math/is_prime.hpp

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• Last update: 2025-06-04 11:53:52+09:00
• Include: #include "math/is_prime.hpp"

Depends on

• math_mod/pow_mod.hpp
• modint/mont_arb.hpp
• type_traits/integral.hpp
• type_traits/io.hpp

Required by

• math/group/rolling_hash.hpp
• math/multiplicative_function/euler_phi.hpp
• math/multiplicative_function/mobius.hpp
• math/multiplicative_function/sigma.hpp
• math/prime_factorize.hpp
• math_mod/primitive_root_64bit.hpp
• random/hash.hpp
• 文字の一点更新が可能文字列に対する動的なローリングハッシュ (string/dynamic_rolling_hash.hpp)
• 文字の変更が行われない文字列に対する静的なローリングハッシュ (string/static_rolling_hash.hpp)

Verified with

• verify/aoj/aoj_alds1_14_b.test.cpp
• verify/aoj/aoj_ntl_1_d.test.cpp
• verify/unit_test/famous_function_table.test.cpp
• verify/unit_test/isprime_table_extend.test.cpp
• verify/unit_test/lpf_table_extend.test.cpp
• verify/unit_test/monoid.test.cpp
• verify/unit_test/prime_factorize_table.test.cpp
• verify/yosupo_math/factrize.test.cpp
• verify/yosupo_math/primality_test.test.cpp
• verify/yosupo_math/primitive_root.test.cpp
• verify/yosupo_string/string_z_roliha.test.cpp

Code

#ifndef KK2_MATH_IS_PRIME_HPP
#define KK2_MATH_IS_PRIME_HPP 1

#include <vector>

#include "../math_mod/pow_mod.hpp"
#include "../modint/mont_arb.hpp"

namespace kk2 {

namespace number_theory {

template <class T, class U> bool miller_rabin(const T &n, const std::vector<T> &ws) {
    if (n <= 2) return n == 2;
    if (~n & 1) return false;

    T d = n - 1;
    while (~d & 1) d >>= 1;
    U e = 1, rev = n - 1;
    for (T w : ws) {
        if (w % n == 0) continue;
        T t = d;
        U y = pow_mod<T, T, U>(w, t, n);
        while (t != n - 1 and y != e and y != rev) {
            y = y * y % n;
            t <<= 1;
        }
        if (y != rev and ~t & 1) return false;
    }
    return true;
}

bool miller_rabin_u64(unsigned long long n) {
    return miller_rabin<unsigned long long, __uint128_t>(
        n, {2, 325, 9375, 28178, 450775, 9780504, 1795265022});
}

template <class mint>
bool miller_rabin_mont(unsigned long long n, const std::vector<unsigned long long> &ws) {
    if (n <= 2) return n == 2;
    if (~n & 1) return false;

    if (mint::getmod() != n) mint::setmod(n);
    unsigned long long d = n - 1;
    while (~d & 1) d >>= 1;
    mint e = 1, rev = n - 1;
    for (unsigned long long w : ws) {
        if (w % n == 0) continue;
        unsigned long long t = d;
        mint y = mint(w).pow(t);
        while (t != n - 1 and y != e and y != rev) {
            y *= y;
            t <<= 1;
        }
        if (y != rev and ~t & 1) return false;
    }
    return true;
}

bool is_prime(unsigned long long n) {
    using mint32 = ArbitraryLazyMontgomeryModInt<54305750>;
    using mint64 = ArbitraryLazyMontgomeryModInt64bit<54305750>;

    if (n <= 2) return n == 2;
    if (~n & 1) return false;
    if (n < (1ull << 30)) {
        return miller_rabin_mont<mint32>(n, {2, 7, 61});
    } else if (n < (1ull << 62)) {
        return miller_rabin_mont<mint64>(n, {2, 325, 9375, 28178, 450775, 9780504, 1795265022});
    } else {
        return miller_rabin_u64(n);
    }
}

}; // namespace number_theory

using number_theory::is_prime;

}; // namespace kk2

#endif // KK2_MATH_IS_PRIME_HPP

Traceback (most recent call last):
  File "/opt/hostedtoolcache/Python/3.12.0/x64/lib/python3.12/site-packages/onlinejudge_verify/documentation/build.py", line 71, in _render_source_code_stat
    bundled_code = language.bundle(stat.path, basedir=basedir, options={'include_paths': [basedir]}).decode()
                   ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/opt/hostedtoolcache/Python/3.12.0/x64/lib/python3.12/site-packages/onlinejudge_verify/languages/cplusplus.py", line 187, in bundle
    bundler.update(path)
  File "/opt/hostedtoolcache/Python/3.12.0/x64/lib/python3.12/site-packages/onlinejudge_verify/languages/cplusplus_bundle.py", line 401, in update
    self.update(self._resolve(pathlib.Path(included), included_from=path))
  File "/opt/hostedtoolcache/Python/3.12.0/x64/lib/python3.12/site-packages/onlinejudge_verify/languages/cplusplus_bundle.py", line 401, in update
    self.update(self._resolve(pathlib.Path(included), included_from=path))
  File "/opt/hostedtoolcache/Python/3.12.0/x64/lib/python3.12/site-packages/onlinejudge_verify/languages/cplusplus_bundle.py", line 312, in update
    raise BundleErrorAt(path, i + 1, "#pragma once found in a non-first line")
onlinejudge_verify.languages.cplusplus_bundle.BundleErrorAt: type_traits/integral.hpp: line 4: #pragma once found in a non-first line

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