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
limits
type_traits
std::enable_if_t
typename enable_if< _Cond, _Tp >::type enable_if_t
Alias template for enable_if.
Definition type_traits:2577
std
ISO C++ entities toplevel namespace is std.
__gnu_cxx
GNU extensions for public use.
__gnu_cxx::__int_traits
__numeric_traits_integer< _Tp > __int_traits
Convenience alias for __numeric_traits<integer-type>.
Definition ext/numeric_traits.h:136
std::__numeric_limits_base::digits
static constexpr int digits
Definition limits:211
std::numeric_limits::max
static constexpr _Tp max() noexcept
Definition limits:321
numeric_traits.h