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// Copyright 2018 The Abseil Authors.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// https://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
//
// -----------------------------------------------------------------------------
// File: hash.h
// -----------------------------------------------------------------------------
//
#ifndef ABSL_HASH_INTERNAL_HASH_H_
#define ABSL_HASH_INTERNAL_HASH_H_
#ifdef __APPLE__
#include <Availability.h>
#include <TargetConditionals.h>
#endif
#include "absl/base/config.h"
// For feature testing and determining which headers can be included.
#if ABSL_INTERNAL_CPLUSPLUS_LANG >= 202002L
#include <version>
#else
#include <ciso646>
#endif
#include <algorithm>
#include <array>
#include <bitset>
#include <cmath>
#include <cstddef>
#include <cstring>
#include <deque>
#include <forward_list>
#include <functional>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <set>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
#include "absl/base/internal/unaligned_access.h"
#include "absl/base/port.h"
#include "absl/container/fixed_array.h"
#include "absl/hash/internal/city.h"
#include "absl/hash/internal/low_level_hash.h"
#include "absl/meta/type_traits.h"
#include "absl/numeric/bits.h"
#include "absl/numeric/int128.h"
#include "absl/strings/string_view.h"
#include "absl/types/optional.h"
#include "absl/types/variant.h"
#include "absl/utility/utility.h"
#if defined(__cpp_lib_filesystem) && __cpp_lib_filesystem >= 201703L && \
!defined(_LIBCPP_HAS_NO_FILESYSTEM_LIBRARY)
#include <filesystem> // NOLINT
#endif
#ifdef ABSL_HAVE_STD_STRING_VIEW
#include <string_view>
#endif
namespace absl {
ABSL_NAMESPACE_BEGIN
class HashState;
namespace hash_internal {
// Internal detail: Large buffers are hashed in smaller chunks. This function
// returns the size of these chunks.
constexpr size_t PiecewiseChunkSize() { return 1024; }
// PiecewiseCombiner
//
// PiecewiseCombiner is an internal-only helper class for hashing a piecewise
// buffer of `char` or `unsigned char` as though it were contiguous. This class
// provides two methods:
//
// H add_buffer(state, data, size)
// H finalize(state)
//
// `add_buffer` can be called zero or more times, followed by a single call to
// `finalize`. This will produce the same hash expansion as concatenating each
// buffer piece into a single contiguous buffer, and passing this to
// `H::combine_contiguous`.
//
// Example usage:
// PiecewiseCombiner combiner;
// for (const auto& piece : pieces) {
// state = combiner.add_buffer(std::move(state), piece.data, piece.size);
// }
// return combiner.finalize(std::move(state));
class PiecewiseCombiner {
public:
PiecewiseCombiner() : position_(0) {}
PiecewiseCombiner(const PiecewiseCombiner&) = delete;
PiecewiseCombiner& operator=(const PiecewiseCombiner&) = delete;
// PiecewiseCombiner::add_buffer()
//
// Appends the given range of bytes to the sequence to be hashed, which may
// modify the provided hash state.
template <typename H>
H add_buffer(H state, const unsigned char* data, size_t size);
template <typename H>
H add_buffer(H state, const char* data, size_t size) {
return add_buffer(std::move(state),
reinterpret_cast<const unsigned char*>(data), size);
}
// PiecewiseCombiner::finalize()
//
// Finishes combining the hash sequence, which may may modify the provided
// hash state.
//
// Once finalize() is called, add_buffer() may no longer be called. The
// resulting hash state will be the same as if the pieces passed to
// add_buffer() were concatenated into a single flat buffer, and then provided
// to H::combine_contiguous().
template <typename H>
H finalize(H state);
private:
unsigned char buf_[PiecewiseChunkSize()];
size_t position_;
};
// is_hashable()
//
// Trait class which returns true if T is hashable by the absl::Hash framework.
// Used for the AbslHashValue implementations for composite types below.
template <typename T>
struct is_hashable;
// HashStateBase
//
// An internal implementation detail that contains common implementation details
// for all of the "hash state objects" objects generated by Abseil. This is not
// a public API; users should not create classes that inherit from this.
//
// A hash state object is the template argument `H` passed to `AbslHashValue`.
// It represents an intermediate state in the computation of an unspecified hash
// algorithm. `HashStateBase` provides a CRTP style base class for hash state
// implementations. Developers adding type support for `absl::Hash` should not
// rely on any parts of the state object other than the following member
// functions:
//
// * HashStateBase::combine()
// * HashStateBase::combine_contiguous()
// * HashStateBase::combine_unordered()
//
// A derived hash state class of type `H` must provide a public member function
// with a signature similar to the following:
//
// `static H combine_contiguous(H state, const unsigned char*, size_t)`.
//
// It must also provide a private template method named RunCombineUnordered.
//
// A "consumer" is a 1-arg functor returning void. Its argument is a reference
// to an inner hash state object, and it may be called multiple times. When
// called, the functor consumes the entropy from the provided state object,
// and resets that object to its empty state.
//
// A "combiner" is a stateless 2-arg functor returning void. Its arguments are
// an inner hash state object and an ElementStateConsumer functor. A combiner
// uses the provided inner hash state object to hash each element of the
// container, passing the inner hash state object to the consumer after hashing
// each element.
//
// Given these definitions, a derived hash state class of type H
// must provide a private template method with a signature similar to the
// following:
//
// `template <typename CombinerT>`
// `static H RunCombineUnordered(H outer_state, CombinerT combiner)`
//
// This function is responsible for constructing the inner state object and
// providing a consumer to the combiner. It uses side effects of the consumer
// and combiner to mix the state of each element in an order-independent manner,
// and uses this to return an updated value of `outer_state`.
//
// This inside-out approach generates efficient object code in the normal case,
// but allows us to use stack storage to implement the absl::HashState type
// erasure mechanism (avoiding heap allocations while hashing).
//
// `HashStateBase` will provide a complete implementation for a hash state
// object in terms of these two methods.
//
// Example:
//
// // Use CRTP to define your derived class.
// struct MyHashState : HashStateBase<MyHashState> {
// static H combine_contiguous(H state, const unsigned char*, size_t);
// using MyHashState::HashStateBase::combine;
// using MyHashState::HashStateBase::combine_contiguous;
// using MyHashState::HashStateBase::combine_unordered;
// private:
// template <typename CombinerT>
// static H RunCombineUnordered(H state, CombinerT combiner);
// };
template <typename H>
class HashStateBase {
public:
// HashStateBase::combine()
//
// Combines an arbitrary number of values into a hash state, returning the
// updated state.
//
// Each of the value types `T` must be separately hashable by the Abseil
// hashing framework.
//
// NOTE:
//
// state = H::combine(std::move(state), value1, value2, value3);
//
// is guaranteed to produce the same hash expansion as:
//
// state = H::combine(std::move(state), value1);
// state = H::combine(std::move(state), value2);
// state = H::combine(std::move(state), value3);
template <typename T, typename... Ts>
static H combine(H state, const T& value, const Ts&... values);
static H combine(H state) { return state; }
// HashStateBase::combine_contiguous()
//
// Combines a contiguous array of `size` elements into a hash state, returning
// the updated state.
//
// NOTE:
//
// state = H::combine_contiguous(std::move(state), data, size);
//
// is NOT guaranteed to produce the same hash expansion as a for-loop (it may
// perform internal optimizations). If you need this guarantee, use the
// for-loop instead.
template <typename T>
static H combine_contiguous(H state, const T* data, size_t size);
template <typename I>
static H combine_unordered(H state, I begin, I end);
using AbslInternalPiecewiseCombiner = PiecewiseCombiner;
template <typename T>
using is_hashable = absl::hash_internal::is_hashable<T>;
private:
// Common implementation of the iteration step of a "combiner", as described
// above.
template <typename I>
struct CombineUnorderedCallback {
I begin;
I end;
template <typename InnerH, typename ElementStateConsumer>
void operator()(InnerH inner_state, ElementStateConsumer cb) {
for (; begin != end; ++begin) {
inner_state = H::combine(std::move(inner_state), *begin);
cb(inner_state);
}
}
};
};
// is_uniquely_represented
//
// `is_uniquely_represented<T>` is a trait class that indicates whether `T`
// is uniquely represented.
//
// A type is "uniquely represented" if two equal values of that type are
// guaranteed to have the same bytes in their underlying storage. In other
// words, if `a == b`, then `memcmp(&a, &b, sizeof(T))` is guaranteed to be
// zero. This property cannot be detected automatically, so this trait is false
// by default, but can be specialized by types that wish to assert that they are
// uniquely represented. This makes them eligible for certain optimizations.
//
// If you have any doubt whatsoever, do not specialize this template.
// The default is completely safe, and merely disables some optimizations
// that will not matter for most types. Specializing this template,
// on the other hand, can be very hazardous.
//
// To be uniquely represented, a type must not have multiple ways of
// representing the same value; for example, float and double are not
// uniquely represented, because they have distinct representations for
// +0 and -0. Furthermore, the type's byte representation must consist
// solely of user-controlled data, with no padding bits and no compiler-
// controlled data such as vptrs or sanitizer metadata. This is usually
// very difficult to guarantee, because in most cases the compiler can
// insert data and padding bits at its own discretion.
//
// If you specialize this template for a type `T`, you must do so in the file
// that defines that type (or in this file). If you define that specialization
// anywhere else, `is_uniquely_represented<T>` could have different meanings
// in different places.
//
// The Enable parameter is meaningless; it is provided as a convenience,
// to support certain SFINAE techniques when defining specializations.
template <typename T, typename Enable = void>
struct is_uniquely_represented : std::false_type {};
// is_uniquely_represented<unsigned char>
//
// unsigned char is a synonym for "byte", so it is guaranteed to be
// uniquely represented.
template <>
struct is_uniquely_represented<unsigned char> : std::true_type {};
// is_uniquely_represented for non-standard integral types
//
// Integral types other than bool should be uniquely represented on any
// platform that this will plausibly be ported to.
template <typename Integral>
struct is_uniquely_represented<
Integral, typename std::enable_if<std::is_integral<Integral>::value>::type>
: std::true_type {};
// is_uniquely_represented<bool>
//
//
template <>
struct is_uniquely_represented<bool> : std::false_type {};
// hash_bytes()
//
// Convenience function that combines `hash_state` with the byte representation
// of `value`.
template <typename H, typename T>
H hash_bytes(H hash_state, const T& value) {
const unsigned char* start = reinterpret_cast<const unsigned char*>(&value);
return H::combine_contiguous(std::move(hash_state), start, sizeof(value));
}
// -----------------------------------------------------------------------------
// AbslHashValue for Basic Types
// -----------------------------------------------------------------------------
// Note: Default `AbslHashValue` implementations live in `hash_internal`. This
// allows us to block lexical scope lookup when doing an unqualified call to
// `AbslHashValue` below. User-defined implementations of `AbslHashValue` can
// only be found via ADL.
// AbslHashValue() for hashing bool values
//
// We use SFINAE to ensure that this overload only accepts bool, not types that
// are convertible to bool.
template <typename H, typename B>
typename std::enable_if<std::is_same<B, bool>::value, H>::type AbslHashValue(
H hash_state, B value) {
return H::combine(std::move(hash_state),
static_cast<unsigned char>(value ? 1 : 0));
}
// AbslHashValue() for hashing enum values
template <typename H, typename Enum>
typename std::enable_if<std::is_enum<Enum>::value, H>::type AbslHashValue(
H hash_state, Enum e) {
// In practice, we could almost certainly just invoke hash_bytes directly,
// but it's possible that a sanitizer might one day want to
// store data in the unused bits of an enum. To avoid that risk, we
// convert to the underlying type before hashing. Hopefully this will get
// optimized away; if not, we can reopen discussion with c-toolchain-team.
return H::combine(std::move(hash_state),
static_cast<typename std::underlying_type<Enum>::type>(e));
}
// AbslHashValue() for hashing floating-point values
template <typename H, typename Float>
typename std::enable_if<std::is_same<Float, float>::value ||
std::is_same<Float, double>::value,
H>::type
AbslHashValue(H hash_state, Float value) {
return hash_internal::hash_bytes(std::move(hash_state),
value == 0 ? 0 : value);
}
// Long double has the property that it might have extra unused bytes in it.
// For example, in x86 sizeof(long double)==16 but it only really uses 80-bits
// of it. This means we can't use hash_bytes on a long double and have to
// convert it to something else first.
template <typename H, typename LongDouble>
typename std::enable_if<std::is_same<LongDouble, long double>::value, H>::type
AbslHashValue(H hash_state, LongDouble value) {
const int category = std::fpclassify(value);
switch (category) {
case FP_INFINITE:
// Add the sign bit to differentiate between +Inf and -Inf
hash_state = H::combine(std::move(hash_state), std::signbit(value));
break;
case FP_NAN:
case FP_ZERO:
default:
// Category is enough for these.
break;
case FP_NORMAL:
case FP_SUBNORMAL:
// We can't convert `value` directly to double because this would have
// undefined behavior if the value is out of range.
// std::frexp gives us a value in the range (-1, -.5] or [.5, 1) that is
// guaranteed to be in range for `double`. The truncation is
// implementation defined, but that works as long as it is deterministic.
int exp;
auto mantissa = static_cast<double>(std::frexp(value, &exp));
hash_state = H::combine(std::move(hash_state), mantissa, exp);
}
return H::combine(std::move(hash_state), category);
}
// Without this overload, an array decays to a pointer and we hash that, which
// is not likely to be what the caller intended.
template <typename H, typename T, size_t N>
H AbslHashValue(H hash_state, T (&)[N]) {
static_assert(
sizeof(T) == -1,
"Hashing C arrays is not allowed. For string literals, wrap the literal "
"in absl::string_view(). To hash the array contents, use "
"absl::MakeSpan() or make the array an std::array. To hash the array "
"address, use &array[0].");
return hash_state;
}
// AbslHashValue() for hashing pointers
template <typename H, typename T>
std::enable_if_t<std::is_pointer<T>::value, H> AbslHashValue(H hash_state,
T ptr) {
auto v = reinterpret_cast<uintptr_t>(ptr);
// Due to alignment, pointers tend to have low bits as zero, and the next few
// bits follow a pattern since they are also multiples of some base value.
// Mixing the pointer twice helps prevent stuck low bits for certain alignment
// values.
return H::combine(std::move(hash_state), v, v);
}
// AbslHashValue() for hashing nullptr_t
template <typename H>
H AbslHashValue(H hash_state, std::nullptr_t) {
return H::combine(std::move(hash_state), static_cast<void*>(nullptr));
}
// AbslHashValue() for hashing pointers-to-member
template <typename H, typename T, typename C>
H AbslHashValue(H hash_state, T C::*ptr) {
auto salient_ptm_size = [](std::size_t n) -> std::size_t {
#if defined(_MSC_VER)
// Pointers-to-member-function on MSVC consist of one pointer plus 0, 1, 2,
// or 3 ints. In 64-bit mode, they are 8-byte aligned and thus can contain
// padding (namely when they have 1 or 3 ints). The value below is a lower
// bound on the number of salient, non-padding bytes that we use for
// hashing.
if (alignof(T C::*) == alignof(int)) {
// No padding when all subobjects have the same size as the total
// alignment. This happens in 32-bit mode.
return n;
} else {
// Padding for 1 int (size 16) or 3 ints (size 24).
// With 2 ints, the size is 16 with no padding, which we pessimize.
return n == 24 ? 20 : n == 16 ? 12 : n;
}
#else
// On other platforms, we assume that pointers-to-members do not have
// padding.
#ifdef __cpp_lib_has_unique_object_representations
static_assert(std::has_unique_object_representations<T C::*>::value);
#endif // __cpp_lib_has_unique_object_representations
return n;
#endif
};
return H::combine_contiguous(std::move(hash_state),
reinterpret_cast<unsigned char*>(&ptr),
salient_ptm_size(sizeof ptr));
}
// -----------------------------------------------------------------------------
// AbslHashValue for Composite Types
// -----------------------------------------------------------------------------
// AbslHashValue() for hashing pairs
template <typename H, typename T1, typename T2>
typename std::enable_if<is_hashable<T1>::value && is_hashable<T2>::value,
H>::type
AbslHashValue(H hash_state, const std::pair<T1, T2>& p) {
return H::combine(std::move(hash_state), p.first, p.second);
}
// hash_tuple()
//
// Helper function for hashing a tuple. The third argument should
// be an index_sequence running from 0 to tuple_size<Tuple> - 1.
template <typename H, typename Tuple, size_t... Is>
H hash_tuple(H hash_state, const Tuple& t, absl::index_sequence<Is...>) {
return H::combine(std::move(hash_state), std::get<Is>(t)...);
}
// AbslHashValue for hashing tuples
template <typename H, typename... Ts>
#if defined(_MSC_VER)
// This SFINAE gets MSVC confused under some conditions. Let's just disable it
// for now.
H
#else // _MSC_VER
typename std::enable_if<absl::conjunction<is_hashable<Ts>...>::value, H>::type
#endif // _MSC_VER
AbslHashValue(H hash_state, const std::tuple<Ts...>& t) {
return hash_internal::hash_tuple(std::move(hash_state), t,
absl::make_index_sequence<sizeof...(Ts)>());
}
// -----------------------------------------------------------------------------
// AbslHashValue for Pointers
// -----------------------------------------------------------------------------
// AbslHashValue for hashing unique_ptr
template <typename H, typename T, typename D>
H AbslHashValue(H hash_state, const std::unique_ptr<T, D>& ptr) {
return H::combine(std::move(hash_state), ptr.get());
}
// AbslHashValue for hashing shared_ptr
template <typename H, typename T>
H AbslHashValue(H hash_state, const std::shared_ptr<T>& ptr) {
return H::combine(std::move(hash_state), ptr.get());
}
// -----------------------------------------------------------------------------
// AbslHashValue for String-Like Types
// -----------------------------------------------------------------------------
// AbslHashValue for hashing strings
//
// All the string-like types supported here provide the same hash expansion for
// the same character sequence. These types are:
//
// - `absl::Cord`
// - `std::string` (and std::basic_string<T, std::char_traits<T>, A> for
// any allocator A and any T in {char, wchar_t, char16_t, char32_t})
// - `absl::string_view`, `std::string_view`, `std::wstring_view`,
// `std::u16string_view`, and `std::u32_string_view`.
//
// For simplicity, we currently support only strings built on `char`, `wchar_t`,
// `char16_t`, or `char32_t`. This support may be broadened, if necessary, but
// with some caution - this overload would misbehave in cases where the traits'
// `eq()` member isn't equivalent to `==` on the underlying character type.
template <typename H>
H AbslHashValue(H hash_state, absl::string_view str) {
return H::combine(
H::combine_contiguous(std::move(hash_state), str.data(), str.size()),
str.size());
}
// Support std::wstring, std::u16string and std::u32string.
template <typename Char, typename Alloc, typename H,
typename = absl::enable_if_t<std::is_same<Char, wchar_t>::value ||
std::is_same<Char, char16_t>::value ||
std::is_same<Char, char32_t>::value>>
H AbslHashValue(
H hash_state,
const std::basic_string<Char, std::char_traits<Char>, Alloc>& str) {
return H::combine(
H::combine_contiguous(std::move(hash_state), str.data(), str.size()),
str.size());
}
#ifdef ABSL_HAVE_STD_STRING_VIEW
// Support std::wstring_view, std::u16string_view and std::u32string_view.
template <typename Char, typename H,
typename = absl::enable_if_t<std::is_same<Char, wchar_t>::value ||
std::is_same<Char, char16_t>::value ||
std::is_same<Char, char32_t>::value>>
H AbslHashValue(H hash_state, std::basic_string_view<Char> str) {
return H::combine(
H::combine_contiguous(std::move(hash_state), str.data(), str.size()),
str.size());
}
#endif // ABSL_HAVE_STD_STRING_VIEW
#if defined(__cpp_lib_filesystem) && __cpp_lib_filesystem >= 201703L && \
!defined(_LIBCPP_HAS_NO_FILESYSTEM_LIBRARY) && \
(!defined(__ENVIRONMENT_IPHONE_OS_VERSION_MIN_REQUIRED__) || \
__ENVIRONMENT_IPHONE_OS_VERSION_MIN_REQUIRED__ >= 130000) && \
(!defined(__ENVIRONMENT_MAC_OS_X_VERSION_MIN_REQUIRED__) || \
__ENVIRONMENT_MAC_OS_X_VERSION_MIN_REQUIRED__ >= 101500)
#define ABSL_INTERNAL_STD_FILESYSTEM_PATH_HASH_AVAILABLE 1
// Support std::filesystem::path. The SFINAE is required because some string
// types are implicitly convertible to std::filesystem::path.
template <typename Path, typename H,
typename = absl::enable_if_t<
std::is_same_v<Path, std::filesystem::path>>>
H AbslHashValue(H hash_state, const Path& path) {
// This is implemented by deferring to the standard library to compute the
// hash. The standard library requires that for two paths, `p1 == p2`, then
// `hash_value(p1) == hash_value(p2)`. `AbslHashValue` has the same
// requirement. Since `operator==` does platform specific matching, deferring
// to the standard library is the simplest approach.
return H::combine(std::move(hash_state), std::filesystem::hash_value(path));
}
#endif // ABSL_INTERNAL_STD_FILESYSTEM_PATH_HASH_AVAILABLE
// -----------------------------------------------------------------------------
// AbslHashValue for Sequence Containers
// -----------------------------------------------------------------------------
// AbslHashValue for hashing std::array
template <typename H, typename T, size_t N>
typename std::enable_if<is_hashable<T>::value, H>::type AbslHashValue(
H hash_state, const std::array<T, N>& array) {
return H::combine_contiguous(std::move(hash_state), array.data(),
array.size());
}
// AbslHashValue for hashing std::deque
template <typename H, typename T, typename Allocator>
typename std::enable_if<is_hashable<T>::value, H>::type AbslHashValue(
H hash_state, const std::deque<T, Allocator>& deque) {
// TODO(gromer): investigate a more efficient implementation taking
// advantage of the chunk structure.
for (const auto& t : deque) {
hash_state = H::combine(std::move(hash_state), t);
}
return H::combine(std::move(hash_state), deque.size());
}
// AbslHashValue for hashing std::forward_list
template <typename H, typename T, typename Allocator>
typename std::enable_if<is_hashable<T>::value, H>::type AbslHashValue(
H hash_state, const std::forward_list<T, Allocator>& list) {
size_t size = 0;
for (const T& t : list) {
hash_state = H::combine(std::move(hash_state), t);
++size;
}
return H::combine(std::move(hash_state), size);
}
// AbslHashValue for hashing std::list
template <typename H, typename T, typename Allocator>
typename std::enable_if<is_hashable<T>::value, H>::type AbslHashValue(
H hash_state, const std::list<T, Allocator>& list) {
for (const auto& t : list) {
hash_state = H::combine(std::move(hash_state), t);
}
return H::combine(std::move(hash_state), list.size());
}
// AbslHashValue for hashing std::vector
//
// Do not use this for vector<bool> on platforms that have a working
// implementation of std::hash. It does not have a .data(), and a fallback for
// std::hash<> is most likely faster.
template <typename H, typename T, typename Allocator>
typename std::enable_if<is_hashable<T>::value && !std::is_same<T, bool>::value,
H>::type
AbslHashValue(H hash_state, const std::vector<T, Allocator>& vector) {
return H::combine(H::combine_contiguous(std::move(hash_state), vector.data(),
vector.size()),
vector.size());
}
// AbslHashValue special cases for hashing std::vector<bool>
#if defined(ABSL_IS_BIG_ENDIAN) && \
(defined(__GLIBCXX__) || defined(__GLIBCPP__))
// std::hash in libstdc++ does not work correctly with vector<bool> on Big
// Endian platforms therefore we need to implement a custom AbslHashValue for
// it. More details on the bug:
// https://gcc.gnu.org/bugzilla/show_bug.cgi?id=102531
template <typename H, typename T, typename Allocator>
typename std::enable_if<is_hashable<T>::value && std::is_same<T, bool>::value,
H>::type
AbslHashValue(H hash_state, const std::vector<T, Allocator>& vector) {
typename H::AbslInternalPiecewiseCombiner combiner;
for (const auto& i : vector) {
unsigned char c = static_cast<unsigned char>(i);
hash_state = combiner.add_buffer(std::move(hash_state), &c, sizeof(c));
}
return H::combine(combiner.finalize(std::move(hash_state)), vector.size());
}
#else
// When not working around the libstdc++ bug above, we still have to contend
// with the fact that std::hash<vector<bool>> is often poor quality, hashing
// directly on the internal words and on no other state. On these platforms,
// vector<bool>{1, 1} and vector<bool>{1, 1, 0} hash to the same value.
//
// Mixing in the size (as we do in our other vector<> implementations) on top
// of the library-provided hash implementation avoids this QOI issue.
template <typename H, typename T, typename Allocator>
typename std::enable_if<is_hashable<T>::value && std::is_same<T, bool>::value,
H>::type
AbslHashValue(H hash_state, const std::vector<T, Allocator>& vector) {
return H::combine(std::move(hash_state),
std::hash<std::vector<T, Allocator>>{}(vector),
vector.size());
}
#endif
// -----------------------------------------------------------------------------
// AbslHashValue for Ordered Associative Containers
// -----------------------------------------------------------------------------
// AbslHashValue for hashing std::map
template <typename H, typename Key, typename T, typename Compare,
typename Allocator>
typename std::enable_if<is_hashable<Key>::value && is_hashable<T>::value,
H>::type
AbslHashValue(H hash_state, const std::map<Key, T, Compare, Allocator>& map) {
for (const auto& t : map) {
hash_state = H::combine(std::move(hash_state), t);
}
return H::combine(std::move(hash_state), map.size());
}
// AbslHashValue for hashing std::multimap
template <typename H, typename Key, typename T, typename Compare,
typename Allocator>
typename std::enable_if<is_hashable<Key>::value && is_hashable<T>::value,
H>::type
AbslHashValue(H hash_state,
const std::multimap<Key, T, Compare, Allocator>& map) {
for (const auto& t : map) {
hash_state = H::combine(std::move(hash_state), t);
}
return H::combine(std::move(hash_state), map.size());
}
// AbslHashValue for hashing std::set
template <typename H, typename Key, typename Compare, typename Allocator>
typename std::enable_if<is_hashable<Key>::value, H>::type AbslHashValue(
H hash_state, const std::set<Key, Compare, Allocator>& set) {
for (const auto& t : set) {
hash_state = H::combine(std::move(hash_state), t);
}
return H::combine(std::move(hash_state), set.size());
}
// AbslHashValue for hashing std::multiset
template <typename H, typename Key, typename Compare, typename Allocator>
typename std::enable_if<is_hashable<Key>::value, H>::type AbslHashValue(
H hash_state, const std::multiset<Key, Compare, Allocator>& set) {
for (const auto& t : set) {
hash_state = H::combine(std::move(hash_state), t);
}
return H::combine(std::move(hash_state), set.size());
}
// -----------------------------------------------------------------------------
// AbslHashValue for Unordered Associative Containers
// -----------------------------------------------------------------------------
// AbslHashValue for hashing std::unordered_set
template <typename H, typename Key, typename Hash, typename KeyEqual,
typename Alloc>
typename std::enable_if<is_hashable<Key>::value, H>::type AbslHashValue(
H hash_state, const std::unordered_set<Key, Hash, KeyEqual, Alloc>& s) {
return H::combine(
H::combine_unordered(std::move(hash_state), s.begin(), s.end()),
s.size());
}
// AbslHashValue for hashing std::unordered_multiset
template <typename H, typename Key, typename Hash, typename KeyEqual,
typename Alloc>
typename std::enable_if<is_hashable<Key>::value, H>::type AbslHashValue(
H hash_state,
const std::unordered_multiset<Key, Hash, KeyEqual, Alloc>& s) {
return H::combine(
H::combine_unordered(std::move(hash_state), s.begin(), s.end()),
s.size());
}
// AbslHashValue for hashing std::unordered_set
template <typename H, typename Key, typename T, typename Hash,
typename KeyEqual, typename Alloc>
typename std::enable_if<is_hashable<Key>::value && is_hashable<T>::value,
H>::type
AbslHashValue(H hash_state,
const std::unordered_map<Key, T, Hash, KeyEqual, Alloc>& s) {
return H::combine(
H::combine_unordered(std::move(hash_state), s.begin(), s.end()),
s.size());
}
// AbslHashValue for hashing std::unordered_multiset
template <typename H, typename Key, typename T, typename Hash,
typename KeyEqual, typename Alloc>
typename std::enable_if<is_hashable<Key>::value && is_hashable<T>::value,
H>::type
AbslHashValue(H hash_state,
const std::unordered_multimap<Key, T, Hash, KeyEqual, Alloc>& s) {
return H::combine(
H::combine_unordered(std::move(hash_state), s.begin(), s.end()),
s.size());
}
// -----------------------------------------------------------------------------
// AbslHashValue for Wrapper Types
// -----------------------------------------------------------------------------
// AbslHashValue for hashing std::reference_wrapper
template <typename H, typename T>
typename std::enable_if<is_hashable<T>::value, H>::type AbslHashValue(
H hash_state, std::reference_wrapper<T> opt) {
return H::combine(std::move(hash_state), opt.get());
}
// AbslHashValue for hashing absl::optional
template <typename H, typename T>
typename std::enable_if<is_hashable<T>::value, H>::type AbslHashValue(
H hash_state, const absl::optional<T>& opt) {
if (opt) hash_state = H::combine(std::move(hash_state), *opt);
return H::combine(std::move(hash_state), opt.has_value());
}
// VariantVisitor
template <typename H>
struct VariantVisitor {
H&& hash_state;
template <typename T>
H operator()(const T& t) const {
return H::combine(std::move(hash_state), t);
}
};
// AbslHashValue for hashing absl::variant
template <typename H, typename... T>
typename std::enable_if<conjunction<is_hashable<T>...>::value, H>::type
AbslHashValue(H hash_state, const absl::variant<T...>& v) {
if (!v.valueless_by_exception()) {
hash_state = absl::visit(VariantVisitor<H>{std::move(hash_state)}, v);
}
return H::combine(std::move(hash_state), v.index());
}
// -----------------------------------------------------------------------------
// AbslHashValue for Other Types
// -----------------------------------------------------------------------------
// AbslHashValue for hashing std::bitset is not defined on Little Endian
// platforms, for the same reason as for vector<bool> (see std::vector above):
// It does not expose the raw bytes, and a fallback to std::hash<> is most
// likely faster.
#if defined(ABSL_IS_BIG_ENDIAN) && \
(defined(__GLIBCXX__) || defined(__GLIBCPP__))
// AbslHashValue for hashing std::bitset
//
// std::hash in libstdc++ does not work correctly with std::bitset on Big Endian
// platforms therefore we need to implement a custom AbslHashValue for it. More
// details on the bug: https://gcc.gnu.org/bugzilla/show_bug.cgi?id=102531
template <typename H, size_t N>
H AbslHashValue(H hash_state, const std::bitset<N>& set) {
typename H::AbslInternalPiecewiseCombiner combiner;
for (size_t i = 0; i < N; i++) {
unsigned char c = static_cast<unsigned char>(set[i]);
hash_state = combiner.add_buffer(std::move(hash_state), &c, sizeof(c));
}
return H::combine(combiner.finalize(std::move(hash_state)), N);
}
#endif
// -----------------------------------------------------------------------------
// hash_range_or_bytes()
//
// Mixes all values in the range [data, data+size) into the hash state.
// This overload accepts only uniquely-represented types, and hashes them by
// hashing the entire range of bytes.
template <typename H, typename T>
typename std::enable_if<is_uniquely_represented<T>::value, H>::type
hash_range_or_bytes(H hash_state, const T* data, size_t size) {
const auto* bytes = reinterpret_cast<const unsigned char*>(data);
return H::combine_contiguous(std::move(hash_state), bytes, sizeof(T) * size);
}
// hash_range_or_bytes()
template <typename H, typename T>
typename std::enable_if<!is_uniquely_represented<T>::value, H>::type
hash_range_or_bytes(H hash_state, const T* data, size_t size) {
for (const auto end = data + size; data < end; ++data) {
hash_state = H::combine(std::move(hash_state), *data);
}
return hash_state;
}
#if defined(ABSL_INTERNAL_LEGACY_HASH_NAMESPACE) && \
ABSL_META_INTERNAL_STD_HASH_SFINAE_FRIENDLY_
#define ABSL_HASH_INTERNAL_SUPPORT_LEGACY_HASH_ 1
#else
#define ABSL_HASH_INTERNAL_SUPPORT_LEGACY_HASH_ 0
#endif
// HashSelect
//
// Type trait to select the appropriate hash implementation to use.
// HashSelect::type<T> will give the proper hash implementation, to be invoked
// as:
// HashSelect::type<T>::Invoke(state, value)
// Also, HashSelect::type<T>::value is a boolean equal to `true` if there is a
// valid `Invoke` function. Types that are not hashable will have a ::value of
// `false`.
struct HashSelect {
private:
struct State : HashStateBase<State> {
static State combine_contiguous(State hash_state, const unsigned char*,
size_t);
using State::HashStateBase::combine_contiguous;
};
struct UniquelyRepresentedProbe {
template <typename H, typename T>
static auto Invoke(H state, const T& value)
-> absl::enable_if_t<is_uniquely_represented<T>::value, H> {
return hash_internal::hash_bytes(std::move(state), value);
}
};
struct HashValueProbe {
template <typename H, typename T>
static auto Invoke(H state, const T& value) -> absl::enable_if_t<
std::is_same<H,
decltype(AbslHashValue(std::move(state), value))>::value,
H> {
return AbslHashValue(std::move(state), value);
}
};
struct LegacyHashProbe {
#if ABSL_HASH_INTERNAL_SUPPORT_LEGACY_HASH_
template <typename H, typename T>
static auto Invoke(H state, const T& value) -> absl::enable_if_t<
std::is_convertible<
decltype(ABSL_INTERNAL_LEGACY_HASH_NAMESPACE::hash<T>()(value)),
size_t>::value,
H> {
return hash_internal::hash_bytes(
std::move(state),
ABSL_INTERNAL_LEGACY_HASH_NAMESPACE::hash<T>{}(value));
}
#endif // ABSL_HASH_INTERNAL_SUPPORT_LEGACY_HASH_
};
struct StdHashProbe {
template <typename H, typename T>
static auto Invoke(H state, const T& value)
-> absl::enable_if_t<type_traits_internal::IsHashable<T>::value, H> {
return hash_internal::hash_bytes(std::move(state), std::hash<T>{}(value));
}
};
template <typename Hash, typename T>
struct Probe : Hash {
private:
template <typename H, typename = decltype(H::Invoke(
std::declval<State>(), std::declval<const T&>()))>
static std::true_type Test(int);
template <typename U>
static std::false_type Test(char);
public:
static constexpr bool value = decltype(Test<Hash>(0))::value;
};
public:
// Probe each implementation in order.
// disjunction provides short circuiting wrt instantiation.
template <typename T>
using Apply = absl::disjunction< //
Probe<UniquelyRepresentedProbe, T>, //
Probe<HashValueProbe, T>, //
Probe<LegacyHashProbe, T>, //
Probe<StdHashProbe, T>, //
std::false_type>;
};
template <typename T>
struct is_hashable
: std::integral_constant<bool, HashSelect::template Apply<T>::value> {};
// MixingHashState
class ABSL_DLL MixingHashState : public HashStateBase<MixingHashState> {
// absl::uint128 is not an alias or a thin wrapper around the intrinsic.
// We use the intrinsic when available to improve performance.
#ifdef ABSL_HAVE_INTRINSIC_INT128
using uint128 = __uint128_t;
#else // ABSL_HAVE_INTRINSIC_INT128
using uint128 = absl::uint128;
#endif // ABSL_HAVE_INTRINSIC_INT128
static constexpr uint64_t kMul =
sizeof(size_t) == 4 ? uint64_t{0xcc9e2d51}
: uint64_t{0x9ddfea08eb382d69};
template <typename T>
using IntegralFastPath =
conjunction<std::is_integral<T>, is_uniquely_represented<T>>;
public:
// Move only
MixingHashState(MixingHashState&&) = default;
MixingHashState& operator=(MixingHashState&&) = default;
// MixingHashState::combine_contiguous()
//
// Fundamental base case for hash recursion: mixes the given range of bytes
// into the hash state.
static MixingHashState combine_contiguous(MixingHashState hash_state,
const unsigned char* first,
size_t size) {
return MixingHashState(
CombineContiguousImpl(hash_state.state_, first, size,
std::integral_constant<int, sizeof(size_t)>{}));
}
using MixingHashState::HashStateBase::combine_contiguous;
// MixingHashState::hash()
//
// For performance reasons in non-opt mode, we specialize this for
// integral types.
// Otherwise we would be instantiating and calling dozens of functions for
// something that is just one multiplication and a couple xor's.
// The result should be the same as running the whole algorithm, but faster.
template <typename T, absl::enable_if_t<IntegralFastPath<T>::value, int> = 0>
static size_t hash(T value) {
return static_cast<size_t>(
Mix(Seed(), static_cast<std::make_unsigned_t<T>>(value)));
}
// Overload of MixingHashState::hash()
template <typename T, absl::enable_if_t<!IntegralFastPath<T>::value, int> = 0>
static size_t hash(const T& value) {
return static_cast<size_t>(combine(MixingHashState{}, value).state_);
}
private:
// Invoked only once for a given argument; that plus the fact that this is
// move-only ensures that there is only one non-moved-from object.
MixingHashState() : state_(Seed()) {}
friend class MixingHashState::HashStateBase;
template <typename CombinerT>
static MixingHashState RunCombineUnordered(MixingHashState state,
CombinerT combiner) {
uint64_t unordered_state = 0;
combiner(MixingHashState{}, [&](MixingHashState& inner_state) {
// Add the hash state of the element to the running total, but mix the
// carry bit back into the low bit. This in intended to avoid losing
// entropy to overflow, especially when unordered_multisets contain
// multiple copies of the same value.
auto element_state = inner_state.state_;
unordered_state += element_state;
if (unordered_state < element_state) {
++unordered_state;
}
inner_state = MixingHashState{};
});
return MixingHashState::combine(std::move(state), unordered_state);
}
// Allow the HashState type-erasure implementation to invoke
// RunCombinedUnordered() directly.
friend class absl::HashState;
// Workaround for MSVC bug.
// We make the type copyable to fix the calling convention, even though we
// never actually copy it. Keep it private to not affect the public API of the
// type.
MixingHashState(const MixingHashState&) = default;
explicit MixingHashState(uint64_t state) : state_(state) {}
// Implementation of the base case for combine_contiguous where we actually
// mix the bytes into the state.
// Dispatch to different implementations of the combine_contiguous depending
// on the value of `sizeof(size_t)`.
static uint64_t CombineContiguousImpl(uint64_t state,
const unsigned char* first, size_t len,
std::integral_constant<int, 4>
/* sizeof_size_t */);
static uint64_t CombineContiguousImpl(uint64_t state,
const unsigned char* first, size_t len,
std::integral_constant<int, 8>
/* sizeof_size_t */);
// Slow dispatch path for calls to CombineContiguousImpl with a size argument
// larger than PiecewiseChunkSize(). Has the same effect as calling
// CombineContiguousImpl() repeatedly with the chunk stride size.
static uint64_t CombineLargeContiguousImpl32(uint64_t state,
const unsigned char* first,
size_t len);
static uint64_t CombineLargeContiguousImpl64(uint64_t state,
const unsigned char* first,
size_t len);
// Reads 9 to 16 bytes from p.
// The least significant 8 bytes are in .first, the rest (zero padded) bytes
// are in .second.
static std::pair<uint64_t, uint64_t> Read9To16(const unsigned char* p,
size_t len) {
uint64_t low_mem = absl::base_internal::UnalignedLoad64(p);
uint64_t high_mem = absl::base_internal::UnalignedLoad64(p + len - 8);
#ifdef ABSL_IS_LITTLE_ENDIAN
uint64_t most_significant = high_mem;
uint64_t least_significant = low_mem;
#else
uint64_t most_significant = low_mem;
uint64_t least_significant = high_mem;
#endif
return {least_significant, most_significant};
}
// Reads 4 to 8 bytes from p. Zero pads to fill uint64_t.
static uint64_t Read4To8(const unsigned char* p, size_t len) {
uint32_t low_mem = absl::base_internal::UnalignedLoad32(p);
uint32_t high_mem = absl::base_internal::UnalignedLoad32(p + len - 4);
#ifdef ABSL_IS_LITTLE_ENDIAN
uint32_t most_significant = high_mem;
uint32_t least_significant = low_mem;
#else
uint32_t most_significant = low_mem;
uint32_t least_significant = high_mem;
#endif
return (static_cast<uint64_t>(most_significant) << (len - 4) * 8) |
least_significant;
}
// Reads 1 to 3 bytes from p. Zero pads to fill uint32_t.
static uint32_t Read1To3(const unsigned char* p, size_t len) {
// The trick used by this implementation is to avoid branches if possible.
unsigned char mem0 = p[0];
unsigned char mem1 = p[len / 2];
unsigned char mem2 = p[len - 1];
#ifdef ABSL_IS_LITTLE_ENDIAN
unsigned char significant2 = mem2;
unsigned char significant1 = mem1;
unsigned char significant0 = mem0;
#else
unsigned char significant2 = mem0;
unsigned char significant1 = len == 2 ? mem0 : mem1;
unsigned char significant0 = mem2;
#endif
return static_cast<uint32_t>(significant0 | //
(significant1 << (len / 2 * 8)) | //
(significant2 << ((len - 1) * 8)));
}
ABSL_ATTRIBUTE_ALWAYS_INLINE static uint64_t Mix(uint64_t state, uint64_t v) {
// Though the 128-bit product on AArch64 needs two instructions, it is
// still a good balance between speed and hash quality.
using MultType =
absl::conditional_t<sizeof(size_t) == 4, uint64_t, uint128>;
// We do the addition in 64-bit space to make sure the 128-bit
// multiplication is fast. If we were to do it as MultType the compiler has
// to assume that the high word is non-zero and needs to perform 2
// multiplications instead of one.
MultType m = state + v;
m *= kMul;
return static_cast<uint64_t>(m ^ (m >> (sizeof(m) * 8 / 2)));
}
// An extern to avoid bloat on a direct call to LowLevelHash() with fixed
// values for both the seed and salt parameters.
static uint64_t LowLevelHashImpl(const unsigned char* data, size_t len);
ABSL_ATTRIBUTE_ALWAYS_INLINE static uint64_t Hash64(const unsigned char* data,
size_t len) {
#ifdef ABSL_HAVE_INTRINSIC_INT128
return LowLevelHashImpl(data, len);
#else
return hash_internal::CityHash64(reinterpret_cast<const char*>(data), len);
#endif
}
// Seed()
//
// A non-deterministic seed.
//
// The current purpose of this seed is to generate non-deterministic results
// and prevent having users depend on the particular hash values.
// It is not meant as a security feature right now, but it leaves the door
// open to upgrade it to a true per-process random seed. A true random seed
// costs more and we don't need to pay for that right now.
//
// On platforms with ASLR, we take advantage of it to make a per-process
// random value.
// See https://en.wikipedia.org/wiki/Address_space_layout_randomization
//
// On other platforms this is still going to be non-deterministic but most
// probably per-build and not per-process.
ABSL_ATTRIBUTE_ALWAYS_INLINE static uint64_t Seed() {
#if (!defined(__clang__) || __clang_major__ > 11) && \
(!defined(__apple_build_version__) || \
__apple_build_version__ >= 19558921) // Xcode 12
return static_cast<uint64_t>(reinterpret_cast<uintptr_t>(&kSeed));
#else
// Workaround the absence of
// https://github.com/llvm/llvm-project/commit/bc15bf66dcca76cc06fe71fca35b74dc4d521021.
return static_cast<uint64_t>(reinterpret_cast<uintptr_t>(kSeed));
#endif
}
static const void* const kSeed;
uint64_t state_;
};
// MixingHashState::CombineContiguousImpl()
inline uint64_t MixingHashState::CombineContiguousImpl(
uint64_t state, const unsigned char* first, size_t len,
std::integral_constant<int, 4> /* sizeof_size_t */) {
// For large values we use CityHash, for small ones we just use a
// multiplicative hash.
uint64_t v;
if (len > 8) {
if (ABSL_PREDICT_FALSE(len > PiecewiseChunkSize())) {
return CombineLargeContiguousImpl32(state, first, len);
}
v = hash_internal::CityHash32(reinterpret_cast<const char*>(first), len);
} else if (len >= 4) {
v = Read4To8(first, len);
} else if (len > 0) {
v = Read1To3(first, len);
} else {
// Empty ranges have no effect.
return state;
}
return Mix(state, v);
}
// Overload of MixingHashState::CombineContiguousImpl()
inline uint64_t MixingHashState::CombineContiguousImpl(
uint64_t state, const unsigned char* first, size_t len,
std::integral_constant<int, 8> /* sizeof_size_t */) {
// For large values we use LowLevelHash or CityHash depending on the platform,
// for small ones we just use a multiplicative hash.
uint64_t v;
if (len > 16) {
if (ABSL_PREDICT_FALSE(len > PiecewiseChunkSize())) {
return CombineLargeContiguousImpl64(state, first, len);
}
v = Hash64(first, len);
} else if (len > 8) {
// This hash function was constructed by the ML-driven algorithm discovery
// using reinforcement learning. We fed the agent lots of inputs from
// microbenchmarks, SMHasher, low hamming distance from generated inputs and
// picked up the one that was good on micro and macrobenchmarks.
auto p = Read9To16(first, len);
uint64_t lo = p.first;
uint64_t hi = p.second;
// Rotation by 53 was found to be most often useful when discovering these
// hashing algorithms with ML techniques.
lo = absl::rotr(lo, 53);
state += kMul;
lo += state;
state ^= hi;
uint128 m = state;
m *= lo;
return static_cast<uint64_t>(m ^ (m >> 64));
} else if (len >= 4) {
v = Read4To8(first, len);
} else if (len > 0) {
v = Read1To3(first, len);
} else {
// Empty ranges have no effect.
return state;
}
return Mix(state, v);
}
struct AggregateBarrier {};
// HashImpl
// Add a private base class to make sure this type is not an aggregate.
// Aggregates can be aggregate initialized even if the default constructor is
// deleted.
struct PoisonedHash : private AggregateBarrier {
PoisonedHash() = delete;
PoisonedHash(const PoisonedHash&) = delete;
PoisonedHash& operator=(const PoisonedHash&) = delete;
};
template <typename T>
struct HashImpl {
size_t operator()(const T& value) const {
return MixingHashState::hash(value);
}
};
template <typename T>
struct Hash
: absl::conditional_t<is_hashable<T>::value, HashImpl<T>, PoisonedHash> {};
template <typename H>
template <typename T, typename... Ts>
H HashStateBase<H>::combine(H state, const T& value, const Ts&... values) {
return H::combine(hash_internal::HashSelect::template Apply<T>::Invoke(
std::move(state), value),
values...);
}
// HashStateBase::combine_contiguous()
template <typename H>
template <typename T>
H HashStateBase<H>::combine_contiguous(H state, const T* data, size_t size) {
return hash_internal::hash_range_or_bytes(std::move(state), data, size);
}
// HashStateBase::combine_unordered()
template <typename H>
template <typename I>
H HashStateBase<H>::combine_unordered(H state, I begin, I end) {
return H::RunCombineUnordered(std::move(state),
CombineUnorderedCallback<I>{begin, end});
}
// HashStateBase::PiecewiseCombiner::add_buffer()
template <typename H>
H PiecewiseCombiner::add_buffer(H state, const unsigned char* data,
size_t size) {
if (position_ + size < PiecewiseChunkSize()) {
// This partial chunk does not fill our existing buffer
memcpy(buf_ + position_, data, size);
position_ += size;
return state;
}
// If the buffer is partially filled we need to complete the buffer
// and hash it.
if (position_ != 0) {
const size_t bytes_needed = PiecewiseChunkSize() - position_;
memcpy(buf_ + position_, data, bytes_needed);
state = H::combine_contiguous(std::move(state), buf_, PiecewiseChunkSize());
data += bytes_needed;
size -= bytes_needed;
}
// Hash whatever chunks we can without copying
while (size >= PiecewiseChunkSize()) {
state = H::combine_contiguous(std::move(state), data, PiecewiseChunkSize());
data += PiecewiseChunkSize();
size -= PiecewiseChunkSize();
}
// Fill the buffer with the remainder
memcpy(buf_, data, size);
position_ = size;
return state;
}
// HashStateBase::PiecewiseCombiner::finalize()
template <typename H>
H PiecewiseCombiner::finalize(H state) {
// Hash the remainder left in the buffer, which may be empty
return H::combine_contiguous(std::move(state), buf_, position_);
}
} // namespace hash_internal
ABSL_NAMESPACE_END
} // namespace absl
#endif // ABSL_HASH_INTERNAL_HASH_H_