number_theory/mod_int.hpp

• View this file on GitHub
• Last update: 2024-07-18 16:56:22+09:00
• Include: #include "number_theory/mod_int.hpp"

Depends on

• number_theory/utils.hpp

Required by

• convolution/index_difference.hpp
• convolution/mul_mod_p_conv.hpp
• poly/fft.hpp
• poly/fps_div_at.hpp
• poly/fps_exp.hpp
• poly/fps_inv.hpp
• poly/fps_log.hpp
• poly/stirling1.hpp
• poly/stirling2.hpp
• poly/taylor_shift.hpp

Verified with

• algebra/test/inverse_matrix.test.cpp
• algebra/test/matrix_det.test.cpp
• algebra/test/matrix_product.test.cpp
• algebra/test/matrix_rank.test.cpp
• algebra/test/system_of_linear_equations.test.cpp
• bit/test/bitwise_xor_convolution.test.cpp
• convolution/test/index_difference.test.cpp
• convolution/test/mul_modp_convolution.test.cpp
• data_structure/test/1891.test.cpp
• data_structure/test/point_set_range_composite.test.cpp
• data_structure/test/queue_operate_all_composite.test.cpp
• data_structure/test/range_affine_point_get.test.cpp
• data_structure/test/range_affine_range_sum.test.cpp
• graph/test/enumerate_triangles.test.cpp
• poly/test/convolution_mod.test.cpp
• poly/test/exp_of_formal_power_series.test.cpp
• poly/test/exp_of_formal_power_series_sparse.test.cpp
• poly/test/find_linear_recurrence.test.cpp
• poly/test/inv_of_formal_power_series.test.cpp
• poly/test/inv_of_formal_power_series_sparse.test.cpp
• poly/test/kth_term_of_linearly_recurrent_sequence.test.cpp
• poly/test/log_of_formal_power_series.test.cpp
• poly/test/log_of_formal_power_series_sparse.test.cpp
• poly/test/polynomial_taylor_shift.test.cpp
• poly/test/pow_of_formal_power_series.test.cpp
• poly/test/prod_of_polys.test.cpp
• poly/test/stirling_number_of_the_first_kind.test.cpp
• poly/test/stirling_number_of_the_second_kind.test.cpp

Code

#pragma once

#include <cassert>
#include <iostream>
#include <type_traits>
#include "utils.hpp"

template <unsigned mod>
struct ModInt {
    static_assert(mod != 0, "`mod` must not be equal to 0.");
    static_assert(mod < (1u << 31),
                  "`mod` must be less than (1u << 31) = 2147483648.");

    unsigned val;

    static constexpr unsigned get_mod() { return mod; }

    constexpr ModInt() : val(0) {}
    template <typename T, std::enable_if_t<std::is_signed_v<T>> * = nullptr>
    constexpr ModInt(T x)
        : val((unsigned)((long long)x % (long long)mod + (x < 0 ? mod : 0))) {}
    template <typename T, std::enable_if_t<std::is_unsigned_v<T>> * = nullptr>
    constexpr ModInt(T x) : val((unsigned)(x % mod)) {}

    static constexpr ModInt raw(unsigned x) {
        ModInt<mod> ret;
        ret.val = x;
        return ret;
    }

    constexpr unsigned get_val() const { return val; }

    constexpr ModInt operator+() const { return *this; }
    constexpr ModInt operator-() const { return ModInt<mod>(0u) - *this; }

    constexpr ModInt &operator+=(const ModInt &rhs) {
        val += rhs.val;
        if (val >= mod) val -= mod;
        return *this;
    }
    constexpr ModInt &operator-=(const ModInt &rhs) {
        val -= rhs.val;
        if (val >= mod) val += mod;
        return *this;
    }
    constexpr ModInt &operator*=(const ModInt &rhs) {
        val = (unsigned long long)val * rhs.val % mod;
        return *this;
    }
    constexpr ModInt &operator/=(const ModInt &rhs) {
        val = (unsigned long long)val * rhs.inv().val % mod;
        return *this;
    }

    friend constexpr ModInt operator+(const ModInt &lhs, const ModInt &rhs) {
        return ModInt<mod>(lhs) += rhs;
    }
    friend constexpr ModInt operator-(const ModInt &lhs, const ModInt &rhs) {
        return ModInt<mod>(lhs) -= rhs;
    }
    friend constexpr ModInt operator*(const ModInt &lhs, const ModInt &rhs) {
        return ModInt<mod>(lhs) *= rhs;
    }
    friend constexpr ModInt operator/(const ModInt &lhs, const ModInt &rhs) {
        return ModInt<mod>(lhs) /= rhs;
    }

    constexpr ModInt pow(unsigned long long x) const {
        ModInt<mod> ret = ModInt<mod>::raw(1);
        ModInt<mod> self = *this;
        while (x != 0) {
            if (x & 1) ret *= self;
            self *= self;
            x >>= 1;
        }
        return ret;
    }
    constexpr ModInt inv() const {
        static_assert(is_prime(mod), "`mod` must be a prime number.");
        assert(val != 0);
        return this->pow(mod - 2);
    }

    friend std::istream &operator>>(std::istream &is, ModInt<mod> &x) {
        long long val;
        is >> val;
        x.val = val % mod + (val < 0 ? mod : 0);
        return is;
    }

    friend std::ostream &operator<<(std::ostream &os, const ModInt<mod> &x) {
        os << x.val;
        return os;
    }

    friend bool operator==(const ModInt &lhs, const ModInt &rhs) {
        return lhs.val == rhs.val;
    }

    friend bool operator!=(const ModInt &lhs, const ModInt &rhs) {
        return lhs.val != rhs.val;
    }
};

template <unsigned mod>
void debug(ModInt<mod> x) {
    std::cerr << x.val;
}

#line 2 "number_theory/mod_int.hpp"

#include <cassert>
#include <iostream>
#include <type_traits>
#line 2 "number_theory/utils.hpp"

#include <utility>

constexpr bool is_prime(unsigned n) {
    if (n == 0 || n == 1) {
        return false;
    }
    for (unsigned i = 2; i * i <= n; ++i) {
        if (n % i == 0) {
            return false;
        }
    }
    return true;
}

constexpr unsigned mod_pow(unsigned x, unsigned y, unsigned mod) {
    unsigned ret = 1, self = x;
    while (y != 0) {
        if (y & 1) {
            ret = (unsigned)((unsigned long long)ret * self % mod);
        }
        self = (unsigned)((unsigned long long)self * self % mod);
        y /= 2;
    }
    return ret;
}

template <unsigned mod>
constexpr unsigned primitive_root() {
    static_assert(is_prime(mod), "`mod` must be a prime number.");
    if (mod == 2) {
        return 1;
    }

    unsigned primes[32] = {};
    int it = 0;
    {
        unsigned m = mod - 1;
        for (unsigned i = 2; i * i <= m; ++i) {
            if (m % i == 0) {
                primes[it++] = i;
                while (m % i == 0) {
                    m /= i;
                }
            }
        }
        if (m != 1) {
            primes[it++] = m;
        }
    }
    for (unsigned i = 2; i < mod; ++i) {
        bool ok = true;
        for (int j = 0; j < it; ++j) {
            if (mod_pow(i, (mod - 1) / primes[j], mod) == 1) {
                ok = false;
                break;
            }
        }
        if (ok) return i;
    }
    return 0;
}

// y >= 1
template <typename T>
constexpr T safe_mod(T x, T y) {
    x %= y;
    if (x < 0) {
        x += y;
    }
    return x;
}

// y != 0
template <typename T>
constexpr T floor_div(T x, T y) {
    if (y < 0) {
        x *= -1;
        y *= -1;
    }
    if (x >= 0) {
        return x / y;
    } else {
        return -((-x + y - 1) / y);
    }
}

// y != 0
template <typename T>
constexpr T ceil_div(T x, T y) {
    if (y < 0) {
        x *= -1;
        y *= -1;
    }
    if (x >= 0) {
        return (x + y - 1) / y;
    } else {
        return -(-x / y);
    }
}

// b >= 1
// returns (g, x) s.t. g = gcd(a, b), a * x = g (mod b), 0 <= x < b / g
// from ACL
template <typename T>
std::pair<T, T> extgcd(T a, T b) {
    a = safe_mod(a, b);
    T s = b, t = a, m0 = 0, m1 = 1;
    while (t) {
        T u = s / t;
        s -= t * u;
        m0 -= m1 * u;
        std::swap(s, t);
        std::swap(m0, m1);
    }
    if (m0 < 0) {
        m0 += b / s;
    }
    return std::pair<T, T>(s, m0);
}

// b >= 1
// returns (g, x, y) s.t. g = gcd(a, b), a * x + b * y = g, 0 <= x < b / g, |y| < max(2, |a| / g)
template <typename T>
std::tuple<T, T, T> extgcd2(T a, T b) {
    T _a = safe_mod(a, b);
    T quot = (a - _a) / b;
    T x00 = 0, x01 = 1, y0 = b;
    T x10 = 1, x11 = -quot, y1 = _a;
    while (y1) {
        T u = y0 / y1;
        x00 -= u * x10;
        x01 -= u * x11;
        y0 -= u * y1;
        std::swap(x00, x10);
        std::swap(x01, x11);
        std::swap(y0, y1);
    }
    if (x00 < 0) {
        x00 += b / y0;
        x01 -= a / y0;
    }
    return std::tuple<T, T, T>(y0, x00, x01);
}

// gcd(x, m) == 1
template <typename T>
T inv_mod(T x, T m) {
    return extgcd(x, m).second;
}
#line 7 "number_theory/mod_int.hpp"

template <unsigned mod>
struct ModInt {
    static_assert(mod != 0, "`mod` must not be equal to 0.");
    static_assert(mod < (1u << 31),
                  "`mod` must be less than (1u << 31) = 2147483648.");

    unsigned val;

    static constexpr unsigned get_mod() { return mod; }

    constexpr ModInt() : val(0) {}
    template <typename T, std::enable_if_t<std::is_signed_v<T>> * = nullptr>
    constexpr ModInt(T x)
        : val((unsigned)((long long)x % (long long)mod + (x < 0 ? mod : 0))) {}
    template <typename T, std::enable_if_t<std::is_unsigned_v<T>> * = nullptr>
    constexpr ModInt(T x) : val((unsigned)(x % mod)) {}

    static constexpr ModInt raw(unsigned x) {
        ModInt<mod> ret;
        ret.val = x;
        return ret;
    }

    constexpr unsigned get_val() const { return val; }

    constexpr ModInt operator+() const { return *this; }
    constexpr ModInt operator-() const { return ModInt<mod>(0u) - *this; }

    constexpr ModInt &operator+=(const ModInt &rhs) {
        val += rhs.val;
        if (val >= mod) val -= mod;
        return *this;
    }
    constexpr ModInt &operator-=(const ModInt &rhs) {
        val -= rhs.val;
        if (val >= mod) val += mod;
        return *this;
    }
    constexpr ModInt &operator*=(const ModInt &rhs) {
        val = (unsigned long long)val * rhs.val % mod;
        return *this;
    }
    constexpr ModInt &operator/=(const ModInt &rhs) {
        val = (unsigned long long)val * rhs.inv().val % mod;
        return *this;
    }

    friend constexpr ModInt operator+(const ModInt &lhs, const ModInt &rhs) {
        return ModInt<mod>(lhs) += rhs;
    }
    friend constexpr ModInt operator-(const ModInt &lhs, const ModInt &rhs) {
        return ModInt<mod>(lhs) -= rhs;
    }
    friend constexpr ModInt operator*(const ModInt &lhs, const ModInt &rhs) {
        return ModInt<mod>(lhs) *= rhs;
    }
    friend constexpr ModInt operator/(const ModInt &lhs, const ModInt &rhs) {
        return ModInt<mod>(lhs) /= rhs;
    }

    constexpr ModInt pow(unsigned long long x) const {
        ModInt<mod> ret = ModInt<mod>::raw(1);
        ModInt<mod> self = *this;
        while (x != 0) {
            if (x & 1) ret *= self;
            self *= self;
            x >>= 1;
        }
        return ret;
    }
    constexpr ModInt inv() const {
        static_assert(is_prime(mod), "`mod` must be a prime number.");
        assert(val != 0);
        return this->pow(mod - 2);
    }

    friend std::istream &operator>>(std::istream &is, ModInt<mod> &x) {
        long long val;
        is >> val;
        x.val = val % mod + (val < 0 ? mod : 0);
        return is;
    }

    friend std::ostream &operator<<(std::ostream &os, const ModInt<mod> &x) {
        os << x.val;
        return os;
    }

    friend bool operator==(const ModInt &lhs, const ModInt &rhs) {
        return lhs.val == rhs.val;
    }

    friend bool operator!=(const ModInt &lhs, const ModInt &rhs) {
        return lhs.val != rhs.val;
    }
};

template <unsigned mod>
void debug(ModInt<mod> x) {
    std::cerr << x.val;
}

Back to top page