number_theory/dynamic_mod_int.hpp

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• Last update: 2026-04-03 09:13:19+09:00
• Include: #include "number_theory/dynamic_mod_int.hpp"

Depends on

• number_theory/barrett.hpp
• number_theory/utils.hpp

Verified with

• number_theory/test/dynamic_modint_stress.test.cpp

Code

#pragma once
#include "barrett.hpp"
#include "utils.hpp"
#include <cassert>
#include <iostream>
#include <type_traits>

template <int ID>
struct DynamicModInt {
    using M = DynamicModInt<ID>;
    static Barrett br;
    unsigned val;
    
    static unsigned get_mod() {
        return br.m;
    }
    static void set_mod(unsigned m) {
        assert(1 <= m && m < (1u << 31));
        br = Barrett(m);
    }
    
    DynamicModInt() : val(0) {}
    template <typename T, std::enable_if_t<std::is_signed_v<T>> * = nullptr>
    DynamicModInt(T x) {
        long long x_ = (long long)x % (long long)br.m;
        if (x_ < 0) {
            x_ += br.m;
        }
        val = x_;
    }
    template <typename T, std::enable_if_t<std::is_unsigned_v<T>> * = nullptr>
    DynamicModInt(T x) : val((unsigned)(x % br.m)) {}
    
    template <typename T>
    M raw(T x) {
        M ret;
        ret.val = x;
        return ret;
    }
    
    unsigned get_val() const {
        return val;
    }
    
    M operator+() const { return *this; }
    M operator-() const { return M() - *this; }

    M &operator+=(const M &rhs) {
        val += rhs.val;
        if (val >= br.m) val -= br.m;
        return *this;
    }
    M &operator-=(const M &rhs) {
        val -= rhs.val;
        if (val >= br.m) val += br.m;
        return *this;
    }
    M &operator*=(const M &rhs) {
        val = br.mul(val, rhs.val);
        return *this;
    }
    M &operator/=(const M &rhs) {
        return *this *= rhs.inv();
    }

    M inv() const {
        auto [g, x] = extgcd(val, br.m);
        assert(g == 1);
        return M::raw(x);
    }
    M pow(unsigned long long x) const {
        M ret = M::raw(1);
        M self = *this;
        while (x != 0) {
            if (x & 1) ret *= self;
            self *= self;
            x >>= 1;
        }
        return ret;
    }
    
    friend M operator+(const M &lhs, const M &rhs) {
        return M(lhs) += rhs;
    }
    friend M operator-(const M &lhs, const M &rhs) {
        return M(lhs) -= rhs;
    }
    friend M operator*(const M &lhs, const M &rhs) {
        return M(lhs) *= rhs;
    }
    friend M operator/(const M &lhs, const M &rhs) {
        return M(lhs) /= rhs;
    }
    friend bool operator==(const M &lhs, const M &rhs) {
        return lhs.val == rhs.val;
    }
    friend bool operator!=(const M &lhs, const M &rhs) {
        return lhs.val != rhs.val;
    }
};

template <int ID>
Barrett DynamicModInt<ID>::br(998244353);

#line 2 "number_theory/barrett.hpp"

struct Barrett {
    unsigned m;
    unsigned long long im;
    explicit Barrett(unsigned m) : m(m), im(-1ull / m + 1) {}
    unsigned mul(unsigned x, unsigned y) const {
        unsigned long long z = (unsigned long long)x * y;
        unsigned long long q = ((__uint128_t)z * im) >> 64;
        unsigned long long t = q * m;
        return z - t + (z < t ? m : 0);
    }
};
#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 4 "number_theory/dynamic_mod_int.hpp"
#include <cassert>
#include <iostream>
#include <type_traits>

template <int ID>
struct DynamicModInt {
    using M = DynamicModInt<ID>;
    static Barrett br;
    unsigned val;
    
    static unsigned get_mod() {
        return br.m;
    }
    static void set_mod(unsigned m) {
        assert(1 <= m && m < (1u << 31));
        br = Barrett(m);
    }
    
    DynamicModInt() : val(0) {}
    template <typename T, std::enable_if_t<std::is_signed_v<T>> * = nullptr>
    DynamicModInt(T x) {
        long long x_ = (long long)x % (long long)br.m;
        if (x_ < 0) {
            x_ += br.m;
        }
        val = x_;
    }
    template <typename T, std::enable_if_t<std::is_unsigned_v<T>> * = nullptr>
    DynamicModInt(T x) : val((unsigned)(x % br.m)) {}
    
    template <typename T>
    M raw(T x) {
        M ret;
        ret.val = x;
        return ret;
    }
    
    unsigned get_val() const {
        return val;
    }
    
    M operator+() const { return *this; }
    M operator-() const { return M() - *this; }

    M &operator+=(const M &rhs) {
        val += rhs.val;
        if (val >= br.m) val -= br.m;
        return *this;
    }
    M &operator-=(const M &rhs) {
        val -= rhs.val;
        if (val >= br.m) val += br.m;
        return *this;
    }
    M &operator*=(const M &rhs) {
        val = br.mul(val, rhs.val);
        return *this;
    }
    M &operator/=(const M &rhs) {
        return *this *= rhs.inv();
    }

    M inv() const {
        auto [g, x] = extgcd(val, br.m);
        assert(g == 1);
        return M::raw(x);
    }
    M pow(unsigned long long x) const {
        M ret = M::raw(1);
        M self = *this;
        while (x != 0) {
            if (x & 1) ret *= self;
            self *= self;
            x >>= 1;
        }
        return ret;
    }
    
    friend M operator+(const M &lhs, const M &rhs) {
        return M(lhs) += rhs;
    }
    friend M operator-(const M &lhs, const M &rhs) {
        return M(lhs) -= rhs;
    }
    friend M operator*(const M &lhs, const M &rhs) {
        return M(lhs) *= rhs;
    }
    friend M operator/(const M &lhs, const M &rhs) {
        return M(lhs) /= rhs;
    }
    friend bool operator==(const M &lhs, const M &rhs) {
        return lhs.val == rhs.val;
    }
    friend bool operator!=(const M &lhs, const M &rhs) {
        return lhs.val != rhs.val;
    }
};

template <int ID>
Barrett DynamicModInt<ID>::br(998244353);

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