Arbitrary Modint
(lib/math/arbitrary_modint.hpp)

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• Last update: 2024-11-03 21:58:22+09:00
• Include: #include "lib/math/arbitrary_modint.hpp"

Arbitrary Modint

概要

Modulus で割ったあまりの値を管理する構造体です。

入力で Modulus が与えられる場合に使用できます。

使い方

• ModInt::setMod(m): Modulus を m に設定します。

Verified with

• test/library_checker/enumerative_combinatorics/binomial_coefficient_prime_mod_1.test.cpp

Code

#pragma once

/**
 * @brief Arbitrary Modint
 * @docs docs/math/arbitrary_modint.md
 */

struct ModInt{
    long long val;
    ModInt(const long long &_val = 0) noexcept : val(_val) {
        normalize();
    }
    static long long &Modulus(){
        static long long mod = 0;
        return mod;
    }
    static long long mod() { return Modulus(); }
    static void setMod(const int &mod){
        Modulus() = mod;
    }
    void normalize(){
        val = (val % Modulus() + Modulus()) % Modulus();
    }
    inline ModInt &operator+=(const ModInt &rhs) noexcept {
        if(val += rhs.val, val >= Modulus()) val -= Modulus();
        return *this;
    }
    inline ModInt &operator-=(const ModInt &rhs) noexcept {
        if(val -= rhs.val, val < 0) val += Modulus();
        return *this;
    }
    inline ModInt &operator*=(const ModInt &rhs) noexcept {
        val = val * rhs.val % Modulus();
        return *this;
    }
    inline ModInt &operator/=(const ModInt &rhs) noexcept {
        val = val * inv(rhs.val).val % Modulus();
        return *this;
    }
    inline ModInt &operator++() noexcept {
        if(++val >= Modulus()) val -= Modulus();
        return *this;
    }
    inline ModInt operator++(int) noexcept {
        ModInt t = val;
        if(++val >= Modulus()) val -= Modulus();
        return t;
    }
    inline ModInt &operator--() noexcept {
        if(--val < 0) val += Modulus();
        return *this;
    }
    inline ModInt operator--(int) noexcept {
        ModInt t = val;
        if(--val < 0) val += Modulus();
        return t;
    }
    inline ModInt operator-() const noexcept { return (Modulus() - val) % Modulus(); }
    inline ModInt inv(void) const { return inv(val); }
    ModInt pow(long long n) const {
        assert(0 <= n);
        ModInt x = *this, r = 1;
        while(n){
            if(n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    ModInt inv(const long long n) const {
        long long a = n, b = Modulus(), u = 1, v = 0;
        while(b){
            long long t = a / b;
            a -= t * b; swap(a, b);
            u -= t * v; swap(u, v);
        }
        u %= Modulus();
        if(u < 0) u += Modulus();
        return u;
    }
    friend inline ModInt operator+(const ModInt &lhs, const ModInt &rhs) noexcept { return ModInt(lhs) += rhs; }
    friend inline ModInt operator-(const ModInt &lhs, const ModInt &rhs) noexcept { return ModInt(lhs) -= rhs; }
    friend inline ModInt operator*(const ModInt &lhs, const ModInt &rhs) noexcept { return ModInt(lhs) *= rhs; }
    friend inline ModInt operator/(const ModInt &lhs, const ModInt &rhs) noexcept { return ModInt(lhs) /= rhs; }
    friend inline bool operator==(const ModInt &lhs, const ModInt &rhs) noexcept { return lhs.val == rhs.val; }
    friend inline bool operator!=(const ModInt &lhs, const ModInt &rhs) noexcept { return lhs.val != rhs.val; }
    friend inline istream &operator>>(istream &is, ModInt &x) noexcept {
        is >> x.val;
        x.normalize();
        return is;
    }
    friend inline ostream &operator<<(ostream &os, const ModInt &x) noexcept { return os << x.val; }
};

#line 2 "lib/math/arbitrary_modint.hpp"

/**
 * @brief Arbitrary Modint
 * @docs docs/math/arbitrary_modint.md
 */

struct ModInt{
    long long val;
    ModInt(const long long &_val = 0) noexcept : val(_val) {
        normalize();
    }
    static long long &Modulus(){
        static long long mod = 0;
        return mod;
    }
    static long long mod() { return Modulus(); }
    static void setMod(const int &mod){
        Modulus() = mod;
    }
    void normalize(){
        val = (val % Modulus() + Modulus()) % Modulus();
    }
    inline ModInt &operator+=(const ModInt &rhs) noexcept {
        if(val += rhs.val, val >= Modulus()) val -= Modulus();
        return *this;
    }
    inline ModInt &operator-=(const ModInt &rhs) noexcept {
        if(val -= rhs.val, val < 0) val += Modulus();
        return *this;
    }
    inline ModInt &operator*=(const ModInt &rhs) noexcept {
        val = val * rhs.val % Modulus();
        return *this;
    }
    inline ModInt &operator/=(const ModInt &rhs) noexcept {
        val = val * inv(rhs.val).val % Modulus();
        return *this;
    }
    inline ModInt &operator++() noexcept {
        if(++val >= Modulus()) val -= Modulus();
        return *this;
    }
    inline ModInt operator++(int) noexcept {
        ModInt t = val;
        if(++val >= Modulus()) val -= Modulus();
        return t;
    }
    inline ModInt &operator--() noexcept {
        if(--val < 0) val += Modulus();
        return *this;
    }
    inline ModInt operator--(int) noexcept {
        ModInt t = val;
        if(--val < 0) val += Modulus();
        return t;
    }
    inline ModInt operator-() const noexcept { return (Modulus() - val) % Modulus(); }
    inline ModInt inv(void) const { return inv(val); }
    ModInt pow(long long n) const {
        assert(0 <= n);
        ModInt x = *this, r = 1;
        while(n){
            if(n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    ModInt inv(const long long n) const {
        long long a = n, b = Modulus(), u = 1, v = 0;
        while(b){
            long long t = a / b;
            a -= t * b; swap(a, b);
            u -= t * v; swap(u, v);
        }
        u %= Modulus();
        if(u < 0) u += Modulus();
        return u;
    }
    friend inline ModInt operator+(const ModInt &lhs, const ModInt &rhs) noexcept { return ModInt(lhs) += rhs; }
    friend inline ModInt operator-(const ModInt &lhs, const ModInt &rhs) noexcept { return ModInt(lhs) -= rhs; }
    friend inline ModInt operator*(const ModInt &lhs, const ModInt &rhs) noexcept { return ModInt(lhs) *= rhs; }
    friend inline ModInt operator/(const ModInt &lhs, const ModInt &rhs) noexcept { return ModInt(lhs) /= rhs; }
    friend inline bool operator==(const ModInt &lhs, const ModInt &rhs) noexcept { return lhs.val == rhs.val; }
    friend inline bool operator!=(const ModInt &lhs, const ModInt &rhs) noexcept { return lhs.val != rhs.val; }
    friend inline istream &operator>>(istream &is, ModInt &x) noexcept {
        is >> x.val;
        x.normalize();
        return is;
    }
    friend inline ostream &operator<<(ostream &os, const ModInt &x) noexcept { return os << x.val; }
};

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