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+// <bit> -*- C++ -*-
+
+// Copyright (C) 2018-2023 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 || __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
+
+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`.
+ /**
+ * @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(_To) && __is_trivially_copyable(_From)
+#endif
+ {
+ return __builtin_bit_cast(_To, __from);
+ }
+#endif
+
+#if __cplusplus > 202002L
+#define __cpp_lib_byteswap 202110L
+
+ /// 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<typename _Tp>
+ [[nodiscard]]
+ constexpr enable_if_t<is_integral<_Tp>::value, _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
+
+ /// @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 (__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.
+ 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
+
+#if __cplusplus > 201703L
+
+#define __cpp_lib_bitops 201907L
+
+ /// @cond undocumented
+ 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); }
+
+ // _GLIBCXX_RESOLVE_LIB_DEFECTS
+ // 3656. Inconsistent bit operations returning a count
+ /// The smallest integer greater than the base-2 logarithm of `x`.
+ template<typename _Tp>
+ constexpr _If_is_unsigned_integer<_Tp, int>
+ bit_width(_Tp __x) noexcept
+ { return std::__bit_width(__x); }
+
+#define __cpp_lib_endian 201907L
+
+ /// 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 // C++2a
+
+ /// @}
+
+_GLIBCXX_END_NAMESPACE_VERSION
+} // namespace std
+
+#endif // C++14
+#endif // _GLIBCXX_BIT