STLExtras.h

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//===- llvm/ADT/STLExtras.h - Useful STL related functions ------*- 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
//
//===----------------------------------------------------------------------===//
///
/// \file
/// This file contains some templates that are useful if you are working with
/// the STL at all.
///
/// No library is required when using these functions.
///
//===----------------------------------------------------------------------===//
 
#ifndef LLVM_ADT_STLEXTRAS_H
#define LLVM_ADT_STLEXTRAS_H
 
#include "llvm/ADT/ADL.h"
#include "llvm/ADT/Hashing.h"
#include "llvm/ADT/STLForwardCompat.h"
#include "llvm/ADT/STLFunctionalExtras.h"
#include "llvm/ADT/iterator.h"
#include "llvm/ADT/iterator_range.h"
#include "llvm/Config/abi-breaking.h"
#include "llvm/Support/ErrorHandling.h"
#include <algorithm>
#include <cassert>
#include <cstddef>
#include <cstdint>
#include <cstdlib>
#include <functional>
#include <initializer_list>
#include <iterator>
#include <limits>
#include <memory>
#include <optional>
#include <tuple>
#include <type_traits>
#include <utility>
 
#ifdef EXPENSIVE_CHECKS
#include <random> // for std::mt19937
#endif
 
namespace llvm {
 
//===----------------------------------------------------------------------===//
//     Extra additions to <type_traits>
//===----------------------------------------------------------------------===//
 
template <typename T> struct make_const_ptr {
  using type = std::add_pointer_t<std::add_const_t<T>>;
};
 
template <typename T> struct make_const_ref {
  using type = std::add_lvalue_reference_t<std::add_const_t<T>>;
};
 
namespace detail {
template <class, template <class...> class Op, class... Args> struct detector {
  using value_t = std::false_type;
};
template <template <class...> class Op, class... Args>
struct detector<std::void_t<Op<Args...>>, Op, Args...> {
  using value_t = std::true_type;
};
} // end namespace detail
 
/// Detects if a given trait holds for some set of arguments 'Args'.
/// For example, the given trait could be used to detect if a given type
/// has a copy assignment operator:
///   template<class T>
///   using has_copy_assign_t = decltype(std::declval<T&>()
///                                                 = std::declval<const T&>());
///   bool fooHasCopyAssign = is_detected<has_copy_assign_t, FooClass>::value;
template <template <class...> class Op, class... Args>
using is_detected = typename detail::detector<void, Op, Args...>::value_t;
 
/// This class provides various trait information about a callable object.
///   * To access the number of arguments: Traits::num_args
///   * To access the type of an argument: Traits::arg_t<Index>
///   * To access the type of the result:  Traits::result_t
template <typename T, bool isClass = std::is_class<T>::value>
struct function_traits : public function_traits<decltype(&T::operator())> {};
 
/// Overload for class function types.
template <typename ClassType, typename ReturnType, typename... Args>
struct function_traits<ReturnType (ClassType::*)(Args...) const, false> {
  /// The number of arguments to this function.
  enum { num_args = sizeof...(Args) };
 
  /// The result type of this function.
  using result_t = ReturnType;
 
  /// The type of an argument to this function.
  template <size_t Index>
  using arg_t = std::tuple_element_t<Index, std::tuple<Args...>>;
};
/// Overload for class function types.
template <typename ClassType, typename ReturnType, typename... Args>
struct function_traits<ReturnType (ClassType::*)(Args...), false>
    : public function_traits<ReturnType (ClassType::*)(Args...) const> {};
/// Overload for non-class function types.
template <typename ReturnType, typename... Args>
struct function_traits<ReturnType (*)(Args...), false> {
  /// The number of arguments to this function.
  enum { num_args = sizeof...(Args) };
 
  /// The result type of this function.
  using result_t = ReturnType;
 
  /// The type of an argument to this function.
  template <size_t i>
  using arg_t = std::tuple_element_t<i, std::tuple<Args...>>;
};
template <typename ReturnType, typename... Args>
struct function_traits<ReturnType (*const)(Args...), false>
    : public function_traits<ReturnType (*)(Args...)> {};
/// Overload for non-class function type references.
template <typename ReturnType, typename... Args>
struct function_traits<ReturnType (&)(Args...), false>
    : public function_traits<ReturnType (*)(Args...)> {};
 
/// traits class for checking whether type T is one of any of the given
/// types in the variadic list.
template <typename T, typename... Ts>
using is_one_of = std::disjunction<std::is_same<T, Ts>...>;
 
/// traits class for checking whether type T is a base class for all
///  the given types in the variadic list.
template <typename T, typename... Ts>
using are_base_of = std::conjunction<std::is_base_of<T, Ts>...>;
 
namespace detail {
template <typename T, typename... Us> struct TypesAreDistinct;
template <typename T, typename... Us>
struct TypesAreDistinct
    : std::integral_constant<bool, !is_one_of<T, Us...>::value &&
                                       TypesAreDistinct<Us...>::value> {};
template <typename T> struct TypesAreDistinct<T> : std::true_type {};
} // namespace detail
 
/// Determine if all types in Ts are distinct.
///
/// Useful to statically assert when Ts is intended to describe a non-multi set
/// of types.
///
/// Expensive (currently quadratic in sizeof(Ts...)), and so should only be
/// asserted once per instantiation of a type which requires it.
template <typename... Ts> struct TypesAreDistinct;
template <> struct TypesAreDistinct<> : std::true_type {};
template <typename... Ts>
struct TypesAreDistinct
    : std::integral_constant<bool, detail::TypesAreDistinct<Ts...>::value> {};
 
/// Find the first index where a type appears in a list of types.
///
/// FirstIndexOfType<T, Us...>::value is the first index of T in Us.
///
/// Typically only meaningful when it is otherwise statically known that the
/// type pack has no duplicate types. This should be guaranteed explicitly with
/// static_assert(TypesAreDistinct<Us...>::value).
///
/// It is a compile-time error to instantiate when T is not present in Us, i.e.
/// if is_one_of<T, Us...>::value is false.
template <typename T, typename... Us> struct FirstIndexOfType;
template <typename T, typename U, typename... Us>
struct FirstIndexOfType<T, U, Us...>
    : std::integral_constant<size_t, 1 + FirstIndexOfType<T, Us...>::value> {};
template <typename T, typename... Us>
struct FirstIndexOfType<T, T, Us...> : std::integral_constant<size_t, 0> {};
 
/// Find the type at a given index in a list of types.
///
/// TypeAtIndex<I, Ts...> is the type at index I in Ts.
template <size_t I, typename... Ts>
using TypeAtIndex = std::tuple_element_t<I, std::tuple<Ts...>>;
 
/// Helper which adds two underlying types of enumeration type.
/// Implicit conversion to a common type is accepted.
template <typename EnumTy1, typename EnumTy2,
          typename UT1 = std::enable_if_t<std::is_enum<EnumTy1>::value,
                                          std::underlying_type_t<EnumTy1>>,
          typename UT2 = std::enable_if_t<std::is_enum<EnumTy2>::value,
                                          std::underlying_type_t<EnumTy2>>>
constexpr auto addEnumValues(EnumTy1 LHS, EnumTy2 RHS) {
  return static_cast<UT1>(LHS) + static_cast<UT2>(RHS);
}
 
//===----------------------------------------------------------------------===//
//     Extra additions to <iterator>
//===----------------------------------------------------------------------===//
 
namespace callable_detail {
 
/// Templated storage wrapper for a callable.
///
/// This class is consistently default constructible, copy / move
/// constructible / assignable.
///
/// Supported callable types:
///  - Function pointer
///  - Function reference
///  - Lambda
///  - Function object
template <typename T,
          bool = std::is_function_v<std::remove_pointer_t<remove_cvref_t<T>>>>
class Callable {
  using value_type = std::remove_reference_t<T>;
  using reference = value_type &;
  using const_reference = value_type const &;
 
  std::optional<value_type> Obj;
 
  static_assert(!std::is_pointer_v<value_type>,
                "Pointers to non-functions are not callable.");
 
public:
  Callable() = default;
  Callable(T const &O) : Obj(std::in_place, O) {}
 
  Callable(Callable const &Other) = default;
  Callable(Callable &&Other) = default;
 
  Callable &operator=(Callable const &Other) {
    Obj = std::nullopt;
    if (Other.Obj)
      Obj.emplace(*Other.Obj);
    return *this;
  }
 
  Callable &operator=(Callable &&Other) {
    Obj = std::nullopt;
    if (Other.Obj)
      Obj.emplace(std::move(*Other.Obj));
    return *this;
  }
 
  template <typename... Pn,
            std::enable_if_t<std::is_invocable_v<T, Pn...>, int> = 0>
  decltype(auto) operator()(Pn &&...Params) {
    return (*Obj)(std::forward<Pn>(Params)...);
  }
 
  template <typename... Pn,
            std::enable_if_t<std::is_invocable_v<T const, Pn...>, int> = 0>
  decltype(auto) operator()(Pn &&...Params) const {
    return (*Obj)(std::forward<Pn>(Params)...);
  }
 
  bool valid() const { return Obj != std::nullopt; }
  bool reset() { return Obj = std::nullopt; }
 
  operator reference() { return *Obj; }
  operator const_reference() const { return *Obj; }
};
 
// Function specialization.  No need to waste extra space wrapping with a
// std::optional.
template <typename T> class Callable<T, true> {
  static constexpr bool IsPtr = std::is_pointer_v<remove_cvref_t<T>>;
 
  using StorageT = std::conditional_t<IsPtr, T, std::remove_reference_t<T> *>;
  using CastT = std::conditional_t<IsPtr, T, T &>;
 
private:
  StorageT Func = nullptr;
 
private:
  template <typename In> static constexpr auto convertIn(In &&I) {
    if constexpr (IsPtr) {
      // Pointer... just echo it back.
      return I;
    } else {
      // Must be a function reference.  Return its address.
      return &I;
    }
  }
 
public:
  Callable() = default;
 
  // Construct from a function pointer or reference.
  //
  // Disable this constructor for references to 'Callable' so we don't violate
  // the rule of 0.
  template < // clang-format off
    typename FnPtrOrRef,
    std::enable_if_t<
      !std::is_same_v<remove_cvref_t<FnPtrOrRef>, Callable>, int
    > = 0
  > // clang-format on
  Callable(FnPtrOrRef &&F) : Func(convertIn(F)) {}
 
  template <typename... Pn,
            std::enable_if_t<std::is_invocable_v<T, Pn...>, int> = 0>
  decltype(auto) operator()(Pn &&...Params) const {
    return Func(std::forward<Pn>(Params)...);
  }
 
  bool valid() const { return Func != nullptr; }
  void reset() { Func = nullptr; }
 
  operator T const &() const {
    if constexpr (IsPtr) {
      // T is a pointer... just echo it back.
      return Func;
    } else {
      static_assert(std::is_reference_v<T>,
                    "Expected a reference to a function.");
      // T is a function reference... dereference the stored pointer.
      return *Func;
    }
  }
};
 
} // namespace callable_detail
 
/// Returns true if the given container only contains a single element.
template <typename ContainerTy> bool hasSingleElement(ContainerTy &&C) {
  auto B = std::begin(C), E = std::end(C);
  return B != E && std::next(B) == E;
}
 
/// Return a range covering \p RangeOrContainer with the first N elements
/// excluded.
template <typename T> auto drop_begin(T &&RangeOrContainer, size_t N = 1) {
  return make_range(std::next(adl_begin(RangeOrContainer), N),
                    adl_end(RangeOrContainer));
}
 
/// Return a range covering \p RangeOrContainer with the last N elements
/// excluded.
template <typename T> auto drop_end(T &&RangeOrContainer, size_t N = 1) {
  return make_range(adl_begin(RangeOrContainer),
                    std::prev(adl_end(RangeOrContainer), N));
}
 
// mapped_iterator - This is a simple iterator adapter that causes a function to
// be applied whenever operator* is invoked on the iterator.
 
template <typename ItTy, typename FuncTy,
          typename ReferenceTy =
              decltype(std::declval<FuncTy>()(*std::declval<ItTy>()))>
class mapped_iterator
    : public iterator_adaptor_base<
          mapped_iterator<ItTy, FuncTy>, ItTy,
          typename std::iterator_traits<ItTy>::iterator_category,
          std::remove_reference_t<ReferenceTy>,
          typename std::iterator_traits<ItTy>::difference_type,
          std::remove_reference_t<ReferenceTy> *, ReferenceTy> {
public:
  mapped_iterator() = default;
  mapped_iterator(ItTy U, FuncTy F)
    : mapped_iterator::iterator_adaptor_base(std::move(U)), F(std::move(F)) {}
 
  ItTy getCurrent() { return this->I; }
 
  const FuncTy &getFunction() const { return F; }
 
  ReferenceTy operator*() const { return F(*this->I); }
 
private:
  callable_detail::Callable<FuncTy> F{};
};
 
// map_iterator - Provide a convenient way to create mapped_iterators, just like
// make_pair is useful for creating pairs...
template <class ItTy, class FuncTy>
inline mapped_iterator<ItTy, FuncTy> map_iterator(ItTy I, FuncTy F) {
  return mapped_iterator<ItTy, FuncTy>(std::move(I), std::move(F));
}
 
template <class ContainerTy, class FuncTy>
auto map_range(ContainerTy &&C, FuncTy F) {
  return make_range(map_iterator(std::begin(C), F),
                    map_iterator(std::end(C), F));
}
 
/// A base type of mapped iterator, that is useful for building derived
/// iterators that do not need/want to store the map function (as in
/// mapped_iterator). These iterators must simply provide a `mapElement` method
/// that defines how to map a value of the iterator to the provided reference
/// type.
template <typename DerivedT, typename ItTy, typename ReferenceTy>
class mapped_iterator_base
    : public iterator_adaptor_base<
          DerivedT, ItTy,
          typename std::iterator_traits<ItTy>::iterator_category,
          std::remove_reference_t<ReferenceTy>,
          typename std::iterator_traits<ItTy>::difference_type,
          std::remove_reference_t<ReferenceTy> *, ReferenceTy> {
public:
  using BaseT = mapped_iterator_base;
 
  mapped_iterator_base(ItTy U)
      : mapped_iterator_base::iterator_adaptor_base(std::move(U)) {}
 
  ItTy getCurrent() { return this->I; }
 
  ReferenceTy operator*() const {
    return static_cast<const DerivedT &>(*this).mapElement(*this->I);
  }
};
 
namespace detail {
template <typename Range>
using check_has_free_function_rbegin =
    decltype(adl_rbegin(std::declval<Range &>()));
 
template <typename Range>
static constexpr bool HasFreeFunctionRBegin =
    is_detected<check_has_free_function_rbegin, Range>::value;
} // namespace detail
 
// Returns an iterator_range over the given container which iterates in reverse.
template <typename ContainerTy> auto reverse(ContainerTy &&C) {
  if constexpr (detail::HasFreeFunctionRBegin<ContainerTy>)
    return make_range(adl_rbegin(C), adl_rend(C));
  else
    return make_range(std::make_reverse_iterator(adl_end(C)),
                      std::make_reverse_iterator(adl_begin(C)));
}
 
/// An iterator adaptor that filters the elements of given inner iterators.
///
/// The predicate parameter should be a callable object that accepts the wrapped
/// iterator's reference type and returns a bool. When incrementing or
/// decrementing the iterator, it will call the predicate on each element and
/// skip any where it returns false.
///
/// \code
///   int A[] = { 1, 2, 3, 4 };
///   auto R = make_filter_range(A, [](int N) { return N % 2 == 1; });
///   // R contains { 1, 3 }.
/// \endcode
///
/// Note: filter_iterator_base implements support for forward iteration.
/// filter_iterator_impl exists to provide support for bidirectional iteration,
/// conditional on whether the wrapped iterator supports it.
template <typename WrappedIteratorT, typename PredicateT, typename IterTag>
class filter_iterator_base
    : public iterator_adaptor_base<
          filter_iterator_base<WrappedIteratorT, PredicateT, IterTag>,
          WrappedIteratorT,
          std::common_type_t<IterTag,
                             typename std::iterator_traits<
                                 WrappedIteratorT>::iterator_category>> {
  using BaseT = typename filter_iterator_base::iterator_adaptor_base;
 
protected:
  WrappedIteratorT End;
  PredicateT Pred;
 
  void findNextValid() {
    while (this->I != End && !Pred(*this->I))
      BaseT::operator++();
  }
 
  filter_iterator_base() = default;
 
  // Construct the iterator. The begin iterator needs to know where the end
  // is, so that it can properly stop when it gets there. The end iterator only
  // needs the predicate to support bidirectional iteration.
  filter_iterator_base(WrappedIteratorT Begin, WrappedIteratorT End,
                       PredicateT Pred)
      : BaseT(Begin), End(End), Pred(Pred) {
    findNextValid();
  }
 
public:
  using BaseT::operator++;
 
  filter_iterator_base &operator++() {
    BaseT::operator++();
    findNextValid();
    return *this;
  }
 
  decltype(auto) operator*() const {
    assert(BaseT::wrapped() != End && "Cannot dereference end iterator!");
    return BaseT::operator*();
  }
 
  decltype(auto) operator->() const {
    assert(BaseT::wrapped() != End && "Cannot dereference end iterator!");
    return BaseT::operator->();
  }
};
 
/// Specialization of filter_iterator_base for forward iteration only.
template <typename WrappedIteratorT, typename PredicateT,
          typename IterTag = std::forward_iterator_tag>
class filter_iterator_impl
    : public filter_iterator_base<WrappedIteratorT, PredicateT, IterTag> {
public:
  filter_iterator_impl() = default;
 
  filter_iterator_impl(WrappedIteratorT Begin, WrappedIteratorT End,
                       PredicateT Pred)
      : filter_iterator_impl::filter_iterator_base(Begin, End, Pred) {}
};
 
/// Specialization of filter_iterator_base for bidirectional iteration.
template <typename WrappedIteratorT, typename PredicateT>
class filter_iterator_impl<WrappedIteratorT, PredicateT,
                           std::bidirectional_iterator_tag>
    : public filter_iterator_base<WrappedIteratorT, PredicateT,
                                  std::bidirectional_iterator_tag> {
  using BaseT = typename filter_iterator_impl::filter_iterator_base;
 
  void findPrevValid() {
    while (!this->Pred(*this->I))
      BaseT::operator--();
  }
 
public:
  using BaseT::operator--;
 
  filter_iterator_impl() = default;
 
  filter_iterator_impl(WrappedIteratorT Begin, WrappedIteratorT End,
                       PredicateT Pred)
      : BaseT(Begin, End, Pred) {}
 
  filter_iterator_impl &operator--() {
    BaseT::operator--();
    findPrevValid();
    return *this;
  }
};
 
namespace detail {
 
template <bool is_bidirectional> struct fwd_or_bidi_tag_impl {
  using type = std::forward_iterator_tag;
};
 
template <> struct fwd_or_bidi_tag_impl<true> {
  using type = std::bidirectional_iterator_tag;
};
 
/// Helper which sets its type member to forward_iterator_tag if the category
/// of \p IterT does not derive from bidirectional_iterator_tag, and to
/// bidirectional_iterator_tag otherwise.
template <typename IterT> struct fwd_or_bidi_tag {
  using type = typename fwd_or_bidi_tag_impl<std::is_base_of<
      std::bidirectional_iterator_tag,
      typename std::iterator_traits<IterT>::iterator_category>::value>::type;
};
 
} // namespace detail
 
/// Defines filter_iterator to a suitable specialization of
/// filter_iterator_impl, based on the underlying iterator's category.
template <typename WrappedIteratorT, typename PredicateT>
using filter_iterator = filter_iterator_impl<
    WrappedIteratorT, PredicateT,
    typename detail::fwd_or_bidi_tag<WrappedIteratorT>::type>;
 
/// Convenience function that takes a range of elements and a predicate,
/// and return a new filter_iterator range.
///
/// FIXME: Currently if RangeT && is a rvalue reference to a temporary, the
/// lifetime of that temporary is not kept by the returned range object, and the
/// temporary is going to be dropped on the floor after the make_iterator_range
/// full expression that contains this function call.
template <typename RangeT, typename PredicateT>
iterator_range<filter_iterator<detail::IterOfRange<RangeT>, PredicateT>>
make_filter_range(RangeT &&Range, PredicateT Pred) {
  using FilterIteratorT =
      filter_iterator<detail::IterOfRange<RangeT>, PredicateT>;
  return make_range(
      FilterIteratorT(std::begin(std::forward<RangeT>(Range)),
                      std::end(std::forward<RangeT>(Range)), Pred),
      FilterIteratorT(std::end(std::forward<RangeT>(Range)),
                      std::end(std::forward<RangeT>(Range)), Pred));
}
 
/// A pseudo-iterator adaptor that is designed to implement "early increment"
/// style loops.
///
/// This is *not a normal iterator* and should almost never be used directly. It
/// is intended primarily to be used with range based for loops and some range
/// algorithms.
///
/// The iterator isn't quite an `OutputIterator` or an `InputIterator` but
/// somewhere between them. The constraints of these iterators are:
///
/// - On construction or after being incremented, it is comparable and
///   dereferencable. It is *not* incrementable.
/// - After being dereferenced, it is neither comparable nor dereferencable, it
///   is only incrementable.
///
/// This means you can only dereference the iterator once, and you can only
/// increment it once between dereferences.
template <typename WrappedIteratorT>
class early_inc_iterator_impl
    : public iterator_adaptor_base<early_inc_iterator_impl<WrappedIteratorT>,
                                   WrappedIteratorT, std::input_iterator_tag> {
  using BaseT = typename early_inc_iterator_impl::iterator_adaptor_base;
 
  using PointerT = typename std::iterator_traits<WrappedIteratorT>::pointer;
 
protected:
#if LLVM_ENABLE_ABI_BREAKING_CHECKS
  bool IsEarlyIncremented = false;
#endif
 
public:
  early_inc_iterator_impl(WrappedIteratorT I) : BaseT(I) {}
 
  using BaseT::operator*;
  decltype(*std::declval<WrappedIteratorT>()) operator*() {
#if LLVM_ENABLE_ABI_BREAKING_CHECKS
    assert(!IsEarlyIncremented && "Cannot dereference twice!");
    IsEarlyIncremented = true;
#endif
    return *(this->I)++;
  }
 
  using BaseT::operator++;
  early_inc_iterator_impl &operator++() {
#if LLVM_ENABLE_ABI_BREAKING_CHECKS
    assert(IsEarlyIncremented && "Cannot increment before dereferencing!");
    IsEarlyIncremented = false;
#endif
    return *this;
  }
 
  friend bool operator==(const early_inc_iterator_impl &LHS,
                         const early_inc_iterator_impl &RHS) {
#if LLVM_ENABLE_ABI_BREAKING_CHECKS
    assert(!LHS.IsEarlyIncremented && "Cannot compare after dereferencing!");
#endif
    return (const BaseT &)LHS == (const BaseT &)RHS;
  }
};
 
/// Make a range that does early increment to allow mutation of the underlying
/// range without disrupting iteration.
///
/// The underlying iterator will be incremented immediately after it is
/// dereferenced, allowing deletion of the current node or insertion of nodes to
/// not disrupt iteration provided they do not invalidate the *next* iterator --
/// the current iterator can be invalidated.
///
/// This requires a very exact pattern of use that is only really suitable to
/// range based for loops and other range algorithms that explicitly guarantee
/// to dereference exactly once each element, and to increment exactly once each
/// element.
template <typename RangeT>
iterator_range<early_inc_iterator_impl<detail::IterOfRange<RangeT>>>
make_early_inc_range(RangeT &&Range) {
  using EarlyIncIteratorT =
      early_inc_iterator_impl<detail::IterOfRange<RangeT>>;
  return make_range(EarlyIncIteratorT(std::begin(std::forward<RangeT>(Range))),
                    EarlyIncIteratorT(std::end(std::forward<RangeT>(Range))));
}
 
// Forward declarations required by zip_shortest/zip_equal/zip_first/zip_longest
template <typename R, typename UnaryPredicate>
bool all_of(R &&range, UnaryPredicate P);
 
template <typename R, typename UnaryPredicate>
bool any_of(R &&range, UnaryPredicate P);
 
template <typename T> bool all_equal(std::initializer_list<T> Values);
 
template <typename R> constexpr size_t range_size(R &&Range);
 
namespace detail {
 
using std::declval;
 
// We have to alias this since inlining the actual type at the usage site
// in the parameter list of iterator_facade_base<> below ICEs MSVC 2017.
template<typename... Iters> struct ZipTupleType {
  using type = std::tuple<decltype(*declval<Iters>())...>;
};
 
template <typename ZipType, typename ReferenceTupleType, typename... Iters>
using zip_traits = iterator_facade_base<
    ZipType,
    std::common_type_t<
        std::bidirectional_iterator_tag,
        typename std::iterator_traits<Iters>::iterator_category...>,
    // ^ TODO: Implement random access methods.
    ReferenceTupleType,
    typename std::iterator_traits<
        std::tuple_element_t<0, std::tuple<Iters...>>>::difference_type,
    // ^ FIXME: This follows boost::make_zip_iterator's assumption that all
    // inner iterators have the same difference_type. It would fail if, for
    // instance, the second field's difference_type were non-numeric while the
    // first is.
    ReferenceTupleType *, ReferenceTupleType>;
 
template <typename ZipType, typename ReferenceTupleType, typename... Iters>
struct zip_common : public zip_traits<ZipType, ReferenceTupleType, Iters...> {
  using Base = zip_traits<ZipType, ReferenceTupleType, Iters...>;
  using IndexSequence = std::index_sequence_for<Iters...>;
  using value_type = typename Base::value_type;
 
  std::tuple<Iters...> iterators;
 
protected:
  template <size_t... Ns> value_type deref(std::index_sequence<Ns...>) const {
    return value_type(*std::get<Ns>(iterators)...);
  }
 
  template <size_t... Ns> void tup_inc(std::index_sequence<Ns...>) {
    (++std::get<Ns>(iterators), ...);
  }
 
  template <size_t... Ns> void tup_dec(std::index_sequence<Ns...>) {
    (--std::get<Ns>(iterators), ...);
  }
 
  template <size_t... Ns>
  bool test_all_equals(const zip_common &other,
                       std::index_sequence<Ns...>) const {
    return ((std::get<Ns>(this->iterators) == std::get<Ns>(other.iterators)) &&
            ...);
  }
 
public:
  zip_common(Iters &&... ts) : iterators(std::forward<Iters>(ts)...) {}
 
  value_type operator*() const { return deref(IndexSequence{}); }
 
  ZipType &operator++() {
    tup_inc(IndexSequence{});
    return static_cast<ZipType &>(*this);
  }
 
  ZipType &operator--() {
    static_assert(Base::IsBidirectional,
                  "All inner iterators must be at least bidirectional.");
    tup_dec(IndexSequence{});
    return static_cast<ZipType &>(*this);
  }
 
  /// Return true if all the iterator are matching `other`'s iterators.
  bool all_equals(zip_common &other) {
    return test_all_equals(other, IndexSequence{});
  }
};
 
template <typename... Iters>
struct zip_first : zip_common<zip_first<Iters...>,
                              typename ZipTupleType<Iters...>::type, Iters...> {
  using zip_common<zip_first, typename ZipTupleType<Iters...>::type,
                   Iters...>::zip_common;
 
  bool operator==(const zip_first &other) const {
    return std::get<0>(this->iterators) == std::get<0>(other.iterators);
  }
};
 
template <typename... Iters>
struct zip_shortest
    : zip_common<zip_shortest<Iters...>, typename ZipTupleType<Iters...>::type,
                 Iters...> {
  using zip_common<zip_shortest, typename ZipTupleType<Iters...>::type,
                   Iters...>::zip_common;
 
  bool operator==(const zip_shortest &other) const {
    return any_iterator_equals(other, std::index_sequence_for<Iters...>{});
  }
 
private:
  template <size_t... Ns>
  bool any_iterator_equals(const zip_shortest &other,
                           std::index_sequence<Ns...>) const {
    return ((std::get<Ns>(this->iterators) == std::get<Ns>(other.iterators)) ||
            ...);
  }
};
 
/// Helper to obtain the iterator types for the tuple storage within `zippy`.
template <template <typename...> class ItType, typename TupleStorageType,
          typename IndexSequence>
struct ZippyIteratorTuple;
 
/// Partial specialization for non-const tuple storage.
template <template <typename...> class ItType, typename... Args,
          std::size_t... Ns>
struct ZippyIteratorTuple<ItType, std::tuple<Args...>,
                          std::index_sequence<Ns...>> {
  using type = ItType<decltype(adl_begin(
      std::get<Ns>(declval<std::tuple<Args...> &>())))...>;
};
 
/// Partial specialization for const tuple storage.
template <template <typename...> class ItType, typename... Args,
          std::size_t... Ns>
struct ZippyIteratorTuple<ItType, const std::tuple<Args...>,
                          std::index_sequence<Ns...>> {
  using type = ItType<decltype(adl_begin(
      std::get<Ns>(declval<const std::tuple<Args...> &>())))...>;
};
 
template <template <typename...> class ItType, typename... Args> class zippy {
private:
  std::tuple<Args...> storage;
  using IndexSequence = std::index_sequence_for<Args...>;
 
public:
  using iterator = typename ZippyIteratorTuple<ItType, decltype(storage),
                                               IndexSequence>::type;
  using const_iterator =
      typename ZippyIteratorTuple<ItType, const decltype(storage),
                                  IndexSequence>::type;
  using iterator_category = typename iterator::iterator_category;
  using value_type = typename iterator::value_type;
  using difference_type = typename iterator::difference_type;
  using pointer = typename iterator::pointer;
  using reference = typename iterator::reference;
  using const_reference = typename const_iterator::reference;
 
  zippy(Args &&...args) : storage(std::forward<Args>(args)...) {}
 
  const_iterator begin() const { return begin_impl(IndexSequence{}); }
  iterator begin() { return begin_impl(IndexSequence{}); }
  const_iterator end() const { return end_impl(IndexSequence{}); }
  iterator end() { return end_impl(IndexSequence{}); }
 
private:
  template <size_t... Ns>
  const_iterator begin_impl(std::index_sequence<Ns...>) const {
    return const_iterator(adl_begin(std::get<Ns>(storage))...);
  }
  template <size_t... Ns> iterator begin_impl(std::index_sequence<Ns...>) {
    return iterator(adl_begin(std::get<Ns>(storage))...);
  }
 
  template <size_t... Ns>
  const_iterator end_impl(std::index_sequence<Ns...>) const {
    return const_iterator(adl_end(std::get<Ns>(storage))...);
  }
  template <size_t... Ns> iterator end_impl(std::index_sequence<Ns...>) {
    return iterator(adl_end(std::get<Ns>(storage))...);
  }
};
 
} // end namespace detail
 
/// zip iterator for two or more iteratable types. Iteration continues until the
/// end of the *shortest* iteratee is reached.
template <typename T, typename U, typename... Args>
detail::zippy<detail::zip_shortest, T, U, Args...> zip(T &&t, U &&u,
                                                       Args &&...args) {
  return detail::zippy<detail::zip_shortest, T, U, Args...>(
      std::forward<T>(t), std::forward<U>(u), std::forward<Args>(args)...);
}
 
/// zip iterator that assumes that all iteratees have the same length.
/// In builds with assertions on, this assumption is checked before the
/// iteration starts.
template <typename T, typename U, typename... Args>
detail::zippy<detail::zip_first, T, U, Args...> zip_equal(T &&t, U &&u,
                                                          Args &&...args) {
  assert(all_equal({range_size(t), range_size(u), range_size(args)...}) &&
         "Iteratees do not have equal length");
  return detail::zippy<detail::zip_first, T, U, Args...>(
      std::forward<T>(t), std::forward<U>(u), std::forward<Args>(args)...);
}
 
/// zip iterator that, for the sake of efficiency, assumes the first iteratee to
/// be the shortest. Iteration continues until the end of the first iteratee is
/// reached. In builds with assertions on, we check that the assumption about
/// the first iteratee being the shortest holds.
template <typename T, typename U, typename... Args>
detail::zippy<detail::zip_first, T, U, Args...> zip_first(T &&t, U &&u,
                                                          Args &&...args) {
  assert(range_size(t) <= std::min({range_size(u), range_size(args)...}) &&
         "First iteratee is not the shortest");
 
  return detail::zippy<detail::zip_first, T, U, Args...>(
      std::forward<T>(t), std::forward<U>(u), std::forward<Args>(args)...);
}
 
namespace detail {
template <typename Iter>
Iter next_or_end(const Iter &I, const Iter &End) {
  if (I == End)
    return End;
  return std::next(I);
}
 
template <typename Iter>
auto deref_or_none(const Iter &I, const Iter &End) -> std::optional<
    std::remove_const_t<std::remove_reference_t<decltype(*I)>>> {
  if (I == End)
    return std::nullopt;
  return *I;
}
 
template <typename Iter> struct ZipLongestItemType {
  using type = std::optional<std::remove_const_t<
      std::remove_reference_t<decltype(*std::declval<Iter>())>>>;
};
 
template <typename... Iters> struct ZipLongestTupleType {
  using type = std::tuple<typename ZipLongestItemType<Iters>::type...>;
};
 
template <typename... Iters>
class zip_longest_iterator
    : public iterator_facade_base<
          zip_longest_iterator<Iters...>,
          std::common_type_t<
              std::forward_iterator_tag,
              typename std::iterator_traits<Iters>::iterator_category...>,
          typename ZipLongestTupleType<Iters...>::type,
          typename std::iterator_traits<
              std::tuple_element_t<0, std::tuple<Iters...>>>::difference_type,
          typename ZipLongestTupleType<Iters...>::type *,
          typename ZipLongestTupleType<Iters...>::type> {
public:
  using value_type = typename ZipLongestTupleType<Iters...>::type;
 
private:
  std::tuple<Iters...> iterators;
  std::tuple<Iters...> end_iterators;
 
  template <size_t... Ns>
  bool test(const zip_longest_iterator<Iters...> &other,
            std::index_sequence<Ns...>) const {
    return ((std::get<Ns>(this->iterators) != std::get<Ns>(other.iterators)) ||
            ...);
  }
 
  template <size_t... Ns> value_type deref(std::index_sequence<Ns...>) const {
    return value_type(
        deref_or_none(std::get<Ns>(iterators), std::get<Ns>(end_iterators))...);
  }
 
  template <size_t... Ns>
  decltype(iterators) tup_inc(std::index_sequence<Ns...>) const {
    return std::tuple<Iters...>(
        next_or_end(std::get<Ns>(iterators), std::get<Ns>(end_iterators))...);
  }
 
public:
  zip_longest_iterator(std::pair<Iters &&, Iters &&>... ts)
      : iterators(std::forward<Iters>(ts.first)...),
        end_iterators(std::forward<Iters>(ts.second)...) {}
 
  value_type operator*() const {
    return deref(std::index_sequence_for<Iters...>{});
  }
 
  zip_longest_iterator<Iters...> &operator++() {
    iterators = tup_inc(std::index_sequence_for<Iters...>{});
    return *this;
  }
 
  bool operator==(const zip_longest_iterator<Iters...> &other) const {
    return !test(other, std::index_sequence_for<Iters...>{});
  }
};
 
template <typename... Args> class zip_longest_range {
public:
  using iterator =
      zip_longest_iterator<decltype(adl_begin(std::declval<Args>()))...>;
  using iterator_category = typename iterator::iterator_category;
  using value_type = typename iterator::value_type;
  using difference_type = typename iterator::difference_type;
  using pointer = typename iterator::pointer;
  using reference = typename iterator::reference;
 
private:
  std::tuple<Args...> ts;
 
  template <size_t... Ns>
  iterator begin_impl(std::index_sequence<Ns...>) const {
    return iterator(std::make_pair(adl_begin(std::get<Ns>(ts)),
                                   adl_end(std::get<Ns>(ts)))...);
  }
 
  template <size_t... Ns> iterator end_impl(std::index_sequence<Ns...>) const {
    return iterator(std::make_pair(adl_end(std::get<Ns>(ts)),
                                   adl_end(std::get<Ns>(ts)))...);
  }
 
public:
  zip_longest_range(Args &&... ts_) : ts(std::forward<Args>(ts_)...) {}
 
  iterator begin() const {
    return begin_impl(std::index_sequence_for<Args...>{});
  }
  iterator end() const { return end_impl(std::index_sequence_for<Args...>{}); }
};
} // namespace detail
 
/// Iterate over two or more iterators at the same time. Iteration continues
/// until all iterators reach the end. The std::optional only contains a value
/// if the iterator has not reached the end.
template <typename T, typename U, typename... Args>
detail::zip_longest_range<T, U, Args...> zip_longest(T &&t, U &&u,
                                                     Args &&... args) {
  return detail::zip_longest_range<T, U, Args...>(
      std::forward<T>(t), std::forward<U>(u), std::forward<Args>(args)...);
}
 
/// Iterator wrapper that concatenates sequences together.
///
/// This can concatenate different iterators, even with different types, into
/// a single iterator provided the value types of all the concatenated
/// iterators expose `reference` and `pointer` types that can be converted to
/// `ValueT &` and `ValueT *` respectively. It doesn't support more
/// interesting/customized pointer or reference types.
///
/// Currently this only supports forward or higher iterator categories as
/// inputs and always exposes a forward iterator interface.
template <typename ValueT, typename... IterTs>
class concat_iterator
    : public iterator_facade_base<concat_iterator<ValueT, IterTs...>,
                                  std::forward_iterator_tag, ValueT> {
  using BaseT = typename concat_iterator::iterator_facade_base;
 
  /// We store both the current and end iterators for each concatenated
  /// sequence in a tuple of pairs.
  ///
  /// Note that something like iterator_range seems nice at first here, but the
  /// range properties are of little benefit and end up getting in the way
  /// because we need to do mutation on the current iterators.
  std::tuple<IterTs...> Begins;
  std::tuple<IterTs...> Ends;
 
  /// Attempts to increment a specific iterator.
  ///
  /// Returns true if it was able to increment the iterator. Returns false if
  /// the iterator is already at the end iterator.
  template <size_t Index> bool incrementHelper() {
    auto &Begin = std::get<Index>(Begins);
    auto &End = std::get<Index>(Ends);
    if (Begin == End)
      return false;
 
    ++Begin;
    return true;
  }
 
  /// Increments the first non-end iterator.
  ///
  /// It is an error to call this with all iterators at the end.
  template <size_t... Ns> void increment(std::index_sequence<Ns...>) {
    // Build a sequence of functions to increment each iterator if possible.
    bool (concat_iterator::*IncrementHelperFns[])() = {
        &concat_iterator::incrementHelper<Ns>...};
 
    // Loop over them, and stop as soon as we succeed at incrementing one.
    for (auto &IncrementHelperFn : IncrementHelperFns)
      if ((this->*IncrementHelperFn)())
        return;
 
    llvm_unreachable("Attempted to increment an end concat iterator!");
  }
 
  /// Returns null if the specified iterator is at the end. Otherwise,
  /// dereferences the iterator and returns the address of the resulting
  /// reference.
  template <size_t Index> ValueT *getHelper() const {
    auto &Begin = std::get<Index>(Begins);
    auto &End = std::get<Index>(Ends);
    if (Begin == End)
      return nullptr;
 
    return &*Begin;
  }
 
  /// Finds the first non-end iterator, dereferences, and returns the resulting
  /// reference.
  ///
  /// It is an error to call this with all iterators at the end.
  template <size_t... Ns> ValueT &get(std::index_sequence<Ns...>) const {
    // Build a sequence of functions to get from iterator if possible.
    ValueT *(concat_iterator::*GetHelperFns[])() const = {
        &concat_iterator::getHelper<Ns>...};
 
    // Loop over them, and return the first result we find.
    for (auto &GetHelperFn : GetHelperFns)
      if (ValueT *P = (this->*GetHelperFn)())
        return *P;
 
    llvm_unreachable("Attempted to get a pointer from an end concat iterator!");
  }
 
public:
  /// Constructs an iterator from a sequence of ranges.
  ///
  /// We need the full range to know how to switch between each of the
  /// iterators.
  template <typename... RangeTs>
  explicit concat_iterator(RangeTs &&... Ranges)
      : Begins(std::begin(Ranges)...), Ends(std::end(Ranges)...) {}
 
  using BaseT::operator++;
 
  concat_iterator &operator++() {
    increment(std::index_sequence_for<IterTs...>());
    return *this;
  }
 
  ValueT &operator*() const {
    return get(std::index_sequence_for<IterTs...>());
  }
 
  bool operator==(const concat_iterator &RHS) const {
    return Begins == RHS.Begins && Ends == RHS.Ends;
  }
};
 
namespace detail {
 
/// Helper to store a sequence of ranges being concatenated and access them.
///
/// This is designed to facilitate providing actual storage when temporaries
/// are passed into the constructor such that we can use it as part of range
/// based for loops.
template <typename ValueT, typename... RangeTs> class concat_range {
public:
  using iterator =
      concat_iterator<ValueT,
                      decltype(std::begin(std::declval<RangeTs &>()))...>;
 
private:
  std::tuple<RangeTs...> Ranges;
 
  template <size_t... Ns>
  iterator begin_impl(std::index_sequence<Ns...>) {
    return iterator(std::get<Ns>(Ranges)...);
  }
  template <size_t... Ns>
  iterator begin_impl(std::index_sequence<Ns...>) const {
    return iterator(std::get<Ns>(Ranges)...);
  }
  template <size_t... Ns> iterator end_impl(std::index_sequence<Ns...>) {
    return iterator(make_range(std::end(std::get<Ns>(Ranges)),
                               std::end(std::get<Ns>(Ranges)))...);
  }
  template <size_t... Ns> iterator end_impl(std::index_sequence<Ns...>) const {
    return iterator(make_range(std::end(std::get<Ns>(Ranges)),
                               std::end(std::get<Ns>(Ranges)))...);
  }
 
public:
  concat_range(RangeTs &&... Ranges)
      : Ranges(std::forward<RangeTs>(Ranges)...) {}
 
  iterator begin() {
    return begin_impl(std::index_sequence_for<RangeTs...>{});
  }
  iterator begin() const {
    return begin_impl(std::index_sequence_for<RangeTs...>{});
  }
  iterator end() {
    return end_impl(std::index_sequence_for<RangeTs...>{});
  }
  iterator end() const {
    return end_impl(std::index_sequence_for<RangeTs...>{});
  }
};
 
} // end namespace detail
 
/// Concatenated range across two or more ranges.
///
/// The desired value type must be explicitly specified.
template <typename ValueT, typename... RangeTs>
detail::concat_range<ValueT, RangeTs...> concat(RangeTs &&... Ranges) {
  static_assert(sizeof...(RangeTs) > 1,
                "Need more than one range to concatenate!");
  return detail::concat_range<ValueT, RangeTs...>(
      std::forward<RangeTs>(Ranges)...);
}
 
/// A utility class used to implement an iterator that contains some base object
/// and an index. The iterator moves the index but keeps the base constant.
template <typename DerivedT, typename BaseT, typename T,
          typename PointerT = T *, typename ReferenceT = T &>
class indexed_accessor_iterator
    : public llvm::iterator_facade_base<DerivedT,
                                        std::random_access_iterator_tag, T,
                                        std::ptrdiff_t, PointerT, ReferenceT> {
public:
  ptrdiff_t operator-(const indexed_accessor_iterator &rhs) const {
    assert(base == rhs.base && "incompatible iterators");
    return index - rhs.index;
  }
  bool operator==(const indexed_accessor_iterator &rhs) const {
    return base == rhs.base && index == rhs.index;
  }
  bool operator<(const indexed_accessor_iterator &rhs) const {
    assert(base == rhs.base && "incompatible iterators");
    return index < rhs.index;
  }
 
  DerivedT &operator+=(ptrdiff_t offset) {
    this->index += offset;
    return static_cast<DerivedT &>(*this);
  }
  DerivedT &operator-=(ptrdiff_t offset) {
    this->index -= offset;
    return static_cast<DerivedT &>(*this);
  }
 
  /// Returns the current index of the iterator.
  ptrdiff_t getIndex() const { return index; }
 
  /// Returns the current base of the iterator.
  const BaseT &getBase() const { return base; }
 
protected:
  indexed_accessor_iterator(BaseT base, ptrdiff_t index)
      : base(base), index(index) {}
  BaseT base;
  ptrdiff_t index;
};
 
namespace detail {
/// The class represents the base of a range of indexed_accessor_iterators. It
/// provides support for many different range functionalities, e.g.
/// drop_front/slice/etc.. Derived range classes must implement the following
/// static methods:
///   * ReferenceT dereference_iterator(const BaseT &base, ptrdiff_t index)
///     - Dereference an iterator pointing to the base object at the given
///       index.
///   * BaseT offset_base(const BaseT &base, ptrdiff_t index)
///     - Return a new base that is offset from the provide base by 'index'
///       elements.
template <typename DerivedT, typename BaseT, typename T,
          typename PointerT = T *, typename ReferenceT = T &>
class indexed_accessor_range_base {
public:
  using RangeBaseT = indexed_accessor_range_base;
 
  /// An iterator element of this range.
  class iterator : public indexed_accessor_iterator<iterator, BaseT, T,
                                                    PointerT, ReferenceT> {
  public:
    // Index into this iterator, invoking a static method on the derived type.
    ReferenceT operator*() const {
      return DerivedT::dereference_iterator(this->getBase(), this->getIndex());
    }
 
  private:
    iterator(BaseT owner, ptrdiff_t curIndex)
        : iterator::indexed_accessor_iterator(owner, curIndex) {}
 
    /// Allow access to the constructor.
    friend indexed_accessor_range_base<DerivedT, BaseT, T, PointerT,
                                       ReferenceT>;
  };
 
  indexed_accessor_range_base(iterator begin, iterator end)
      : base(offset_base(begin.getBase(), begin.getIndex())),
        count(end.getIndex() - begin.getIndex()) {}
  indexed_accessor_range_base(const iterator_range<iterator> &range)
      : indexed_accessor_range_base(range.begin(), range.end()) {}
  indexed_accessor_range_base(BaseT base, ptrdiff_t count)
      : base(base), count(count) {}
 
  iterator begin() const { return iterator(base, 0); }
  iterator end() const { return iterator(base, count); }
  ReferenceT operator[](size_t Index) const {
    assert(Index < size() && "invalid index for value range");
    return DerivedT::dereference_iterator(base, static_cast<ptrdiff_t>(Index));
  }
  ReferenceT front() const {
    assert(!empty() && "expected non-empty range");
    return (*this)[0];
  }
  ReferenceT back() const {
    assert(!empty() && "expected non-empty range");
    return (*this)[size() - 1];
  }
 
  /// Return the size of this range.
  size_t size() const { return count; }
 
  /// Return if the range is empty.
  bool empty() const { return size() == 0; }
 
  /// Drop the first N elements, and keep M elements.
  DerivedT slice(size_t n, size_t m) const {
    assert(n + m <= size() && "invalid size specifiers");
    return DerivedT(offset_base(base, n), m);
  }
 
  /// Drop the first n elements.
  DerivedT drop_front(size_t n = 1) const {
    assert(size() >= n && "Dropping more elements than exist");
    return slice(n, size() - n);
  }
  /// Drop the last n elements.
  DerivedT drop_back(size_t n = 1) const {
    assert(size() >= n && "Dropping more elements than exist");
    return DerivedT(base, size() - n);
  }
 
  /// Take the first n elements.
  DerivedT take_front(size_t n = 1) const {
    return n < size() ? drop_back(size() - n)
                      : static_cast<const DerivedT &>(*this);
  }
 
  /// Take the last n elements.
  DerivedT take_back(size_t n = 1) const {
    return n < size() ? drop_front(size() - n)
                      : static_cast<const DerivedT &>(*this);
  }
 
  /// Allow conversion to any type accepting an iterator_range.
  template <typename RangeT, typename = std::enable_if_t<std::is_constructible<
                                 RangeT, iterator_range<iterator>>::value>>
  operator RangeT() const {
    return RangeT(iterator_range<iterator>(*this));
  }
 
  /// Returns the base of this range.
  const BaseT &getBase() const { return base; }
 
private:
  /// Offset the given base by the given amount.
  static BaseT offset_base(const BaseT &base, size_t n) {
    return n == 0 ? base : DerivedT::offset_base(base, n);
  }
 
protected:
  indexed_accessor_range_base(const indexed_accessor_range_base &) = default;
  indexed_accessor_range_base(indexed_accessor_range_base &&) = default;
  indexed_accessor_range_base &
  operator=(const indexed_accessor_range_base &) = default;
 
  /// The base that owns the provided range of values.
  BaseT base;
  /// The size from the owning range.
  ptrdiff_t count;
};
/// Compare this range with another.
/// FIXME: Make me a member function instead of friend when it works in C++20.
template <typename OtherT, typename DerivedT, typename BaseT, typename T,
          typename PointerT, typename ReferenceT>
bool operator==(const indexed_accessor_range_base<DerivedT, BaseT, T, PointerT,
                                                  ReferenceT> &lhs,
                const OtherT &rhs) {
  return std::equal(lhs.begin(), lhs.end(), rhs.begin(), rhs.end());
}
 
template <typename OtherT, typename DerivedT, typename BaseT, typename T,
          typename PointerT, typename ReferenceT>
bool operator!=(const indexed_accessor_range_base<DerivedT, BaseT, T, PointerT,
                                                  ReferenceT> &lhs,
                const OtherT &rhs) {
  return !(lhs == rhs);
}
} // end namespace detail
 
/// This class provides an implementation of a range of
/// indexed_accessor_iterators where the base is not indexable. Ranges with
/// bases that are offsetable should derive from indexed_accessor_range_base
/// instead. Derived range classes are expected to implement the following
/// static method:
///   * ReferenceT dereference(const BaseT &base, ptrdiff_t index)
///     - Dereference an iterator pointing to a parent base at the given index.
template <typename DerivedT, typename BaseT, typename T,
          typename PointerT = T *, typename ReferenceT = T &>
class indexed_accessor_range
    : public detail::indexed_accessor_range_base<
          DerivedT, std::pair<BaseT, ptrdiff_t>, T, PointerT, ReferenceT> {
public:
  indexed_accessor_range(BaseT base, ptrdiff_t startIndex, ptrdiff_t count)
      : detail::indexed_accessor_range_base<
            DerivedT, std::pair<BaseT, ptrdiff_t>, T, PointerT, ReferenceT>(
            std::make_pair(base, startIndex), count) {}
  using detail::indexed_accessor_range_base<
      DerivedT, std::pair<BaseT, ptrdiff_t>, T, PointerT,
      ReferenceT>::indexed_accessor_range_base;
 
  /// Returns the current base of the range.
  const BaseT &getBase() const { return this->base.first; }
 
  /// Returns the current start index of the range.
  ptrdiff_t getStartIndex() const { return this->base.second; }
 
  /// See `detail::indexed_accessor_range_base` for details.
  static std::pair<BaseT, ptrdiff_t>
  offset_base(const std::pair<BaseT, ptrdiff_t> &base, ptrdiff_t index) {
    // We encode the internal base as a pair of the derived base and a start
    // index into the derived base.
    return std::make_pair(base.first, base.second + index);
  }
  /// See `detail::indexed_accessor_range_base` for details.
  static ReferenceT
  dereference_iterator(const std::pair<BaseT, ptrdiff_t> &base,
                       ptrdiff_t index) {
    return DerivedT::dereference(base.first, base.second + index);
  }
};
 
namespace detail {
/// Return a reference to the first or second member of a reference. Otherwise,
/// return a copy of the member of a temporary.
///
/// When passing a range whose iterators return values instead of references,
/// the reference must be dropped from `decltype((elt.first))`, which will
/// always be a reference, to avoid returning a reference to a temporary.
template <typename EltTy, typename FirstTy> class first_or_second_type {
public:
  using type = std::conditional_t<std::is_reference<EltTy>::value, FirstTy,
                                  std::remove_reference_t<FirstTy>>;
};
} // end namespace detail
 
/// Given a container of pairs, return a range over the first elements.
template <typename ContainerTy> auto make_first_range(ContainerTy &&c) {
  using EltTy = decltype((*std::begin(c)));
  return llvm::map_range(std::forward<ContainerTy>(c),
                         [](EltTy elt) -> typename detail::first_or_second_type<
                                           EltTy, decltype((elt.first))>::type {
                           return elt.first;
                         });
}
 
/// Given a container of pairs, return a range over the second elements.
template <typename ContainerTy> auto make_second_range(ContainerTy &&c) {
  using EltTy = decltype((*std::begin(c)));
  return llvm::map_range(
      std::forward<ContainerTy>(c),
      [](EltTy elt) ->
      typename detail::first_or_second_type<EltTy,
                                            decltype((elt.second))>::type {
        return elt.second;
      });
}
 
//===----------------------------------------------------------------------===//
//     Extra additions to <utility>
//===----------------------------------------------------------------------===//
 
/// Function object to check whether the first component of a container
/// supported by std::get (like std::pair and std::tuple) compares less than the
/// first component of another container.
struct less_first {
  template <typename T> bool operator()(const T &lhs, const T &rhs) const {
    return std::less<>()(std::get<0>(lhs), std::get<0>(rhs));
  }
};
 
/// Function object to check whether the second component of a container
/// supported by std::get (like std::pair and std::tuple) compares less than the
/// second component of another container.
struct less_second {
  template <typename T> bool operator()(const T &lhs, const T &rhs) const {
    return std::less<>()(std::get<1>(lhs), std::get<1>(rhs));
  }
};
 
/// \brief Function object to apply a binary function to the first component of
/// a std::pair.
template<typename FuncTy>
struct on_first {
  FuncTy func;
 
  template <typename T>
  decltype(auto) operator()(const T &lhs, const T &rhs) const {
    return func(lhs.first, rhs.first);
  }
};
 
/// Utility type to build an inheritance chain that makes it easy to rank
/// overload candidates.
template <int N> struct rank : rank<N - 1> {};
template <> struct rank<0> {};
 
namespace detail {
template <typename... Ts> struct Visitor;
 
template <typename HeadT, typename... TailTs>
struct Visitor<HeadT, TailTs...> : remove_cvref_t<HeadT>, Visitor<TailTs...> {
  explicit constexpr Visitor(HeadT &&Head, TailTs &&...Tail)
      : remove_cvref_t<HeadT>(std::forward<HeadT>(Head)),
        Visitor<TailTs...>(std::forward<TailTs>(Tail)...) {}
  using remove_cvref_t<HeadT>::operator();
  using Visitor<TailTs...>::operator();
};
 
template <typename HeadT> struct Visitor<HeadT> : remove_cvref_t<HeadT> {
  explicit constexpr Visitor(HeadT &&Head)
      : remove_cvref_t<HeadT>(std::forward<HeadT>(Head)) {}
  using remove_cvref_t<HeadT>::operator();
};
} // namespace detail
 
/// Returns an opaquely-typed Callable object whose operator() overload set is
/// the sum of the operator() overload sets of each CallableT in CallableTs.
///
/// The type of the returned object derives from each CallableT in CallableTs.
/// The returned object is constructed by invoking the appropriate copy or move
/// constructor of each CallableT, as selected by overload resolution on the
/// corresponding argument to makeVisitor.
///
/// Example:
///
/// \code
/// auto visitor = makeVisitor([](auto) { return "unhandled type"; },
///                            [](int i) { return "int"; },
///                            [](std::string s) { return "str"; });
/// auto a = visitor(42);    // `a` is now "int".
/// auto b = visitor("foo"); // `b` is now "str".
/// auto c = visitor(3.14f); // `c` is now "unhandled type".
/// \endcode
///
/// Example of making a visitor with a lambda which captures a move-only type:
///
/// \code
/// std::unique_ptr<FooHandler> FH = /* ... */;
/// auto visitor = makeVisitor(
///     [FH{std::move(FH)}](Foo F) { return FH->handle(F); },
///     [](int i) { return i; },
///     [](std::string s) { return atoi(s); });
/// \endcode
template <typename... CallableTs>
constexpr decltype(auto) makeVisitor(CallableTs &&...Callables) {
  return detail::Visitor<CallableTs...>(std::forward<CallableTs>(Callables)...);
}
 
//===----------------------------------------------------------------------===//
//     Extra additions to <algorithm>
//===----------------------------------------------------------------------===//
 
// We have a copy here so that LLVM behaves the same when using different
// standard libraries.
template <class Iterator, class RNG>
void shuffle(Iterator first, Iterator last, RNG &&g) {
  // It would be better to use a std::uniform_int_distribution,
  // but that would be stdlib dependent.
  typedef
      typename std::iterator_traits<Iterator>::difference_type difference_type;
  for (auto size = last - first; size > 1; ++first, (void)--size) {
    difference_type offset = g() % size;
    // Avoid self-assignment due to incorrect assertions in libstdc++
    // containers (https://gcc.gnu.org/bugzilla/show_bug.cgi?id=85828).
    if (offset != difference_type(0))
      std::iter_swap(first, first + offset);
  }
}
 
/// Adapt std::less<T> for array_pod_sort.
template<typename T>
inline int array_pod_sort_comparator(const void *P1, const void *P2) {
  if (std::less<T>()(*reinterpret_cast<const T*>(P1),
                     *reinterpret_cast<const T*>(P2)))
    return -1;
  if (std::less<T>()(*reinterpret_cast<const T*>(P2),
                     *reinterpret_cast<const T*>(P1)))
    return 1;
  return 0;
}
 
/// get_array_pod_sort_comparator - This is an internal helper function used to
/// get type deduction of T right.
template<typename T>
inline int (*get_array_pod_sort_comparator(const T &))
             (const void*, const void*) {
  return array_pod_sort_comparator<T>;
}
 
#ifdef EXPENSIVE_CHECKS
namespace detail {
 
inline unsigned presortShuffleEntropy() {
  static unsigned Result(std::random_device{}());
  return Result;
}
 
template <class IteratorTy>
inline void presortShuffle(IteratorTy Start, IteratorTy End) {
  std::mt19937 Generator(presortShuffleEntropy());
  llvm::shuffle(Start, End, Generator);
}
 
} // end namespace detail
#endif
 
/// array_pod_sort - This sorts an array with the specified start and end
/// extent.  This is just like std::sort, except that it calls qsort instead of
/// using an inlined template.  qsort is slightly slower than std::sort, but
/// most sorts are not performance critical in LLVM and std::sort has to be
/// template instantiated for each type, leading to significant measured code
/// bloat.  This function should generally be used instead of std::sort where
/// possible.
///
/// This function assumes that you have simple POD-like types that can be
/// compared with std::less and can be moved with memcpy.  If this isn't true,
/// you should use std::sort.
///
/// NOTE: If qsort_r were portable, we could allow a custom comparator and
/// default to std::less.
template<class IteratorTy>
inline void array_pod_sort(IteratorTy Start, IteratorTy End) {
  // Don't inefficiently call qsort with one element or trigger undefined
  // behavior with an empty sequence.
  auto NElts = End - Start;
  if (NElts <= 1) return;
#ifdef EXPENSIVE_CHECKS
  detail::presortShuffle<IteratorTy>(Start, End);
#endif
  qsort(&*Start, NElts, sizeof(*Start), get_array_pod_sort_comparator(*Start));
}
 
template <class IteratorTy>
inline void array_pod_sort(
    IteratorTy Start, IteratorTy End,
    int (*Compare)(
        const typename std::iterator_traits<IteratorTy>::value_type *,
        const typename std::iterator_traits<IteratorTy>::value_type *)) {
  // Don't inefficiently call qsort with one element or trigger undefined
  // behavior with an empty sequence.
  auto NElts = End - Start;
  if (NElts <= 1) return;
#ifdef EXPENSIVE_CHECKS
  detail::presortShuffle<IteratorTy>(Start, End);
#endif
  qsort(&*Start, NElts, sizeof(*Start),
        reinterpret_cast<int (*)(const void *, const void *)>(Compare));
}
 
namespace detail {
template <typename T>
// We can use qsort if the iterator type is a pointer and the underlying value
// is trivially copyable.
using sort_trivially_copyable = std::conjunction<
    std::is_pointer<T>,
    std::is_trivially_copyable<typename std::iterator_traits<T>::value_type>>;
} // namespace detail
 
// Provide wrappers to std::sort which shuffle the elements before sorting
// to help uncover non-deterministic behavior (PR35135).
template <typename IteratorTy>
inline void sort(IteratorTy Start, IteratorTy End) {
  if constexpr (detail::sort_trivially_copyable<IteratorTy>::value) {
    // Forward trivially copyable types to array_pod_sort. This avoids a large
    // amount of code bloat for a minor performance hit.
    array_pod_sort(Start, End);
  } else {
#ifdef EXPENSIVE_CHECKS
    detail::presortShuffle<IteratorTy>(Start, End);
#endif
    std::sort(Start, End);
  }
}
 
template <typename Container> inline void sort(Container &&C) {
  llvm::sort(adl_begin(C), adl_end(C));
}
 
template <typename IteratorTy, typename Compare>
inline void sort(IteratorTy Start, IteratorTy End, Compare Comp) {
#ifdef EXPENSIVE_CHECKS
  detail::presortShuffle<IteratorTy>(Start, End);
#endif
  std::sort(Start, End, Comp);
}
 
template <typename Container, typename Compare>
inline void sort(Container &&C, Compare Comp) {
  llvm::sort(adl_begin(C), adl_end(C), Comp);
}
 
/// Get the size of a range. This is a wrapper function around std::distance
/// which is only enabled when the operation is O(1).
template <typename R>
auto size(R &&Range,
          std::enable_if_t<
              std::is_base_of<std::random_access_iterator_tag,
                              typename std::iterator_traits<decltype(
                                  Range.begin())>::iterator_category>::value,
              void> * = nullptr) {
  return std::distance(Range.begin(), Range.end());
}
 
namespace detail {
template <typename Range>
using check_has_free_function_size =
    decltype(adl_size(std::declval<Range &>()));
 
template <typename Range>
static constexpr bool HasFreeFunctionSize =
    is_detected<check_has_free_function_size, Range>::value;
} // namespace detail
 
/// Returns the size of the \p Range, i.e., the number of elements. This
/// implementation takes inspiration from `std::ranges::size` from C++20 and
/// delegates the size check to `adl_size` or `std::distance`, in this order of
/// preference. Unlike `llvm::size`, this function does *not* guarantee O(1)
/// running time, and is intended to be used in generic code that does not know
/// the exact range type.
template <typename R> constexpr size_t range_size(R &&Range) {
  if constexpr (detail::HasFreeFunctionSize<R>)
    return adl_size(Range);
  else
    return static_cast<size_t>(std::distance(adl_begin(Range), adl_end(Range)));
}
 
/// Provide wrappers to std::for_each which take ranges instead of having to
/// pass begin/end explicitly.
template <typename R, typename UnaryFunction>
UnaryFunction for_each(R &&Range, UnaryFunction F) {
  return std::for_each(adl_begin(Range), adl_end(Range), F);
}
 
/// Provide wrappers to std::all_of which take ranges instead of having to pass
/// begin/end explicitly.
template <typename R, typename UnaryPredicate>
bool all_of(R &&Range, UnaryPredicate P) {
  return std::all_of(adl_begin(Range), adl_end(Range), P);
}
 
/// Provide wrappers to std::any_of which take ranges instead of having to pass
/// begin/end explicitly.
template <typename R, typename UnaryPredicate>
bool any_of(R &&Range, UnaryPredicate P) {
  return std::any_of(adl_begin(Range), adl_end(Range), P);
}
 
/// Provide wrappers to std::none_of which take ranges instead of having to pass
/// begin/end explicitly.
template <typename R, typename UnaryPredicate>
bool none_of(R &&Range, UnaryPredicate P) {
  return std::none_of(adl_begin(Range), adl_end(Range), P);
}
 
/// Provide wrappers to std::find which take ranges instead of having to pass
/// begin/end explicitly.
template <typename R, typename T> auto find(R &&Range, const T &Val) {
  return std::find(adl_begin(Range), adl_end(Range), Val);
}
 
/// Provide wrappers to std::find_if which take ranges instead of having to pass
/// begin/end explicitly.
template <typename R, typename UnaryPredicate>
auto find_if(R &&Range, UnaryPredicate P) {
  return std::find_if(adl_begin(Range), adl_end(Range), P);
}
 
template <typename R, typename UnaryPredicate>
auto find_if_not(R &&Range, UnaryPredicate P) {
  return std::find_if_not(adl_begin(Range), adl_end(Range), P);
}
 
/// Provide wrappers to std::remove_if which take ranges instead of having to
/// pass begin/end explicitly.
template <typename R, typename UnaryPredicate>
auto remove_if(R &&Range, UnaryPredicate P) {
  return std::remove_if(adl_begin(Range), adl_end(Range), P);
}
 
/// Provide wrappers to std::copy_if which take ranges instead of having to
/// pass begin/end explicitly.
template <typename R, typename OutputIt, typename UnaryPredicate>
OutputIt copy_if(R &&Range, OutputIt Out, UnaryPredicate P) {
  return std::copy_if(adl_begin(Range), adl_end(Range), Out, P);
}
 
/// Return the single value in \p Range that satisfies
/// \p P(<member of \p Range> *, AllowRepeats)->T * returning nullptr
/// when no values or multiple values were found.
/// When \p AllowRepeats is true, multiple values that compare equal
/// are allowed.
template <typename T, typename R, typename Predicate>
T *find_singleton(R &&Range, Predicate P, bool AllowRepeats = false) {
  T *RC = nullptr;
  for (auto &&A : Range) {
    if (T *PRC = P(A, AllowRepeats)) {
      if (RC) {
        if (!AllowRepeats || PRC != RC)
          return nullptr;
      } else
        RC = PRC;
    }
  }
  return RC;
}
 
/// Return a pair consisting of the single value in \p Range that satisfies
/// \p P(<member of \p Range> *, AllowRepeats)->std::pair<T*, bool> returning
/// nullptr when no values or multiple values were found, and a bool indicating
/// whether multiple values were found to cause the nullptr.
/// When \p AllowRepeats is true, multiple values that compare equal are
/// allowed.  The predicate \p P returns a pair<T *, bool> where T is the
/// singleton while the bool indicates whether multiples have already been
/// found.  It is expected that first will be nullptr when second is true.
/// This allows using find_singleton_nested within the predicate \P.
template <typename T, typename R, typename Predicate>
std::pair<T *, bool> find_singleton_nested(R &&Range, Predicate P,
                                           bool AllowRepeats = false) {
  T *RC = nullptr;
  for (auto *A : Range) {
    std::pair<T *, bool> PRC = P(A, AllowRepeats);
    if (PRC.second) {
      assert(PRC.first == nullptr &&
             "Inconsistent return values in find_singleton_nested.");
      return PRC;
    }
    if (PRC.first) {
      if (RC) {
        if (!AllowRepeats || PRC.first != RC)
          return {nullptr, true};
      } else
        RC = PRC.first;
    }
  }
  return {RC, false};
}
 
template <typename R, typename OutputIt>
OutputIt copy(R &&Range, OutputIt Out) {
  return std::copy(adl_begin(Range), adl_end(Range), Out);
}
 
/// Provide wrappers to std::replace_copy_if which take ranges instead of having
/// to pass begin/end explicitly.
template <typename R, typename OutputIt, typename UnaryPredicate, typename T>
OutputIt replace_copy_if(R &&Range, OutputIt Out, UnaryPredicate P,
                         const T &NewValue) {
  return std::replace_copy_if(adl_begin(Range), adl_end(Range), Out, P,
                              NewValue);
}
 
/// Provide wrappers to std::replace_copy which take ranges instead of having to
/// pass begin/end explicitly.
template <typename R, typename OutputIt, typename T>
OutputIt replace_copy(R &&Range, OutputIt Out, const T &OldValue,
                      const T &NewValue) {
  return std::replace_copy(adl_begin(Range), adl_end(Range), Out, OldValue,
                           NewValue);
}
 
/// Provide wrappers to std::replace which take ranges instead of having to pass
/// begin/end explicitly.
template <typename R, typename T>
void replace(R &&Range, const T &OldValue, const T &NewValue) {
  std::replace(adl_begin(Range), adl_end(Range), OldValue, NewValue);
}
 
/// Provide wrappers to std::move which take ranges instead of having to
/// pass begin/end explicitly.
template <typename R, typename OutputIt>
OutputIt move(R &&Range, OutputIt Out) {
  return std::move(adl_begin(Range), adl_end(Range), Out);
}
 
namespace detail {
template <typename Range, typename Element>
using check_has_member_contains_t =
    decltype(std::declval<Range &>().contains(std::declval<const Element &>()));
 
template <typename Range, typename Element>
static constexpr bool HasMemberContains =
    is_detected<check_has_member_contains_t, Range, Element>::value;
 
template <typename Range, typename Element>
using check_has_member_find_t =
    decltype(std::declval<Range &>().find(std::declval<const Element &>()) !=
             std::declval<Range &>().end());
 
template <typename Range, typename Element>
static constexpr bool HasMemberFind =
    is_detected<check_has_member_find_t, Range, Element>::value;
 
} // namespace detail
 
/// Returns true if \p Element is found in \p Range. Delegates the check to
/// either `.contains(Element)`, `.find(Element)`, or `std::find`, in this
/// order of preference. This is intended as the canonical way to check if an
/// element exists in a range in generic code or range type that does not
/// expose a `.contains(Element)` member.
template <typename R, typename E>
bool is_contained(R &&Range, const E &Element) {
  if constexpr (detail::HasMemberContains<R, E>)
    return Range.contains(Element);
  else if constexpr (detail::HasMemberFind<R, E>)
    return Range.find(Element) != Range.end();
  else
    return std::find(adl_begin(Range), adl_end(Range), Element) !=
           adl_end(Range);
}
 
/// Returns true iff \p Element exists in \p Set. This overload takes \p Set as
/// an initializer list and is `constexpr`-friendly.
template <typename T, typename E>
constexpr bool is_contained(std::initializer_list<T> Set, const E &Element) {
  // TODO: Use std::find when we switch to C++20.
  for (const T &V : Set)
    if (V == Element)
      return true;
  return false;
}
 
/// Wrapper function around std::is_sorted to check if elements in a range \p R
/// are sorted with respect to a comparator \p C.
template <typename R, typename Compare> bool is_sorted(R &&Range, Compare C) {
  return std::is_sorted(adl_begin(Range), adl_end(Range), C);
}
 
/// Wrapper function around std::is_sorted to check if elements in a range \p R
/// are sorted in non-descending order.
template <typename R> bool is_sorted(R &&Range) {
  return std::is_sorted(adl_begin(Range), adl_end(Range));
}
 
/// Wrapper function around std::count to count the number of times an element
/// \p Element occurs in the given range \p Range.
template <typename R, typename E> auto count(R &&Range, const E &Element) {
  return std::count(adl_begin(Range), adl_end(Range), Element);
}
 
/// Wrapper function around std::count_if to count the number of times an
/// element satisfying a given predicate occurs in a range.
template <typename R, typename UnaryPredicate>
auto count_if(R &&Range, UnaryPredicate P) {
  return std::count_if(adl_begin(Range), adl_end(Range), P);
}
 
/// Wrapper function around std::transform to apply a function to a range and
/// store the result elsewhere.
template <typename R, typename OutputIt, typename UnaryFunction>
OutputIt transform(R &&Range, OutputIt d_first, UnaryFunction F) {
  return std::transform(adl_begin(Range), adl_end(Range), d_first, F);
}
 
/// Provide wrappers to std::partition which take ranges instead of having to
/// pass begin/end explicitly.
template <typename R, typename UnaryPredicate>
auto partition(R &&Range, UnaryPredicate P) {
  return std::partition(adl_begin(Range), adl_end(Range), P);
}
 
/// Provide wrappers to std::binary_search which take ranges instead of having
/// to pass begin/end explicitly.
template <typename R, typename T> auto binary_search(R &&Range, T &&Value) {
  return std::binary_search(adl_begin(Range), adl_end(Range),
                            std::forward<T>(Value));
}
 
template <typename R, typename T, typename Compare>
auto binary_search(R &&Range, T &&Value, Compare C) {
  return std::binary_search(adl_begin(Range), adl_end(Range),
                            std::forward<T>(Value), C);
}
 
/// Provide wrappers to std::lower_bound which take ranges instead of having to
/// pass begin/end explicitly.
template <typename R, typename T> auto lower_bound(R &&Range, T &&Value) {
  return std::lower_bound(adl_begin(Range), adl_end(Range),
                          std::forward<T>(Value));
}
 
template <typename R, typename T, typename Compare>
auto lower_bound(R &&Range, T &&Value, Compare C) {
  return std::lower_bound(adl_begin(Range), adl_end(Range),
                          std::forward<T>(Value), C);
}
 
/// Provide wrappers to std::upper_bound which take ranges instead of having to
/// pass begin/end explicitly.
template <typename R, typename T> auto upper_bound(R &&Range, T &&Value) {
  return std::upper_bound(adl_begin(Range), adl_end(Range),
                          std::forward<T>(Value));
}
 
template <typename R, typename T, typename Compare>
auto upper_bound(R &&Range, T &&Value, Compare C) {
  return std::upper_bound(adl_begin(Range), adl_end(Range),
                          std::forward<T>(Value), C);
}
 
/// Provide wrappers to std::min_element which take ranges instead of having to
/// pass begin/end explicitly.
template <typename R> auto min_element(R &&Range) {
  return std::min_element(adl_begin(Range), adl_end(Range));
}
 
template <typename R, typename Compare> auto min_element(R &&Range, Compare C) {
  return std::min_element(adl_begin(Range), adl_end(Range), C);
}
 
/// Provide wrappers to std::max_element which take ranges instead of having to
/// pass begin/end explicitly.
template <typename R> auto max_element(R &&Range) {
  return std::max_element(adl_begin(Range), adl_end(Range));
}
 
template <typename R, typename Compare> auto max_element(R &&Range, Compare C) {
  return std::max_element(adl_begin(Range), adl_end(Range), C);
}
 
/// Provide wrappers to std::mismatch which take ranges instead of having to
/// pass begin/end explicitly.
/// This function returns a pair of iterators for the first mismatching elements
/// from `R1` and `R2`. As an example, if:
///
/// R1 = [0, 1, 4, 6], R2 = [0, 1, 5, 6]
///
/// this function will return a pair of iterators, first pointing to R1[2] and
/// second pointing to R2[2].
template <typename R1, typename R2> auto mismatch(R1 &&Range1, R2 &&Range2) {
  return std::mismatch(adl_begin(Range1), adl_end(Range1), adl_begin(Range2),
                       adl_end(Range2));
}
 
template <typename R>
void stable_sort(R &&Range) {
  std::stable_sort(adl_begin(Range), adl_end(Range));
}
 
template <typename R, typename Compare>
void stable_sort(R &&Range, Compare C) {
  std::stable_sort(adl_begin(Range), adl_end(Range), C);
}
 
/// Binary search for the first iterator in a range where a predicate is false.
/// Requires that C is always true below some limit, and always false above it.
template <typename R, typename Predicate,
          typename Val = decltype(*adl_begin(std::declval<R>()))>
auto partition_point(R &&Range, Predicate P) {
  return std::partition_point(adl_begin(Range), adl_end(Range), P);
}
 
template<typename Range, typename Predicate>
auto unique(Range &&R, Predicate P) {
  return std::unique(adl_begin(R), adl_end(R), P);
}
 
/// Wrapper function around std::unique to allow calling unique on a
/// container without having to specify the begin/end iterators.
template <typename Range> auto unique(Range &&R) {
  return std::unique(adl_begin(R), adl_end(R));
}
 
/// Wrapper function around std::equal to detect if pair-wise elements between
/// two ranges are the same.
template <typename L, typename R> bool equal(L &&LRange, R &&RRange) {
  return std::equal(adl_begin(LRange), adl_end(LRange), adl_begin(RRange),
                    adl_end(RRange));
}
 
template <typename L, typename R, typename BinaryPredicate>
bool equal(L &&LRange, R &&RRange, BinaryPredicate P) {
  return std::equal(adl_begin(LRange), adl_end(LRange), adl_begin(RRange),
                    adl_end(RRange), P);
}
 
/// Returns true if all elements in Range are equal or when the Range is empty.
template <typename R> bool all_equal(R &&Range) {
  auto Begin = adl_begin(Range);
  auto End = adl_end(Range);
  return Begin == End || std::equal(Begin + 1, End, Begin);
}
 
/// Returns true if all Values in the initializer lists are equal or the list
// is empty.
template <typename T> bool all_equal(std::initializer_list<T> Values) {
  return all_equal<std::initializer_list<T>>(std::move(Values));
}
 
/// Provide a container algorithm similar to C++ Library Fundamentals v2's
/// `erase_if` which is equivalent to:
///
///   C.erase(remove_if(C, pred), C.end());
///
/// This version works for any container with an erase method call accepting
/// two iterators.
template <typename Container, typename UnaryPredicate>
void erase_if(Container &C, UnaryPredicate P) {
  C.erase(remove_if(C, P), C.end());
}
 
/// Wrapper function to remove a value from a container:
///
/// C.erase(remove(C.begin(), C.end(), V), C.end());
template <typename Container, typename ValueType>
void erase(Container &C, ValueType V) {
  C.erase(std::remove(C.begin(), C.end(), V), C.end());
}
 
/// Wrapper function to append range `R` to container `C`.
///
/// C.insert(C.end(), R.begin(), R.end());
template <typename Container, typename Range>
void append_range(Container &C, Range &&R) {
  C.insert(C.end(), adl_begin(R), adl_end(R));
}
 
/// Appends all `Values` to container `C`.
template <typename Container, typename... Args>
void append_values(Container &C, Args &&...Values) {
  C.reserve(range_size(C) + sizeof...(Args));
  // Append all values one by one.
  ((void)C.insert(C.end(), std::forward<Args>(Values)), ...);
}
 
/// Given a sequence container Cont, replace the range [ContIt, ContEnd) with
/// the range [ValIt, ValEnd) (which is not from the same container).
template<typename Container, typename RandomAccessIterator>
void replace(Container &Cont, typename Container::iterator ContIt,
             typename Container::iterator ContEnd, RandomAccessIterator ValIt,
             RandomAccessIterator ValEnd) {
  while (true) {
    if (ValIt == ValEnd) {
      Cont.erase(ContIt, ContEnd);
      return;
    } else if (ContIt == ContEnd) {
      Cont.insert(ContIt, ValIt, ValEnd);
      return;
    }
    *ContIt++ = *ValIt++;
  }
}
 
/// Given a sequence container Cont, replace the range [ContIt, ContEnd) with
/// the range R.
template<typename Container, typename Range = std::initializer_list<
                                 typename Container::value_type>>
void replace(Container &Cont, typename Container::iterator ContIt,
             typename Container::iterator ContEnd, Range R) {
  replace(Cont, ContIt, ContEnd, R.begin(), R.end());
}
 
/// An STL-style algorithm similar to std::for_each that applies a second
/// functor between every pair of elements.
///
/// This provides the control flow logic to, for example, print a
/// comma-separated list:
/// \code
///   interleave(names.begin(), names.end(),
///              [&](StringRef name) { os << name; },
///              [&] { os << ", "; });
/// \endcode
template <typename ForwardIterator, typename UnaryFunctor,
          typename NullaryFunctor,
          typename = std::enable_if_t<
              !std::is_constructible<StringRef, UnaryFunctor>::value &&
              !std::is_constructible<StringRef, NullaryFunctor>::value>>
inline void interleave(ForwardIterator begin, ForwardIterator end,
                       UnaryFunctor each_fn, NullaryFunctor between_fn) {
  if (begin == end)
    return;
  each_fn(*begin);
  ++begin;
  for (; begin != end; ++begin) {
    between_fn();
    each_fn(*begin);
  }
}
 
template <typename Container, typename UnaryFunctor, typename NullaryFunctor,
          typename = std::enable_if_t<
              !std::is_constructible<StringRef, UnaryFunctor>::value &&
              !std::is_constructible<StringRef, NullaryFunctor>::value>>
inline void interleave(const Container &c, UnaryFunctor each_fn,
                       NullaryFunctor between_fn) {
  interleave(adl_begin(c), adl_end(c), each_fn, between_fn);
}
 
/// Overload of interleave for the common case of string separator.
template <typename Container, typename UnaryFunctor, typename StreamT,
          typename T = detail::ValueOfRange<Container>>
inline void interleave(const Container &c, StreamT &os, UnaryFunctor each_fn,
                       const StringRef &separator) {
  interleave(adl_begin(c), adl_end(c), each_fn, [&] { os << separator; });
}
template <typename Container, typename StreamT,
          typename T = detail::ValueOfRange<Container>>
inline void interleave(const Container &c, StreamT &os,
                       const StringRef &separator) {
  interleave(
      c, os, [&](const T &a) { os << a; }, separator);
}
 
template <typename Container, typename UnaryFunctor, typename StreamT,
          typename T = detail::ValueOfRange<Container>>
inline void interleaveComma(const Container &c, StreamT &os,
                            UnaryFunctor each_fn) {
  interleave(c, os, each_fn, ", ");
}
template <typename Container, typename StreamT,
          typename T = detail::ValueOfRange<Container>>
inline void interleaveComma(const Container &c, StreamT &os) {
  interleaveComma(c, os, [&](const T &a) { os << a; });
}
 
//===----------------------------------------------------------------------===//
//     Extra additions to <memory>
//===----------------------------------------------------------------------===//
 
struct FreeDeleter {
  void operator()(void* v) {
    ::free(v);
  }
};
 
template<typename First, typename Second>
struct pair_hash {
  size_t operator()(const std::pair<First, Second> &P) const {
    return std::hash<First>()(P.first) * 31 + std::hash<Second>()(P.second);
  }
};
 
/// Binary functor that adapts to any other binary functor after dereferencing
/// operands.
template <typename T> struct deref {
  T func;
 
  // Could be further improved to cope with non-derivable functors and
  // non-binary functors (should be a variadic template member function
  // operator()).
  template <typename A, typename B> auto operator()(A &lhs, B &rhs) const {
    assert(lhs);
    assert(rhs);
    return func(*lhs, *rhs);
  }
};
 
namespace detail {
 
/// Tuple-like type for `zip_enumerator` dereference.
template <typename... Refs> struct enumerator_result;
 
template <typename... Iters>
using EnumeratorTupleType = enumerator_result<decltype(*declval<Iters>())...>;
 
/// Zippy iterator that uses the second iterator for comparisons. For the
/// increment to be safe, the second range has to be the shortest.
/// Returns `enumerator_result` on dereference to provide `.index()` and
/// `.value()` member functions.
/// Note: Because the dereference operator returns `enumerator_result` as a
/// value instead of a reference and does not strictly conform to the C++17's
/// definition of forward iterator. However, it satisfies all the
/// forward_iterator requirements that the `zip_common` and `zippy` depend on
/// and fully conforms to the C++20 definition of forward iterator.
/// This is similar to `std::vector<bool>::iterator` that returns bit reference
/// wrappers on dereference.
template <typename... Iters>
struct zip_enumerator : zip_common<zip_enumerator<Iters...>,
                                   EnumeratorTupleType<Iters...>, Iters...> {
  static_assert(sizeof...(Iters) >= 2, "Expected at least two iteratees");
  using zip_common<zip_enumerator<Iters...>, EnumeratorTupleType<Iters...>,
                   Iters...>::zip_common;
 
  bool operator==(const zip_enumerator &Other) const {
    return std::get<1>(this->iterators) == std::get<1>(Other.iterators);
  }
};
 
template <typename... Refs> struct enumerator_result<std::size_t, Refs...> {
  static constexpr std::size_t NumRefs = sizeof...(Refs);
  static_assert(NumRefs != 0);
  // `NumValues` includes the index.
  static constexpr std::size_t NumValues = NumRefs + 1;
 
  // Tuple type whose element types are references for each `Ref`.
  using range_reference_tuple = std::tuple<Refs...>;
  // Tuple type who elements are references to all values, including both
  // the index and `Refs` reference types.
  using value_reference_tuple = std::tuple<std::size_t, Refs...>;
 
  enumerator_result(std::size_t Index, Refs &&...Rs)
      : Idx(Index), Storage(std::forward<Refs>(Rs)...) {}
 
  /// Returns the 0-based index of the current position within the original
  /// input range(s).
  std::size_t index() const { return Idx; }
 
  /// Returns the value(s) for the current iterator. This does not include the
  /// index.
  decltype(auto) value() const {
    if constexpr (NumRefs == 1)
      return std::get<0>(Storage);
    else
      return Storage;
  }
 
  /// Returns the value at index `I`. This case covers the index.
  template <std::size_t I, typename = std::enable_if_t<I == 0>>
  friend std::size_t get(const enumerator_result &Result) {
    return Result.Idx;
  }
 
  /// Returns the value at index `I`. This case covers references to the
  /// iteratees.
  template <std::size_t I, typename = std::enable_if_t<I != 0>>
  friend decltype(auto) get(const enumerator_result &Result) {
    // Note: This is a separate function from the other `get`, instead of an
    // `if constexpr` case, to work around an MSVC 19.31.31XXX compiler
    // (Visual Studio 2022 17.1) return type deduction bug.
    return std::get<I - 1>(Result.Storage);
  }
 
  template <typename... Ts>
  friend bool operator==(const enumerator_result &Result,
                         const std::tuple<std::size_t, Ts...> &Other) {
    static_assert(NumRefs == sizeof...(Ts), "Size mismatch");
    if (Result.Idx != std::get<0>(Other))
      return false;
    return Result.is_value_equal(Other, std::make_index_sequence<NumRefs>{});
  }
 
private:
  template <typename Tuple, std::size_t... Idx>
  bool is_value_equal(const Tuple &Other, std::index_sequence<Idx...>) const {
    return ((std::get<Idx>(Storage) == std::get<Idx + 1>(Other)) && ...);
  }
 
  std::size_t Idx;
  // Make this tuple mutable to avoid casts that obfuscate const-correctness
  // issues. Const-correctness of references is taken care of by `zippy` that
  // defines const-non and const iterator types that will propagate down to
  // `enumerator_result`'s `Refs`.
  //  Note that unlike the results of `zip*` functions, `enumerate`'s result are
  //  supposed to be modifiable even when defined as
  // `const`.
  mutable range_reference_tuple Storage;
};
 
struct index_iterator
    : llvm::iterator_facade_base<index_iterator,
                                 std::random_access_iterator_tag, std::size_t> {
  index_iterator(std::size_t Index) : Index(Index) {}
 
  index_iterator &operator+=(std::ptrdiff_t N) {
    Index += N;
    return *this;
  }
 
  index_iterator &operator-=(std::ptrdiff_t N) {
    Index -= N;
    return *this;
  }
 
  std::ptrdiff_t operator-(const index_iterator &R) const {
    return Index - R.Index;
  }
 
  // Note: This dereference operator returns a value instead of a reference
  // and does not strictly conform to the C++17's definition of forward
  // iterator. However, it satisfies all the forward_iterator requirements
  // that the `zip_common` depends on and fully conforms to the C++20
  // definition of forward iterator.
  std::size_t operator*() const { return Index; }
 
  friend bool operator==(const index_iterator &Lhs, const index_iterator &Rhs) {
    return Lhs.Index == Rhs.Index;
  }
 
  friend bool operator<(const index_iterator &Lhs, const index_iterator &Rhs) {
    return Lhs.Index < Rhs.Index;
  }
 
private:
  std::size_t Index;
};
 
/// Infinite stream of increasing 0-based `size_t` indices.
struct index_stream {
  index_iterator begin() const { return {0}; }
  index_iterator end() const {
    // We approximate 'infinity' with the max size_t value, which should be good
    // enough to index over any container.
    return index_iterator{std::numeric_limits<std::size_t>::max()};
  }
};
 
} // end namespace detail
 
/// Increasing range of `size_t` indices.
class index_range {
  std::size_t Begin;
  std::size_t End;
 
public:
  index_range(std::size_t Begin, std::size_t End) : Begin(Begin), End(End) {}
  detail::index_iterator begin() const { return {Begin}; }
  detail::index_iterator end() const { return {End}; }
};
 
/// Given two or more input ranges, returns a new range whose values are
/// tuples (A, B, C, ...), such that A is the 0-based index of the item in the
/// sequence, and B, C, ..., are the values from the original input ranges. All
/// input ranges are required to have equal lengths. Note that the returned
/// iterator allows for the values (B, C, ...) to be modified.  Example:
///
/// ```c++
/// std::vector<char> Letters = {'A', 'B', 'C', 'D'};
/// std::vector<int> Vals = {10, 11, 12, 13};
///
/// for (auto [Index, Letter, Value] : enumerate(Letters, Vals)) {
///   printf("Item %zu - %c: %d\n", Index, Letter, Value);
///   Value -= 10;
/// }
/// ```
///
/// Output:
///   Item 0 - A: 10
///   Item 1 - B: 11
///   Item 2 - C: 12
///   Item 3 - D: 13
///
/// or using an iterator:
/// ```c++
/// for (auto it : enumerate(Vals)) {
///   it.value() += 10;
///   printf("Item %zu: %d\n", it.index(), it.value());
/// }
/// ```
///
/// Output:
///   Item 0: 20
///   Item 1: 21
///   Item 2: 22
///   Item 3: 23
///
template <typename FirstRange, typename... RestRanges>
auto enumerate(FirstRange &&First, RestRanges &&...Rest) {
  if constexpr (sizeof...(Rest) != 0) {
#ifndef NDEBUG
    // Note: Create an array instead of an initializer list to work around an
    // Apple clang 14 compiler bug.
    size_t sizes[] = {range_size(First), range_size(Rest)...};
    assert(all_equal(sizes) && "Ranges have different length");
#endif
  }
  using enumerator = detail::zippy<detail::zip_enumerator, detail::index_stream,
                                   FirstRange, RestRanges...>;
  return enumerator(detail::index_stream{}, std::forward<FirstRange>(First),
                    std::forward<RestRanges>(Rest)...);
}
 
namespace detail {
 
template <typename Predicate, typename... Args>
bool all_of_zip_predicate_first(Predicate &&P, Args &&...args) {
  auto z = zip(args...);
  auto it = z.begin();
  auto end = z.end();
  while (it != end) {
    if (!std::apply([&](auto &&...args) { return P(args...); }, *it))
      return false;
    ++it;
  }
  return it.all_equals(end);
}
 
// Just an adaptor to switch the order of argument and have the predicate before
// the zipped inputs.
template <typename... ArgsThenPredicate, size_t... InputIndexes>
bool all_of_zip_predicate_last(
    std::tuple<ArgsThenPredicate...> argsThenPredicate,
    std::index_sequence<InputIndexes...>) {
  auto constexpr OutputIndex =
      std::tuple_size<decltype(argsThenPredicate)>::value - 1;
  return all_of_zip_predicate_first(std::get<OutputIndex>(argsThenPredicate),
                             std::get<InputIndexes>(argsThenPredicate)...);
}
 
} // end namespace detail
 
/// Compare two zipped ranges using the provided predicate (as last argument).
/// Return true if all elements satisfy the predicate and false otherwise.
//  Return false if the zipped iterator aren't all at end (size mismatch).
template <typename... ArgsAndPredicate>
bool all_of_zip(ArgsAndPredicate &&...argsAndPredicate) {
  return detail::all_of_zip_predicate_last(
      std::forward_as_tuple(argsAndPredicate...),
      std::make_index_sequence<sizeof...(argsAndPredicate) - 1>{});
}
 
/// Return true if the sequence [Begin, End) has exactly N items. Runs in O(N)
/// time. Not meant for use with random-access iterators.
/// Can optionally take a predicate to filter lazily some items.
template <typename IterTy,
          typename Pred = bool (*)(const decltype(*std::declval<IterTy>()) &)>
bool hasNItems(
    IterTy &&Begin, IterTy &&End, unsigned N,
    Pred &&ShouldBeCounted =
        [](const decltype(*std::declval<IterTy>()) &) { return true; },
    std::enable_if_t<
        !std::is_base_of<std::random_access_iterator_tag,
                         typename std::iterator_traits<std::remove_reference_t<
                             decltype(Begin)>>::iterator_category>::value,
        void> * = nullptr) {
  for (; N; ++Begin) {
    if (Begin == End)
      return false; // Too few.
    N -= ShouldBeCounted(*Begin);
  }
  for (; Begin != End; ++Begin)
    if (ShouldBeCounted(*Begin))
      return false; // Too many.
  return true;
}
 
/// Return true if the sequence [Begin, End) has N or more items. Runs in O(N)
/// time. Not meant for use with random-access iterators.
/// Can optionally take a predicate to lazily filter some items.
template <typename IterTy,
          typename Pred = bool (*)(const decltype(*std::declval<IterTy>()) &)>
bool hasNItemsOrMore(
    IterTy &&Begin, IterTy &&End, unsigned N,
    Pred &&ShouldBeCounted =
        [](const decltype(*std::declval<IterTy>()) &) { return true; },
    std::enable_if_t<
        !std::is_base_of<std::random_access_iterator_tag,
                         typename std::iterator_traits<std::remove_reference_t<
                             decltype(Begin)>>::iterator_category>::value,
        void> * = nullptr) {
  for (; N; ++Begin) {
    if (Begin == End)
      return false; // Too few.
    N -= ShouldBeCounted(*Begin);
  }
  return true;
}
 
/// Returns true if the sequence [Begin, End) has N or less items. Can
/// optionally take a predicate to lazily filter some items.
template <typename IterTy,
          typename Pred = bool (*)(const decltype(*std::declval<IterTy>()) &)>
bool hasNItemsOrLess(
    IterTy &&Begin, IterTy &&End, unsigned N,
    Pred &&ShouldBeCounted = [](const decltype(*std::declval<IterTy>()) &) {
      return true;
    }) {
  assert(N != std::numeric_limits<unsigned>::max());
  return !hasNItemsOrMore(Begin, End, N + 1, ShouldBeCounted);
}
 
/// Returns true if the given container has exactly N items
template <typename ContainerTy> bool hasNItems(ContainerTy &&C, unsigned N) {
  return hasNItems(std::begin(C), std::end(C), N);
}
 
/// Returns true if the given container has N or more items
template <typename ContainerTy>
bool hasNItemsOrMore(ContainerTy &&C, unsigned N) {
  return hasNItemsOrMore(std::begin(C), std::end(C), N);
}
 
/// Returns true if the given container has N or less items
template <typename ContainerTy>
bool hasNItemsOrLess(ContainerTy &&C, unsigned N) {
  return hasNItemsOrLess(std::begin(C), std::end(C), N);
}
 
/// Returns a raw pointer that represents the same address as the argument.
///
/// This implementation can be removed once we move to C++20 where it's defined
/// as std::to_address().
///
/// The std::pointer_traits<>::to_address(p) variations of these overloads has
/// not been implemented.
template <class Ptr> auto to_address(const Ptr &P) { return P.operator->(); }
template <class T> constexpr T *to_address(T *P) { return P; }
 
// Detect incomplete types, relying on the fact that their size is unknown.
namespace detail {
template <typename T> using has_sizeof = decltype(sizeof(T));
} // namespace detail
 
/// Detects when type `T` is incomplete. This is true for forward declarations
/// and false for types with a full definition.
template <typename T>
constexpr bool is_incomplete_v = !is_detected<detail::has_sizeof, T>::value;
 
} // end namespace llvm
 
namespace std {
template <typename... Refs>
struct tuple_size<llvm::detail::enumerator_result<Refs...>>
    : std::integral_constant<std::size_t, sizeof...(Refs)> {};
 
template <std::size_t I, typename... Refs>
struct tuple_element<I, llvm::detail::enumerator_result<Refs...>>
    : std::tuple_element<I, std::tuple<Refs...>> {};
 
template <std::size_t I, typename... Refs>
struct tuple_element<I, const llvm::detail::enumerator_result<Refs...>>
    : std::tuple_element<I, std::tuple<Refs...>> {};
 
} // namespace std
 
#endif // LLVM_ADT_STLEXTRAS_H