snix/absl/container/internal/layout.h

// Copyright 2018 The Abseil Authors.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//      https://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
//
//                           MOTIVATION AND TUTORIAL
//
// If you want to put in a single heap allocation N doubles followed by M ints,
// it's easy if N and M are known at compile time.
//
//   struct S {
//     double a[N];
//     int b[M];
//   };
//
//   S* p = new S;
//
// But what if N and M are known only in run time? Class template Layout to the
// rescue! It's a portable generalization of the technique known as struct hack.
//
//   // This object will tell us everything we need to know about the memory
//   // layout of double[N] followed by int[M]. It's structurally identical to
//   // size_t[2] that stores N and M. It's very cheap to create.
//   const Layout<double, int> layout(N, M);
//
//   // Allocate enough memory for both arrays. `AllocSize()` tells us how much
//   // memory is needed. We are free to use any allocation function we want as
//   // long as it returns aligned memory.
//   std::unique_ptr<unsigned char[]> p(new unsigned char[layout.AllocSize()]);
//
//   // Obtain the pointer to the array of doubles.
//   // Equivalent to `reinterpret_cast<double*>(p.get())`.
//   //
//   // We could have written layout.Pointer<0>(p) instead. If all the types are
//   // unique you can use either form, but if some types are repeated you must
//   // use the index form.
//   double* a = layout.Pointer<double>(p.get());
//
//   // Obtain the pointer to the array of ints.
//   // Equivalent to `reinterpret_cast<int*>(p.get() + N * 8)`.
//   int* b = layout.Pointer<int>(p);
//
// If we are unable to specify sizes of all fields, we can pass as many sizes as
// we can to `Partial()`. In return, it'll allow us to access the fields whose
// locations and sizes can be computed from the provided information.
// `Partial()` comes in handy when the array sizes are embedded into the
// allocation.
//
//   // size_t[1] containing N, size_t[1] containing M, double[N], int[M].
//   using L = Layout<size_t, size_t, double, int>;
//
//   unsigned char* Allocate(size_t n, size_t m) {
//     const L layout(1, 1, n, m);
//     unsigned char* p = new unsigned char[layout.AllocSize()];
//     *layout.Pointer<0>(p) = n;
//     *layout.Pointer<1>(p) = m;
//     return p;
//   }
//
//   void Use(unsigned char* p) {
//     // First, extract N and M.
//     // Specify that the first array has only one element. Using `prefix` we
//     // can access the first two arrays but not more.
//     constexpr auto prefix = L::Partial(1);
//     size_t n = *prefix.Pointer<0>(p);
//     size_t m = *prefix.Pointer<1>(p);
//
//     // Now we can get pointers to the payload.
//     const L layout(1, 1, n, m);
//     double* a = layout.Pointer<double>(p);
//     int* b = layout.Pointer<int>(p);
//   }
//
// The layout we used above combines fixed-size with dynamically-sized fields.
// This is quite common. Layout is optimized for this use case and generates
// optimal code. All computations that can be performed at compile time are
// indeed performed at compile time.
//
// Efficiency tip: The order of fields matters. In `Layout<T1, ..., TN>` try to
// ensure that `alignof(T1) >= ... >= alignof(TN)`. This way you'll have no
// padding in between arrays.
//
// You can manually override the alignment of an array by wrapping the type in
// `Aligned<T, N>`. `Layout<..., Aligned<T, N>, ...>` has exactly the same API
// and behavior as `Layout<..., T, ...>` except that the first element of the
// array of `T` is aligned to `N` (the rest of the elements follow without
// padding). `N` cannot be less than `alignof(T)`.
//
// `AllocSize()` and `Pointer()` are the most basic methods for dealing with
// memory layouts. Check out the reference or code below to discover more.
//
//                            EXAMPLE
//
//   // Immutable move-only string with sizeof equal to sizeof(void*). The
//   // string size and the characters are kept in the same heap allocation.
//   class CompactString {
//    public:
//     CompactString(const char* s = "") {
//       const size_t size = strlen(s);
//       // size_t[1] followed by char[size + 1].
//       const L layout(1, size + 1);
//       p_.reset(new unsigned char[layout.AllocSize()]);
//       // If running under ASAN, mark the padding bytes, if any, to catch
//       // memory errors.
//       layout.PoisonPadding(p_.get());
//       // Store the size in the allocation.
//       *layout.Pointer<size_t>(p_.get()) = size;
//       // Store the characters in the allocation.
//       memcpy(layout.Pointer<char>(p_.get()), s, size + 1);
//     }
//
//     size_t size() const {
//       // Equivalent to reinterpret_cast<size_t&>(*p).
//       return *L::Partial().Pointer<size_t>(p_.get());
//     }
//
//     const char* c_str() const {
//       // Equivalent to reinterpret_cast<char*>(p.get() + sizeof(size_t)).
//       // The argument in Partial(1) specifies that we have size_t[1] in front
//       // of the characters.
//       return L::Partial(1).Pointer<char>(p_.get());
//     }
//
//    private:
//     // Our heap allocation contains a size_t followed by an array of chars.
//     using L = Layout<size_t, char>;
//     std::unique_ptr<unsigned char[]> p_;
//   };
//
//   int main() {
//     CompactString s = "hello";
//     assert(s.size() == 5);
//     assert(strcmp(s.c_str(), "hello") == 0);
//   }
//
//                               DOCUMENTATION
//
// The interface exported by this file consists of:
// - class `Layout<>` and its public members.
// - The public members of class `internal_layout::LayoutImpl<>`. That class
//   isn't intended to be used directly, and its name and template parameter
//   list are internal implementation details, but the class itself provides
//   most of the functionality in this file. See comments on its members for
//   detailed documentation.
//
// `Layout<T1,... Tn>::Partial(count1,..., countm)` (where `m` <= `n`) returns a
// `LayoutImpl<>` object. `Layout<T1,..., Tn> layout(count1,..., countn)`
// creates a `Layout` object, which exposes the same functionality by inheriting
// from `LayoutImpl<>`.

#ifndef ABSL_CONTAINER_INTERNAL_LAYOUT_H_
#define ABSL_CONTAINER_INTERNAL_LAYOUT_H_

#include <assert.h>
#include <stddef.h>
#include <stdint.h>
#include <ostream>
#include <string>
#include <tuple>
#include <type_traits>
#include <typeinfo>
#include <utility>

#ifdef ADDRESS_SANITIZER
#include <sanitizer/asan_interface.h>
#endif

#include "absl/meta/type_traits.h"
#include "absl/strings/str_cat.h"
#include "absl/types/span.h"
#include "absl/utility/utility.h"

#if defined(__GXX_RTTI)
#define ABSL_INTERNAL_HAS_CXA_DEMANGLE
#endif

#ifdef ABSL_INTERNAL_HAS_CXA_DEMANGLE
#include <cxxabi.h>
#endif

namespace absl {
namespace container_internal {

// A type wrapper that instructs `Layout` to use the specific alignment for the
// array. `Layout<..., Aligned<T, N>, ...>` has exactly the same API
// and behavior as `Layout<..., T, ...>` except that the first element of the
// array of `T` is aligned to `N` (the rest of the elements follow without
// padding).
//
// Requires: `N >= alignof(T)` and `N` is a power of 2.
template <class T, size_t N>
struct Aligned;

namespace internal_layout {

template <class T>
struct NotAligned {};

template <class T, size_t N>
struct NotAligned<const Aligned<T, N>> {
  static_assert(sizeof(T) == 0, "Aligned<T, N> cannot be const-qualified");
};

template <size_t>
using IntToSize = size_t;

template <class>
using TypeToSize = size_t;

template <class T>
struct Type : NotAligned<T> {
  using type = T;
};

template <class T, size_t N>
struct Type<Aligned<T, N>> {
  using type = T;
};

template <class T>
struct SizeOf : NotAligned<T>, std::integral_constant<size_t, sizeof(T)> {};

template <class T, size_t N>
struct SizeOf<Aligned<T, N>> : std::integral_constant<size_t, sizeof(T)> {};

// Note: workaround for https://gcc.gnu.org/PR88115
template <class T>
struct AlignOf : NotAligned<T> {
  static constexpr size_t value = alignof(T);
};

template <class T, size_t N>
struct AlignOf<Aligned<T, N>> {
  static_assert(N % alignof(T) == 0,
                "Custom alignment can't be lower than the type's alignment");
  static constexpr size_t value = N;
};

// Does `Ts...` contain `T`?
template <class T, class... Ts>
using Contains = absl::disjunction<std::is_same<T, Ts>...>;

template <class From, class To>
using CopyConst =
    typename std::conditional<std::is_const<From>::value, const To, To>::type;

// Note: We're not qualifying this with absl:: because it doesn't compile under
// MSVC.
template <class T>
using SliceType = Span<T>;

// This namespace contains no types. It prevents functions defined in it from
// being found by ADL.
namespace adl_barrier {

template <class Needle, class... Ts>
constexpr size_t Find(Needle, Needle, Ts...) {
  static_assert(!Contains<Needle, Ts...>(), "Duplicate element type");
  return 0;
}

template <class Needle, class T, class... Ts>
constexpr size_t Find(Needle, T, Ts...) {
  return adl_barrier::Find(Needle(), Ts()...) + 1;
}

constexpr bool IsPow2(size_t n) { return !(n & (n - 1)); }

// Returns `q * m` for the smallest `q` such that `q * m >= n`.
// Requires: `m` is a power of two. It's enforced by IsLegalElementType below.
constexpr size_t Align(size_t n, size_t m) { return (n + m - 1) & ~(m - 1); }

constexpr size_t Min(size_t a, size_t b) { return b < a ? b : a; }

constexpr size_t Max(size_t a) { return a; }

template <class... Ts>
constexpr size_t Max(size_t a, size_t b, Ts... rest) {
  return adl_barrier::Max(b < a ? a : b, rest...);
}

template <class T>
std::string TypeName() {
  std::string out;
  int status = 0;
  char* demangled = nullptr;
#ifdef ABSL_INTERNAL_HAS_CXA_DEMANGLE
  demangled = abi::__cxa_demangle(typeid(T).name(), nullptr, nullptr, &status);
#endif
  if (status == 0 && demangled != nullptr) {  // Demangling succeeded.
    absl::StrAppend(&out, "<", demangled, ">");
    free(demangled);
  } else {
#if defined(__GXX_RTTI) || defined(_CPPRTTI)
    absl::StrAppend(&out, "<", typeid(T).name(), ">");
#endif
  }
  return out;
}

}  // namespace adl_barrier

template <bool C>
using EnableIf = typename std::enable_if<C, int>::type;

// Can `T` be a template argument of `Layout`?
template <class T>
using IsLegalElementType = std::integral_constant<
    bool, !std::is_reference<T>::value && !std::is_volatile<T>::value &&
              !std::is_reference<typename Type<T>::type>::value &&
              !std::is_volatile<typename Type<T>::type>::value &&
              adl_barrier::IsPow2(AlignOf<T>::value)>;

template <class Elements, class SizeSeq, class OffsetSeq>
class LayoutImpl;

// Public base class of `Layout` and the result type of `Layout::Partial()`.
//
// `Elements...` contains all template arguments of `Layout` that created this
// instance.
//
// `SizeSeq...` is `[0, NumSizes)` where `NumSizes` is the number of arguments
// passed to `Layout::Partial()` or `Layout::Layout()`.
//
// `OffsetSeq...` is `[0, NumOffsets)` where `NumOffsets` is
// `Min(sizeof...(Elements), NumSizes + 1)` (the number of arrays for which we
// can compute offsets).
template <class... Elements, size_t... SizeSeq, size_t... OffsetSeq>
class LayoutImpl<std::tuple<Elements...>, absl::index_sequence<SizeSeq...>,
                 absl::index_sequence<OffsetSeq...>> {
 private:
  static_assert(sizeof...(Elements) > 0, "At least one field is required");
  static_assert(absl::conjunction<IsLegalElementType<Elements>...>::value,
                "Invalid element type (see IsLegalElementType)");

  enum {
    NumTypes = sizeof...(Elements),
    NumSizes = sizeof...(SizeSeq),
    NumOffsets = sizeof...(OffsetSeq),
  };

  // These are guaranteed by `Layout`.
  static_assert(NumOffsets == adl_barrier::Min(NumTypes, NumSizes + 1),
                "Internal error");
  static_assert(NumTypes > 0, "Internal error");

  // Returns the index of `T` in `Elements...`. Results in a compilation error
  // if `Elements...` doesn't contain exactly one instance of `T`.
  template <class T>
  static constexpr size_t ElementIndex() {
    static_assert(Contains<Type<T>, Type<typename Type<Elements>::type>...>(),
                  "Type not found");
    return adl_barrier::Find(Type<T>(),
                             Type<typename Type<Elements>::type>()...);
  }

  template <size_t N>
  using ElementAlignment =
      AlignOf<typename std::tuple_element<N, std::tuple<Elements...>>::type>;

 public:
  // Element types of all arrays packed in a tuple.
  using ElementTypes = std::tuple<typename Type<Elements>::type...>;

  // Element type of the Nth array.
  template <size_t N>
  using ElementType = typename std::tuple_element<N, ElementTypes>::type;

  constexpr explicit LayoutImpl(IntToSize<SizeSeq>... sizes)
      : size_{sizes...} {}

  // Alignment of the layout, equal to the strictest alignment of all elements.
  // All pointers passed to the methods of layout must be aligned to this value.
  static constexpr size_t Alignment() {
    return adl_barrier::Max(AlignOf<Elements>::value...);
  }

  // Offset in bytes of the Nth array.
  //
  //   // int[3], 4 bytes of padding, double[4].
  //   Layout<int, double> x(3, 4);
  //   assert(x.Offset<0>() == 0);   // The ints starts from 0.
  //   assert(x.Offset<1>() == 16);  // The doubles starts from 16.
  //
  // Requires: `N <= NumSizes && N < sizeof...(Ts)`.
  template <size_t N, EnableIf<N == 0> = 0>
  constexpr size_t Offset() const {
    return 0;
  }

  template <size_t N, EnableIf<N != 0> = 0>
  constexpr size_t Offset() const {
    static_assert(N < NumOffsets, "Index out of bounds");
    return adl_barrier::Align(
        Offset<N - 1>() + SizeOf<ElementType<N - 1>>() * size_[N - 1],
        ElementAlignment<N>::value);
  }

  // Offset in bytes of the array with the specified element type. There must
  // be exactly one such array and its zero-based index must be at most
  // `NumSizes`.
  //
  //   // int[3], 4 bytes of padding, double[4].
  //   Layout<int, double> x(3, 4);
  //   assert(x.Offset<int>() == 0);      // The ints starts from 0.
  //   assert(x.Offset<double>() == 16);  // The doubles starts from 16.
  template <class T>
  constexpr size_t Offset() const {
    return Offset<ElementIndex<T>()>();
  }

  // Offsets in bytes of all arrays for which the offsets are known.
  constexpr std::array<size_t, NumOffsets> Offsets() const {
    return {{Offset<OffsetSeq>()...}};
  }

  // The number of elements in the Nth array. This is the Nth argument of
  // `Layout::Partial()` or `Layout::Layout()` (zero-based).
  //
  //   // int[3], 4 bytes of padding, double[4].
  //   Layout<int, double> x(3, 4);
  //   assert(x.Size<0>() == 3);
  //   assert(x.Size<1>() == 4);
  //
  // Requires: `N < NumSizes`.
  template <size_t N>
  constexpr size_t Size() const {
    static_assert(N < NumSizes, "Index out of bounds");
    return size_[N];
  }

  // The number of elements in the array with the specified element type.
  // There must be exactly one such array and its zero-based index must be
  // at most `NumSizes`.
  //
  //   // int[3], 4 bytes of padding, double[4].
  //   Layout<int, double> x(3, 4);
  //   assert(x.Size<int>() == 3);
  //   assert(x.Size<double>() == 4);
  template <class T>
  constexpr size_t Size() const {
    return Size<ElementIndex<T>()>();
  }

  // The number of elements of all arrays for which they are known.
  constexpr std::array<size_t, NumSizes> Sizes() const {
    return {{Size<SizeSeq>()...}};
  }

  // Pointer to the beginning of the Nth array.
  //
  // `Char` must be `[const] [signed|unsigned] char`.
  //
  //   // int[3], 4 bytes of padding, double[4].
  //   Layout<int, double> x(3, 4);
  //   unsigned char* p = new unsigned char[x.AllocSize()];
  //   int* ints = x.Pointer<0>(p);
  //   double* doubles = x.Pointer<1>(p);
  //
  // Requires: `N <= NumSizes && N < sizeof...(Ts)`.
  // Requires: `p` is aligned to `Alignment()`.
  template <size_t N, class Char>
  CopyConst<Char, ElementType<N>>* Pointer(Char* p) const {
    using C = typename std::remove_const<Char>::type;
    static_assert(
        std::is_same<C, char>() || std::is_same<C, unsigned char>() ||
            std::is_same<C, signed char>(),
        "The argument must be a pointer to [const] [signed|unsigned] char");
    constexpr size_t alignment = Alignment();
    (void)alignment;
    assert(reinterpret_cast<uintptr_t>(p) % alignment == 0);
    return reinterpret_cast<CopyConst<Char, ElementType<N>>*>(p + Offset<N>());
  }

  // Pointer to the beginning of the array with the specified element type.
  // There must be exactly one such array and its zero-based index must be at
  // most `NumSizes`.
  //
  // `Char` must be `[const] [signed|unsigned] char`.
  //
  //   // int[3], 4 bytes of padding, double[4].
  //   Layout<int, double> x(3, 4);
  //   unsigned char* p = new unsigned char[x.AllocSize()];
  //   int* ints = x.Pointer<int>(p);
  //   double* doubles = x.Pointer<double>(p);
  //
  // Requires: `p` is aligned to `Alignment()`.
  template <class T, class Char>
  CopyConst<Char, T>* Pointer(Char* p) const {
    return Pointer<ElementIndex<T>()>(p);
  }

  // Pointers to all arrays for which pointers are known.
  //
  // `Char` must be `[const] [signed|unsigned] char`.
  //
  //   // int[3], 4 bytes of padding, double[4].
  //   Layout<int, double> x(3, 4);
  //   unsigned char* p = new unsigned char[x.AllocSize()];
  //
  //   int* ints;
  //   double* doubles;
  //   std::tie(ints, doubles) = x.Pointers(p);
  //
  // Requires: `p` is aligned to `Alignment()`.
  //
  // Note: We're not using ElementType alias here because it does not compile
  // under MSVC.
  template <class Char>
  std::tuple<CopyConst<
      Char, typename std::tuple_element<OffsetSeq, ElementTypes>::type>*...>
  Pointers(Char* p) const {
    return std::tuple<CopyConst<Char, ElementType<OffsetSeq>>*...>(
        Pointer<OffsetSeq>(p)...);
  }

  // The Nth array.
  //
  // `Char` must be `[const] [signed|unsigned] char`.
  //
  //   // int[3], 4 bytes of padding, double[4].
  //   Layout<int, double> x(3, 4);
  //   unsigned char* p = new unsigned char[x.AllocSize()];
  //   Span<int> ints = x.Slice<0>(p);
  //   Span<double> doubles = x.Slice<1>(p);
  //
  // Requires: `N < NumSizes`.
  // Requires: `p` is aligned to `Alignment()`.
  template <size_t N, class Char>
  SliceType<CopyConst<Char, ElementType<N>>> Slice(Char* p) const {
    return SliceType<CopyConst<Char, ElementType<N>>>(Pointer<N>(p), Size<N>());
  }

  // The array with the specified element type. There must be exactly one
  // such array and its zero-based index must be less than `NumSizes`.
  //
  // `Char` must be `[const] [signed|unsigned] char`.
  //
  //   // int[3], 4 bytes of padding, double[4].
  //   Layout<int, double> x(3, 4);
  //   unsigned char* p = new unsigned char[x.AllocSize()];
  //   Span<int> ints = x.Slice<int>(p);
  //   Span<double> doubles = x.Slice<double>(p);
  //
  // Requires: `p` is aligned to `Alignment()`.
  template <class T, class Char>
  SliceType<CopyConst<Char, T>> Slice(Char* p) const {
    return Slice<ElementIndex<T>()>(p);
  }

  // All arrays with known sizes.
  //
  // `Char` must be `[const] [signed|unsigned] char`.
  //
  //   // int[3], 4 bytes of padding, double[4].
  //   Layout<int, double> x(3, 4);
  //   unsigned char* p = new unsigned char[x.AllocSize()];
  //
  //   Span<int> ints;
  //   Span<double> doubles;
  //   std::tie(ints, doubles) = x.Slices(p);
  //
  // Requires: `p` is aligned to `Alignment()`.
  //
  // Note: We're not using ElementType alias here because it does not compile
  // under MSVC.
  template <class Char>
  std::tuple<SliceType<CopyConst<
      Char, typename std::tuple_element<SizeSeq, ElementTypes>::type>>...>
  Slices(Char* p) const {
    // Workaround for https://gcc.gnu.org/bugzilla/show_bug.cgi?id=63875 (fixed
    // in 6.1).
    (void)p;
    return std::tuple<SliceType<CopyConst<Char, ElementType<SizeSeq>>>...>(
        Slice<SizeSeq>(p)...);
  }

  // The size of the allocation that fits all arrays.
  //
  //   // int[3], 4 bytes of padding, double[4].
  //   Layout<int, double> x(3, 4);
  //   unsigned char* p = new unsigned char[x.AllocSize()];  // 48 bytes
  //
  // Requires: `NumSizes == sizeof...(Ts)`.
  constexpr size_t AllocSize() const {
    static_assert(NumTypes == NumSizes, "You must specify sizes of all fields");
    return Offset<NumTypes - 1>() +
           SizeOf<ElementType<NumTypes - 1>>() * size_[NumTypes - 1];
  }

  // If built with --config=asan, poisons padding bytes (if any) in the
  // allocation. The pointer must point to a memory block at least
  // `AllocSize()` bytes in length.
  //
  // `Char` must be `[const] [signed|unsigned] char`.
  //
  // Requires: `p` is aligned to `Alignment()`.
  template <class Char, size_t N = NumOffsets - 1, EnableIf<N == 0> = 0>
  void PoisonPadding(const Char* p) const {
    Pointer<0>(p);  // verify the requirements on `Char` and `p`
  }

  template <class Char, size_t N = NumOffsets - 1, EnableIf<N != 0> = 0>
  void PoisonPadding(const Char* p) const {
    static_assert(N < NumOffsets, "Index out of bounds");
    (void)p;
#ifdef ADDRESS_SANITIZER
    PoisonPadding<Char, N - 1>(p);
    // The `if` is an optimization. It doesn't affect the observable behaviour.
    if (ElementAlignment<N - 1>::value % ElementAlignment<N>::value) {
      size_t start =
          Offset<N - 1>() + SizeOf<ElementType<N - 1>>() * size_[N - 1];
      ASAN_POISON_MEMORY_REGION(p + start, Offset<N>() - start);
    }
#endif
  }

  // Human-readable description of the memory layout. Useful for debugging.
  // Slow.
  //
  //   // char[5], 3 bytes of padding, int[3], 4 bytes of padding, followed
  //   // by an unknown number of doubles.
  //   auto x = Layout<char, int, double>::Partial(5, 3);
  //   assert(x.DebugString() ==
  //          "@0<char>(1)[5]; @8<int>(4)[3]; @24<double>(8)");
  //
  // Each field is in the following format: @offset<type>(sizeof)[size] (<type>
  // may be missing depending on the target platform). For example,
  // @8<int>(4)[3] means that at offset 8 we have an array of ints, where each
  // int is 4 bytes, and we have 3 of those ints. The size of the last field may
  // be missing (as in the example above). Only fields with known offsets are
  // described. Type names may differ across platforms: one compiler might
  // produce "unsigned*" where another produces "unsigned int *".
  std::string DebugString() const {
    const auto offsets = Offsets();
    const size_t sizes[] = {SizeOf<ElementType<OffsetSeq>>()...};
    const std::string types[] = {
        adl_barrier::TypeName<ElementType<OffsetSeq>>()...};
    std::string res = absl::StrCat("@0", types[0], "(", sizes[0], ")");
    for (size_t i = 0; i != NumOffsets - 1; ++i) {
      absl::StrAppend(&res, "[", size_[i], "]; @", offsets[i + 1], types[i + 1],
                      "(", sizes[i + 1], ")");
    }
    // NumSizes is a constant that may be zero. Some compilers cannot see that
    // inside the if statement "size_[NumSizes - 1]" must be valid.
    int last = static_cast<int>(NumSizes) - 1;
    if (NumTypes == NumSizes && last >= 0) {
      absl::StrAppend(&res, "[", size_[last], "]");
    }
    return res;
  }

 private:
  // Arguments of `Layout::Partial()` or `Layout::Layout()`.
  size_t size_[NumSizes > 0 ? NumSizes : 1];
};

template <size_t NumSizes, class... Ts>
using LayoutType = LayoutImpl<
    std::tuple<Ts...>, absl::make_index_sequence<NumSizes>,
    absl::make_index_sequence<adl_barrier::Min(sizeof...(Ts), NumSizes + 1)>>;

}  // namespace internal_layout

// Descriptor of arrays of various types and sizes laid out in memory one after
// another. See the top of the file for documentation.
//
// Check out the public API of internal_layout::LayoutImpl above. The type is
// internal to the library but its methods are public, and they are inherited
// by `Layout`.
template <class... Ts>
class Layout : public internal_layout::LayoutType<sizeof...(Ts), Ts...> {
 public:
  static_assert(sizeof...(Ts) > 0, "At least one field is required");
  static_assert(
      absl::conjunction<internal_layout::IsLegalElementType<Ts>...>::value,
      "Invalid element type (see IsLegalElementType)");

  // The result type of `Partial()` with `NumSizes` arguments.
  template <size_t NumSizes>
  using PartialType = internal_layout::LayoutType<NumSizes, Ts...>;

  // `Layout` knows the element types of the arrays we want to lay out in
  // memory but not the number of elements in each array.
  // `Partial(size1, ..., sizeN)` allows us to specify the latter. The
  // resulting immutable object can be used to obtain pointers to the
  // individual arrays.
  //
  // It's allowed to pass fewer array sizes than the number of arrays. E.g.,
  // if all you need is to the offset of the second array, you only need to
  // pass one argument -- the number of elements in the first array.
  //
  //   // int[3] followed by 4 bytes of padding and an unknown number of
  //   // doubles.
  //   auto x = Layout<int, double>::Partial(3);
  //   // doubles start at byte 16.
  //   assert(x.Offset<1>() == 16);
  //
  // If you know the number of elements in all arrays, you can still call
  // `Partial()` but it's more convenient to use the constructor of `Layout`.
  //
  //   Layout<int, double> x(3, 5);
  //
  // Note: The sizes of the arrays must be specified in number of elements,
  // not in bytes.
  //
  // Requires: `sizeof...(Sizes) <= sizeof...(Ts)`.
  // Requires: all arguments are convertible to `size_t`.
  template <class... Sizes>
  static constexpr PartialType<sizeof...(Sizes)> Partial(Sizes&&... sizes) {
    static_assert(sizeof...(Sizes) <= sizeof...(Ts), "");
    return PartialType<sizeof...(Sizes)>(absl::forward<Sizes>(sizes)...);
  }

  // Creates a layout with the sizes of all arrays specified. If you know
  // only the sizes of the first N arrays (where N can be zero), you can use
  // `Partial()` defined above. The constructor is essentially equivalent to
  // calling `Partial()` and passing in all array sizes; the constructor is
  // provided as a convenient abbreviation.
  //
  // Note: The sizes of the arrays must be specified in number of elements,
  // not in bytes.
  constexpr explicit Layout(internal_layout::TypeToSize<Ts>... sizes)
      : internal_layout::LayoutType<sizeof...(Ts), Ts...>(sizes...) {}
};

}  // namespace container_internal
}  // namespace absl

#endif  // ABSL_CONTAINER_INTERNAL_LAYOUT_H_