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- //===----------------------------------------------------------------------===//
- //
- // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
- // See https://llvm.org/LICENSE.txt for license information.
- // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
- //
- //===----------------------------------------------------------------------===//
- #ifndef _LIBCPP___FUNCTIONAL_HASH_H
- #define _LIBCPP___FUNCTIONAL_HASH_H
- #include <__config>
- #include <__functional/invoke.h>
- #include <__functional/unary_function.h>
- #include <__fwd/hash.h>
- #include <__tuple_dir/sfinae_helpers.h>
- #include <__type_traits/is_copy_constructible.h>
- #include <__type_traits/is_default_constructible.h>
- #include <__type_traits/is_enum.h>
- #include <__type_traits/is_move_constructible.h>
- #include <__type_traits/underlying_type.h>
- #include <__utility/forward.h>
- #include <__utility/move.h>
- #include <__utility/pair.h>
- #include <__utility/swap.h>
- #include <cstddef>
- #include <cstdint>
- #include <cstring>
- #include <limits>
- #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
- # pragma GCC system_header
- #endif
- _LIBCPP_BEGIN_NAMESPACE_STD
- template <class _Size>
- inline _LIBCPP_INLINE_VISIBILITY
- _Size
- __loadword(const void* __p)
- {
- _Size __r;
- _VSTD::memcpy(&__r, __p, sizeof(__r));
- return __r;
- }
- // We use murmur2 when size_t is 32 bits, and cityhash64 when size_t
- // is 64 bits. This is because cityhash64 uses 64bit x 64bit
- // multiplication, which can be very slow on 32-bit systems.
- template <class _Size, size_t = sizeof(_Size)*__CHAR_BIT__>
- struct __murmur2_or_cityhash;
- template <class _Size>
- struct __murmur2_or_cityhash<_Size, 32>
- {
- inline _Size operator()(const void* __key, _Size __len)
- _LIBCPP_DISABLE_UBSAN_UNSIGNED_INTEGER_CHECK;
- };
- // murmur2
- template <class _Size>
- _Size
- __murmur2_or_cityhash<_Size, 32>::operator()(const void* __key, _Size __len)
- {
- const _Size __m = 0x5bd1e995;
- const _Size __r = 24;
- _Size __h = __len;
- const unsigned char* __data = static_cast<const unsigned char*>(__key);
- for (; __len >= 4; __data += 4, __len -= 4)
- {
- _Size __k = std::__loadword<_Size>(__data);
- __k *= __m;
- __k ^= __k >> __r;
- __k *= __m;
- __h *= __m;
- __h ^= __k;
- }
- switch (__len)
- {
- case 3:
- __h ^= static_cast<_Size>(__data[2] << 16);
- _LIBCPP_FALLTHROUGH();
- case 2:
- __h ^= static_cast<_Size>(__data[1] << 8);
- _LIBCPP_FALLTHROUGH();
- case 1:
- __h ^= __data[0];
- __h *= __m;
- }
- __h ^= __h >> 13;
- __h *= __m;
- __h ^= __h >> 15;
- return __h;
- }
- template <class _Size>
- struct __murmur2_or_cityhash<_Size, 64>
- {
- inline _Size operator()(const void* __key, _Size __len) _LIBCPP_DISABLE_UBSAN_UNSIGNED_INTEGER_CHECK;
- private:
- // Some primes between 2^63 and 2^64.
- static const _Size __k0 = 0xc3a5c85c97cb3127ULL;
- static const _Size __k1 = 0xb492b66fbe98f273ULL;
- static const _Size __k2 = 0x9ae16a3b2f90404fULL;
- static const _Size __k3 = 0xc949d7c7509e6557ULL;
- static _Size __rotate(_Size __val, int __shift) {
- return __shift == 0 ? __val : ((__val >> __shift) | (__val << (64 - __shift)));
- }
- static _Size __rotate_by_at_least_1(_Size __val, int __shift) {
- return (__val >> __shift) | (__val << (64 - __shift));
- }
- static _Size __shift_mix(_Size __val) {
- return __val ^ (__val >> 47);
- }
- static _Size __hash_len_16(_Size __u, _Size __v)
- _LIBCPP_DISABLE_UBSAN_UNSIGNED_INTEGER_CHECK
- {
- const _Size __mul = 0x9ddfea08eb382d69ULL;
- _Size __a = (__u ^ __v) * __mul;
- __a ^= (__a >> 47);
- _Size __b = (__v ^ __a) * __mul;
- __b ^= (__b >> 47);
- __b *= __mul;
- return __b;
- }
- static _Size __hash_len_0_to_16(const char* __s, _Size __len)
- _LIBCPP_DISABLE_UBSAN_UNSIGNED_INTEGER_CHECK
- {
- if (__len > 8) {
- const _Size __a = std::__loadword<_Size>(__s);
- const _Size __b = std::__loadword<_Size>(__s + __len - 8);
- return __hash_len_16(__a, __rotate_by_at_least_1(__b + __len, __len)) ^ __b;
- }
- if (__len >= 4) {
- const uint32_t __a = std::__loadword<uint32_t>(__s);
- const uint32_t __b = std::__loadword<uint32_t>(__s + __len - 4);
- #ifdef _LIBCPP_ABI_FIX_CITYHASH_IMPLEMENTATION
- return __hash_len_16(__len + (static_cast<_Size>(__a) << 3), __b);
- #else
- return __hash_len_16(__len + (__a << 3), __b);
- #endif
- }
- if (__len > 0) {
- const unsigned char __a = static_cast<unsigned char>(__s[0]);
- const unsigned char __b = static_cast<unsigned char>(__s[__len >> 1]);
- const unsigned char __c = static_cast<unsigned char>(__s[__len - 1]);
- const uint32_t __y = static_cast<uint32_t>(__a) +
- (static_cast<uint32_t>(__b) << 8);
- const uint32_t __z = __len + (static_cast<uint32_t>(__c) << 2);
- return __shift_mix(__y * __k2 ^ __z * __k3) * __k2;
- }
- return __k2;
- }
- static _Size __hash_len_17_to_32(const char *__s, _Size __len)
- _LIBCPP_DISABLE_UBSAN_UNSIGNED_INTEGER_CHECK
- {
- const _Size __a = std::__loadword<_Size>(__s) * __k1;
- const _Size __b = std::__loadword<_Size>(__s + 8);
- const _Size __c = std::__loadword<_Size>(__s + __len - 8) * __k2;
- const _Size __d = std::__loadword<_Size>(__s + __len - 16) * __k0;
- return __hash_len_16(__rotate(__a - __b, 43) + __rotate(__c, 30) + __d,
- __a + __rotate(__b ^ __k3, 20) - __c + __len);
- }
- // Return a 16-byte hash for 48 bytes. Quick and dirty.
- // Callers do best to use "random-looking" values for a and b.
- static pair<_Size, _Size> __weak_hash_len_32_with_seeds(
- _Size __w, _Size __x, _Size __y, _Size __z, _Size __a, _Size __b)
- _LIBCPP_DISABLE_UBSAN_UNSIGNED_INTEGER_CHECK
- {
- __a += __w;
- __b = __rotate(__b + __a + __z, 21);
- const _Size __c = __a;
- __a += __x;
- __a += __y;
- __b += __rotate(__a, 44);
- return pair<_Size, _Size>(__a + __z, __b + __c);
- }
- // Return a 16-byte hash for s[0] ... s[31], a, and b. Quick and dirty.
- static pair<_Size, _Size> __weak_hash_len_32_with_seeds(
- const char* __s, _Size __a, _Size __b)
- _LIBCPP_DISABLE_UBSAN_UNSIGNED_INTEGER_CHECK
- {
- return __weak_hash_len_32_with_seeds(std::__loadword<_Size>(__s),
- std::__loadword<_Size>(__s + 8),
- std::__loadword<_Size>(__s + 16),
- std::__loadword<_Size>(__s + 24),
- __a,
- __b);
- }
- // Return an 8-byte hash for 33 to 64 bytes.
- static _Size __hash_len_33_to_64(const char *__s, size_t __len)
- _LIBCPP_DISABLE_UBSAN_UNSIGNED_INTEGER_CHECK
- {
- _Size __z = std::__loadword<_Size>(__s + 24);
- _Size __a = std::__loadword<_Size>(__s) +
- (__len + std::__loadword<_Size>(__s + __len - 16)) * __k0;
- _Size __b = __rotate(__a + __z, 52);
- _Size __c = __rotate(__a, 37);
- __a += std::__loadword<_Size>(__s + 8);
- __c += __rotate(__a, 7);
- __a += std::__loadword<_Size>(__s + 16);
- _Size __vf = __a + __z;
- _Size __vs = __b + __rotate(__a, 31) + __c;
- __a = std::__loadword<_Size>(__s + 16) + std::__loadword<_Size>(__s + __len - 32);
- __z += std::__loadword<_Size>(__s + __len - 8);
- __b = __rotate(__a + __z, 52);
- __c = __rotate(__a, 37);
- __a += std::__loadword<_Size>(__s + __len - 24);
- __c += __rotate(__a, 7);
- __a += std::__loadword<_Size>(__s + __len - 16);
- _Size __wf = __a + __z;
- _Size __ws = __b + __rotate(__a, 31) + __c;
- _Size __r = __shift_mix((__vf + __ws) * __k2 + (__wf + __vs) * __k0);
- return __shift_mix(__r * __k0 + __vs) * __k2;
- }
- };
- // cityhash64
- template <class _Size>
- _Size
- __murmur2_or_cityhash<_Size, 64>::operator()(const void* __key, _Size __len)
- {
- const char* __s = static_cast<const char*>(__key);
- if (__len <= 32) {
- if (__len <= 16) {
- return __hash_len_0_to_16(__s, __len);
- } else {
- return __hash_len_17_to_32(__s, __len);
- }
- } else if (__len <= 64) {
- return __hash_len_33_to_64(__s, __len);
- }
- // For strings over 64 bytes we hash the end first, and then as we
- // loop we keep 56 bytes of state: v, w, x, y, and z.
- _Size __x = std::__loadword<_Size>(__s + __len - 40);
- _Size __y = std::__loadword<_Size>(__s + __len - 16) +
- std::__loadword<_Size>(__s + __len - 56);
- _Size __z = __hash_len_16(std::__loadword<_Size>(__s + __len - 48) + __len,
- std::__loadword<_Size>(__s + __len - 24));
- pair<_Size, _Size> __v = __weak_hash_len_32_with_seeds(__s + __len - 64, __len, __z);
- pair<_Size, _Size> __w = __weak_hash_len_32_with_seeds(__s + __len - 32, __y + __k1, __x);
- __x = __x * __k1 + std::__loadword<_Size>(__s);
- // Decrease len to the nearest multiple of 64, and operate on 64-byte chunks.
- __len = (__len - 1) & ~static_cast<_Size>(63);
- do {
- __x = __rotate(__x + __y + __v.first + std::__loadword<_Size>(__s + 8), 37) * __k1;
- __y = __rotate(__y + __v.second + std::__loadword<_Size>(__s + 48), 42) * __k1;
- __x ^= __w.second;
- __y += __v.first + std::__loadword<_Size>(__s + 40);
- __z = __rotate(__z + __w.first, 33) * __k1;
- __v = __weak_hash_len_32_with_seeds(__s, __v.second * __k1, __x + __w.first);
- __w = __weak_hash_len_32_with_seeds(__s + 32, __z + __w.second,
- __y + std::__loadword<_Size>(__s + 16));
- _VSTD::swap(__z, __x);
- __s += 64;
- __len -= 64;
- } while (__len != 0);
- return __hash_len_16(
- __hash_len_16(__v.first, __w.first) + __shift_mix(__y) * __k1 + __z,
- __hash_len_16(__v.second, __w.second) + __x);
- }
- template <class _Tp, size_t = sizeof(_Tp) / sizeof(size_t)>
- struct __scalar_hash;
- template <class _Tp>
- struct __scalar_hash<_Tp, 0>
- : public __unary_function<_Tp, size_t>
- {
- _LIBCPP_INLINE_VISIBILITY
- size_t operator()(_Tp __v) const _NOEXCEPT
- {
- union
- {
- _Tp __t;
- size_t __a;
- } __u;
- __u.__a = 0;
- __u.__t = __v;
- return __u.__a;
- }
- };
- template <class _Tp>
- struct __scalar_hash<_Tp, 1>
- : public __unary_function<_Tp, size_t>
- {
- _LIBCPP_INLINE_VISIBILITY
- size_t operator()(_Tp __v) const _NOEXCEPT
- {
- union
- {
- _Tp __t;
- size_t __a;
- } __u;
- __u.__t = __v;
- return __u.__a;
- }
- };
- template <class _Tp>
- struct __scalar_hash<_Tp, 2>
- : public __unary_function<_Tp, size_t>
- {
- _LIBCPP_INLINE_VISIBILITY
- size_t operator()(_Tp __v) const _NOEXCEPT
- {
- union
- {
- _Tp __t;
- struct
- {
- size_t __a;
- size_t __b;
- } __s;
- } __u;
- __u.__t = __v;
- return __murmur2_or_cityhash<size_t>()(&__u, sizeof(__u));
- }
- };
- template <class _Tp>
- struct __scalar_hash<_Tp, 3>
- : public __unary_function<_Tp, size_t>
- {
- _LIBCPP_INLINE_VISIBILITY
- size_t operator()(_Tp __v) const _NOEXCEPT
- {
- union
- {
- _Tp __t;
- struct
- {
- size_t __a;
- size_t __b;
- size_t __c;
- } __s;
- } __u;
- __u.__t = __v;
- return __murmur2_or_cityhash<size_t>()(&__u, sizeof(__u));
- }
- };
- template <class _Tp>
- struct __scalar_hash<_Tp, 4>
- : public __unary_function<_Tp, size_t>
- {
- _LIBCPP_INLINE_VISIBILITY
- size_t operator()(_Tp __v) const _NOEXCEPT
- {
- union
- {
- _Tp __t;
- struct
- {
- size_t __a;
- size_t __b;
- size_t __c;
- size_t __d;
- } __s;
- } __u;
- __u.__t = __v;
- return __murmur2_or_cityhash<size_t>()(&__u, sizeof(__u));
- }
- };
- struct _PairT {
- size_t first;
- size_t second;
- };
- _LIBCPP_INLINE_VISIBILITY
- inline size_t __hash_combine(size_t __lhs, size_t __rhs) _NOEXCEPT {
- typedef __scalar_hash<_PairT> _HashT;
- const _PairT __p = {__lhs, __rhs};
- return _HashT()(__p);
- }
- template<class _Tp>
- struct _LIBCPP_TEMPLATE_VIS hash<_Tp*>
- : public __unary_function<_Tp*, size_t>
- {
- _LIBCPP_INLINE_VISIBILITY
- size_t operator()(_Tp* __v) const _NOEXCEPT
- {
- union
- {
- _Tp* __t;
- size_t __a;
- } __u;
- __u.__t = __v;
- return __murmur2_or_cityhash<size_t>()(&__u, sizeof(__u));
- }
- };
- template <>
- struct _LIBCPP_TEMPLATE_VIS hash<bool>
- : public __unary_function<bool, size_t>
- {
- _LIBCPP_INLINE_VISIBILITY
- size_t operator()(bool __v) const _NOEXCEPT {return static_cast<size_t>(__v);}
- };
- template <>
- struct _LIBCPP_TEMPLATE_VIS hash<char>
- : public __unary_function<char, size_t>
- {
- _LIBCPP_INLINE_VISIBILITY
- size_t operator()(char __v) const _NOEXCEPT {return static_cast<size_t>(__v);}
- };
- template <>
- struct _LIBCPP_TEMPLATE_VIS hash<signed char>
- : public __unary_function<signed char, size_t>
- {
- _LIBCPP_INLINE_VISIBILITY
- size_t operator()(signed char __v) const _NOEXCEPT {return static_cast<size_t>(__v);}
- };
- template <>
- struct _LIBCPP_TEMPLATE_VIS hash<unsigned char>
- : public __unary_function<unsigned char, size_t>
- {
- _LIBCPP_INLINE_VISIBILITY
- size_t operator()(unsigned char __v) const _NOEXCEPT {return static_cast<size_t>(__v);}
- };
- #ifndef _LIBCPP_HAS_NO_CHAR8_T
- template <>
- struct _LIBCPP_TEMPLATE_VIS hash<char8_t>
- : public __unary_function<char8_t, size_t>
- {
- _LIBCPP_INLINE_VISIBILITY
- size_t operator()(char8_t __v) const _NOEXCEPT {return static_cast<size_t>(__v);}
- };
- #endif // !_LIBCPP_HAS_NO_CHAR8_T
- template <>
- struct _LIBCPP_TEMPLATE_VIS hash<char16_t>
- : public __unary_function<char16_t, size_t>
- {
- _LIBCPP_INLINE_VISIBILITY
- size_t operator()(char16_t __v) const _NOEXCEPT {return static_cast<size_t>(__v);}
- };
- template <>
- struct _LIBCPP_TEMPLATE_VIS hash<char32_t>
- : public __unary_function<char32_t, size_t>
- {
- _LIBCPP_INLINE_VISIBILITY
- size_t operator()(char32_t __v) const _NOEXCEPT {return static_cast<size_t>(__v);}
- };
- #ifndef _LIBCPP_HAS_NO_WIDE_CHARACTERS
- template <>
- struct _LIBCPP_TEMPLATE_VIS hash<wchar_t>
- : public __unary_function<wchar_t, size_t>
- {
- _LIBCPP_INLINE_VISIBILITY
- size_t operator()(wchar_t __v) const _NOEXCEPT {return static_cast<size_t>(__v);}
- };
- #endif // _LIBCPP_HAS_NO_WIDE_CHARACTERS
- template <>
- struct _LIBCPP_TEMPLATE_VIS hash<short>
- : public __unary_function<short, size_t>
- {
- _LIBCPP_INLINE_VISIBILITY
- size_t operator()(short __v) const _NOEXCEPT {return static_cast<size_t>(__v);}
- };
- template <>
- struct _LIBCPP_TEMPLATE_VIS hash<unsigned short>
- : public __unary_function<unsigned short, size_t>
- {
- _LIBCPP_INLINE_VISIBILITY
- size_t operator()(unsigned short __v) const _NOEXCEPT {return static_cast<size_t>(__v);}
- };
- template <>
- struct _LIBCPP_TEMPLATE_VIS hash<int>
- : public __unary_function<int, size_t>
- {
- _LIBCPP_INLINE_VISIBILITY
- size_t operator()(int __v) const _NOEXCEPT {return static_cast<size_t>(__v);}
- };
- template <>
- struct _LIBCPP_TEMPLATE_VIS hash<unsigned int>
- : public __unary_function<unsigned int, size_t>
- {
- _LIBCPP_INLINE_VISIBILITY
- size_t operator()(unsigned int __v) const _NOEXCEPT {return static_cast<size_t>(__v);}
- };
- template <>
- struct _LIBCPP_TEMPLATE_VIS hash<long>
- : public __unary_function<long, size_t>
- {
- _LIBCPP_INLINE_VISIBILITY
- size_t operator()(long __v) const _NOEXCEPT {return static_cast<size_t>(__v);}
- };
- template <>
- struct _LIBCPP_TEMPLATE_VIS hash<unsigned long>
- : public __unary_function<unsigned long, size_t>
- {
- _LIBCPP_INLINE_VISIBILITY
- size_t operator()(unsigned long __v) const _NOEXCEPT {return static_cast<size_t>(__v);}
- };
- template <>
- struct _LIBCPP_TEMPLATE_VIS hash<long long>
- : public __scalar_hash<long long>
- {
- };
- template <>
- struct _LIBCPP_TEMPLATE_VIS hash<unsigned long long>
- : public __scalar_hash<unsigned long long>
- {
- };
- #ifndef _LIBCPP_HAS_NO_INT128
- template <>
- struct _LIBCPP_TEMPLATE_VIS hash<__int128_t>
- : public __scalar_hash<__int128_t>
- {
- };
- template <>
- struct _LIBCPP_TEMPLATE_VIS hash<__uint128_t>
- : public __scalar_hash<__uint128_t>
- {
- };
- #endif
- template <>
- struct _LIBCPP_TEMPLATE_VIS hash<float>
- : public __scalar_hash<float>
- {
- _LIBCPP_INLINE_VISIBILITY
- size_t operator()(float __v) const _NOEXCEPT
- {
- // -0.0 and 0.0 should return same hash
- if (__v == 0.0f)
- return 0;
- return __scalar_hash<float>::operator()(__v);
- }
- };
- template <>
- struct _LIBCPP_TEMPLATE_VIS hash<double>
- : public __scalar_hash<double>
- {
- _LIBCPP_INLINE_VISIBILITY
- size_t operator()(double __v) const _NOEXCEPT
- {
- // -0.0 and 0.0 should return same hash
- if (__v == 0.0)
- return 0;
- return __scalar_hash<double>::operator()(__v);
- }
- };
- template <>
- struct _LIBCPP_TEMPLATE_VIS hash<long double>
- : public __scalar_hash<long double>
- {
- _LIBCPP_INLINE_VISIBILITY
- size_t operator()(long double __v) const _NOEXCEPT
- {
- // -0.0 and 0.0 should return same hash
- if (__v == 0.0L)
- return 0;
- #if defined(__i386__) || (defined(__x86_64__) && defined(__ILP32__))
- // Zero out padding bits
- union
- {
- long double __t;
- struct
- {
- size_t __a;
- size_t __b;
- size_t __c;
- size_t __d;
- } __s;
- } __u;
- __u.__s.__a = 0;
- __u.__s.__b = 0;
- __u.__s.__c = 0;
- __u.__s.__d = 0;
- __u.__t = __v;
- return __u.__s.__a ^ __u.__s.__b ^ __u.__s.__c ^ __u.__s.__d;
- #elif defined(__x86_64__)
- // Zero out padding bits
- union
- {
- long double __t;
- struct
- {
- size_t __a;
- size_t __b;
- } __s;
- } __u;
- __u.__s.__a = 0;
- __u.__s.__b = 0;
- __u.__t = __v;
- return __u.__s.__a ^ __u.__s.__b;
- #else
- return __scalar_hash<long double>::operator()(__v);
- #endif
- }
- };
- template <class _Tp, bool = is_enum<_Tp>::value>
- struct _LIBCPP_TEMPLATE_VIS __enum_hash
- : public __unary_function<_Tp, size_t>
- {
- _LIBCPP_INLINE_VISIBILITY
- size_t operator()(_Tp __v) const _NOEXCEPT
- {
- typedef typename underlying_type<_Tp>::type type;
- return hash<type>()(static_cast<type>(__v));
- }
- };
- template <class _Tp>
- struct _LIBCPP_TEMPLATE_VIS __enum_hash<_Tp, false> {
- __enum_hash() = delete;
- __enum_hash(__enum_hash const&) = delete;
- __enum_hash& operator=(__enum_hash const&) = delete;
- };
- template <class _Tp>
- struct _LIBCPP_TEMPLATE_VIS hash : public __enum_hash<_Tp>
- {
- };
- #if _LIBCPP_STD_VER > 14
- template <>
- struct _LIBCPP_TEMPLATE_VIS hash<nullptr_t>
- : public __unary_function<nullptr_t, size_t>
- {
- _LIBCPP_INLINE_VISIBILITY
- size_t operator()(nullptr_t) const _NOEXCEPT {
- return 662607004ull;
- }
- };
- #endif
- #ifndef _LIBCPP_CXX03_LANG
- template <class _Key, class _Hash>
- using __check_hash_requirements _LIBCPP_NODEBUG = integral_constant<bool,
- is_copy_constructible<_Hash>::value &&
- is_move_constructible<_Hash>::value &&
- __invokable_r<size_t, _Hash, _Key const&>::value
- >;
- template <class _Key, class _Hash = hash<_Key> >
- using __has_enabled_hash _LIBCPP_NODEBUG = integral_constant<bool,
- __check_hash_requirements<_Key, _Hash>::value &&
- is_default_constructible<_Hash>::value
- >;
- #if _LIBCPP_STD_VER > 14
- template <class _Type, class>
- using __enable_hash_helper_imp _LIBCPP_NODEBUG = _Type;
- template <class _Type, class ..._Keys>
- using __enable_hash_helper _LIBCPP_NODEBUG = __enable_hash_helper_imp<_Type,
- typename enable_if<__all<__has_enabled_hash<_Keys>::value...>::value>::type
- >;
- #else
- template <class _Type, class ...>
- using __enable_hash_helper _LIBCPP_NODEBUG = _Type;
- #endif
- #endif // !_LIBCPP_CXX03_LANG
- _LIBCPP_END_NAMESPACE_STD
- #endif // _LIBCPP___FUNCTIONAL_HASH_H
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