What has my Standard Library Done for me Lately? - the boolean specialization of std::vector

This short post explores the std::vector<bool> specialization of std::vector in the C++ standard library. Specifically, we look at how the standard library writers achieve a space-optimized implementation without sacrificing (most) of the semantics we expect from standard containers, and why this optimization sometimes leads to unexpected behavior.


The boolean specialization of std::vector (aka std::vector<bool>) has received criticism from the C++ community for years. I will leave the debate over the utility of the container to more experienced developers, but I would still like to understand the source of the “weirdness” associated with std::vector<bool>. To that end, we’ll first look at some examples of std::vector<bool>’s misbehavior before diving into the source to determine where it originates.

In his classic Effective STL, Scott Meyers advises readers to avoid use of std::vector<bool> because it is not a proper STL container. He demonstrates this idea with a simple example:

std::vector<int> v{1, 2, 3};
int* i = &v[0];

This is perfectly valid C++. However, by replacing int with bool, we produce code that no longer compiles:

std::vector<bool> v{true, true, false};
bool* i = &v[0];

In this instance, the compiler will report that we cannot assign the result of &v[0] to bool* because the types are incompatible. With this example, Meyers demonstrates that std::vector<bool> does not support some of the semantics we expect from an STL container - namely we cannot get the location of an element (its address) in a familiar way.

As a more realistic example, suppose that we want to write our own version of the STL’s std::for_each. Naturally, this implementation must be generic over the type of the element in the container. If we constrain the container type to be std::vector, our implementation might resemble the following:

template <typename T, typename F>
auto for_each(std::vector<T> const& container, F func) -> void {
  for (auto& item : container) {

This algorithm works fine for nearly all types for the contained elements. For int, it works as expected:

auto main() -> int {
  std::vector<int> container{1, 2, 3};
  for_each(container, [](int const& i) { printf("%d\n", i); });



However, this code breaks when we attempt to pass a std::vector<bool> to our algorithm. The version of main() below

auto main() -> int {
  std::vector<bool> container{true, true, false};
  for_each(container, [](bool const& i){ printf("%d\n", i); });

produces the following error message (on GCC x86-64 12.2):

<source>: In instantiation of 'void for_each(const std::vector<T>&, F) [with T = bool; F = main()::<lambda(const int&)>]':
<source>:13:13:   required from here
<source>:6:5: error: cannot bind non-const lvalue reference of type 'bool&' to an rvalue of type 'std::_Bit_const_iterator::const_reference' {aka 'bool'}
    6 |     for (auto& item : container) {
      |     ^~~
Compiler returned: 1

Again we see that the error stems from the fact that the range-for construct expects a bool& type, but the container’s iterator is failing to provide this type and is instead returning a std::_Bit_const_iterator::const_reference type. Next we’ll look at the implementation of a simplified version of std::vector<bool> to understand why this type-mismatch occurs.

A Naive std::vector<bool>

Before working on our implementation of std::vector<bool>, let us first consider why this specialization is provided in the first place. Why not just let bool follow the same rules as all of the other types?

With most compilers and standard library implementations, the size of a single bool object is 1 byte (8 bits). With GCC, the code

printf("%zu\n", sizeof(bool));

prints the value 1. Furthermore, in the implementation of std::vector, each item in the container is allocated its own storage area in a contiguous memory region (subject to alignment constraints). Together, these two facts imply that for a non-specialized implementation of std::vector<bool>, each boolean element takes 1 byte.

It is easy to see that such an implementation is space-efficient. Each boolean element consumes a full byte of space, when we know that the information contained in a bool can be expressed by a single bit.

However, there is no primitive type in C++ that has a storage requirement that is smaller than a single byte. For this reason, C++ standard authors advocate a clever implementation that introduces some “hacks” to compress the space allocated to each element of the std::vector down to a single bit.

A More Efficient Implementation

To demonstrate a boolean std::vector specialization in the spirit of those offered by the C++ standard library, we’ll write our own BitVector type. The complete implementation is here. Note that this implementation is considerably stripped-down and does not offer the full interface provided by std::vector. furthermore, it is implemented in a style that would never be utilized within the standard library (for instance, it uses std::unique_ptr internally). This is by design, as I believe it demonstrates the topics of interest without getting bogged-down in the complexities of a more mature implementation.

Our key implementation strategy for space-efficiency is representing many bool items in the vector with a single element in the underlying storage area. We manage individual bits of a primitive integer type and provide some logic on top to encode and decode bool values from these bits.

We begin by declaring a BitType type alias that defines the type that we will use in the implementation of our underlying storage array - in this case, unsigned long (the same used by GCC / libstdc++). We then declare an array of these elements owned by a std::unique_ptr to automatically handle deallocation.

using BitType = unsigned long;

class BitVector {
  /** The number of elements in the vector */
  std::size_t size_;
  /** The total capacity of the vector */
  std::size_t capacity_;
  /** The underlying storage */
  std::unique_ptr<BitType[]> storage_;

The At() member function demonstrates how we read boolean values from our underlying storage:

auto At(std::size_t index) const -> bool {
  if (index >= size_) {
    throw std::out_of_range("Index out of range.");
  ASSERT(index < size_, "Broken precondition.");
  const auto mask = 1UL << index % sizeof(BitType);
  return storage_[index / sizeof(BitType)] & mask;

First, we select the “bucket” (really, the word) in which the bit of interest is stored. Then, we construct a mask that isolates the bit of interest and apply this to the word to read a bool value.

The PushBack() member works similarly to write new values to our BitVector:

auto PushBack(bool const val) -> void {
  if (size_ == capacity_) {
  ASSERT(capacity_ > size_, "Broken invariant.");
  if (val) {
    // The 'bucket' in which new bit is set
    auto const bucket = size_ / sizeof(BitType);
    storage_[bucket] |= (1UL << size_ % sizeof(BitType));

Initially, we note that we do not need to update the underlying storage at all in the event that a false value is inserted - only the metadata member size_ needs to be updated. In the event that true is inserted into the BitVector, we follow the same procedure as before to isolate the bit of interest, and we write to the word in which it resides using the bitwise or (|=) operator.

Now we have seen how we can read and write boolean values to our BitVector while only allocating each a single bit of storage space. The final piece of the puzzle is the mechanism for returning (possibly mutable) references to individual bits in our container. As noted earlier in this post, C++ offers us no mechanism by which we can address a location that consists of a single bit. This complicates the implementation of certain member functions, like operator[]. Consider what the prototype for this function might look like:

auto operator[](std::size_t index) -> ??? {
  # ???

We have to provide a way to read and write an individual bit in the container without the ability to directly return a reference to it. The way that the C++ standard library implementors solve this problem is through the use of reference proxies.

Reference Proxies

Our final implementation of operator[] ends up looking like:

auto operator[](std::size_t index) -> BitRef {
  if (index >= size_) {
    throw std::out_of_range("Index out of range.");
  ASSERT(index < size_, "Broken precondition.");
  auto* bucket = &storage_[index / sizeof(BitType)];
  const auto mask = 1UL << index % sizeof(BitType);
  return BitRef{bucket, mask};

The magic of this implementation lies in the BitRef type which implements a reference proxy for the individual bits in our BitVector. It consists of a pointer to the word that it references in the BitVector (BitType*) combined with the mask that isolates the bit of interest within the word:

class BitRef {
  /** The 'bucket' in which the bit is located */
  BitType* const bucket_;
  /** The mask to isolate the target bit */
  BitType const mask_;

  BitRef(BitType* bucket, BitType const mask)
      : bucket_{bucket}
      , mask_{mask} {}

The operator bool() member function demonstrates how BitRef “reaches back” to its originating BitVector instance to read the boolean value that it represents:

operator bool() const { return !!(*bucket_ & mask_); }

Likewise, operator=(bool) demonstrates how we can use the BitRef to assign to an individual bit in the originating BitVector:

auto operator=(bool const val) -> BitRef& {
  if (val) {
    *bucket_ |= mask_;
  } else {
    *bucket_ &= ~mask_;
  return *this;

These two member functions illustrate the core functionality of the BitRef proxy type. See the complete implementation for more details.


This implementation only demonstrates the use of reference proxies to aid the implementation of member functions like operator[], Front(), and Back(). A distinct but related technique, that of an iterator proxy, is employed by the standard library to allow std::vector<bool> to be used with constructs like the range-for loop.

Hopefully this quick walkthrough demystifies the errors that arise when working with std::vector<bool>. We see that the core of the issue stems from the fact that the specialization introduces a space-efficient implementation that allocates a single bit for each bool element. Because we cannot return a reference to an individual bit, we introduce a proxy object. These proxies provide the illusion of a reference to a single bit in the container but the illusion breaks down under some conditions, and this can make working with this type perilous.


Written on September 10, 2022