Wording for fundamental bit manipulation utilities

Table of Contents

• History and feedback
• Introduction
• Examples
• Proposed wording
• Design questions
• Acknowledgements

History and feedback

Original wording [February 2016 (pre-Jacksonville) → June 2016 (pre-Oulu)] (P0237R0 → P0237R1)

The idea of bit manipulation utilities has been originally proposed in the 2016 pre-Jacksonville mailing and has been discussed in both SG6 and LEWG in Jacksonville. The original document, P0237R0 fully describes and discusses the idea of fundamental bit manipulation utilities for the C++ language. Another proposal, P0161R0 had the same motivations but was focusing on bitsets. As P0237R0 seemed more generic and not restrained to the scope of std::bitset, we decided to push forward P0237R0, while still keeping in mind the functionalities and performances allowed by P0161R0. The genericity and abstraction offered by P0237R0 should not introduce a performance overhead (at least with the -O2 optimization level on most compilers) when compared to P0161R0 and N3864.

The feedback from the Jacksonville meeting was positive: in top of their intrinsics functionalities, bit manipulation utilities have the potential to serve as a common basis for a std::dynamic_bitset replacement of std::vector<bool> and for bounded and unbounded precision arithmetic as discussed in N4038.

In terms of design, the following guidance was given by LEWG:

• Restrain std::bit_reference to unsigned fundamental integer types?
  → [SF: 6, F: 3, N: 0, A: 0, SA :0]
• std::bit_reference provides no arithmetic except what the paper provides explicitly?
  → [Unanimous consent]
• In small discussion groups, introducing std::bit_value was considered to be good idea

In Jacksonville, the following questions were raised:

• How to deal with word endianness?
• How to provide the possibility to get a mask from the bit position?
• How to deal with infinite ranges of bits, particularly for unbounded precision arithmetic?
• What bitwise logic operators should bits provide?
• How to make std::bit_iterator compatible with proxy iterators presented in P0022R1?

These questions can be answered in the following way:

• The endianness is not a problem since std::bit_iterator is an iterator adaptor: the word-endianness is determined by the iterator provided as the template parameter
• A mask member function has been added
• Infinite ranges of bits still need discussions with SG6
• A bit should provide an equivalent of and, or and xor
• The compatibility with proxy iterators presented in P0022R1 still need discussions

First update [June 2016 (pre-Oulu) → July 2016 (post-Oulu)] (P0237R1 → P0237R2)

The following polls were taken in LEWG:

• Should bit_value default-initialize to false?
  → [SF: 2, F: 5, N: 2, A: 4, SA :0] (no consensus)
• What std::bit_pointer::difference_type should be?
  → [intmax_t: 0, ptrdiff_t: 3, implementation defined >= ptrdiff_t: 15, int64_t: 0, unconstrained implementation defined: 7]

The following additional questions were answered in small group dicussions:

• Should the classes have an independent constructor when the bit position is zero?
  template <class UIntType>
  explicit constexpr bit_value(UIntType val) noexcept;
  explicit constexpr bit_reference(underlying_type& ref) noexcept;
  explicit constexpr bit_pointer(underlying_type* ptr) noexcept;
  explicit constexpr bit_iterator(iterator_type i);
  → [Not really necessary since constructors with a default position set to zero allow implementations to create independent constructors of the preceding form.]
• What should happen when the position exceeds std::binary_digits, and in particular should the constructors taking a position parameter be marked noexcept?
  template <class UIntType>
  constexpr bit_value(UIntType val, size_type pos);
  constexpr bit_reference(underlying_type& ref, size_type pos);
  constexpr bit_pointer(underlying_type* ptr, size_type pos);
  constexpr bit_iterator(iterator_type i, size_type pos);
  → [It should result in an undefined behavior]
• Should the bit utility classes have an assignment operator taking the last bit of a UIntType?
  template <class UIntType>
  bit_value& operator=(UIntType val) noexcept;
  bit_reference& operator=(underlying_type val) noexcept;
  bit_pointer& operator=(underlying_type* ptr) noexcept;
  bit_iterator& operator=(iterator_type i);
  → [Misleading and dangerous, use an assign function instead.]
• Should std::bit_value and std::bit_reference have a set function member taking a bool?
  void set(bool b) noexcept;
  → [Use an assign function instead.]
• Should bit modification functions be free functions or member functions (name conflict for set)?
  void set(bool b) noexcept;
  void set() noexcept;
  void reset() noexcept;
  void flip() noexcept;
  → [Member functions are ok.]
• Should std::bit_value and std::bit_reference have a facet for input and output operations?
  → [Yes, but they can be added later.]
• What should happen in the streaming functions when a value that is not 0 or 1 is read as an input?
  → [The same as for integral types.]
• Should std::bit_value, std::bit_reference, std::bit_pointer and std::bit_iterator have maker functions?
  template <class T>
  constexpr bit_value make_bit_value(T val) noexcept;
  template <class T>
  constexpr bit_value make_bit_value(T val, typename bit_value::size_type pos);
  template <class T>
  constexpr bit_reference<T> make_bit_reference(T& ref) noexcept;
  template <class T>
  constexpr bit_reference<T> make_bit_reference(T& ref, typename bit_reference<T>::size_type pos)
  template <class T>
  constexpr bit_pointer<T> make_bit_pointer(T* ptr) noexcept;
  template <class T>
  constexpr bit_pointer<T> make_bit_pointer(T* ptr, typename bit_pointer<T>::size_type pos);
  template <class T>
  constexpr bit_iterator<T> make_bit_iterator(T i);
  template <class T>
  constexpr bit_iterator<T> make_bit_iterator(T i, typename bit_iterator<T>::size_type pos);
  → [Not necessary if argument deduction get accepted.]
• Should std::bit_value have member swap functions?
  template <class T>
  void swap(bit_reference<T> other);
  void swap(bit_value& other);
  → [Do the same as in the current state of the standard library.]
• Should we have the whole set of swap functions?
  template <class T, class U>
  void swap(bit_reference<T> lhs, bit_reference<U> rhs) noexcept;
  template <class T>
  void swap(bit_reference<T> lhs, bit_value& rhs) noexcept;
  template <class U>
  void swap(bit_value& lhs, bit_reference<U> rhs) noexcept;
  → [Yes.]
• Should std::exchange be overloaded for std::bit_reference?
  template <class T, class U = bit_value>
  bit_value exchange(bit_reference<T> x, U&& val);
  → [Probably yes.]
• Should we have specific comparison operators for std::bit_reference for optimization purposes (which ones?) instead of using implicit conversion to std::bit_value?
  → [The choice can be left to implementers.]
• Should std::bit_pointer have a constructor and an assignment operator taking a nullptr, and should the constructor be explicit?
  explicit constexpr bit_pointer(std::nullptr_t) noexcept;
  bit_pointer& operator=(underlying_type* ptr) noexcept;
  → [Yes and the constructor should be implicit.]
• What should happen when a nullptr is provided with a non-zero position, and should a specific constructor exist for this case?
  constexpr bit_pointer(std::nullptr_t, size_type);
  → [Undefined behavior.]
• Bikeshed the following names:
  address
  position
  mask
  underlying_type
  binary_digits
  → [The small group was ok with these names.]

The following important design questions were also suggested during the meeting:

• What about concurrency and parellelism on std::bit_reference?
• What about infinite ranges of bits?
• What bitwise operations should be allowed on bit values and bit references?
• Should std::bit_value take a template parameter and provides the same interface as std::bit_reference?

As a consequence, the wording has been updated in the following way, compared to P0237R1:

• The assignment operators from unsigned integral types have been removed:
  template <class UIntType>
  bit_value& operator=(UIntType val) noexcept;
  bit_reference& operator=(underlying_type val) noexcept;
  
• The maker functions have been removed because of argument deduction for class templates P0091R2. They may be reintroduced later if argument deduction for class templates do not make it into the standard:
  template <class T>
  constexpr bit_value make_bit_value(T val) noexcept;
  template <class T>
  constexpr bit_value make_bit_value(T val, typename bit_value::size_type pos);
  template <class T>
  constexpr bit_reference<T> make_bit_reference(T& ref) noexcept;
  template <class T>
  constexpr bit_reference<T> make_bit_reference(T& ref, typename bit_reference<T>::size_type pos)
  template <class T>
  constexpr bit_pointer<T> make_bit_pointer(T* ptr) noexcept;
  template <class T>
  constexpr bit_pointer<T> make_bit_pointer(T* ptr, typename bit_pointer<T>::size_type pos);
  template <class T>
  constexpr bit_iterator<T> make_bit_iterator(T i);
  template <class T>
  constexpr bit_iterator<T> make_bit_iterator(T i, typename bit_iterator<T>::size_type pos);
  
• The assignment operators with an implicit zero position have been removed because they were considered misleading:
  template <class UIntType>
  bit_value& operator=(UIntType val) noexcept;
  bit_reference& operator=(underlying_type val) noexcept;
  bit_pointer& operator=(underlying_type* ptr) noexcept;
  bit_iterator& operator=(iterator_type i);
  

The future revision of this proposal will include assign functions, swap members for std::bit_value, and bitwise operators. Several alternative designs for std::bit_value with a template parameter will also be included.

Second update [July 2016 (post-Oulu) → October 2016 (pre-Issaquah)] (P0237R2 → P0237R3)

According to the feedback received in Oulu, the following elements have been added or removed:

• Assign member functions have been added to both std::bit_value and std::bit_reference:
  template <class UIntType>
  void assign(UIntType val) noexcept;
  template <class UIntType>
  void assign(UIntType val, size_type pos);
  void assign(underlying_type val) noexcept;
  void assign(underlying_type val, size_type pos);
  
• Bitwise operators have been added to both std::bit_value and std::bit_reference:
  bit_value& operator&=(bit_value other) noexcept;
  bit_value& operator|=(bit_value other) noexcept;
  bit_value& operator^=(bit_value other) noexcept;
  constexpr bit_value operator&(bit_value lhs, bit_value rhs) noexcept;
  constexpr bit_value operator|(bit_value lhs, bit_value rhs) noexcept;
  constexpr bit_value operator^(bit_value lhs, bit_value rhs) noexcept;
  bit_reference& operator&=(bit_value other) noexcept;
  bit_reference& operator|=(bit_value other) noexcept;
  bit_reference& operator^=(bit_value other) noexcept;
  
• Swap members have been added to std::bit_value to match the interface of std::bit_reference:
  void swap(bit_value& other);
  template <class T>
  void swap(bit_reference<T> other);
  
• Constructors of std::bit_pointer from nullptr have been updated:
  explicit constexpr bit_pointer(std::nullptr_t) noexcept;
  constexpr bit_pointer(std::nullptr_t, size_type);
  

On top of it, the two following constants were added:

• static constexpr bit_value zero_bit(0U);
  static constexpr bit_value one_bit(1U);
  

Introduction

This paper proposes a wording for fundamental bit utilities: std::bit_value, std::bit_reference, std::bit_pointer and std::bit_iterator. An in-depth discussion of the motivations and an in-depth exploration of the design space can be found in P0237R0. In short, this paper proposes a set of 4 main utility classes to serve as bit abstractions in order to offer a common and standardized interface for libraries and programs that require bit manipulations. These bit utilities both emulate bits that are easy to use for users, and provide an interface to access the underlying words to implement efficient low-level algorithms.

Examples

An implementation of the fundamental bit utilities is available at https://github.com/vreverdy/bit. Before presenting a wording, we illustrate some of the functionalities of the library.

First, std::bit_value and std::bit_reference:

  // First, we create an integer
  using uint_t = unsigned long long int;
  uint_t intval = 42;                                        // 101010
  
  // Then we create aligned bit values and a bit references on this integer
  std::bit_value bval0(intval);                              // Creates a bit value from the bit at position 0 of intval
  std::bit_reference<uint_t> bref0(intval);                  // Creates a bit reference from the bit at position 0 of intval

  // And unaligned bit values and a bit references on this integer
  std::bit_value bval5(intval, 5);                           // Creates a bit value from the bit at position 5 of intval 
  std::bit_reference<uint_t> bref5(intval, 5);               // Creates a bit reference from the bit at position 5 of intval

  // Display them
  std::cout<<bval0<<bref0<<bval5<<bref5<<std::endl;          // Prints 0011
  
  // Change their values conditionnally
  if (static_cast<bool>(bval5)) {
    bval0.flip();  // Flips the bit without affecting the integer
    bref5.reset(); // Resets the bit to zero and affects the integer
  }
  std::cout<<bval0<<bref0<<bval5<<bref5<<std::endl;          //  Prints 1010
  
  // Prints the location and the corresponding mask of bit references
  std::cout<<bref0.position()<<" "<<bref0.mask()<<std::endl; // Prints 0 and 1
  std::cout<<bref5.position()<<" "<<bref5.mask()<<std::endl; // Prints 5 and 32

Then, with std::bit_pointer:

  // First, we create an array of integers
  using uint_t = unsigned long long int;
  std::array<uint_t, 2> intarr = {42, 314};
  
  // Then we create a bit reference and a bit pointer
  std::bit_reference<uint_t> bref5(intarr[0], 5);            // Creates a bit reference from the bit at position 5 of the first element of the array
  std::bit_pointer<uint_t> bptr(intarr.data());              // Creates a bit pointer from the bit at position 0 of the first element of the array

  // We flip the first bit, and sets the second one to 1 with two methods
  bptr->flip();                                              // Flips the bit
  ++bptr;                                                    // Goes to the next bit
  *bptr.set();                                               // Sets the bit
  
  // Then we advance the bit pointer by more than 64 bits and display its position
  bptr += 71;
  std::cout<<bptr->position()<<std::endl;                    // Prints 7 as the bit is now in the second element of the array
  
  // And finally we set the bit pointer to the position of the bit reference
  bptr = &bref5;

And finally std::bit_iterator, which can serve as a basis of bit algorithm:

  // First, we create a list of integers
  using uint_t = unsigned short int;
  std::list<uint_t> intlst = {40, 41, 42, 43, 44};
  
  // Then we create a pair of aligned bit iterators
  auto bfirst = std::bit_iterator<typename std::list<uint_t>::iterator>(std::begin(intlst));
  auto bend = std::bit_iterator<typename std::list<uint_t>::iterator>(std::end(intlst));

  // Then we count the number of bits set to 1
  auto result = std::count(bfirst, bend, std::bit(1));
  
  // We take a subset of the list
  auto bfirst2 = std::make_bit_iterator(std::begin(intlst), 5);
  auto bend2 = std::make_bit_iterator(std::end(intlst) - 1, 2);
  
  // And we reverse the subset
  std::reverse(bfirst2, bend2);

The count algorithm can be implemented as:

// Counts the number of bits equal to the provided bit value
template <class InputIt, class T> 
typename bit_iterator<InputIt>::difference_type
count(
  bit_iterator<InputIt> first, 
  bit_iterator<InputIt> last, 
  const T& value
)
{
  // Initialization
  using underlying_type = typename bit_iterator<InputIt>::underlying_type;
  using difference_type = typename bit_iterator<InputIt>::difference_type;
  constexpr difference_type digits = binary_digits<underlying_type>::value;
  const bit_value input = value;
  difference_type result = 0;
  auto it = first.base();
    
  // Computation when bits belong to several underlying values
  if (first.base() != last.base()) {
    if (first.position() != 0) {
      result = _popcnt(*first.base() >> first.position());
      ++it;
    }
    for (; it != last.base(); ++it) {
      result += _popcnt(*it);
    }
    if (last.position() != 0) {
      result += _popcnt(*last.base() << (digits - last.position()));
    }
  // Computation when bits belong to the same underlying value
  } else {
    result = _popcnt(_bextr(
      *first.base(), 
      static_cast<underlying_type>(first.position()), 
      static_cast<underlying_type>(last.position() - first.position())
    ));
  }
    
  // Negates when the number of zero bits is requested
  if (!static_cast<bool>(input)) {
    result = (last - first) - result;
  }
    
  // Finalization
  return result;
}

As illustrated in these examples, bit utilities act as a convenient interface between high level code that can use bit manipulation through bit iterators, and low level algorithms that can call dedicated instruction sets and compiler intrinsics.

More information as well as more examples can be found in the presentation From Numerical Cosmology to Efficient Bit Abstractions for the Standard Library that was given during CppCon 2016.

Proposed Wording

Header <bit>

Add the following header to the standard:

<bit>

Helper struct std::binary_digits

Add to the <bit> synopsis:

// Binary digits structure definition
template <class T>
struct binary_digits 
: std::enable_if<
  std::is_integral<T>::value && std::is_unsigned<T>::value,
  std::integral_constant<std::size_t, std::numeric_limits<T>::digits>
>::type
{};

Class std::bit_value

Add to the <bit> synopsis:

// Bit value class definition
class bit_value
{public:
    
  // Types
  using size_type = std::size_t;
    
  // Lifecycle
  bit_value() noexcept = default;
  template <class T> 
  constexpr bit_value(bit_reference<T> val) noexcept;
  template <class UIntType>
  explicit constexpr bit_value(UIntType val) noexcept;
  template <class UIntType> 
  constexpr bit_value(UIntType val, size_type pos);
    
  // Assignment
  template <class T> 
  bit_value& operator=(bit_reference<T> val) noexcept;
  template <class UIntType>
  void assign(UIntType val) noexcept;
  template <class UIntType> 
  void assign(UIntType val, size_type pos);
  
  // Bitwise assignment
  bit_value& operator&=(bit_value other) noexcept;
  bit_value& operator|=(bit_value other) noexcept;
  bit_value& operator^=(bit_value other) noexcept;

  // Conversion
  explicit constexpr operator bool() const noexcept;

  // Swap members
  void swap(bit_value& other);
  template <class T> 
  void swap(bit_reference<T> other);

  // Bit manipulation
  void set(bool b) noexcept;
  void set() noexcept;
  void reset() noexcept;
  void flip() noexcept;
};

// Bitwise operators
constexpr bit_value operator&(bit_value lhs, bit_value rhs) noexcept;
constexpr bit_value operator|(bit_value lhs, bit_value rhs) noexcept;
constexpr bit_value operator^(bit_value lhs, bit_value rhs) noexcept;

// Comparison operators
constexpr bool operator==(bit_value lhs, bit_value rhs) noexcept;
constexpr bool operator!=(bit_value lhs, bit_value rhs) noexcept;
constexpr bool operator<(bit_value lhs, bit_value rhs) noexcept;
constexpr bool operator<=(bit_value lhs, bit_value rhs) noexcept;
constexpr bool operator>(bit_value lhs, bit_value rhs) noexcept;
constexpr bool operator>=(bit_value lhs, bit_value rhs) noexcept;

// Stream functions
template <class CharT, class Traits>
std::basic_ostream<CharT, Traits>& operator<<(
  std::basic_ostream<CharT, Traits>& os,
  bit_value x
);
template <class CharT, class Traits>
std::basic_istream<CharT, Traits>& operator>>(
  std::basic_istream<CharT, Traits>& is,
  bit_value& x
);

// Constants
static constexpr bit_value zero_bit(0U);
static constexpr bit_value one_bit(1U);

Lifecycle

Assignment

Bitwise assignment

Conversion

Swap members

Bit manipulation

Bitwise operators

Comparison operators

Stream functions

Class template std::bit_reference

Add to the <bit> synopsis:

// Bit reference class definition
template <class UIntType>
class bit_reference
{public:
    
  // Types
  using underlying_type = UIntType;
  using size_type = std::size_t;

  // Lifecycle
  template <class T> 
  constexpr bit_reference(const bit_reference<T>& other) noexcept;
  explicit constexpr bit_reference(underlying_type& ref) noexcept;
  constexpr bit_reference(underlying_type& ref, size_type pos);

  // Assignment
  bit_reference& operator=(const bit_reference& other) noexcept;
  template <class T> 
  bit_reference& operator=(const bit_reference<T>& other) noexcept;
  bit_reference& operator=(bit_value val) noexcept;
  void assign(underlying_type val) noexcept;
  void assign(underlying_type val, size_type pos);

  // Bitwise assignment
  bit_reference& operator&=(bit_value other) noexcept;
  bit_reference& operator|=(bit_value other) noexcept;
  bit_reference& operator^=(bit_value other) noexcept;
    
  // Conversion
  explicit constexpr operator bool() const noexcept;

  // Access
  constexpr bit_pointer<UIntType> operator&() const noexcept;
    
  // Swap members
  template <class T> 
  void swap(bit_reference<T> other);
  void swap(bit_value& other);

  // Bit manipulation
  void set(bool b) noexcept;
  void set() noexcept;
  void reset() noexcept;
  void flip() noexcept;

  // Underlying details
  constexpr underlying_type* address() const noexcept;
  constexpr size_type position() const noexcept;
  constexpr underlying_type mask() const noexcept;
};

// Swap and exchange
template <class T, class U>
void swap(bit_reference<T> lhs, bit_reference<U> rhs) noexcept;
template <class T>
void swap(bit_reference<T> lhs, bit_value& rhs) noexcept;
template <class U>
void swap(bit_value& lhs, bit_reference<U> rhs) noexcept;
template <class T, class U = bit_value>
bit_value exchange(bit_reference<T> x, U&& val);

// Stream functions
template <class CharT, class Traits, class T>
std::basic_ostream<CharT, Traits>& operator<<(
  std::basic_ostream<CharT, Traits>& os,
  bit_reference<T> x
);
template <class CharT, class Traits, class T>
std::basic_istream<CharT, Traits>& operator>>(
  std::basic_istream<CharT, Traits>& is,
  bit_reference<T>& x
);

Lifecycle

Assignment

Bitwise assignment

Conversion

Access

Swap members

Bit manipulation

Underlying details

Swap and exchange

Stream functions

Class template std::bit_pointer

Add to the <bit> synopsis:

// Bit pointer class definition
template <class UIntType>
class bit_pointer
{public:
    
  // Types
  using underlying_type = UIntType;
  using size_type = std::size_t;
  using difference_type = /* Implementation defined, at least std::ptrdiff_t */;

  // Lifecycle
  bit_pointer() noexcept = default;
  template <class T> 
  constexpr bit_pointer(const bit_pointer<T>& other) noexcept;
  constexpr bit_pointer(std::nullptr_t) noexcept;
  explicit constexpr bit_pointer(underlying_type* ptr) noexcept;
  constexpr bit_pointer(underlying_type* ptr, size_type pos);
    
  // Assignment
  bit_pointer& operator=(std::nullptr_t) noexcept;
  bit_pointer& operator=(const bit_pointer& other) noexcept;
  template <class T> 
  bit_pointer& operator=(const bit_pointer<T>& other) noexcept;
    
  // Conversion
  explicit constexpr operator bool() const noexcept;

  // Access
  constexpr bit_reference<UIntType> operator*() const noexcept;
  constexpr bit_reference<UIntType>* operator->() const noexcept;
  constexpr bit_reference<UIntType> operator[](difference_type n) const;
    
  // Increment and decrement operators
  bit_pointer& operator++();
  bit_pointer& operator--();
  bit_pointer operator++(int);
  bit_pointer operator--(int);
  constexpr bit_pointer operator+(difference_type n) const;
  constexpr bit_pointer operator-(difference_type n) const;
  bit_pointer& operator+=(difference_type n);
  bit_pointer& operator-=(difference_type n);
};

// Non-member arithmetic operators
template <class T>
constexpr bit_pointer<T> operator+(
  typename bit_pointer<T>::difference_type n,
  bit_pointer<T> x
);
template <class T, class U>
constexpr typename std::common_type<
  typename bit_pointer<T>::difference_type,
  typename bit_pointer<U>::difference_type
>::type operator-(
  bit_pointer<T> lhs,
  bit_pointer<U> rhs
);

// Comparison operators
template <class T, class U>
constexpr bool operator==(bit_pointer<T> lhs, bit_pointer<U> rhs) noexcept;
template <class T, class U>
constexpr bool operator!=(bit_pointer<T> lhs, bit_pointer<U> rhs) noexcept;
template <class T, class U>
constexpr bool operator<(bit_pointer<T> lhs, bit_pointer<U> rhs) noexcept;
template <class T, class U>
constexpr bool operator<=(bit_pointer<T> lhs, bit_pointer<U> rhs) noexcept;
template <class T, class U>
constexpr bool operator>(bit_pointer<T> lhs, bit_pointer<U> rhs) noexcept;
template <class T, class U>
constexpr bool operator>=(bit_pointer<T> lhs, bit_pointer<U> rhs) noexcept;

Lifecycle

Assignment

Conversion

Access

Increment and decrement operators

Non-member arithmetic operators

Comparison operators

Class template std::bit_iterator

Add to the <bit> synopsis:

// Bit iterator class definition
template <class Iterator>
class bit_iterator
{public:
  
  // Types
  using iterator_type = Iterator;
  using underlying_type = typename _cv_iterator_traits<Iterator>::value_type;
  using iterator_category = typename std::iterator_traits<Iterator>::iterator_category;
  using value_type = bit_value;
  using difference_type = /* Implementation defined, at least std::ptrdiff_t */;
  using pointer = bit_pointer<underlying_type>;
  using reference = bit_reference<underlying_type>;
  using size_type = std::size_t;

  // Lifecycle
  constexpr bit_iterator();
  template <class T> 
  constexpr bit_iterator(const bit_iterator<T>& other);
  explicit constexpr bit_iterator(iterator_type i);
  constexpr bit_iterator(iterator_type i, size_type pos);

  // Assignment
  template <class T>
  bit_iterator& operator=(const bit_iterator<T>& other);

  // Access
  constexpr reference operator*() const noexcept;
  constexpr pointer operator->() const noexcept;
  constexpr reference operator[](difference_type n) const;

  // Increment and decrement operators
  bit_iterator& operator++();
  bit_iterator& operator--();
  bit_iterator operator++(int);
  bit_iterator operator--(int);
  constexpr bit_iterator operator+(difference_type n) const;
  constexpr bit_iterator operator-(difference_type n) const;
  bit_iterator& operator+=(difference_type n);
  bit_iterator& operator-=(difference_type n);

  // Underlying details
  constexpr iterator_type base() const;
  constexpr size_type position() const noexcept;
  constexpr underlying_type mask() const noexcept;
};

// Non-member arithmetic operators
template <class T>
constexpr bit_iterator<T> operator+(
  typename bit_iterator<T>::difference_type n,
  const bit_iterator<T>& i
);
template <class T, class U>
constexpr typename std::common_type<
  typename bit_iterator<T>::difference_type,
  typename bit_iterator<U>::difference_type
>::type operator-(
  const bit_iterator<T>& lhs,
  const bit_iterator<U>& rhs
);

// Comparison operators
template <class T, class U>
constexpr bool operator==(const bit_iterator<T>& lhs, const bit_iterator<U>& rhs);
template <class T, class U>
constexpr bool operator!=(const bit_iterator<T>& lhs, const bit_iterator<U>& rhs);
template <class T, class U>
constexpr bool operator<(const bit_iterator<T>& lhs, const bit_iterator<U>& rhs);
template <class T, class U>
constexpr bool operator<=(const bit_iterator<T>& lhs, const bit_iterator<U>& rhs);
template <class T, class U>
constexpr bool operator>(const bit_iterator<T>& lhs, const bit_iterator<U>& rhs);
template <class T, class U>
constexpr bool operator>=(const bit_iterator<T>& lhs, const bit_iterator<U>& rhs);

Lifecycle

Assignment

Access

Increment and decrement operators

Underlying details

Non-member arithmetic operators

Comparison operators

Design questions

The following minor questions will need to be answered:

• When the position exceeds std::binary_digits, it leads to undefined behavior. In that context, can the constructors taking a position parameter be marked noexcept?
  
• Should std::bit_value and std::bit_reference have a set function member taking a bool?
  void set(bool b) noexcept;
  
• Should std::bit_value and std::bit_reference have a facet for input and output operations? If so, how to design this facet?
• Should std::exchange be overloaded for std::bit_reference?
  template <class T, class U = bit_value>
  bit_value exchange(bit_reference<T> x, U&& val);
  
• Should we have specific bitwise and comparison operators for std::bit_reference for optimization purposes (which ones?) instead of using implicit conversion to std::bit_value?
• What functions should be marked constexpr? In particular, should non-const members be marked constexpr?
• Bikeshed the following names:
  zero_bit
  one_bit
  

Additionally, a major design question has been raised during the Oulu meeting: should std::bit_value be a template class? The major advantage would be to allow implicit conversions from std::bit_value& to std::bit_reference, and from std::bit_value* to std::bit_pointer. Three main possibilities should be considered and discussed:

• std::bit_value is a non-template class as in the current design
• std::bit_value is a template class, and stores the bit inside as the first bit of the underlying value, losing information about the position
• std::bit_value is a template class, and stores the bit inside at the specified position, basically operating as a std::bit_reference that copies the underlying value

• How to manage cv-qualified bit values and references as well as conversions between them? For example, what should the semantics of const bit_value<T>, bit_value<const T>, const bit_reference<T>, and bit_reference<const T> be and how should they interact with each other? Furthermore, what should a const bit_value<volatile T> or a volatile bit_reference<const T> represent? The question has been detailed on the ISO C++ Standard - Future Proposals board. As the question goes beyond the sole scope of the bit manipulation library and concerns all template class wrappers, it may also be asked to LWG.
• Temporary bit values with a defaulted underlying type will be required anyway. Two possible solutions are: a specialized version of std::bit_value such as std::bit_value<void>, or a new non-template class, whose name has to be defined.

Acknowledgements

The authors would like to thank Tomasz Kaminski, Lawrence Crowl, Howard Hinnant, Jens Maurer, Tony Van Eerd, Klemens Morgenstern, Vicente Botet Escriba, Odin Holmes and the other contributors of the ISO C++ Standard - Discussion and of the ISO C++ Standard - Future Proposals groups for their initial reviews and comments.

Vincent Reverdy and Robert J. Brunner have been supported by the National Science Foundation Grant AST-1313415. Robert J. Brunner has been supported in part by the Center for Advanced Studies at the University of Illinois.