tourist's modular arithmetic class
7846 ワード
#include
using namespace std;
template
T inverse(T a, T m) {
T u = 0, v = 1;
while (a != 0) {
T t = m / a;
m -= t * a; swap(a, m);
u -= t * v; swap(u, v);
}
assert(m == 1);
return u;
}
template
class Modular {
public:
using Type = typename decay::type;
constexpr Modular() : value() {}
template
Modular(const U& x) {
value = normalize(x);
}
template
static Type normalize(const U& x) {
Type v;
if (-mod() <= x && x < mod()) v = static_cast(x);
else v = static_cast(x % mod());
if (v < 0) v += mod();
return v;
}
const Type& operator()() const { return value; }
template
explicit operator U() const { return static_cast(value); }
constexpr static Type mod() { return T::value; }
Modular& operator+=(const Modular& other) { if ((value += other.value) >= mod()) value -= mod(); return *this; }
Modular& operator-=(const Modular& other) { if ((value -= other.value) < 0) value += mod(); return *this; }
template Modular& operator+=(const U& other) { return *this += Modular(other); }
template Modular& operator-=(const U& other) { return *this -= Modular(other); }
Modular& operator++() { return *this += 1; }
Modular& operator--() { return *this -= 1; }
Modular operator++(int) { Modular result(*this); *this += 1; return result; }
Modular operator--(int) { Modular result(*this); *this -= 1; return result; }
Modular operator-() const { return Modular(-value); }
template
typename enable_if::Type, int>::value, Modular>::type& operator*=(const Modular& rhs) {
#ifdef _WIN32
uint64_t x = static_cast(value) * static_cast(rhs.value);
uint32_t xh = static_cast(x >> 32), xl = static_cast(x), d, m;
asm(
"divl %4;
\t"
: "=a" (d), "=d" (m)
: "d" (xh), "a" (xl), "r" (mod())
);
value = m;
#else
value = normalize(static_cast(value) * static_cast(rhs.value));
#endif
return *this;
}
template
typename enable_if::Type, int64_t>::value, Modular>::type& operator*=(const Modular& rhs) {
int64_t q = static_cast(static_cast(value) * rhs.value / mod());
value = normalize(value * rhs.value - q * mod());
return *this;
}
template
typename enable_if::Type>::value, Modular>::type& operator*=(const Modular& rhs) {
value = normalize(value * rhs.value);
return *this;
}
Modular& operator/=(const Modular& other) { return *this *= Modular(inverse(other.value, mod())); }
template
friend const Modular& abs(const Modular& v) { return v; }
template
friend bool operator==(const Modular& lhs, const Modular& rhs);
template
friend bool operator& lhs, const Modular& rhs);
template
friend std::istream& operator>>(std::istream& stream, Modular& number);
private:
Type value;
};
template bool operator==(const Modular& lhs, const Modular& rhs) { return lhs.value == rhs.value; }
template bool operator==(const Modular& lhs, U rhs) { return lhs == Modular(rhs); }
template bool operator==(U lhs, const Modular& rhs) { return Modular(lhs) == rhs; }
template bool operator!=(const Modular& lhs, const Modular& rhs) { return !(lhs == rhs); }
template bool operator!=(const Modular& lhs, U rhs) { return !(lhs == rhs); }
template bool operator!=(U lhs, const Modular& rhs) { return !(lhs == rhs); }
template bool operator& lhs, const Modular& rhs) { return lhs.value < rhs.value; }
template Modular operator+(const Modular& lhs, const Modular& rhs) { return Modular(lhs) += rhs; }
template Modular operator+(const Modular& lhs, U rhs) { return Modular(lhs) += rhs; }
template Modular operator+(U lhs, const Modular& rhs) { return Modular(lhs) += rhs; }
template Modular operator-(const Modular& lhs, const Modular& rhs) { return Modular(lhs) -= rhs; }
template Modular operator-(const Modular& lhs, U rhs) { return Modular(lhs) -= rhs; }
template Modular operator-(U lhs, const Modular& rhs) { return Modular(lhs) -= rhs; }
template Modular operator*(const Modular& lhs, const Modular& rhs) { return Modular(lhs) *= rhs; }
template Modular operator*(const Modular& lhs, U rhs) { return Modular(lhs) *= rhs; }
template Modular operator*(U lhs, const Modular& rhs) { return Modular(lhs) *= rhs; }
template Modular operator/(const Modular& lhs, const Modular& rhs) { return Modular(lhs) /= rhs; }
template Modular operator/(const Modular& lhs, U rhs) { return Modular(lhs) /= rhs; }
template Modular operator/(U lhs, const Modular& rhs) { return Modular(lhs) /= rhs; }
template
Modular power(const Modular& a, const U& b) {
assert(b >= 0);
Modular x = a, res = 1;
U p = b;
while (p > 0) {
if (p & 1) res *= x;
x *= x;
p >>= 1;
}
return res;
}
template
bool IsZero(const Modular& number) {
return number() == 0;
}
template
string to_string(const Modular& number) {
return to_string(number());
}
template
std::ostream& operator<& number) {
return stream << number();
}
template
std::istream& operator>>(std::istream& stream, Modular& number) {
typename common_type::Type, int64_t>::type x;
stream >> x;
number.value = Modular::normalize(x);
return stream;
}
/*
using ModType = int;
struct VarMod { static ModType value; };
ModType VarMod::value;
ModType& md = VarMod::value;
using Mint = Modular;
*/
constexpr int md = 998244353;
using Mint = Modular<:integral_constant>::type, md>>;