//===-- llvm/ADT/Hashing.h - Utilities for hashing --------------*- C++ -*-===//
//
// 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
//
//===----------------------------------------------------------------------===//
//
// This file implements the newly proposed standard C++ interfaces for hashing
// arbitrary data and building hash functions for user-defined types. This
// interface was originally proposed in N3333[1] and is currently under review
// for inclusion in a future TR and/or standard.
//
// The primary interfaces provide are comprised of one type and three functions:
//
// -- 'hash_code' class is an opaque type representing the hash code for some
// data. It is the intended product of hashing, and can be used to implement
// hash tables, checksumming, and other common uses of hashes. It is not an
// integer type (although it can be converted to one) because it is risky
// to assume much about the internals of a hash_code. In particular, each
// execution of the program has a high probability of producing a different
// hash_code for a given input. Thus their values are not stable to save or
// persist, and should only be used during the execution for the
// construction of hashing datastructures.
//
// -- 'hash_value' is a function designed to be overloaded for each
// user-defined type which wishes to be used within a hashing context. It
// should be overloaded within the user-defined type's namespace and found
// via ADL. Overloads for primitive types are provided by this library.
//
// -- 'hash_combine' and 'hash_combine_range' are functions designed to aid
// programmers in easily and intuitively combining a set of data into
// a single hash_code for their object. They should only logically be used
// within the implementation of a 'hash_value' routine or similar context.
//
// Note that 'hash_combine_range' contains very special logic for hashing
// a contiguous array of integers or pointers. This logic is *extremely* fast,
// on a modern Intel "Gainestown" Xeon (Nehalem uarch) @2.2 GHz, these were
// benchmarked at over 6.5 GiB/s for large keys, and <20 cycles/hash for keys
// under 32-bytes.
//
//===----------------------------------------------------------------------===//
#ifndef LLVM_ADT_HASHING_H
#define LLVM_ADT_HASHING_H
#include "llvm/Support/DataTypes.h"
#include "llvm/Support/ErrorHandling.h"
#include "llvm/Support/SwapByteOrder.h"
#include "llvm/Support/type_traits.h"
#include <algorithm>
#include <cassert>
#include <cstring>
#include <optional>
#include <string>
#include <tuple>
#include <utility>
namespace llvm {
template <typename T, typename Enable> struct DenseMapInfo;
/// An opaque object representing a hash code.
///
/// This object represents the result of hashing some entity. It is intended to
/// be used to implement hashtables or other hashing-based data structures.
/// While it wraps and exposes a numeric value, this value should not be
/// trusted to be stable or predictable across processes or executions.
///
/// In order to obtain the hash_code for an object 'x':
/// \code
/// using llvm::hash_value;
/// llvm::hash_code code = hash_value(x);
/// \endcode
class hash_code {
size_t value;
public:
/// Default construct a hash_code.
/// Note that this leaves the value uninitialized.
hash_code() = default;
/// Form a hash code directly from a numerical value.
hash_code(size_t value) : value(value) {}
/// Convert the hash code to its numerical value for use.
/*explicit*/ operator size_t() const { return value; }
friend bool operator==(const hash_code &lhs, const hash_code &rhs) {
return lhs.value == rhs.value;
}
friend bool operator!=(const hash_code &lhs, const hash_code &rhs) {
return lhs.value != rhs.value;
}
/// Allow a hash_code to be directly run through hash_value.
friend size_t hash_value(const hash_code &code) { return code.value; }
};
/// Compute a hash_code for any integer value.
///
/// Note that this function is intended to compute the same hash_code for
/// a particular value without regard to the pre-promotion type. This is in
/// contrast to hash_combine which may produce different hash_codes for
/// differing argument types even if they would implicit promote to a common
/// type without changing the value.
template <typename T>
std::enable_if_t<is_integral_or_enum<T>::value, hash_code> hash_value(T value);
/// Compute a hash_code for a pointer's address.
///
/// N.B.: This hashes the *address*. Not the value and not the type.
template <typename T> hash_code hash_value(const T *ptr);
/// Compute a hash_code for a pair of objects.
template <typename T, typename U>
hash_code hash_value(const std::pair<T, U> &arg);
/// Compute a hash_code for a tuple.
template <typename... Ts>
hash_code hash_value(const std::tuple<Ts...> &arg);
/// Compute a hash_code for a standard string.
template <typename T>
hash_code hash_value(const std::basic_string<T> &arg);
/// Compute a hash_code for a standard string.
template <typename T> hash_code hash_value(const std::optional<T> &arg);
/// Override the execution seed with a fixed value.
///
/// This hashing library uses a per-execution seed designed to change on each
/// run with high probability in order to ensure that the hash codes are not
/// attackable and to ensure that output which is intended to be stable does
/// not rely on the particulars of the hash codes produced.
///
/// That said, there are use cases where it is important to be able to
/// reproduce *exactly* a specific behavior. To that end, we provide a function
/// which will forcibly set the seed to a fixed value. This must be done at the
/// start of the program, before any hashes are computed. Also, it cannot be
/// undone. This makes it thread-hostile and very hard to use outside of
/// immediately on start of a simple program designed for reproducible
/// behavior.
void set_fixed_execution_hash_seed(uint64_t fixed_value);
// All of the implementation details of actually computing the various hash
// code values are held within this namespace. These routines are included in
// the header file mainly to allow inlining and constant propagation.
namespace hashing {
namespace detail {
inline uint64_t fetch64(const char *p) {
uint64_t result;
memcpy(&result, p, sizeof(result));
if (sys::IsBigEndianHost)
sys::swapByteOrder(result);
return result;
}
inline uint32_t fetch32(const char *p) {
uint32_t result;
memcpy(&result, p, sizeof(result));
if (sys::IsBigEndianHost)
sys::swapByteOrder(result);
return result;
}
/// Some primes between 2^63 and 2^64 for various uses.
static constexpr uint64_t k0 = 0xc3a5c85c97cb3127ULL;
static constexpr uint64_t k1 = 0xb492b66fbe98f273ULL;
static constexpr uint64_t k2 = 0x9ae16a3b2f90404fULL;
static constexpr uint64_t k3 = 0xc949d7c7509e6557ULL;
/// Bitwise right rotate.
/// Normally this will compile to a single instruction, especially if the
/// shift is a manifest constant.
inline uint64_t rotate(uint64_t val, size_t shift) {
// Avoid shifting by 64: doing so yields an undefined result.
return shift == 0 ? val : ((val >> shift) | (val << (64 - shift)));
}
inline uint64_t shift_mix(uint64_t val) {
return val ^ (val >> 47);
}
inline uint64_t hash_16_bytes(uint64_t low, uint64_t high) {
// Murmur-inspired hashing.
const uint64_t kMul = 0x9ddfea08eb382d69ULL;
uint64_t a = (low ^ high) * kMul;
a ^= (a >> 47);
uint64_t b = (high ^ a) * kMul;
b ^= (b >> 47);
b *= kMul;
return b;
}
inline uint64_t hash_1to3_bytes(const char *s, size_t len, uint64_t seed) {
uint8_t a = s[0];
uint8_t b = s[len >> 1];
uint8_t c = s[len - 1];
uint32_t y = static_cast<uint32_t>(a) + (static_cast<uint32_t>(b) << 8);
uint32_t z = static_cast<uint32_t>(len) + (static_cast<uint32_t>(c) << 2);
return shift_mix(y * k2 ^ z * k3 ^ seed) * k2;
}
inline uint64_t hash_4to8_bytes(const char *s, size_t len, uint64_t seed) {
uint64_t a = fetch32(s);
return hash_16_bytes(len + (a << 3), seed ^ fetch32(s + len - 4));
}
inline uint64_t hash_9to16_bytes(const char *s, size_t len, uint64_t seed) {
uint64_t a = fetch64(s);
uint64_t b = fetch64(s + len - 8);
return hash_16_bytes(seed ^ a, rotate(b + len, len)) ^ b;
}
inline uint64_t hash_17to32_bytes(const char *s, size_t len, uint64_t seed) {
uint64_t a = fetch64(s) * k1;
uint64_t b = fetch64(s + 8);
uint64_t c = fetch64(s + len - 8) * k2;
uint64_t d = fetch64(s + len - 16) * k0;
return hash_16_bytes(rotate(a - b, 43) + rotate(c ^ seed, 30) + d,
a + rotate(b ^ k3, 20) - c + len + seed);
}
inline uint64_t hash_33to64_bytes(const char *s, size_t len, uint64_t seed) {
uint64_t z = fetch64(s + 24);
uint64_t a = fetch64(s) + (len + fetch64(s + len - 16)) * k0;
uint64_t b = rotate(a + z, 52);
uint64_t c = rotate(a, 37);
a += fetch64(s + 8);
c += rotate(a, 7);
a += fetch64(s + 16);
uint64_t vf = a + z;
uint64_t vs = b + rotate(a, 31) + c;
a = fetch64(s + 16) + fetch64(s + len - 32);
z = fetch64(s + len - 8);
b = rotate(a + z, 52);
c = rotate(a, 37);
a += fetch64(s + len - 24);
c += rotate(a, 7);
a += fetch64(s + len - 16);
uint64_t wf = a + z;
uint64_t ws = b + rotate(a, 31) + c;
uint64_t r = shift_mix((vf + ws) * k2 + (wf + vs) * k0);
return shift_mix((seed ^ (r * k0)) + vs) * k2;
}
inline uint64_t hash_short(const char *s, size_t length, uint64_t seed) {
if (length >= 4 && length <= 8)
return hash_4to8_bytes(s, length, seed);
if (length > 8 && length <= 16)
return hash_9to16_bytes(s, length, seed);
if (length > 16 && length <= 32)
return hash_17to32_bytes(s, length, seed);
if (length > 32)
return hash_33to64_bytes(s, length, seed);
if (length != 0)
return hash_1to3_bytes(s, length, seed);
return k2 ^ seed;
}
/// The intermediate state used during hashing.
/// Currently, the algorithm for computing hash codes is based on CityHash and
/// keeps 56 bytes of arbitrary state.
struct hash_state {
uint64_t h0 = 0, h1 = 0, h2 = 0, h3 = 0, h4 = 0, h5 = 0, h6 = 0;
/// Create a new hash_state structure and initialize it based on the
/// seed and the first 64-byte chunk.
/// This effectively performs the initial mix.
static hash_state create(const char *s, uint64_t seed) {
hash_state state = {
0, seed, hash_16_bytes(seed, k1), rotate(seed ^ k1, 49),
seed * k1, shift_mix(seed), 0 };
state.h6 = hash_16_bytes(state.h4, state.h5);
state.mix(s);
return state;
}
/// Mix 32-bytes from the input sequence into the 16-bytes of 'a'
/// and 'b', including whatever is already in 'a' and 'b'.
static void mix_32_bytes(const char *s, uint64_t &a, uint64_t &b) {
a += fetch64(s);
uint64_t c = fetch64(s + 24);
b = rotate(b + a + c, 21);
uint64_t d = a;
a += fetch64(s + 8) + fetch64(s + 16);
b += rotate(a, 44) + d;
a += c;
}
/// Mix in a 64-byte buffer of data.
/// We mix all 64 bytes even when the chunk length is smaller, but we
/// record the actual length.
void mix(const char *s) {
h0 = rotate(h0 + h1 + h3 + fetch64(s + 8), 37) * k1;
h1 = rotate(h1 + h4 + fetch64(s + 48), 42) * k1;
h0 ^= h6;
h1 += h3 + fetch64(s + 40);
h2 = rotate(h2 + h5, 33) * k1;
h3 = h4 * k1;
h4 = h0 + h5;
mix_32_bytes(s, h3, h4);
h5 = h2 + h6;
h6 = h1 + fetch64(s + 16);
mix_32_bytes(s + 32, h5, h6);
std::swap(h2, h0);
}
/// Compute the final 64-bit hash code value based on the current
/// state and the length of bytes hashed.
uint64_t finalize(size_t length) {
return hash_16_bytes(hash_16_bytes(h3, h5) + shift_mix(h1) * k1 + h2,
hash_16_bytes(h4, h6) + shift_mix(length) * k1 + h0);
}
};
/// A global, fixed seed-override variable.
///
/// This variable can be set using the \see llvm::set_fixed_execution_seed
/// function. See that function for details. Do not, under any circumstances,
/// set or read this variable.
extern uint64_t fixed_seed_override;
inline uint64_t get_execution_seed() {
// FIXME: This needs to be a per-execution seed. This is just a placeholder
// implementation. Switching to a per-execution seed is likely to flush out
// instability bugs and so will happen as its own commit.
//
// However, if there is a fixed seed override set the first time this is
// called, return that instead of the per-execution seed.
const uint64_t seed_prime = 0xff51afd7ed558ccdULL;
static uint64_t seed = fixed_seed_override ? fixed_seed_override : seed_prime;
return seed;
}
/// Trait to indicate whether a type's bits can be hashed directly.
///
/// A type trait which is true if we want to combine values for hashing by
/// reading the underlying data. It is false if values of this type must
/// first be passed to hash_value, and the resulting hash_codes combined.
//
// FIXME: We want to replace is_integral_or_enum and is_pointer here with
// a predicate which asserts that comparing the underlying storage of two
// values of the type for equality is equivalent to comparing the two values
// for equality. For all the platforms we care about, this holds for integers
// and pointers, but there are platforms where it doesn't and we would like to
// support user-defined types which happen to satisfy this property.
template <typename T> struct is_hashable_data
: std::integral_constant<bool, ((is_integral_or_enum<T>::value ||
std::is_pointer<T>::value) &&
64 % sizeof(T) == 0)> {};
// Special case std::pair to detect when both types are viable and when there
// is no alignment-derived padding in the pair. This is a bit of a lie because
// std::pair isn't truly POD, but it's close enough in all reasonable
// implementations for our use case of hashing the underlying data.
template <typename T, typename U> struct is_hashable_data<std::pair<T, U> >
: std::integral_constant<bool, (is_hashable_data<T>::value &&
is_hashable_data<U>::value &&
(sizeof(T) + sizeof(U)) ==
sizeof(std::pair<T, U>))> {};
/// Helper to get the hashable data representation for a type.
/// This variant is enabled when the type itself can be used.
template <typename T>
std::enable_if_t<is_hashable_data<T>::value, T>
get_hashable_data(const T &value) {
return value;
}
/// Helper to get the hashable data representation for a type.
/// This variant is enabled when we must first call hash_value and use the
/// result as our data.
template <typename T>
std::enable_if_t<!is_hashable_data<T>::value, size_t>
get_hashable_data(const T &value) {
using ::llvm::hash_value;
return hash_value(value);
}
/// Helper to store data from a value into a buffer and advance the
/// pointer into that buffer.
///
/// This routine first checks whether there is enough space in the provided
/// buffer, and if not immediately returns false. If there is space, it
/// copies the underlying bytes of value into the buffer, advances the
/// buffer_ptr past the copied bytes, and returns true.
template <typename T>
bool store_and_advance(char *&buffer_ptr, char *buffer_end, const T& value,
size_t offset = 0) {
size_t store_size = sizeof(value) - offset;
if (buffer_ptr + store_size > buffer_end)
return false;
const char *value_data = reinterpret_cast<const char *>(&value);
memcpy(buffer_ptr, value_data + offset, store_size);
buffer_ptr += store_size;
return true;
}
/// Implement the combining of integral values into a hash_code.
///
/// This overload is selected when the value type of the iterator is
/// integral. Rather than computing a hash_code for each object and then
/// combining them, this (as an optimization) directly combines the integers.
template <typename InputIteratorT>
hash_code hash_combine_range_impl(InputIteratorT first, InputIteratorT last) {
const uint64_t seed = get_execution_seed();
char buffer[64], *buffer_ptr = buffer;
char *const buffer_end = std::end(buffer);
while (first != last && store_and_advance(buffer_ptr, buffer_end,
get_hashable_data(*first)))
++first;
if (first == last)
return hash_short(buffer, buffer_ptr - buffer, seed);
assert(buffer_ptr == buffer_end);
hash_state state = state.create(buffer, seed);
size_t length = 64;
while (first != last) {
// Fill up the buffer. We don't clear it, which re-mixes the last round
// when only a partial 64-byte chunk is left.
buffer_ptr = buffer;
while (first != last && store_and_advance(buffer_ptr, buffer_end,
get_hashable_data(*first)))
++first;
// Rotate the buffer if we did a partial fill in order to simulate doing
// a mix of the last 64-bytes. That is how the algorithm works when we
// have a contiguous byte sequence, and we want to emulate that here.
std::rotate(buffer, buffer_ptr, buffer_end);
// Mix this chunk into the current state.
state.mix(buffer);
length += buffer_ptr - buffer;
};
return state.finalize(length);
}
/// Implement the combining of integral values into a hash_code.
///
/// This overload is selected when the value type of the iterator is integral
/// and when the input iterator is actually a pointer. Rather than computing
/// a hash_code for each object and then combining them, this (as an
/// optimization) directly combines the integers. Also, because the integers
/// are stored in contiguous memory, this routine avoids copying each value
/// and directly reads from the underlying memory.
template <typename ValueT>
std::enable_if_t<is_hashable_data<ValueT>::value, hash_code>
hash_combine_range_impl(ValueT *first, ValueT *last) {
const uint64_t seed = get_execution_seed();
const char *s_begin = reinterpret_cast<const char *>(first);
const char *s_end = reinterpret_cast<const char *>(last);
const size_t length = std::distance(s_begin, s_end);
if (length <= 64)
return hash_short(s_begin, length, seed);
const char *s_aligned_end = s_begin + (length & ~63);
hash_state state = state.create(s_begin, seed);
s_begin += 64;
while (s_begin != s_aligned_end) {
state.mix(s_begin);
s_begin += 64;
}
if (length & 63)
state.mix(s_end - 64);
return state.finalize(length);
}
} // namespace detail
} // namespace hashing
/// Compute a hash_code for a sequence of values.
///
/// This hashes a sequence of values. It produces the same hash_code as
/// 'hash_combine(a, b, c, ...)', but can run over arbitrary sized sequences
/// and is significantly faster given pointers and types which can be hashed as
/// a sequence of bytes.
template <typename InputIteratorT>
hash_code hash_combine_range(InputIteratorT first, InputIteratorT last) {
return ::llvm::hashing::detail::hash_combine_range_impl(first, last);
}
// Implementation details for hash_combine.
namespace hashing {
namespace detail {
/// Helper class to manage the recursive combining of hash_combine
/// arguments.
///
/// This class exists to manage the state and various calls involved in the
/// recursive combining of arguments used in hash_combine. It is particularly
/// useful at minimizing the code in the recursive calls to ease the pain
/// caused by a lack of variadic functions.
struct hash_combine_recursive_helper {
char buffer[64] = {};
hash_state state;
const uint64_t seed;
public:
/// Construct a recursive hash combining helper.
///
/// This sets up the state for a recursive hash combine, including getting
/// the seed and buffer setup.
hash_combine_recursive_helper()
: seed(get_execution_seed()) {}
/// Combine one chunk of data into the current in-flight hash.
///
/// This merges one chunk of data into the hash. First it tries to buffer
/// the data. If the buffer is full, it hashes the buffer into its
/// hash_state, empties it, and then merges the new chunk in. This also
/// handles cases where the data straddles the end of the buffer.
template <typename T>
char *combine_data(size_t &length, char *buffer_ptr, char *buffer_end, T data) {
if (!store_and_advance(buffer_ptr, buffer_end, data)) {
// Check for skew which prevents the buffer from being packed, and do
// a partial store into the buffer to fill it. This is only a concern
// with the variadic combine because that formation can have varying
// argument types.
size_t partial_store_size = buffer_end - buffer_ptr;
memcpy(buffer_ptr, &data, partial_store_size);
// If the store fails, our buffer is full and ready to hash. We have to
// either initialize the hash state (on the first full buffer) or mix
// this buffer into the existing hash state. Length tracks the *hashed*
// length, not the buffered length.
if (length == 0) {
state = state.create(buffer, seed);
length = 64;
} else {
// Mix this chunk into the current state and bump length up by 64.
state.mix(buffer);
length += 64;
}
// Reset the buffer_ptr to the head of the buffer for the next chunk of
// data.
buffer_ptr = buffer;
// Try again to store into the buffer -- this cannot fail as we only
// store types smaller than the buffer.
if (!store_and_advance(buffer_ptr, buffer_end, data,
partial_store_size))
llvm_unreachable("buffer smaller than stored type");
}
return buffer_ptr;
}
/// Recursive, variadic combining method.
///
/// This function recurses through each argument, combining that argument
/// into a single hash.
template <typename T, typename ...Ts>
hash_code combine(size_t length, char *buffer_ptr, char *buffer_end,
const T &arg, const Ts &...args) {
buffer_ptr = combine_data(length, buffer_ptr, buffer_end, get_hashable_data(arg));
// Recurse to the next argument.
return combine(length, buffer_ptr, buffer_end, args...);
}
/// Base case for recursive, variadic combining.
///
/// The base case when combining arguments recursively is reached when all
/// arguments have been handled. It flushes the remaining buffer and
/// constructs a hash_code.
hash_code combine(size_t length, char *buffer_ptr, char *buffer_end) {
// Check whether the entire set of values fit in the buffer. If so, we'll
// use the optimized short hashing routine and skip state entirely.
if (length == 0)
return hash_short(buffer, buffer_ptr - buffer, seed);
// Mix the final buffer, rotating it if we did a partial fill in order to
// simulate doing a mix of the last 64-bytes. That is how the algorithm
// works when we have a contiguous byte sequence, and we want to emulate
// that here.
std::rotate(buffer, buffer_ptr, buffer_end);
// Mix this chunk into the current state.
state.mix(buffer);
length += buffer_ptr - buffer;
return state.finalize(length);
}
};
} // namespace detail
} // namespace hashing
/// Combine values into a single hash_code.
///
/// This routine accepts a varying number of arguments of any type. It will
/// attempt to combine them into a single hash_code. For user-defined types it
/// attempts to call a \see hash_value overload (via ADL) for the type. For
/// integer and pointer types it directly combines their data into the
/// resulting hash_code.
///
/// The result is suitable for returning from a user's hash_value
/// *implementation* for their user-defined type. Consumers of a type should
/// *not* call this routine, they should instead call 'hash_value'.
template <typename ...Ts> hash_code hash_combine(const Ts &...args) {
// Recursively hash each argument using a helper class.
::llvm::hashing::detail::hash_combine_recursive_helper helper;
return helper.combine(0, helper.buffer, helper.buffer + 64, args...);
}
// Implementation details for implementations of hash_value overloads provided
// here.
namespace hashing {
namespace detail {
/// Helper to hash the value of a single integer.
///
/// Overloads for smaller integer types are not provided to ensure consistent
/// behavior in the presence of integral promotions. Essentially,
/// "hash_value('4')" and "hash_value('0' + 4)" should be the same.
inline hash_code hash_integer_value(uint64_t value) {
// Similar to hash_4to8_bytes but using a seed instead of length.
const uint64_t seed = get_execution_seed();
const char *s = reinterpret_cast<const char *>(&value);
const uint64_t a = fetch32(s);
return hash_16_bytes(seed + (a << 3), fetch32(s + 4));
}
} // namespace detail
} // namespace hashing
// Declared and documented above, but defined here so that any of the hashing
// infrastructure is available.
template <typename T>
std::enable_if_t<is_integral_or_enum<T>::value, hash_code> hash_value(T value) {
return ::llvm::hashing::detail::hash_integer_value(
static_cast<uint64_t>(value));
}
// Declared and documented above, but defined here so that any of the hashing
// infrastructure is available.
template <typename T> hash_code hash_value(const T *ptr) {
return ::llvm::hashing::detail::hash_integer_value(
reinterpret_cast<uintptr_t>(ptr));
}
// Declared and documented above, but defined here so that any of the hashing
// infrastructure is available.
template <typename T, typename U>
hash_code hash_value(const std::pair<T, U> &arg) {
return hash_combine(arg.first, arg.second);
}
template <typename... Ts> hash_code hash_value(const std::tuple<Ts...> &arg) {
return std::apply([](const auto &...xs) { return hash_combine(xs...); }, arg);
}
// Declared and documented above, but defined here so that any of the hashing
// infrastructure is available.
template <typename T>
hash_code hash_value(const std::basic_string<T> &arg) {
return hash_combine_range(arg.begin(), arg.end());
}
template <typename T> hash_code hash_value(const std::optional<T> &arg) {
return arg ? hash_combine(true, *arg) : hash_value(false);
}
template <> struct DenseMapInfo<hash_code, void> {
static inline hash_code getEmptyKey() { return hash_code(-1); }
static inline hash_code getTombstoneKey() { return hash_code(-2); }
static unsigned getHashValue(hash_code val) { return val; }
static bool isEqual(hash_code LHS, hash_code RHS) { return LHS == RHS; }
};
} // namespace llvm
#endif