StaticModint
(src/template/static_modint.hpp)

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• Last update: 2024-11-09 01:34:39+09:00
• Include: #include "src/template/static_modint.hpp"

StaticModint

自動で $\mathrm{mod}$ をとる構造体です．
$\mathrm{mod}$ はコンパイル時定数である必要があります．

基本的には modint998244353 か modint1000000007 を使えば十分で，以下のように使えます．

#include "template/template.hpp"
#include "template/static_modint.hpp"
using mint = modint998244353;
int main(void) {
    mint sum = 0;
    for(int i = 0; i < 10000; i++) {
        sum += i;
    }
    cout << sum << '\n';  // 8828235 (= 5000050000 % 998244353)
}

その他の $\mathrm{mod}$ で使いたい場合はページ下部の Tips を参照してください．

コンストラクタ

mint x

• mint のデフォルトコンストラクタです．
• 初期化しない場合， $0$ が格納されます．

制約

• 初期化で代入する数は ll に収まる値であること

計算量

• $O(1)$

mod

unsigned int mint::mod()

$\mathrm{mod}$ を返します．

計算量

• $O(1)$

val

unsigned int x.val()

$x$ に格納されている値を int 型で返します．

計算量

• $O(1)$

各種演算

-mint;

mint++;
mint--;
--mint;
++mint;

mint += mint;
mint -= mint;
mint *= mint;
mint /= mint;

mint + mint;
mint - mint;
mint * mint;
mint / mint;

mint == mint;
mint != mint;

が動きます．

mint x = 58;
1 + x;

なども，

mint(1) + x

と (自動で解釈されるので) 動きます．

また，

mint x;
cin >> x;
cout << x;

により入出力もできます．

制約

• a / b と a /= b を行うとき， $gcd(b, \mathrm{mod}) = 1$

計算量

• $O(1)$ (割り算以外)
• $O(\log \mathrm{mod})$ (割り算)

pow

mint x.pow(ll n)

$x^n$ を返します．

制約

• $0 \leq n$

計算量

• $O(\log n)$

inv

mint x.inv()

$xy \equiv 1$ なる $y$ を返します．

制約

• $gcd(x, \mathrm{mod}) = 1$

計算量

• $O(\log \mathrm{mod})$

raw

mint mint::raw(int x)

$x$ に対して $\mathrm{mod}$ を取らずに mint(x) を返します．
定数倍高速化のための関数です．

値が $\mathrm{mod}$ 以上になる場合の挙動は未定義です．

制約

• $0 \leq x < \mathrm{mod}$

計算量

• $O(1)$

Tips (other mod)

$998244353$ と $1000000007$ 以外で modint を使いたい場合は以下のように書けます．
ただし，冒頭でも述べた通り， $\mathrm{mod}$ に指定する整数はコンパイル時定数である必要があります．

using mint = StaticModint<1234567891>;

modint998244353 と modint1000000007 はそれぞれ StaticModint<998244353> と StaticModint<1000000007> のエイリアスになっています．

Depends on

• template (src/template/template.hpp)

Required by

• convolution_arbitrary (src/convolution/convolution_arbitrary.hpp)
• convolution_ll (src/convolution/convolution_ll.hpp)
• FormalPowerSeriesArbitrary (src/fps/formal_power_series_arbitrary.hpp)
• FormalPowerSeriesLL (src/fps/formal_power_series_ll.hpp)
• wildcard_pattern_matching (src/string/wildcard_pattern_matching.hpp)
• debug (src/template/debug.hpp)

Verified with

• verify/library_checker/convolution/bitwise_and_convolution.test.cpp
• verify/library_checker/convolution/bitwise_xor_convolution.test.cpp
• verify/library_checker/convolution/convolution.test.cpp
• verify/library_checker/convolution/convolution_mod_1000000007.test.cpp
• verify/library_checker/convolution/gcd_convolution.test.cpp
• verify/library_checker/convolution/lcm_convolution.test.cpp
• verify/library_checker/data_structure/deque_operate_all_composite.test.cpp
• verify/library_checker/data_structure/point_set_range_composite.test.cpp
• verify/library_checker/data_structure/queue_operate_all_composite.test.cpp
• verify/library_checker/data_structure/range_affine_point_get.test.cpp
• verify/library_checker/data_structure/range_affine_range_sum.test.cpp
• verify/library_checker/data_structure/unionfind_with_potential.test.cpp
• verify/library_checker/enumerative_combinatrics/counting_spanning_tree_directed.test.cpp
• verify/library_checker/enumerative_combinatrics/counting_spanning_tree_undirected.test.cpp
• verify/library_checker/linear_algebra/determinant_of_matric.test.cpp
• verify/library_checker/linear_algebra/inverse_matrix.test.cpp
• verify/library_checker/linear_algebra/matrix_product.test.cpp
• verify/library_checker/linear_algebra/pow_of_matrix.test.cpp
• verify/library_checker/linear_algebra/rank_of_matrix.test.cpp
• verify/library_checker/linear_algebra/system_of_linear_equations.test.cpp
• verify/library_checker/other/find_linear_recurrence.test.cpp
• verify/library_checker/other/kth_term_of_linearly_recurrent_sequence.test.cpp
• verify/library_checker/polynomial/division_of_polynomial.test.cpp
• verify/library_checker/polynomial/exp_of_formal_power_series.test.cpp
• verify/library_checker/polynomial/inv_of_formal_power_series.test.cpp
• verify/library_checker/polynomial/log_of_formal_power_series.test.cpp
• verify/library_checker/polynomial/polynomial_taylor_shift.test.cpp
• verify/library_checker/polynomial/pow_of_formal_power_series.test.cpp
• verify/library_checker/polynomial/product_of_polynomial_sequence.test.cpp
• verify/library_checker/string/wildcard_pattern_matching.test.cpp
• verify/library_checker/tree/frequency_table_of_tree_distance.test.cpp
• verify/library_checker/tree/tree_path_composite_sum.test.cpp
• verify/library_checker/tree/vertex_set_path_composite.test.cpp
• verify/unit_test/convolution/convolution_ll.test.cpp
• verify/unit_test/template/debug.test.cpp
• verify/yukicoder/1559.test.cpp

Code

#pragma once
#include "./template.hpp"
template <uint32_t m>
struct StaticModint {
    using mint = StaticModint;
    static constexpr uint32_t mod() {
        return m;
    }
    static constexpr mint raw(const uint32_t v) {
        mint a;
        a._v = v;
        return a;
    }
    constexpr StaticModint()
        : _v(0) {}
    template <class T>
    constexpr StaticModint(const T& v) {
        static_assert(is_integral_v<T>);
        if constexpr(is_signed_v<T>) {
            int64_t x = int64_t(v % int64_t(m));
            if(x < 0) x += m;
            _v = uint32_t(x);
        } else _v = uint32_t(v % m);
    }
    constexpr uint32_t val() const {
        return _v;
    }
    constexpr mint& operator++() {
        return *this += 1;
    }
    constexpr mint& operator--() {
        return *this -= 1;
    }
    constexpr mint operator++(int) {
        mint res = *this;
        ++*this;
        return res;
    }
    constexpr mint operator--(int) {
        mint res = *this;
        --*this;
        return res;
    }
    constexpr mint& operator+=(mint rhs) {
        if(_v >= m - rhs._v) _v -= m;
        _v += rhs._v;
        return *this;
    }
    constexpr mint& operator-=(mint rhs) {
        if(_v < rhs._v) _v += m;
        _v -= rhs._v;
        return *this;
    }
    constexpr mint& operator*=(mint rhs) {
        return *this = *this * rhs;
    }
    constexpr mint& operator/=(mint rhs) {
        return *this *= rhs.inv();
    }
    constexpr mint operator+() const {
        return *this;
    }
    constexpr mint operator-() const {
        return mint{} - *this;
    }
    constexpr mint pow(long long n) const {
        assert(0 <= n);
        if(n == 0) return 1;
        mint x = *this, r = 1;
        while(1) {
            if(n & 1) r *= x;
            n >>= 1;
            if(n == 0) return r;
            x *= x;
        }
    }
    constexpr mint inv() const {
        if constexpr(prime) {
            assert(_v);
            return pow(m - 2);
        } else {
            const auto eg = inv_gcd(_v, m);
            assert(eg.first == 1);
            return eg.second;
        }
    }
    friend constexpr mint operator+(mint lhs, mint rhs) {
        return lhs += rhs;
    }
    friend constexpr mint operator-(mint lhs, mint rhs) {
        return lhs -= rhs;
    }
    friend constexpr mint operator*(mint lhs, mint rhs) {
        return uint64_t(lhs._v) * rhs._v;
    }
    friend constexpr mint operator/(mint lhs, mint rhs) {
        return lhs /= rhs;
    }
    friend constexpr bool operator==(mint lhs, mint rhs) {
        return lhs._v == rhs._v;
    }
    friend constexpr bool operator!=(mint lhs, mint rhs) {
        return lhs._v != rhs._v;
    }
    friend istream& operator>>(istream& in, mint& x) {
        long long a;
        in >> a;
        x = a;
        return in;
    }
    friend ostream& operator<<(ostream& out, const mint& x) {
        return out << x.val();
    }

   private:
    uint32_t _v = 0;
    static constexpr bool prime = []() -> bool {
        if(m == 1) return 0;
        if(m == 2 or m == 7 or m == 61) return 1;
        if(m % 2 == 0) return 0;
        uint32_t d = m - 1;
        while(d % 2 == 0) d /= 2;
        for(uint32_t a : {2, 7, 61}) {
            uint32_t t = d;
            mint y = mint(a).pow(t);
            while(t != m - 1 && y != 1 && y != m - 1) {
                y *= y;
                t <<= 1;
            }
            if(y != m - 1 && t % 2 == 0) return 0;
        }
        return 1;
    }();
    static constexpr pair<int32_t, int32_t> inv_gcd(const int32_t a, const int32_t b) {
        if(a == 0) return {b, 0};
        int32_t s = b, t = a, m0 = 0, m1 = 1;
        while(t) {
            const int32_t u = s / t;
            s -= t * u;
            m0 -= m1 * u;
            swap(s, t);
            swap(m0, m1);
        }
        if(m0 < 0) m0 += b / s;
        return {s, m0};
    }
};
using modint998244353 = StaticModint<998244353>;
using modint1000000007 = StaticModint<1000000007>;

#line 2 "src/template/template.hpp"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using P = pair<long long, long long>;
#define rep(i, a, b) for(long long i = (a); i < (b); ++i)
#define rrep(i, a, b) for(long long i = (a); i >= (b); --i)
constexpr long long inf = 4e18;
struct SetupIO {
    SetupIO() {
        ios::sync_with_stdio(0);
        cin.tie(0);
        cout << fixed << setprecision(30);
    }
} setup_io;
#line 3 "src/template/static_modint.hpp"
template <uint32_t m>
struct StaticModint {
    using mint = StaticModint;
    static constexpr uint32_t mod() {
        return m;
    }
    static constexpr mint raw(const uint32_t v) {
        mint a;
        a._v = v;
        return a;
    }
    constexpr StaticModint()
        : _v(0) {}
    template <class T>
    constexpr StaticModint(const T& v) {
        static_assert(is_integral_v<T>);
        if constexpr(is_signed_v<T>) {
            int64_t x = int64_t(v % int64_t(m));
            if(x < 0) x += m;
            _v = uint32_t(x);
        } else _v = uint32_t(v % m);
    }
    constexpr uint32_t val() const {
        return _v;
    }
    constexpr mint& operator++() {
        return *this += 1;
    }
    constexpr mint& operator--() {
        return *this -= 1;
    }
    constexpr mint operator++(int) {
        mint res = *this;
        ++*this;
        return res;
    }
    constexpr mint operator--(int) {
        mint res = *this;
        --*this;
        return res;
    }
    constexpr mint& operator+=(mint rhs) {
        if(_v >= m - rhs._v) _v -= m;
        _v += rhs._v;
        return *this;
    }
    constexpr mint& operator-=(mint rhs) {
        if(_v < rhs._v) _v += m;
        _v -= rhs._v;
        return *this;
    }
    constexpr mint& operator*=(mint rhs) {
        return *this = *this * rhs;
    }
    constexpr mint& operator/=(mint rhs) {
        return *this *= rhs.inv();
    }
    constexpr mint operator+() const {
        return *this;
    }
    constexpr mint operator-() const {
        return mint{} - *this;
    }
    constexpr mint pow(long long n) const {
        assert(0 <= n);
        if(n == 0) return 1;
        mint x = *this, r = 1;
        while(1) {
            if(n & 1) r *= x;
            n >>= 1;
            if(n == 0) return r;
            x *= x;
        }
    }
    constexpr mint inv() const {
        if constexpr(prime) {
            assert(_v);
            return pow(m - 2);
        } else {
            const auto eg = inv_gcd(_v, m);
            assert(eg.first == 1);
            return eg.second;
        }
    }
    friend constexpr mint operator+(mint lhs, mint rhs) {
        return lhs += rhs;
    }
    friend constexpr mint operator-(mint lhs, mint rhs) {
        return lhs -= rhs;
    }
    friend constexpr mint operator*(mint lhs, mint rhs) {
        return uint64_t(lhs._v) * rhs._v;
    }
    friend constexpr mint operator/(mint lhs, mint rhs) {
        return lhs /= rhs;
    }
    friend constexpr bool operator==(mint lhs, mint rhs) {
        return lhs._v == rhs._v;
    }
    friend constexpr bool operator!=(mint lhs, mint rhs) {
        return lhs._v != rhs._v;
    }
    friend istream& operator>>(istream& in, mint& x) {
        long long a;
        in >> a;
        x = a;
        return in;
    }
    friend ostream& operator<<(ostream& out, const mint& x) {
        return out << x.val();
    }

   private:
    uint32_t _v = 0;
    static constexpr bool prime = []() -> bool {
        if(m == 1) return 0;
        if(m == 2 or m == 7 or m == 61) return 1;
        if(m % 2 == 0) return 0;
        uint32_t d = m - 1;
        while(d % 2 == 0) d /= 2;
        for(uint32_t a : {2, 7, 61}) {
            uint32_t t = d;
            mint y = mint(a).pow(t);
            while(t != m - 1 && y != 1 && y != m - 1) {
                y *= y;
                t <<= 1;
            }
            if(y != m - 1 && t % 2 == 0) return 0;
        }
        return 1;
    }();
    static constexpr pair<int32_t, int32_t> inv_gcd(const int32_t a, const int32_t b) {
        if(a == 0) return {b, 0};
        int32_t s = b, t = a, m0 = 0, m1 = 1;
        while(t) {
            const int32_t u = s / t;
            s -= t * u;
            m0 -= m1 * u;
            swap(s, t);
            swap(m0, m1);
        }
        if(m0 < 0) m0 += b / s;
        return {s, m0};
    }
};
using modint998244353 = StaticModint<998244353>;
using modint1000000007 = StaticModint<1000000007>;

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