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//usr/include/c++/11/bit

// <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;

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;

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