Sieve of Atkin
(Mylib/Number/Prime/sieve_atkin.cpp)

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• Last update: 2021-04-23 23:44:44+09:00
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Operations

Requirements

Notes

Problems

References

Verified with

• test/yosupo-judge/enumerate_primes/main.atkin.test.cpp

Code

#pragma once
#include <cstdint>
#include <vector>

namespace haar_lib {
  class atkin_sieve {
    std::vector<bool> is_prime_;

  public:
    atkin_sieve() {}
    atkin_sieve(int MAX) : is_prime_(MAX + 1) {
      for (int64_t i = 1; i * i <= MAX; ++i) {
        for (int64_t j = 1; j * j <= MAX; ++j) {
          {
            auto n = 4LL * i * i + j * j;
            if (n <= MAX and (n % 12 == 1 or n % 12 == 5)) {
              is_prime_[n] = not is_prime_[n];
            }
          }
          {
            auto n = 3LL * i * i + j * j;
            if (n <= MAX and n % 12 == 7) {
              is_prime_[n] = not is_prime_[n];
            }
          }
          if (i > j) {
            auto n = 3LL * i * i - j * j;
            if (n <= MAX and n % 12 == 11) {
              is_prime_[n] = not is_prime_[n];
            }
          }
        }
      }

      for (int64_t i = 5; i * i <= MAX; ++i) {
        if (is_prime_[i]) {
          for (int64_t k = i * i, j = k; j <= MAX; j += k) {
            is_prime_[j] = false;
          }
        }
      }

      is_prime_[2] = is_prime_[3] = true;
    }

    bool operator()(int i) const {
      return is_prime_[i];
    }
  };
}  // namespace haar_lib

#line 2 "Mylib/Number/Prime/sieve_atkin.cpp"
#include <cstdint>
#include <vector>

namespace haar_lib {
  class atkin_sieve {
    std::vector<bool> is_prime_;

  public:
    atkin_sieve() {}
    atkin_sieve(int MAX) : is_prime_(MAX + 1) {
      for (int64_t i = 1; i * i <= MAX; ++i) {
        for (int64_t j = 1; j * j <= MAX; ++j) {
          {
            auto n = 4LL * i * i + j * j;
            if (n <= MAX and (n % 12 == 1 or n % 12 == 5)) {
              is_prime_[n] = not is_prime_[n];
            }
          }
          {
            auto n = 3LL * i * i + j * j;
            if (n <= MAX and n % 12 == 7) {
              is_prime_[n] = not is_prime_[n];
            }
          }
          if (i > j) {
            auto n = 3LL * i * i - j * j;
            if (n <= MAX and n % 12 == 11) {
              is_prime_[n] = not is_prime_[n];
            }
          }
        }
      }

      for (int64_t i = 5; i * i <= MAX; ++i) {
        if (is_prime_[i]) {
          for (int64_t k = i * i, j = k; j <= MAX; j += k) {
            is_prime_[j] = false;
          }
        }
      }

      is_prime_[2] = is_prime_[3] = true;
    }

    bool operator()(int i) const {
      return is_prime_[i];
    }
  };
}  // namespace haar_lib

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