<T, MAX_PRECOMPUTE_NUM_DIGIT>(-x);
            return *this;
          }
        }
        _write_uint_root<T, MAX_PRECOMPUTE_NUM_DIGIT>(x);
        return *this;
      }

      // ===== Common ====== //

      public:
      FastIO() {
        read_ptr = read_buffer.begin();
        write_ptr = write_buffer.begin();
        load();
      }

      ~FastIO() { flush(); }
    };
  }  // namespace _internal

  _internal::FastIO FastIO;
}  // namespace asalib
#line 2 "library/math/miller-rabin.hpp"

#line 7 "library/math/miller-rabin.hpp"
using namespace std;

namespace asalib {
  namespace math {
    template<integral T>
    constexpr bool miller_rabin_test(T n) {
      if (n < 2) [[unlikely]]
        return false;
      if (n % 2 == 0) return n == 2;
      T d = n - 1, s = 0;
      while (d % 2 == 0) d >>= 1, ++s;
      assert(d % 2 == 1);

      static_assert(sizeof(T) == 4 || sizeof(T) == 8, "T must be 32-bit or 64-bit integer type");
      constexpr bool is_64bit = sizeof(T) == 8;

      function<T(T, T, T)> modpow = [&](T a, T n, T mod) {
        T res = 1;
        while (n) {
          if constexpr (is_64bit) {
            if (n & 1) res = (__uint128_t) res * a % mod;
            a = (__uint128_t) a * a % mod;
          }
          else {
            if (n & 1) res = (unsigned long long) res * a % mod;
            a = (unsigned long long) a * a % mod;
          }
          n >>= 1;
        }
        return res;
      };

      function<bool(T)> test = [&](T a) {
        T x = modpow(a, d, n);
        if (x == 0) [[unlikely]]
          return false;
        if (x == 1) [[unlikely]]
          return true;
        for (T _ = 0; _ < s; ++_) {
          T y;
          if constexpr (is_64bit)
            y = (__uint128_t) x * x % n;
          else
            y = (unsigned long long) x * x % n;
          if (y == 1 && x != 1 && x != n - 1) return false;
          x = y;
        }
        return x == 1;
      };

      function<bool(vector<T>)> tests = [&](vector<T> basis) {
        for (T a : basis)
          if (!test(a)) return false;
        return true;
      };

      if (n < 2'047) return test(2);
      if (n < 1'373'653) return tests({ 2, 3 });
      if (n < 9'080'191) return tests({ 31, 73 });
      if (n < 25'326'001) return tests({ 2, 3, 5 });
      if (n < 3'215'031'751) return tests({ 2, 3, 5, 7 });
      if (n < 4'759'123'141) return tests({ 2, 7, 61 });
      if (n < 1'122'004'669'633) return tests({ 2, 13, 23, 1662803 });
      if (n < 2'152'302'898'747) return tests({ 2, 3, 5, 7, 11 });
      if (n < 3'474'749'660'383) return tests({ 2, 3, 5, 7, 11, 13 });
      if (n < 341'550'071'728'321) return tests({ 2, 3, 5, 7, 11, 13, 17 });
      if (n < 3'825'123'056'546'413'051) return tests({ 2, 3, 5, 7, 11, 13, 17, 19, 23 });
      if (ull(n) <= 18'446'744'073'709'551'615ULL) return tests({ 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37 });
      // 18'446'744'073'709'551'616 は 2^64 であり、これ以上の数は 64 ビット整数型では表現できない
      // TODO: 多倍長整数を使う場合は if を追加する
      // TODO: C++23 以降なら __builtin_unreachable() -> std::unreachable() に変更可能
      __builtin_unreachable();
    }
  }  // namespace math
}  // namespace asalib
#line 9 "tests/math/miller-rabin/libchecker.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/primality_test"

int main() {
  int q;
  asalib::FastIO >> q;
  while (q--) {
    ull n;
    asalib::FastIO >> n;
    asalib::FastIO << (asalib::math::miller_rabin_test(n) ? "Yes" : "No") << '\n';
  }
  return 0;
}

Back to top page