internal-hash.hpp

#pragma once

namespace internal {
using i64 = long long;
using u64 = unsigned long long;
using u128 = __uint128_t;

template <int BASE_NUM = 2>
struct Hash : array<u64, BASE_NUM> {
  using array<u64, BASE_NUM>::operator[];
  static constexpr int n = BASE_NUM;

  Hash() : array<u64, BASE_NUM>() {}

  static constexpr u64 md = (1ull << 61) - 1;

  constexpr static Hash set(const i64 &a) {
    Hash res;
    fill(begin(res), end(res), cast(a));
    return res;
  }
  Hash &operator+=(const Hash &r) {
    for (int i = 0; i < n; i++)
      if (((*this)[i] += r[i]) >= md) (*this)[i] -= md;
    return *this;
  }
  Hash &operator+=(const i64 &r) {
    u64 s = cast(r);
    for (int i = 0; i < n; i++)
      if (((*this)[i] += s) >= md) (*this)[i] -= md;
    return *this;
  }
  Hash &operator-=(const Hash &r) {
    for (int i = 0; i < n; i++)
      if (((*this)[i] += md - r[i]) >= md) (*this)[i] -= md;
    return *this;
  }
  Hash &operator-=(const i64 &r) {
    u64 s = cast(r);
    for (int i = 0; i < n; i++)
      if (((*this)[i] += md - s) >= md) (*this)[i] -= md;
    return *this;
  }
  Hash &operator*=(const Hash &r) {
    for (int i = 0; i < n; i++) (*this)[i] = modmul((*this)[i], r[i]);
    return *this;
  }
  Hash &operator*=(const i64 &r) {
    u64 s = cast(r);
    for (int i = 0; i < n; i++) (*this)[i] = modmul((*this)[i], s);
    return *this;
  }

  Hash operator+(const Hash &r) { return Hash(*this) += r; }
  Hash operator+(const i64 &r) { return Hash(*this) += r; }
  Hash operator-(const Hash &r) { return Hash(*this) -= r; }
  Hash operator-(const i64 &r) { return Hash(*this) -= r; }
  Hash operator*(const Hash &r) { return Hash(*this) *= r; }
  Hash operator*(const i64 &r) { return Hash(*this) *= r; }
  Hash operator-() const {
    Hash res;
    for (int i = 0; i < n; i++) res[i] = (*this)[i] == 0 ? 0 : md - (*this)[i];
    return res;
  }
  friend Hash pfma(const Hash &a, const Hash &b, const Hash &c) {
    Hash res;
    for (int i = 0; i < n; i++) res[i] = modfma(a[i], b[i], c[i]);
    return res;
  }
  friend Hash pfma(const Hash &a, const Hash &b, const i64 &c) {
    Hash res;
    u64 s = cast(c);
    for (int i = 0; i < n; i++) res[i] = modfma(a[i], b[i], s);
    return res;
  }

  Hash pow(long long e) {
    Hash a{*this}, res{Hash::set(1)};
    for (; e; a *= a, e >>= 1) {
      if (e & 1) res *= a;
    }
    return res;
  }

  static Hash get_basis() {
    static auto rand_time =
        chrono::duration_cast<chrono::nanoseconds>(
            chrono::high_resolution_clock::now().time_since_epoch())
            .count();
    static mt19937_64 rng(rand_time);
    Hash h;
    for (int i = 0; i < n; i++) {
      while (isPrimitive(h[i] = rng() % (md - 1) + 1) == false)
        ;
    }
    return h;
  }

 private:
  static u64 modpow(u64 a, u64 b) {
    u64 r = 1;
    for (a %= md; b; a = modmul(a, a), b >>= 1) r = modmul(r, a);
    return r;
  }
  static bool isPrimitive(u64 x) {
    for (auto &d : vector<u64>{2, 3, 5, 7, 11, 13, 31, 41, 61, 151, 331, 1321})
      if (modpow(x, (md - 1) / d) <= 1) return false;
    return true;
  }
  static inline constexpr u64 cast(const long long &a) {
    return a < 0 ? a + md : a;
  }
  static inline constexpr u64 modmul(const u64 &a, const u64 &b) { 
    u128 d = u128(a) * b;
    u64 ret = (u64(d) & md) + u64(d >> 61);
    return ret >= md ? ret - md : ret;
  }
  static inline constexpr u64 modfma(const u64 &a, const u64 &b, const u64 &c) {
    u128 d = u128(a) * b + c;
    u64 ret = (d >> 61) + (u64(d) & md);
    return ret >= md ? ret - md : ret;
  }
};

}  // namespace internal

/**
 * @brief ハッシュ構造体
 * @docs docs/internal/internal-hash.md
 */