math/combinatorics/montgomery-mod-int.hpp

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• Last update: 2024-04-27 01:27:28+09:00
• Include: #include "math/combinatorics/montgomery-mod-int.hpp"

Required by

• Vertex Set Path Composite (structure/develop/vertex-set-path-composite.hpp)

Verified with

• test/verify/aoj-2405.test.cpp
• test/verify/aoj-dpl-5-g.test.cpp
• test/verify/aoj-dpl-5-i.test.cpp
• test/verify/aoj-dpl-5-j.test.cpp
• test/verify/yosupo-bernoulli-number.test.cpp
• test/verify/yosupo-bitwise-and-convolution-2.test.cpp
• test/verify/yosupo-bitwise-and-convolution.test.cpp
• test/verify/yosupo-bitwise-xor-convolution.test.cpp
• test/verify/yosupo-convolution-mod-2.test.cpp
• test/verify/yosupo-division-of-polynomials.test.cpp
• test/verify/yosupo-dynamic-tree-vertex-set-path-composite-2.test.cpp
• test/verify/yosupo-dynamic-tree-vertex-set-path-composite-3.test.cpp
• test/verify/yosupo-dynamic-tree-vertex-set-path-composite.test.cpp
• test/verify/yosupo-exp-of-formal-power-series.test.cpp
• test/verify/yosupo-find-linear-recurrence.test.cpp
• test/verify/yosupo-inv-of-formal-power-series.test.cpp
• test/verify/yosupo-kth-term-of-linearly-recurrent-sequence.test.cpp
• test/verify/yosupo-log-of-formal-power-series.test.cpp
• test/verify/yosupo-matrix-det.test.cpp
• test/verify/yosupo-multipoint-evaluation.test.cpp
• test/verify/yosupo-partition-function.test.cpp
• test/verify/yosupo-point-set-range-composite-2.test.cpp
• test/verify/yosupo-point-set-range-composite-3.test.cpp
• test/verify/yosupo-point-set-range-composite.test.cpp
• test/verify/yosupo-polynomial-interpolation.test.cpp
• test/verify/yosupo-polynomial-taylor-shift.test.cpp
• test/verify/yosupo-pow-of-formal-power-series.test.cpp
• test/verify/yosupo-queue-operate-all-composite.test.cpp
• test/verify/yosupo-range-affine-range-sum-2.test.cpp
• test/verify/yosupo-range-affine-range-sum-3.test.cpp
• test/verify/yosupo-range-affine-range-sum.test.cpp
• test/verify/yosupo-sharp-p-subset-sum.test.cpp
• test/verify/yosupo-shift-of-sampling-points-of-polynomial.test.cpp
• test/verify/yosupo-sparse-matrix-det.test.cpp
• test/verify/yosupo-sqrt-of-formal-power-series.test.cpp
• test/verify/yosupo-stirling-number-of-the-first-kind.test.cpp
• test/verify/yosupo-stirling-number-of-the-second-kind.test.cpp
• test/verify/yosupo-subset-convolution.test.cpp
• test/verify/yukicoder-1720.test.cpp
• test/verify/yukicoder-215.test.cpp
• test/verify/yukicoder-3046.test.cpp
• test/verify/yukicoder-502.test.cpp
• test/verify/yukicoder-650.test.cpp

Code

#pragma once

template <uint32_t mod_, bool fast = false>
struct MontgomeryModInt {
 private:
  using mint = MontgomeryModInt;
  using i32 = int32_t;
  using i64 = int64_t;
  using u32 = uint32_t;
  using u64 = uint64_t;

  static constexpr u32 get_r() {
    u32 ret = mod_;
    for (i32 i = 0; i < 4; i++) ret *= 2 - mod_ * ret;
    return ret;
  }

  static constexpr u32 r = get_r();

  static constexpr u32 n2 = -u64(mod_) % mod_;

  static_assert(r * mod_ == 1, "invalid, r * mod != 1");
  static_assert(mod_ < (1 << 30), "invalid, mod >= 2 ^ 30");
  static_assert((mod_ & 1) == 1, "invalid, mod % 2 == 0");

  u32 x;

 public:
  MontgomeryModInt() : x{} {}

  MontgomeryModInt(const i64 &a)
      : x(reduce(u64(fast ? a : (a % mod() + mod())) * n2)) {}

  static constexpr u32 reduce(const u64 &b) {
    return u32(b >> 32) + mod() - u32((u64(u32(b) * r) * mod()) >> 32);
  }

  mint &operator+=(const mint &p) {
    if (i32(x += p.x - 2 * mod()) < 0) x += 2 * mod();
    return *this;
  }

  mint &operator-=(const mint &p) {
    if (i32(x -= p.x) < 0) x += 2 * mod();
    return *this;
  }

  mint &operator*=(const mint &p) {
    x = reduce(u64(x) * p.x);
    return *this;
  }

  mint &operator/=(const mint &p) {
    *this *= p.inv();
    return *this;
  }

  mint operator-() const { return mint() - *this; }

  mint operator+(const mint &p) const { return mint(*this) += p; }

  mint operator-(const mint &p) const { return mint(*this) -= p; }

  mint operator*(const mint &p) const { return mint(*this) *= p; }

  mint operator/(const mint &p) const { return mint(*this) /= p; }

  bool operator==(const mint &p) const {
    return (x >= mod() ? x - mod() : x) == (p.x >= mod() ? p.x - mod() : p.x);
  }

  bool operator!=(const mint &p) const {
    return (x >= mod() ? x - mod() : x) != (p.x >= mod() ? p.x - mod() : p.x);
  }

  u32 val() const {
    u32 ret = reduce(x);
    return ret >= mod() ? ret - mod() : ret;
  }

  mint pow(u64 n) const {
    mint ret(1), mul(*this);
    while (n > 0) {
      if (n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }

  mint inv() const { return pow(mod() - 2); }

  friend ostream &operator<<(ostream &os, const mint &p) {
    return os << p.val();
  }

  friend istream &operator>>(istream &is, mint &a) {
    i64 t;
    is >> t;
    a = mint(t);
    return is;
  }

  static constexpr u32 mod() { return mod_; }
};

template <uint32_t mod>
using modint = MontgomeryModInt<mod>;
using modint998244353 = modint<998244353>;
using modint1000000007 = modint<1000000007>;

#line 2 "math/combinatorics/montgomery-mod-int.hpp"

template <uint32_t mod_, bool fast = false>
struct MontgomeryModInt {
 private:
  using mint = MontgomeryModInt;
  using i32 = int32_t;
  using i64 = int64_t;
  using u32 = uint32_t;
  using u64 = uint64_t;

  static constexpr u32 get_r() {
    u32 ret = mod_;
    for (i32 i = 0; i < 4; i++) ret *= 2 - mod_ * ret;
    return ret;
  }

  static constexpr u32 r = get_r();

  static constexpr u32 n2 = -u64(mod_) % mod_;

  static_assert(r * mod_ == 1, "invalid, r * mod != 1");
  static_assert(mod_ < (1 << 30), "invalid, mod >= 2 ^ 30");
  static_assert((mod_ & 1) == 1, "invalid, mod % 2 == 0");

  u32 x;

 public:
  MontgomeryModInt() : x{} {}

  MontgomeryModInt(const i64 &a)
      : x(reduce(u64(fast ? a : (a % mod() + mod())) * n2)) {}

  static constexpr u32 reduce(const u64 &b) {
    return u32(b >> 32) + mod() - u32((u64(u32(b) * r) * mod()) >> 32);
  }

  mint &operator+=(const mint &p) {
    if (i32(x += p.x - 2 * mod()) < 0) x += 2 * mod();
    return *this;
  }

  mint &operator-=(const mint &p) {
    if (i32(x -= p.x) < 0) x += 2 * mod();
    return *this;
  }

  mint &operator*=(const mint &p) {
    x = reduce(u64(x) * p.x);
    return *this;
  }

  mint &operator/=(const mint &p) {
    *this *= p.inv();
    return *this;
  }

  mint operator-() const { return mint() - *this; }

  mint operator+(const mint &p) const { return mint(*this) += p; }

  mint operator-(const mint &p) const { return mint(*this) -= p; }

  mint operator*(const mint &p) const { return mint(*this) *= p; }

  mint operator/(const mint &p) const { return mint(*this) /= p; }

  bool operator==(const mint &p) const {
    return (x >= mod() ? x - mod() : x) == (p.x >= mod() ? p.x - mod() : p.x);
  }

  bool operator!=(const mint &p) const {
    return (x >= mod() ? x - mod() : x) != (p.x >= mod() ? p.x - mod() : p.x);
  }

  u32 val() const {
    u32 ret = reduce(x);
    return ret >= mod() ? ret - mod() : ret;
  }

  mint pow(u64 n) const {
    mint ret(1), mul(*this);
    while (n > 0) {
      if (n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }

  mint inv() const { return pow(mod() - 2); }

  friend ostream &operator<<(ostream &os, const mint &p) {
    return os << p.val();
  }

  friend istream &operator>>(istream &is, mint &a) {
    i64 t;
    is >> t;
    a = mint(t);
    return is;
  }

  static constexpr u32 mod() { return mod_; }
};

template <uint32_t mod>
using modint = MontgomeryModInt<mod>;
using modint998244353 = modint<998244353>;
using modint1000000007 = modint<1000000007>;

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