bit

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// <bit> -*- C++ -*-
 
// Copyright (C) 2018-2021 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
 
#pragma GCC system_header
 
#if __cplusplus >= 201402L
 
#include <type_traits>
 
#if _GLIBCXX_HOSTED
# 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
 
namespace std _GLIBCXX_VISIBILITY(default)
{
_GLIBCXX_BEGIN_NAMESPACE_VERSION
 
  /**
   * @defgroup bit_manip Bit manipulation
   * @ingroup numerics
   *
   * Utilities for examining and manipulating individual bits.
   *
   * @{
   */
 
#if __cplusplus > 201703l && __has_builtin(__builtin_bit_cast)
#define __cpp_lib_bit_cast 201806L
 
  /// Create a value of type `To` from the bits of `from`.
  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(_To) && __is_trivially_copyable(_From)
#endif
    {
      return __builtin_bit_cast(_To, __from);
    }
#endif
 
  /// @cond undoc
 
  template<typename _Tp>
    constexpr _Tp
    __rotl(_Tp __x, int __s) noexcept
    {
      constexpr auto _Nd = __gnu_cxx::__int_traits<_Tp>::__digits;
      if _GLIBCXX17_CONSTEXPR ((_Nd & (_Nd - 1)) == 0)
        {
          // Variant for power of two _Nd which the compiler can
          // easily pattern match.
          constexpr unsigned __uNd = _Nd;
          const unsigned __r = __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>
    constexpr _Tp
    __rotr(_Tp __x, int __s) noexcept
    {
      constexpr auto _Nd = __gnu_cxx::__int_traits<_Tp>::__digits;
      if _GLIBCXX17_CONSTEXPR ((_Nd & (_Nd - 1)) == 0)
        {
          // Variant for power of two _Nd which the compiler can
          // easily pattern match.
          constexpr unsigned __uNd = _Nd;
          const unsigned __r = __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)
    }
 
  template<typename _Tp>
    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 _GLIBCXX17_CONSTEXPR (_Nd <= _Nd_u)
        {
          constexpr int __diff = _Nd_u - _Nd;
          return __builtin_clz(__x) - __diff;
        }
      else if _GLIBCXX17_CONSTEXPR (_Nd <= _Nd_ul)
        {
          constexpr int __diff = _Nd_ul - _Nd;
          return __builtin_clzl(__x) - __diff;
        }
      else if _GLIBCXX17_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);
        }
    }
 
  template<typename _Tp>
    constexpr int
    __countl_one(_Tp __x) noexcept
    {
      return std::__countl_zero<_Tp>((_Tp)~__x);
    }
 
  template<typename _Tp>
    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 _GLIBCXX17_CONSTEXPR (_Nd <= _Nd_u)
        return __builtin_ctz(__x);
      else if _GLIBCXX17_CONSTEXPR (_Nd <= _Nd_ul)
        return __builtin_ctzl(__x);
      else if _GLIBCXX17_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;
        }
    }
 
  template<typename _Tp>
    constexpr int
    __countr_one(_Tp __x) noexcept
    {
      return std::__countr_zero((_Tp)~__x);
    }
 
  template<typename _Tp>
    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 _GLIBCXX17_CONSTEXPR (_Nd <= _Nd_u)
        return __builtin_popcount(__x);
      else if _GLIBCXX17_CONSTEXPR (_Nd <= _Nd_ul)
        return __builtin_popcountl(__x);
      else if _GLIBCXX17_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);
        }
    }
 
  template<typename _Tp>
    constexpr bool
    __has_single_bit(_Tp __x) noexcept
    { return std::__popcount(__x) == 1; }
 
  template<typename _Tp>
    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.
#ifdef _GLIBCXX_HAVE_BUILTIN_IS_CONSTANT_EVALUATED
      if (!__builtin_is_constant_evaluated())
        {
          __glibcxx_assert( __shift_exponent != __int_traits<_Tp>::__digits );
        }
#endif
      using __promoted_type = decltype(__x << 1);
      if _GLIBCXX17_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;
    }
 
  template<typename _Tp>
    constexpr _Tp
    __bit_floor(_Tp __x) noexcept
    {
      constexpr auto _Nd = __gnu_cxx::__int_traits<_Tp>::__digits;
      if (__x == 0)
        return 0;
      return (_Tp)1u << (_Nd - std::__countl_zero((_Tp)(__x >> 1)));
    }
 
  template<typename _Tp>
    constexpr _Tp
    __bit_width(_Tp __x) noexcept
    {
      constexpr auto _Nd = __gnu_cxx::__int_traits<_Tp>::__digits;
      return _Nd - std::__countl_zero(__x);
    }
 
  /// @endcond
 
#if __cplusplus > 201703L
 
#define __cpp_lib_bitops 201907L
 
  /// @cond undoc
  template<typename _Tp, typename _Up = _Tp>
    using _If_is_unsigned_integer
      = enable_if_t<__is_unsigned_integer<_Tp>::value, _Up>;
  /// @endcond
 
  // [bit.rot], rotating
 
  /// Rotate `x` to the left by `s` bits.
  template<typename _Tp>
    [[nodiscard]] constexpr _If_is_unsigned_integer<_Tp>
    rotl(_Tp __x, int __s) noexcept
    { return std::__rotl(__x, __s); }
 
  /// Rotate `x` to the right by `s` bits.
  template<typename _Tp>
    [[nodiscard]] constexpr _If_is_unsigned_integer<_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<typename _Tp>
    constexpr _If_is_unsigned_integer<_Tp, int>
    countl_zero(_Tp __x) noexcept
    { return std::__countl_zero(__x); }
 
  /// The number of contiguous one bits, starting from the highest bit.
  template<typename _Tp>
    constexpr _If_is_unsigned_integer<_Tp, int>
    countl_one(_Tp __x) noexcept
    { return std::__countl_one(__x); }
 
  /// The number of contiguous zero bits, starting from the lowest bit.
  template<typename _Tp>
    constexpr _If_is_unsigned_integer<_Tp, int>
    countr_zero(_Tp __x) noexcept
    { return std::__countr_zero(__x); }
 
  /// The number of contiguous one bits, starting from the lowest bit.
  template<typename _Tp>
    constexpr _If_is_unsigned_integer<_Tp, int>
    countr_one(_Tp __x) noexcept
    { return std::__countr_one(__x); }
 
  /// The number of bits set in `x`.
  template<typename _Tp>
    constexpr _If_is_unsigned_integer<_Tp, int>
    popcount(_Tp __x) noexcept
    { return std::__popcount(__x); }
 
  // [bit.pow.two], integral powers of 2
 
#define __cpp_lib_int_pow2 202002L
 
  /// True if `x` is a power of two, false otherwise.
  template<typename _Tp>
    constexpr _If_is_unsigned_integer<_Tp, bool>
    has_single_bit(_Tp __x) noexcept
    { return std::__has_single_bit(__x); }
 
  /// The smallest power-of-two not less than `x`.
  template<typename _Tp>
    constexpr _If_is_unsigned_integer<_Tp>
    bit_ceil(_Tp __x) noexcept
    { return std::__bit_ceil(__x); }
 
  /// The largest power-of-two not greater than `x`.
  template<typename _Tp>
    constexpr _If_is_unsigned_integer<_Tp>
    bit_floor(_Tp __x) noexcept
    { return std::__bit_floor(__x); }
 
  /// The smallest integer greater than the base-2 logarithm of `x`.
  template<typename _Tp>
    constexpr _If_is_unsigned_integer<_Tp>
    bit_width(_Tp __x) noexcept
    { return std::__bit_width(__x); }
 
#define __cpp_lib_endian 201907L
 
  /// Byte order
  enum class endian
  {
    little = __ORDER_LITTLE_ENDIAN__,
    big    = __ORDER_BIG_ENDIAN__,
    native = __BYTE_ORDER__
  };
#endif // C++2a
 
  /// @}
 
_GLIBCXX_END_NAMESPACE_VERSION
} // namespace std
 
#endif // C++14
#endif // _GLIBCXX_BIT