bit

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// <bit> -*- C++ -*-
 
// Copyright (C) 2018-2026 Free Software Foundation, Inc.
//
// This file is part of the GNU ISO C++ Library.  This library is free
// software; you can redistribute it and/or modify it under the
// terms of the GNU General Public License as published by the
// Free Software Foundation; either version 3, or (at your option)
// any later version.
 
// This library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.
 
// Under Section 7 of GPL version 3, you are granted additional
// permissions described in the GCC Runtime Library Exception, version
// 3.1, as published by the Free Software Foundation.
 
// You should have received a copy of the GNU General Public License and
// a copy of the GCC Runtime Library Exception along with this program;
// see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
// <http://www.gnu.org/licenses/>.
 
/** @file include/bit
 *  This is a Standard C++ Library header.
 */
 
#ifndef _GLIBCXX_BIT
#define _GLIBCXX_BIT 1
 
#ifdef _GLIBCXX_SYSHDR
#pragma GCC system_header
#endif
 
#if __cplusplus >= 201103L
 
#include <concepts> // for std::integral
#include <type_traits>
 
#if _GLIBCXX_HOSTED || __has_include(<ext/numeric_traits.h>)
# include <ext/numeric_traits.h>
#else
# include <limits>
/// @cond undocumented
namespace __gnu_cxx
{
  template<typename _Tp>
    struct __int_traits
    {
      static constexpr int __digits = std::numeric_limits<_Tp>::digits;
      static constexpr _Tp __max = std::numeric_limits<_Tp>::max();
    };
}
/// @endcond
#endif
 
#define __glibcxx_want_bit_cast
#define __glibcxx_want_byteswap
#define __glibcxx_want_bitops
#define __glibcxx_want_int_pow2
#define __glibcxx_want_endian
#include <bits/version.h>
 
namespace std _GLIBCXX_VISIBILITY(default)
{
_GLIBCXX_BEGIN_NAMESPACE_VERSION
 
  /**
   * @defgroup bit_manip Bit manipulation
   * @ingroup numerics
   *
   * Utilities for examining and manipulating individual bits.
   *
   * @{
   */
 
#ifdef __cpp_lib_bit_cast // C++ >= 20
 
  /// Create a value of type `To` from the bits of `from`.
  /**
   * @tparam _To   A trivially-copyable type.
   * @param __from A trivially-copyable object of the same size as `_To`.
   * @return       An object of type `_To`.
   * @since C++20
   */
  template<typename _To, typename _From>
    [[nodiscard]]
    constexpr _To
    bit_cast(const _From& __from) noexcept
#ifdef __cpp_concepts
    requires (sizeof(_To) == sizeof(_From))
      && is_trivially_copyable_v<_To> && is_trivially_copyable_v<_From>
#endif
    {
      return __builtin_bit_cast(_To, __from);
    }
#endif // __cpp_lib_bit_cast
 
#ifdef __cpp_lib_byteswap // C++ >= 23
 
  /// Reverse order of bytes in the object representation of `value`.
  /**
   * @tparam _Tp     An integral type.
   * @param __value  An object of integer type.
   * @return         An object of the same type, with the bytes reversed.
   * @since C++23
   */
  template<integral _Tp>
    [[nodiscard]]
    constexpr _Tp
    byteswap(_Tp __value) noexcept
    {
      if constexpr (sizeof(_Tp) == 1)
        return __value;
#if __cpp_if_consteval >= 202106L && __CHAR_BIT__ == 8
      if !consteval
        {
          if constexpr (sizeof(_Tp) == 2)
            return __builtin_bswap16(__value);
          if constexpr (sizeof(_Tp) == 4)
            return __builtin_bswap32(__value);
          if constexpr (sizeof(_Tp) == 8)
            return __builtin_bswap64(__value);
          if constexpr (sizeof(_Tp) == 16)
#if __has_builtin(__builtin_bswap128)
            return __builtin_bswap128(__value);
#else
            return (__builtin_bswap64(__value >> 64)
                    | (static_cast<_Tp>(__builtin_bswap64(__value)) << 64));
#endif
        }
#endif
 
      // Fallback implementation that handles even __int24 etc.
      using _Up = typename __make_unsigned<__remove_cv_t<_Tp>>::__type;
      size_t __diff = __CHAR_BIT__ * (sizeof(_Tp) - 1);
      _Up __mask1 = static_cast<unsigned char>(~0);
      _Up __mask2 = __mask1 << __diff;
      _Up __val = __value;
      for (size_t __i = 0; __i < sizeof(_Tp) / 2; ++__i)
        {
          _Up __byte1 = __val & __mask1;
          _Up __byte2 = __val & __mask2;
          __val = (__val ^ __byte1 ^ __byte2
                   ^ (__byte1 << __diff) ^ (__byte2 >> __diff));
          __mask1 <<= __CHAR_BIT__;
          __mask2 >>= __CHAR_BIT__;
          __diff -= 2 * __CHAR_BIT__;
        }
      return __val;
    }
#endif // __cpp_lib_byteswap
 
  /// @cond undocumented
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wc++17-extensions" // if constexpr
 
  template<typename _Tp>
    _GLIBCXX14_CONSTEXPR _Tp
    __rotl(_Tp __x, int __s) noexcept
    {
      constexpr auto _Nd = __gnu_cxx::__int_traits<_Tp>::__digits;
      if constexpr ((_Nd & (_Nd - 1)) == 0)
        {
          // Variant for power of two _Nd which the compiler can
          // easily pattern match.
          constexpr unsigned __uNd = _Nd;
          const auto __r = static_cast<unsigned>(__s);
          return (__x << (__r % __uNd)) | (__x >> ((-__r) % __uNd));
        }
      const int __r = __s % _Nd;
      if (__r == 0)
        return __x;
      else if (__r > 0)
        return (__x << __r) | (__x >> ((_Nd - __r) % _Nd));
      else
        return (__x >> -__r) | (__x << ((_Nd + __r) % _Nd)); // rotr(x, -r)
    }
 
  template<typename _Tp>
    _GLIBCXX14_CONSTEXPR _Tp
    __rotr(_Tp __x, int __s) noexcept
    {
      constexpr auto _Nd = __gnu_cxx::__int_traits<_Tp>::__digits;
      if constexpr ((_Nd & (_Nd - 1)) == 0)
        {
          // Variant for power of two _Nd which the compiler can
          // easily pattern match.
          constexpr unsigned __uNd = _Nd;
          const auto __r = static_cast<unsigned>(__s);
          return (__x >> (__r % __uNd)) | (__x << ((-__r) % __uNd));
        }
      const int __r = __s % _Nd;
      if (__r == 0)
        return __x;
      else if (__r > 0)
        return (__x >> __r) | (__x << ((_Nd - __r) % _Nd));
      else
        return (__x << -__r) | (__x >> ((_Nd + __r) % _Nd)); // rotl(x, -r)
    }
 
#if _GLIBCXX_USE_BUILTIN_TRAIT(__builtin_clzg)
  template<typename _Tp>
    constexpr int
    __countl_zero(_Tp __x) noexcept
    {
      return __builtin_clzg(__x, __gnu_cxx::__int_traits<_Tp>::__digits);
    }
#else
  template<typename _Tp>
    _GLIBCXX14_CONSTEXPR int
    __countl_zero(_Tp __x) noexcept
    {
      using __gnu_cxx::__int_traits;
      constexpr auto _Nd = __int_traits<_Tp>::__digits;
      if (__x == 0)
        return _Nd;
 
      constexpr auto _Nd_ull = __int_traits<unsigned long long>::__digits;
      constexpr auto _Nd_ul = __int_traits<unsigned long>::__digits;
      constexpr auto _Nd_u = __int_traits<unsigned>::__digits;
 
      if constexpr (_Nd <= _Nd_u)
        {
          constexpr int __diff = _Nd_u - _Nd;
          return __builtin_clz(__x) - __diff;
        }
      else if constexpr (_Nd <= _Nd_ul)
        {
          constexpr int __diff = _Nd_ul - _Nd;
          return __builtin_clzl(__x) - __diff;
        }
      else if constexpr (_Nd <= _Nd_ull)
        {
          constexpr int __diff = _Nd_ull - _Nd;
          return __builtin_clzll(__x) - __diff;
        }
      else // (_Nd > _Nd_ull)
        {
          static_assert(_Nd <= (2 * _Nd_ull),
                        "Maximum supported integer size is 128-bit");
 
          unsigned long long __high = __x >> _Nd_ull;
          if (__high != 0)
            {
              constexpr int __diff = (2 * _Nd_ull) - _Nd;
              return __builtin_clzll(__high) - __diff;
            }
          constexpr auto __max_ull = __int_traits<unsigned long long>::__max;
          unsigned long long __low = __x & __max_ull;
          return (_Nd - _Nd_ull) + __builtin_clzll(__low);
        }
    }
#endif
 
  template<typename _Tp>
    constexpr int
    __countl_one(_Tp __x) noexcept
    {
      return std::__countl_zero<_Tp>((_Tp)~__x);
    }
 
#if _GLIBCXX_USE_BUILTIN_TRAIT(__builtin_ctzg)
   template<typename _Tp>
    constexpr int
    __countr_zero(_Tp __x) noexcept
    {
      return __builtin_ctzg(__x, __gnu_cxx::__int_traits<_Tp>::__digits);
    }
#else
  template<typename _Tp>
    _GLIBCXX14_CONSTEXPR int
    __countr_zero(_Tp __x) noexcept
    {
      using __gnu_cxx::__int_traits;
      constexpr auto _Nd = __int_traits<_Tp>::__digits;
      if (__x == 0)
        return _Nd;
 
      constexpr auto _Nd_ull = __int_traits<unsigned long long>::__digits;
      constexpr auto _Nd_ul = __int_traits<unsigned long>::__digits;
      constexpr auto _Nd_u = __int_traits<unsigned>::__digits;
 
      if constexpr (_Nd <= _Nd_u)
        return __builtin_ctz(__x);
      else if constexpr (_Nd <= _Nd_ul)
        return __builtin_ctzl(__x);
      else if constexpr (_Nd <= _Nd_ull)
        return __builtin_ctzll(__x);
      else // (_Nd > _Nd_ull)
        {
          static_assert(_Nd <= (2 * _Nd_ull),
                        "Maximum supported integer size is 128-bit");
 
          constexpr auto __max_ull = __int_traits<unsigned long long>::__max;
          unsigned long long __low = __x & __max_ull;
          if (__low != 0)
            return __builtin_ctzll(__low);
          unsigned long long __high = __x >> _Nd_ull;
          return __builtin_ctzll(__high) + _Nd_ull;
        }
    }
#endif
 
  template<typename _Tp>
    constexpr int
    __countr_one(_Tp __x) noexcept
    {
      return std::__countr_zero((_Tp)~__x);
    }
 
#if _GLIBCXX_USE_BUILTIN_TRAIT(__builtin_popcountg)
  template<typename _Tp>
    constexpr int
    __popcount(_Tp __x) noexcept
    {
      return __builtin_popcountg(__x);
    }
#else
  template<typename _Tp>
    _GLIBCXX14_CONSTEXPR int
    __popcount(_Tp __x) noexcept
    {
      using __gnu_cxx::__int_traits;
      constexpr auto _Nd = __int_traits<_Tp>::__digits;
 
      constexpr auto _Nd_ull = __int_traits<unsigned long long>::__digits;
      constexpr auto _Nd_ul = __int_traits<unsigned long>::__digits;
      constexpr auto _Nd_u = __int_traits<unsigned>::__digits;
 
      if constexpr (_Nd <= _Nd_u)
        return __builtin_popcount(__x);
      else if constexpr (_Nd <= _Nd_ul)
        return __builtin_popcountl(__x);
      else if constexpr (_Nd <= _Nd_ull)
        return __builtin_popcountll(__x);
      else // (_Nd > _Nd_ull)
        {
          static_assert(_Nd <= (2 * _Nd_ull),
                        "Maximum supported integer size is 128-bit");
 
          constexpr auto __max_ull = __int_traits<unsigned long long>::__max;
          unsigned long long __low = __x & __max_ull;
          unsigned long long __high = __x >> _Nd_ull;
          return __builtin_popcountll(__low) + __builtin_popcountll(__high);
        }
    }
#endif
 
  template<typename _Tp>
    constexpr bool
    __has_single_bit(_Tp __x) noexcept
    { return std::__popcount(__x) == 1; }
 
  template<typename _Tp>
    constexpr int
    __bit_width(_Tp __x) noexcept
    {
      return __gnu_cxx::__int_traits<_Tp>::__digits - std::__countl_zero(__x);
    }
 
  template<typename _Tp>
    constexpr _Tp
    __bit_floor(_Tp __x) noexcept
    {
      return (__x == 0) ? (_Tp)0 : ((_Tp)1u << (std::__bit_width(__x) - 1));
    }
 
  template<typename _Tp>
    _GLIBCXX14_CONSTEXPR _Tp
    __bit_ceil(_Tp __x) noexcept
    {
      using __gnu_cxx::__int_traits;
      constexpr auto _Nd = __int_traits<_Tp>::__digits;
      if (__x == 0 || __x == 1)
        return 1;
      auto __shift_exponent = _Nd - std::__countl_zero((_Tp)(__x - 1u));
      // If the shift exponent equals _Nd then the correct result is not
      // representable as a value of _Tp, and so the result is undefined.
      // Want that undefined behaviour to be detected in constant expressions,
      // by UBSan, and by debug assertions.
      if (!std::__is_constant_evaluated())
        {
          __glibcxx_assert( __shift_exponent != __int_traits<_Tp>::__digits );
        }
 
      using __promoted_type = decltype(__x << 1);
      if constexpr (!is_same<__promoted_type, _Tp>::value)
        {
          // If __x undergoes integral promotion then shifting by _Nd is
          // not undefined. In order to make the shift undefined, so that
          // it is diagnosed in constant expressions and by UBsan, we also
          // need to "promote" the shift exponent to be too large for the
          // promoted type.
          const int __extra_exp = sizeof(__promoted_type) / sizeof(_Tp) / 2;
          __shift_exponent |= (__shift_exponent & _Nd) << __extra_exp;
        }
      return (_Tp)1u << __shift_exponent;
    }
 
#pragma GCC diagnostic pop
  /// @endcond
 
#ifdef __cpp_lib_bitops // C++ >= 20
 
  /// @cond undocumented
  template<typename _Tp>
    concept __unsigned_integer = __is_unsigned_integer<_Tp>::value;
 
  template<typename _Tp>
    concept __signed_or_unsigned_integer
      = __is_signed_or_unsigned_integer<_Tp>::value;
  /// @endcond
 
#if __cpp_lib_bitops >= 202606L // >= C++29
  // [bit.shift], shifting
  template<__signed_or_unsigned_integer _Tp, __signed_or_unsigned_integer _Sp>
    [[nodiscard]] constexpr _Tp
    shl(_Tp __x, _Sp __s) noexcept
    {
      constexpr auto _Nd = __gnu_cxx::__int_traits<_Tp>::__digits
                           + is_signed_v<_Tp>;
      if (__s < 0)
        return __s > -_Nd ? __x >> -__s : static_cast<_Tp>(__x < 0 ? -1 : 0);
      return __s < _Nd ? __x << __s : static_cast<_Tp>(0);
    }
 
  template<__signed_or_unsigned_integer _Tp, __signed_or_unsigned_integer _Sp>
    [[nodiscard]] constexpr _Tp
    shr(_Tp __x, _Sp __s) noexcept
    {
      constexpr auto _Nd = __gnu_cxx::__int_traits<_Tp>::__digits
                           + is_signed_v<_Tp>;
      if (__s < 0)
        return __s > -_Nd ? __x << -__s : static_cast<_Tp>(0);
      return __s < _Nd ? __x >> __s : static_cast<_Tp>(__x < 0 ? -1 : 0);
    }
#endif
 
  // [bit.rotate], rotating
 
  /// Rotate `x` to the left by `s` bits.
  template<__unsigned_integer _Tp>
    [[nodiscard]] constexpr _Tp
    rotl(_Tp __x, int __s) noexcept
    { return std::__rotl(__x, __s); }
 
  /// Rotate `x` to the right by `s` bits.
  template<__unsigned_integer _Tp>
    [[nodiscard]] constexpr _Tp
    rotr(_Tp __x, int __s) noexcept
    { return std::__rotr(__x, __s); }
 
  // [bit.count], counting
 
  /// The number of contiguous zero bits, starting from the highest bit.
  template<__unsigned_integer _Tp>
    constexpr int
    countl_zero(_Tp __x) noexcept
    { return std::__countl_zero(__x); }
 
  /// The number of contiguous one bits, starting from the highest bit.
  template<__unsigned_integer _Tp>
    constexpr int
    countl_one(_Tp __x) noexcept
    { return std::__countl_one(__x); }
 
  /// The number of contiguous zero bits, starting from the lowest bit.
  template<__unsigned_integer _Tp>
    constexpr int
    countr_zero(_Tp __x) noexcept
    { return std::__countr_zero(__x); }
 
  /// The number of contiguous one bits, starting from the lowest bit.
  template<__unsigned_integer _Tp>
    constexpr int
    countr_one(_Tp __x) noexcept
    { return std::__countr_one(__x); }
 
  /// The number of bits set in `x`.
  template<__unsigned_integer _Tp>
    constexpr int
    popcount(_Tp __x) noexcept
    { return std::__popcount(__x); }
#endif // __cpp_lib_bitops
 
#ifdef __cpp_lib_int_pow2 // C++ >= 20
  // [bit.pow.two], integral powers of 2
 
  /// True if `x` is a power of two, false otherwise.
  template<__unsigned_integer _Tp>
    constexpr bool
    has_single_bit(_Tp __x) noexcept
    { return std::__has_single_bit(__x); }
 
  /// The smallest power-of-two not less than `x`.
  template<__unsigned_integer _Tp>
    constexpr _Tp
    bit_ceil(_Tp __x) noexcept
    { return std::__bit_ceil(__x); }
 
  /// The largest power-of-two not greater than `x`.
  template<__unsigned_integer _Tp>
    constexpr _Tp
    bit_floor(_Tp __x) noexcept
    { return std::__bit_floor(__x); }
 
  // _GLIBCXX_RESOLVE_LIB_DEFECTS
  // 3656. Inconsistent bit operations returning a count
  /// The smallest integer greater than the base-2 logarithm of `x`.
  template<__unsigned_integer _Tp>
    constexpr int
    bit_width(_Tp __x) noexcept
    { return std::__bit_width(__x); }
#endif // defined (__cpp_lib_int_pow2)
 
#if __cpp_lib_bitops >= 202607L // >= C++29
  // [bit.permute], permutation
  template<__unsigned_integer _Tp>
    [[nodiscard]] constexpr _Tp
    bit_repeat(_Tp __x, int __l)
    {
      __glibcxx_assert( __l > 0 );
      constexpr auto _Nd = __gnu_cxx::__int_traits<_Tp>::__digits;
      if (__l >= _Nd)
        return __x;
      __x &= ((_Tp)1 << __l) - 1;
      do
        {
          __x |= __x << __l;
          __l <<= 1;
        }
      while (__l < _Nd);
      return __x;
    }
 
  template<__unsigned_integer _Tp>
    [[nodiscard]] constexpr _Tp
    bit_reverse(_Tp __x) noexcept
    {
#if _GLIBCXX_USE_BUILTIN_TRAIT(__builtin_bitreverseg)
      return __builtin_bitreverseg(__x);
#else
      constexpr auto _Nd = __gnu_cxx::__int_traits<_Tp>::__digits;
      if constexpr (_Nd % __CHAR_BIT__ == 0 && __CHAR_BIT__ == 8)
        {
          __x = std::byteswap(__x);
          constexpr auto __m1 = std::bit_repeat<_Tp>(15, 8);
          constexpr auto __m2 = std::bit_repeat<_Tp>(3, 4);
          constexpr auto __m3 = std::bit_repeat<_Tp>(1, 2);
          __x = ((__x >> 4) & __m1) | ((__x & __m1) << 4);
          __x = ((__x >> 2) & __m2) | ((__x & __m2) << 2);
          __x = ((__x >> 1) & __m3) | ((__x & __m3) << 1);
          return __x;
        }
      else
        {
          _Tp __r = 0;
          for (int __i = 0; __i < _Nd; ++__i)
            {
              __r <<= 1;
              __r |= (__x & 1);
              __x >>= 1;
            }
          return __r;
        }
#endif
    }
 
  template<__unsigned_integer _Tp>
    [[nodiscard]] constexpr _Tp
    bit_compress(_Tp __x, _Tp __m) noexcept
    {
#if _GLIBCXX_USE_BUILTIN_TRAIT(__builtin_elementwise_pext)
      return __builtin_elementwise_pext(__x, __m);
#else
      constexpr auto _Nd = __gnu_cxx::__int_traits<_Tp>::__digits;
      // Based on "Compress, or Generalized Extract" in Hacker's Delight
      __x &= __m;
      _Tp __mk = ~__m << 1;
      for (int __i = 1; __i < _Nd; __i <<= 1)
        {
          _Tp __mp = __mk;
          for (int __j = 1; __j < _Nd; __j <<= 1)
            __mp ^= __mp << __j;
          _Tp __mv = __mp & __m;
          __m = (__m ^ __mv) | (__mv >> __i);
          _Tp __t = __x & __mv;
          __x = (__x ^ __t) | (__t >> __i);
          __mk = __mk & ~__mp;
        }
      return __x;
#endif
    }
 
  template<__unsigned_integer _Tp>
    [[nodiscard]] constexpr _Tp
    bit_expand(_Tp __x, _Tp __m) noexcept
    {
#if _GLIBCXX_USE_BUILTIN_TRAIT(__builtin_elementwise_pdep)
      return __builtin_elementwise_pdep(__x, __m);
#else
      constexpr auto _Nd = __gnu_cxx::__int_traits<_Tp>::__digits;
      if constexpr (_Nd == 1)
        return __x & __m;
      constexpr auto __log2_Nd
        = _Nd == 1 ? 1 : (__gnu_cxx::__int_traits<unsigned>::__digits
                          - std::__countl_zero<unsigned>(_Nd - 1));
      // Based on "Expand, or Generalized Insert" in Hacker's Delight
      _Tp __m0 = __m;
      _Tp __mk = ~__m << 1;
      _Tp __array[__log2_Nd];
      for (int __i = 0; __i < __log2_Nd; __i++)
        {
          _Tp __mp = __mk;
          for (int __j = 1; __j < _Nd; __j <<= 1)
            __mp ^= __mp << __j;
          _Tp __mv = __mp & __m;
          __array[__i] = __mv;
          __m = (__m ^ __mv) | (__mv >> (_Tp(1) << __i));
          __mk = __mk & ~__mp;
        }
      for (int __i = __log2_Nd - 1; __i >= 0; __i--)
        {
          _Tp __mv = __array[__i];
          _Tp __t = __x << (_Tp(1) << __i);
          __x = (__x & ~__mv) | (__t & __mv);
        }
      return __x & __m0;
#endif
    }
#endif // __cpp_lib_bitops >= 202607L
 
#ifdef __cpp_lib_endian // C++ >= 20
 
  /// Byte order constants
  /**
   * The platform endianness can be checked by comparing `std::endian::native`
   * to one of `std::endian::big` or `std::endian::little`.
   *
   * @since C++20
   */
  enum class endian
  {
    little = __ORDER_LITTLE_ENDIAN__,
    big    = __ORDER_BIG_ENDIAN__,
    native = __BYTE_ORDER__
  };
#endif // __cpp_lib_endian
 
  /// @}
 
_GLIBCXX_END_NAMESPACE_VERSION
} // namespace std
 
#endif // C++11
#endif // _GLIBCXX_BIT