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//===-- 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