CP-Algorithms Library
This documentation is automatically generated by competitive-verifier/competitive-verifier
cp-algo/number_theory/modint.hpp
- View this file on GitHub
- Last update: 2025-05-27 14:25:18+02:00
- Include:
#include "cp-algo/number_theory/modint.hpp"
Depends on
Required by
- cp-algo/linalg/frobenius.hpp
- cp-algo/linalg/matrix.hpp
- cp-algo/linalg/vector.hpp
- cp-algo/math/factorials.hpp
- cp-algo/math/fft.hpp
- cp-algo/math/multivar.hpp
- cp-algo/math/poly.hpp
- cp-algo/math/poly/impl/div.hpp
- cp-algo/math/poly/impl/euclid.hpp
cp-algo/number_theory.hpp- cp-algo/number_theory/discrete_log.hpp
- cp-algo/number_theory/discrete_sqrt.hpp
- cp-algo/number_theory/euler.hpp
- cp-algo/number_theory/factorize.hpp
- cp-algo/number_theory/primality.hpp
- cp-algo/number_theory/two_squares.hpp
Verified with
- Binomial Coefficient (Prime Mod) (verify/combi/binom.test.cpp)
- Many Factorials (verify/combi/many_facts.test.cpp)
- Many Factorials (dynamic Mod) (verify/combi/many_facts_dynamic.test.cpp)
- Adjugate Matrix (verify/linalg/adj.test.cpp)
- Characteristic Polynomial (verify/linalg/characteristic.test.cpp)
- Matrix Determinant (verify/linalg/det.test.cpp)
- Counting Eulerian Circuits (verify/linalg/euler_circs.test.cpp)
- Inverse Matrix (verify/linalg/inv.test.cpp)
- Matching on General Graph (verify/linalg/matching.test.cpp)
- Pow of Matrix (verify/linalg/pow.test.cpp)
- Pow of Matrix (Frobenius) (verify/linalg/pow_fast.test.cpp)
- Matrix Product (verify/linalg/prod.test.cpp)
- Matrix Product (dynamic modint) (verify/linalg/prod_dynamic_modint.test.cpp)
- Rank of Matrix (verify/linalg/rank.test.cpp)
- Counting Spanning Trees (Directed) (verify/linalg/spanning_directed.test.cpp)
- Counting Spanning Trees (Undirected) (verify/linalg/spanning_undirected.test.cpp)
- System of Linear Equations (verify/linalg/system.test.cpp)
- Matching on General Graph (Tutte matrix) (verify/linalg/tutte.test.cpp)
- Discrete Logarithm (verify/number_theory/discrete_log.test.cpp)
- Factorize (verify/number_theory/factorize.test.cpp)
- Sqrt Mod (verify/number_theory/modsqrt.test.cpp)
- Primality Test (verify/number_theory/primality.test.cpp)
- Primitive Root (verify/number_theory/primitive_root.test.cpp)
- Represent A Number As Two Square Sum (verify/number_theory/two_squares.test.cpp)
- Bell Number (verify/poly/bell.test.cpp)
- Convolution mod $10^9+7$ (verify/poly/convolution107.test.cpp)
- Convolution (Large) (verify/poly/convolution_large.test.cpp)
- Convolution on the Multiplicative Monoid of $\mathbb Z/p\mathbb{Z}$ (verify/poly/convolution_mul.test.cpp)
- Division of Polynomials (verify/poly/div.test.cpp)
- Exp of Power Series (verify/poly/exp.test.cpp)
- Find Linear Recurrence (verify/poly/find_linrec.test.cpp)
- Polynomial Interpolation (verify/poly/inter.test.cpp)
- Polynomial Interpolation (Geometric Sequence) (verify/poly/inter_geo.test.cpp)
- Inv of Power Series (verify/poly/inv.test.cpp)
- Inv of Polynomials (verify/poly/inv_mod.test.cpp)
- Consecutive Terms of Linear Recursion (verify/poly/linrec_consecutive.test.cpp)
- Kth term of Linearly Recurrent Sequence (verify/poly/linrec_single.test.cpp)
- Log of Power Series (verify/poly/log.test.cpp)
- Multipoint Evaluation (verify/poly/multieval.test.cpp)
- Multipoint Evaluation (Geometric Sequence) (verify/poly/multieval_geo.test.cpp)
- Multidimensional Convolution (Truncated) (verify/poly/multivar.test.cpp)
- Conversion to Newton Basis (verify/poly/newton.test.cpp)
- Pow of Power Series (verify/poly/pow.test.cpp)
- Product of Polynomial Sequence (verify/poly/prod_sequence.test.cpp)
- Polynomial Root Finding (verify/poly/roots.test.cpp)
- Shift of Sampling Points of Polynomial (verify/poly/sampling.test.cpp)
- Sqrt of Power Series (verify/poly/sqrt.test.cpp)
- $\sum\limits_{i=0}^\infty r^i i^d$ (verify/poly/sum_exp_poly.test.cpp)
- Polynomial Taylor Shift (verify/poly/taylor.test.cpp)
- Range Affine Range Sum (verify/structures/segtree/range_affine_range_sum.test.cpp)
- Dynamic Range Affine Range Sum (verify/structures/treap/dynamic_sequence_range_affine_range_sum.test.cpp)
Code
#ifndef CP_ALGO_NUMBER_THEORY_MODINT_HPP
#define CP_ALGO_NUMBER_THEORY_MODINT_HPP
#include "../math/common.hpp"
#include <iostream>
#include <cassert>
namespace cp_algo::math {
template<typename modint, typename _Int>
struct modint_base {
using Int = _Int;
using UInt = std::make_unsigned_t<Int>;
static constexpr size_t bits = sizeof(Int) * 8;
using Int2 = std::conditional_t<bits <= 32, int64_t, __int128_t>;
using UInt2 = std::conditional_t<bits <= 32, uint64_t, __uint128_t>;
constexpr static Int mod() {
return modint::mod();
}
constexpr static Int remod() {
return modint::remod();
}
constexpr static UInt2 modmod() {
return UInt2(mod()) * mod();
}
constexpr modint_base() = default;
constexpr modint_base(Int2 rr) {
to_modint().setr(UInt((rr + modmod()) % mod()));
}
modint inv() const {
return bpow(to_modint(), mod() - 2);
}
modint operator - () const {
modint neg;
neg.r = std::min(-r, remod() - r);
return neg;
}
modint& operator /= (const modint &t) {
return to_modint() *= t.inv();
}
modint& operator *= (const modint &t) {
r = UInt(UInt2(r) * t.r % mod());
return to_modint();
}
modint& operator += (const modint &t) {
r += t.r; r = std::min(r, r - remod());
return to_modint();
}
modint& operator -= (const modint &t) {
r -= t.r; r = std::min(r, r + remod());
return to_modint();
}
modint operator + (const modint &t) const {return modint(to_modint()) += t;}
modint operator - (const modint &t) const {return modint(to_modint()) -= t;}
modint operator * (const modint &t) const {return modint(to_modint()) *= t;}
modint operator / (const modint &t) const {return modint(to_modint()) /= t;}
// Why <=> doesn't work?..
auto operator == (const modint &t) const {return to_modint().getr() == t.getr();}
auto operator != (const modint &t) const {return to_modint().getr() != t.getr();}
auto operator <= (const modint &t) const {return to_modint().getr() <= t.getr();}
auto operator >= (const modint &t) const {return to_modint().getr() >= t.getr();}
auto operator < (const modint &t) const {return to_modint().getr() < t.getr();}
auto operator > (const modint &t) const {return to_modint().getr() > t.getr();}
Int rem() const {
UInt R = to_modint().getr();
return R - (R > (UInt)mod() / 2) * mod();
}
constexpr void setr(UInt rr) {
r = rr;
}
constexpr UInt getr() const {
return r;
}
// Only use these if you really know what you're doing!
static UInt modmod8() {return UInt(8 * modmod());}
void add_unsafe(UInt t) {r += t;}
void pseudonormalize() {r = std::min(r, r - modmod8());}
modint const& normalize() {
if(r >= (UInt)mod()) {
r %= mod();
}
return to_modint();
}
void setr_direct(UInt rr) {r = rr;}
UInt getr_direct() const {return r;}
protected:
UInt r;
private:
constexpr modint& to_modint() {return static_cast<modint&>(*this);}
constexpr modint const& to_modint() const {return static_cast<modint const&>(*this);}
};
template<typename modint>
concept modint_type = std::is_base_of_v<modint_base<modint, typename modint::Int>, modint>;
template<modint_type modint>
decltype(std::cin)& operator >> (decltype(std::cin) &in, modint &x) {
typename modint::UInt r;
auto &res = in >> r;
x.setr(r);
return res;
}
template<modint_type modint>
decltype(std::cout)& operator << (decltype(std::cout) &out, modint const& x) {
return out << x.getr();
}
template<auto m>
struct modint: modint_base<modint<m>, decltype(m)> {
using Base = modint_base<modint<m>, decltype(m)>;
using Base::Base;
static constexpr Base::Int mod() {return m;}
static constexpr Base::UInt remod() {return m;}
auto getr() const {return Base::r;}
};
template<typename Int = int>
struct dynamic_modint: modint_base<dynamic_modint<Int>, Int> {
using Base = modint_base<dynamic_modint<Int>, Int>;
using Base::Base;
static Base::UInt m_reduce(Base::UInt2 ab) {
if(mod() % 2 == 0) [[unlikely]] {
return typename Base::UInt(ab % mod());
} else {
typename Base::UInt2 m = typename Base::UInt(ab) * imod();
return typename Base::UInt((ab + m * mod()) >> Base::bits);
}
}
static Base::UInt m_transform(Base::UInt a) {
if(mod() % 2 == 0) [[unlikely]] {
return a;
} else {
return m_reduce(a * pw128());
}
}
dynamic_modint& operator *= (const dynamic_modint &t) {
Base::r = m_reduce(typename Base::UInt2(Base::r) * t.r);
return *this;
}
void setr(Base::UInt rr) {
Base::r = m_transform(rr);
}
Base::UInt getr() const {
typename Base::UInt res = m_reduce(Base::r);
return std::min(res, res - mod());
}
static Int mod() {return m;}
static Int remod() {return 2 * m;}
static Base::UInt imod() {return im;}
static Base::UInt2 pw128() {return r2;}
static void switch_mod(Int nm) {
m = nm;
im = m % 2 ? inv2(-m) : 0;
r2 = static_cast<Base::UInt>(static_cast<Base::UInt2>(-1) % m + 1);
}
// Wrapper for temp switching
auto static with_mod(Int tmp, auto callback) {
struct scoped {
Int prev = mod();
~scoped() {switch_mod(prev);}
} _;
switch_mod(tmp);
return callback();
}
private:
static thread_local Int m;
static thread_local Base::UInt im, r2;
};
template<typename Int>
Int thread_local dynamic_modint<Int>::m = 1;
template<typename Int>
dynamic_modint<Int>::Base::UInt thread_local dynamic_modint<Int>::im = -1;
template<typename Int>
dynamic_modint<Int>::Base::UInt thread_local dynamic_modint<Int>::r2 = 0;
}
#endif // CP_ALGO_MATH_MODINT_HPP
#line 1 "cp-algo/number_theory/modint.hpp"
#line 1 "cp-algo/math/common.hpp"
#include <functional>
#include <cstdint>
#include <cassert>
namespace cp_algo::math {
#ifdef CP_ALGO_MAXN
const int maxn = CP_ALGO_MAXN;
#else
const int maxn = 1 << 19;
#endif
const int magic = 64; // threshold for sizes to run the naive algo
auto bpow(auto const& x, auto n, auto const& one, auto op) {
if(n == 0) {
return one;
} else {
auto t = bpow(x, n / 2, one, op);
t = op(t, t);
if(n % 2) {
t = op(t, x);
}
return t;
}
}
auto bpow(auto x, auto n, auto ans) {
return bpow(x, n, ans, std::multiplies{});
}
template<typename T>
T bpow(T const& x, auto n) {
return bpow(x, n, T(1));
}
inline constexpr auto inv2(auto x) {
assert(x % 2);
std::make_unsigned_t<decltype(x)> y = 1;
while(y * x != 1) {
y *= 2 - x * y;
}
return y;
}
}
#line 4 "cp-algo/number_theory/modint.hpp"
#include <iostream>
#line 6 "cp-algo/number_theory/modint.hpp"
namespace cp_algo::math {
template<typename modint, typename _Int>
struct modint_base {
using Int = _Int;
using UInt = std::make_unsigned_t<Int>;
static constexpr size_t bits = sizeof(Int) * 8;
using Int2 = std::conditional_t<bits <= 32, int64_t, __int128_t>;
using UInt2 = std::conditional_t<bits <= 32, uint64_t, __uint128_t>;
constexpr static Int mod() {
return modint::mod();
}
constexpr static Int remod() {
return modint::remod();
}
constexpr static UInt2 modmod() {
return UInt2(mod()) * mod();
}
constexpr modint_base() = default;
constexpr modint_base(Int2 rr) {
to_modint().setr(UInt((rr + modmod()) % mod()));
}
modint inv() const {
return bpow(to_modint(), mod() - 2);
}
modint operator - () const {
modint neg;
neg.r = std::min(-r, remod() - r);
return neg;
}
modint& operator /= (const modint &t) {
return to_modint() *= t.inv();
}
modint& operator *= (const modint &t) {
r = UInt(UInt2(r) * t.r % mod());
return to_modint();
}
modint& operator += (const modint &t) {
r += t.r; r = std::min(r, r - remod());
return to_modint();
}
modint& operator -= (const modint &t) {
r -= t.r; r = std::min(r, r + remod());
return to_modint();
}
modint operator + (const modint &t) const {return modint(to_modint()) += t;}
modint operator - (const modint &t) const {return modint(to_modint()) -= t;}
modint operator * (const modint &t) const {return modint(to_modint()) *= t;}
modint operator / (const modint &t) const {return modint(to_modint()) /= t;}
// Why <=> doesn't work?..
auto operator == (const modint &t) const {return to_modint().getr() == t.getr();}
auto operator != (const modint &t) const {return to_modint().getr() != t.getr();}
auto operator <= (const modint &t) const {return to_modint().getr() <= t.getr();}
auto operator >= (const modint &t) const {return to_modint().getr() >= t.getr();}
auto operator < (const modint &t) const {return to_modint().getr() < t.getr();}
auto operator > (const modint &t) const {return to_modint().getr() > t.getr();}
Int rem() const {
UInt R = to_modint().getr();
return R - (R > (UInt)mod() / 2) * mod();
}
constexpr void setr(UInt rr) {
r = rr;
}
constexpr UInt getr() const {
return r;
}
// Only use these if you really know what you're doing!
static UInt modmod8() {return UInt(8 * modmod());}
void add_unsafe(UInt t) {r += t;}
void pseudonormalize() {r = std::min(r, r - modmod8());}
modint const& normalize() {
if(r >= (UInt)mod()) {
r %= mod();
}
return to_modint();
}
void setr_direct(UInt rr) {r = rr;}
UInt getr_direct() const {return r;}
protected:
UInt r;
private:
constexpr modint& to_modint() {return static_cast<modint&>(*this);}
constexpr modint const& to_modint() const {return static_cast<modint const&>(*this);}
};
template<typename modint>
concept modint_type = std::is_base_of_v<modint_base<modint, typename modint::Int>, modint>;
template<modint_type modint>
decltype(std::cin)& operator >> (decltype(std::cin) &in, modint &x) {
typename modint::UInt r;
auto &res = in >> r;
x.setr(r);
return res;
}
template<modint_type modint>
decltype(std::cout)& operator << (decltype(std::cout) &out, modint const& x) {
return out << x.getr();
}
template<auto m>
struct modint: modint_base<modint<m>, decltype(m)> {
using Base = modint_base<modint<m>, decltype(m)>;
using Base::Base;
static constexpr Base::Int mod() {return m;}
static constexpr Base::UInt remod() {return m;}
auto getr() const {return Base::r;}
};
template<typename Int = int>
struct dynamic_modint: modint_base<dynamic_modint<Int>, Int> {
using Base = modint_base<dynamic_modint<Int>, Int>;
using Base::Base;
static Base::UInt m_reduce(Base::UInt2 ab) {
if(mod() % 2 == 0) [[unlikely]] {
return typename Base::UInt(ab % mod());
} else {
typename Base::UInt2 m = typename Base::UInt(ab) * imod();
return typename Base::UInt((ab + m * mod()) >> Base::bits);
}
}
static Base::UInt m_transform(Base::UInt a) {
if(mod() % 2 == 0) [[unlikely]] {
return a;
} else {
return m_reduce(a * pw128());
}
}
dynamic_modint& operator *= (const dynamic_modint &t) {
Base::r = m_reduce(typename Base::UInt2(Base::r) * t.r);
return *this;
}
void setr(Base::UInt rr) {
Base::r = m_transform(rr);
}
Base::UInt getr() const {
typename Base::UInt res = m_reduce(Base::r);
return std::min(res, res - mod());
}
static Int mod() {return m;}
static Int remod() {return 2 * m;}
static Base::UInt imod() {return im;}
static Base::UInt2 pw128() {return r2;}
static void switch_mod(Int nm) {
m = nm;
im = m % 2 ? inv2(-m) : 0;
r2 = static_cast<Base::UInt>(static_cast<Base::UInt2>(-1) % m + 1);
}
// Wrapper for temp switching
auto static with_mod(Int tmp, auto callback) {
struct scoped {
Int prev = mod();
~scoped() {switch_mod(prev);}
} _;
switch_mod(tmp);
return callback();
}
private:
static thread_local Int m;
static thread_local Base::UInt im, r2;
};
template<typename Int>
Int thread_local dynamic_modint<Int>::m = 1;
template<typename Int>
dynamic_modint<Int>::Base::UInt thread_local dynamic_modint<Int>::im = -1;
template<typename Int>
dynamic_modint<Int>::Base::UInt thread_local dynamic_modint<Int>::r2 = 0;
}