:heavy_check_mark: 高速 Möbius 変換 (algorithm/moebius_transform.cpp)

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#ifndef H_moebius_transform
#define H_moebius_transform

/**
 * @brief 高速 Möbius 変換
 * @author えびちゃん
 */

#include "integer/bit.cpp"
#include "utility/literals.cpp"

template <typename RandomIt>
void moebius_transform(RandomIt first, RandomIt last) {
  size_t n = ctz(last-first);
  for (size_t j = 0; j < n; ++j)
    for (size_t i = 0; i < (1_zu << n); ++i)
      if (i >> j & 1) first[i] -= first[i ^ (1_zu << j)];
}

#endif  /* !defined(H_moebius_transform) */

#line 1 "algorithm/moebius_transform.cpp"



/**
 * @brief 高速 Möbius 変換
 * @author えびちゃん
 */

#line 1 "integer/bit.cpp"



/** 
 * @brief ビット演算
 * @author えびちゃん
 */

// XXX integral promotion 関連の注意をあまりしていません

#include <climits>
#include <type_traits>

template <typename Tp>
constexpr auto countl_zero(Tp n)
  -> typename std::enable_if<std::is_unsigned<Tp>::value, int>::type
{
  using value_type = typename std::make_unsigned<Tp>::type;
  int bits = (sizeof(value_type) * CHAR_BIT);
  if (n == 0) return bits;
  int res = 0;
  for (int i = bits / 2; i > 0; i /= 2) {
    value_type mask = ((static_cast<value_type>(1) << i) - 1) << i;
    if (n & mask) n >>= i;
    else res += i;
  }
  return res;
}
template <typename Tp>
constexpr auto countl_one(Tp n)
  -> typename std::enable_if<std::is_unsigned<Tp>::value, int>::type
{
  using value_type = typename std::make_unsigned<Tp>::type;
  return countl_zero(static_cast<value_type>(~n));
}

template <typename Tp>
constexpr auto countr_zero(Tp n)
  -> typename std::enable_if<std::is_unsigned<Tp>::value, int>::type
{
  using value_type = typename std::make_unsigned<Tp>::type;
  int bits = (sizeof(value_type) * CHAR_BIT);
  if (n == 0) return bits;
  int res = 0;
  for (int i = bits / 2; i > 0; i /= 2) {
    value_type mask = ((static_cast<value_type>(1) << i) - 1);
    if (!(n & mask)) res += i, n >>= i;
  }
  return res;
}
template <typename Tp>
constexpr auto countr_one(Tp n)
  -> typename std::enable_if<std::is_unsigned<Tp>::value, int>::type
{
  using value_type = typename std::make_unsigned<Tp>::type;
  return countr_zero(static_cast<value_type>(~n));
}

constexpr unsigned long long half_mask[] = {
  0x5555555555555555uLL, 0x3333333333333333uLL, 0x0F0F0F0F0F0F0F0FuLL,
  0x00FF00FF00FF00FFuLL, 0x0000FFFF0000FFFFuLL, 0x00000000FFFFFFFFuLL
};

template <typename Tp>
constexpr auto popcount(Tp n)
  -> typename std::enable_if<std::is_unsigned<Tp>::value, int>::type
{
  int bits = static_cast<int>((sizeof n) * CHAR_BIT);
  for (int i = 0, j = 1; j < bits; ++i, j *= 2) {
    if (j <= 8) n = (n & half_mask[i]) + ((n >> j) & half_mask[i]);
    else n += n >> j;
  }
  return n & 0xFF;
}

template <typename Tp>
constexpr auto parity(Tp n)
  -> typename std::enable_if<std::is_unsigned<Tp>::value, int>::type
{ return popcount(n) & 1; }


template <typename Tp>
int clz(Tp n) { return countl_zero(static_cast<typename std::make_unsigned<Tp>::type>(n)); }
template <typename Tp>
int ctz(Tp n) { return countr_zero(static_cast<typename std::make_unsigned<Tp>::type>(n)); }

template <typename Tp>
int ilog2(Tp n) {
  return (CHAR_BIT * sizeof(Tp) - 1) - clz(static_cast<typename std::make_unsigned<Tp>::type>(n));
}
template <typename Tp>
bool is_pow2(Tp n) { return (n > 0) && ((n & (n-1)) == 0); }
template <typename Tp>
Tp floor2(Tp n) { return is_pow2(n)? n: static_cast<Tp>(1) << ilog2(n); }
template <typename Tp>
Tp ceil2(Tp n) { return is_pow2(n)? n: static_cast<Tp>(2) << ilog2(n); }

template <typename Tp>
constexpr auto reverse(Tp n)
  -> typename std::enable_if<std::is_unsigned<Tp>::value, Tp>::type
{
  int bits = static_cast<int>((sizeof n) * CHAR_BIT);
  for (int i = 0, j = 1; j < bits; ++i, j *= 2) {
    n = ((n & half_mask[i]) << j) | ((n >> j) & half_mask[i]);
  }
  return n;
}


#line 1 "utility/literals.cpp"



/**
 * @brief ユーザ定義リテラル
 * @author えびちゃん
 */

#include <cstddef>
#include <cstdint>

constexpr intmax_t  operator ""_jd(unsigned long long n) { return n; }
constexpr uintmax_t operator ""_ju(unsigned long long n) { return n; }
constexpr size_t    operator ""_zu(unsigned long long n) { return n; }
constexpr ptrdiff_t operator ""_td(unsigned long long n) { return n; }

constexpr int8_t   operator ""_i8(unsigned long long n)  { return n; }
constexpr int16_t  operator ""_i16(unsigned long long n) { return n; }
constexpr int32_t  operator ""_i32(unsigned long long n) { return n; }
constexpr int64_t  operator ""_i64(unsigned long long n) { return n; }
constexpr uint8_t  operator ""_u8(unsigned long long n)  { return n; }
constexpr uint16_t operator ""_u16(unsigned long long n) { return n; }
constexpr uint32_t operator ""_u32(unsigned long long n) { return n; }
constexpr uint64_t operator ""_u64(unsigned long long n) { return n; }


#line 11 "algorithm/moebius_transform.cpp"

template <typename RandomIt>
void moebius_transform(RandomIt first, RandomIt last) {
  size_t n = ctz(last-first);
  for (size_t j = 0; j < n; ++j)
    for (size_t i = 0; i < (1_zu << n); ++i)
      if (i >> j & 1) first[i] -= first[i ^ (1_zu << j)];
}



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