bit
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// <bit> -*- C++ -*-
// Copyright (C) 2018-2025 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 >= 201402L
#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
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 _GLIBCXX_USE_BUILTIN_TRAIT(__builtin_clzg)
return __builtin_clzg(__x, _Nd);
#else
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);
}
#endif
}
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 _GLIBCXX_USE_BUILTIN_TRAIT(__builtin_ctzg)
return __builtin_ctzg(__x, _Nd);
#else
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;
}
#endif
}
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
{
#if _GLIBCXX_USE_BUILTIN_TRAIT(__builtin_popcountg)
return __builtin_popcountg(__x);
#else
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);
}
#endif
}
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.
if (!std::__is_constant_evaluated())
{
__glibcxx_assert( __shift_exponent != __int_traits<_Tp>::__digits );
}
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 int
__bit_width(_Tp __x) noexcept
{
constexpr auto _Nd = __gnu_cxx::__int_traits<_Tp>::__digits;
return _Nd - std::__countl_zero(__x);
}
/// @endcond
#ifdef __cpp_lib_bitops // C++ >= 20
/// @cond undocumented
template<typename _Tp>
concept __unsigned_integer = __is_unsigned_integer<_Tp>::value;
/// @endcond
// [bit.rot], 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)
#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++14
#endif // _GLIBCXX_BIT
concepts
limits
type_traits
version.h
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:140
std::__numeric_limits_base::digits
static constexpr int digits
Definition limits:218
std::numeric_limits::max
static constexpr _Tp max() noexcept
Definition limits:328
std::is_same
is_same
Definition type_traits:1535
numeric_traits.h