# dynamic_bitset<Block, Allocator>

## Contents

Description
Synopsis
Definitions
Examples
Rationale
Header Files
Template Parameters
Concepts modeled
Type requirements
Public base classes
Nested type names
Public data members
Constructors
Destructor
Member functions
Non-member functions
Exception guarantees
Changes from previous version(s)
See also
Acknowledgements

### Description

The `dynamic_bitset` class represents a set of bits. It provides accesses to the value of individual bits via an `operator[]` and provides all of the bitwise operators that one can apply to builtin integers, such as `operator&` and `operator<<`. The number of bits in the set is specified at runtime via a parameter to the constructor of the `dynamic_bitset`.

The `dynamic_bitset` class is nearly identical to the `std::bitset` class. The difference is that the size of the `dynamic_bitset` (the number of bits) is specified at run-time during the construction of a `dynamic_bitset` object, whereas the size of a `std::bitset` is specified at compile-time through an integer template parameter.

The main problem that `dynamic_bitset` is designed to solve is that of representing a subset of a finite set. Each bit represents whether an element of the finite set is in the subset or not. As such the bitwise operations of `dynamic_bitset`, such as `operator&` and `operator|`, correspond to set operations, such as intersection and union.

### Synopsis

    namespace boost {

    template <typename Block, typename Allocator>
    class dynamic_bitset
    {
    public:
        typedef Block block_type;
        typedef Allocator allocator_type;
        typedef implementation-defined size_type;

        static const int bits_per_block = implementation-defined;
        static const size_type npos = implementation-defined;

        class reference
        {
            void operator&(); // not defined

        public:
            // An automatically generated copy constructor.

            reference& operator=(bool value);
            reference& operator=(const reference& rhs);

            reference& operator|=(bool value);
            reference& operator&=(bool value);
            reference& operator^=(bool value);
            reference& operator-=(bool value);

            bool operator~() const;
            operator bool() const;
            reference& flip();
        };

        typedef bool const_reference;

        explicit dynamic_bitset(const Allocator& alloc = Allocator());

        explicit dynamic_bitset(size_type num_bits, unsigned long value = 0,
                                const Allocator& alloc = Allocator());

        template <typename CharT, typename Traits, typename Alloc>
        explicit dynamic_bitset(const std::basic_string<CharT, Traits, Alloc>& s,
            typename std::basic_string<CharT, Traits, Alloc>::size_type pos = 0,
            typename std::basic_string<CharT, Traits, Alloc>::size_type n = std::basic_string<CharT, Traits, Alloc>::npos,
            const Allocator& alloc = Allocator());

        template <typename BlockInputIterator>
        dynamic_bitset(BlockInputIterator first, BlockInputIterator last,
                       const Allocator& alloc = Allocator());

        dynamic_bitset(const dynamic_bitset& b);

        void swap(dynamic_bitset& b);

        dynamic_bitset& operator=(const dynamic_bitset& b);

        allocator_type get_allocator() const;

        void resize(size_type num_bits, bool value = false);
        void clear();
        void push_back(bool bit);
        void append(Block block);

        template <typename BlockInputIterator>
        void append(BlockInputIterator first, BlockInputIterator last);

        dynamic_bitset& operator&=(const dynamic_bitset& b);
        dynamic_bitset& operator|=(const dynamic_bitset& b);
        dynamic_bitset& operator^=(const dynamic_bitset& b);
        dynamic_bitset& operator-=(const dynamic_bitset& b);
        dynamic_bitset& operator<<=(size_type n);
        dynamic_bitset& operator>>=(size_type n);
        dynamic_bitset operator<<(size_type n) const;
        dynamic_bitset operator>>(size_type n) const;

        dynamic_bitset& set(size_type n, bool val = true);
        dynamic_bitset& set();
        dynamic_bitset& reset(size_type n);
        dynamic_bitset& reset();
        dynamic_bitset& flip(size_type n);
        dynamic_bitset& flip();
        bool test(size_type n) const;
        bool any() const;
        bool none() const;
        dynamic_bitset operator~() const;
        size_type count() const;

        reference operator[](size_type pos);
        bool operator[](size_type pos) const;

        unsigned long to_ulong() const;

        size_type size() const;
        size_type num_blocks() const;
        size_type max_size() const;
        bool empty() const;

        bool is_subset_of(const dynamic_bitset& a) const;
        bool is_proper_subset_of(const dynamic_bitset& a) const;
        bool intersects(const dynamic_bitset& a) const;

        size_type find_first() const;
        size_type find_next(size_type pos) const;

    };

    template <typename B, typename A>
    bool operator==(const dynamic_bitset<B, A>& a, const dynamic_bitset<B, A>& b);

    template <typename Block, typename Allocator>
    bool operator!=(const dynamic_bitset<Block, Allocator>& a, const dynamic_bitset<Block, Allocator>& b);

    template <typename B, typename A>
    bool operator<(const dynamic_bitset<B, A>& a, const dynamic_bitset<B, A>& b);

    template <typename Block, typename Allocator>
    bool operator<=(const dynamic_bitset<Block, Allocator>& a, const dynamic_bitset<Block, Allocator>& b);

    template <typename Block, typename Allocator>
    bool operator>(const dynamic_bitset<Block, Allocator>& a, const dynamic_bitset<Block, Allocator>& b);

    template <typename Block, typename Allocator>
    bool operator>=(const dynamic_bitset<Block, Allocator>& a, const dynamic_bitset<Block, Allocator>& b);

    template <typename Block, typename Allocator>
    dynamic_bitset<Block, Allocator>
    operator&(const dynamic_bitset<Block, Allocator>& b1, const dynamic_bitset<Block, Allocator>& b2);

    template <typename Block, typename Allocator>
    dynamic_bitset<Block, Allocator>
    operator|(const dynamic_bitset<Block, Allocator>& b1, const dynamic_bitset<Block, Allocator>& b2);

    template <typename Block, typename Allocator>
    dynamic_bitset<Block, Allocator>
    operator^(const dynamic_bitset<Block, Allocator>& b1, const dynamic_bitset<Block, Allocator>& b2);

    template <typename Block, typename Allocator>
    dynamic_bitset<Block, Allocator>
    operator-(const dynamic_bitset<Block, Allocator>& b1, const dynamic_bitset<Block, Allocator>& b2);

    template <typename Block, typename Allocator, typename CharT, typename Alloc>
    void to_string(const dynamic_bitset<Block, Allocator>& b,
              std::basic_string<CharT, Alloc>& s);

    template <typename Block, typename Allocator, typename BlockOutputIterator>
    void to_block_range(const dynamic_bitset<Block, Allocator>& b,
                        BlockOutputIterator result);

    template <typename CharT, typename Traits, typename Block, typename Allocator>
    std::basic_ostream<CharT, Traits>&
    operator<<(std::basic_ostream<CharT, Traits>& os, const dynamic_bitset<Block, Allocator>& b);

    template <typename CharT, typename Traits, typename Block, typename Allocator>
    std::basic_istream<CharT, Traits>&
    operator>>(std::basic_istream<CharT, Traits>& is, dynamic_bitset<Block, Allocator>& b);

    } // namespace boost

### Definitions

Each bit represents either the Boolean value true or false (1 or 0). To set a bit is to assign it 1. To clear or reset a bit is to assign it 0. To flip a bit is to change the value to 1 if it was 0 and to 0 if it was 1. Each bit has a non-negative position. A bitset `x` contains `x.size()` bits, with each bit assigned a unique position in the range `[0,x.size())`. The bit at position 0 is called the least significant bit and the bit at position `size() - 1` is the most significant bit. When converting an instance of `dynamic_bitset` to or from an unsigned long `n`, the bit at position `i` of the bitset has the same value as `(n >> i) & 1`.

### Examples

Example 1 (setting and reading some bits)

Example 2 (creating some bitsets from integers)

Example 3 (performing input/output and some bitwise operations).

### Rationale

`dynamic_bitset` is not a Container and does not provide iterators for the following reason:

- A container with a proxy `reference` type can not fulfill the container requirements as specified in the C++ standard (unless one resorts to strange iterator semantics). `std::vector<bool>` has a proxy `reference` type and does not fulfill the container requirements and as a result has caused many problems. One common problem is when people try to use iterators from `std::vector<bool>` with a Standard algorithm such as `std::search`. The `std::search` requirements say that the iterator must be a Forward Iterator, but the `std::vector<bool>::iterator` does not meet this requirement because of the proxy reference. Depending on the implementation, they may or not be a compile error or even a run-time error due to this misuse. For further discussion of the problem see Effective STL by Scott Meyers). So `dynamic_bitset` tries to avoid these problems by not pretending to be a container.

Some people prefer the name "toggle" to "flip". The name "flip" was chosen because that is the name used in `std::bitset`. In fact, most of the function names for `dynamic_bitset` were chosen for this reason.

`dynamic_bitset` does not throw exceptions when a precondition is violated (as is done in `std::bitset`). Instead `assert` is used. See the guidelines for Error and Exception Handling for the explanation.

### Header Files

The class `dynamic_bitset` is defined in the header boost/dynamic_bitset.hpp. Also, there is a forward declaration for `dynamic_bitset` in the header boost/dynamic_bitset_fwd.hpp.

### Template parameters

Parameter | Description | Default
--- | --- | ---
`Block` | The integer type in which the bits are stored. | `unsigned long`
`Allocator` | The allocator type used for all internal memory management. | `std::allocator<Block>`

### Concepts Modeled

Assignable, Default Constructible, Equality Comparable, LessThan Comparable.

### Type requirements

`Block` is an unsigned integer type. `Allocator` satisfies the Standard requirements for an allocator.

### Public base classes

None.

### Nested type names

    dynamic_bitset::reference

A proxy class that acts as a reference to a single bit. It contains an assignment operator, a conversion to `bool`, an `operator~`, and a member function `flip`. It exists only as a helper class for `dynamic_bitset`'s `operator[]`. The following table describes the valid operations on the `reference` type. Assume that `b` is an instance of `dynamic_bitset`, `i, j` are of `size_type` and in the range `[0,b.size())`. Also, note that when we write `b[i]` we mean an object of type `reference` that was initialized from `b[i]`. The variable `x` is a `bool`.

Expression | Semantics
--- | ---
`x = b[i]` | Assign the ith bit of `b` to `x`.
`(bool)b[i]` | Return the ith bit of `b`.
`b[i] = x` | Set the ith bit of `b` to the value of `x` and return `b[i]`.
`b[i] |= x` | Or the ith bit of `b` with the value of `x` and return `b[i]`.
`b[i] &= x` | And the ith bit of `b` with the value of `x` and return `b[i]`.
`b[i] ^= x` | Exclusive-Or the ith bit of `b` with the value of `x` and return `b[i]`.
`b[i] -= x` | If `x==true`, clear the ith bit of `b`. Returns `b[i]`.
`b[i] = b[j]` | Set the ith bit of `b` to the value of the jth bit of `b` and return `b[i]`.
`b[i] |= b[j]` | Or the ith bit of `b` with the jth bit of `b` and return `b[i]`.
`b[i] &= b[j]` | And the ith bit of `b` with the jth bit of `b` and return `b[i]`.
`b[i] ^= b[j]` | Exclusive-Or the ith bit of `b` with the jth bit of `b` and return `b[i]`.
`b[i] -= b[j]` | If the jth bit of `b` is set, clear the ith bit of `b`. Returns `b[i]`.
`x = ~b[i]` | Assign the opposite of the ith bit of `b` to `x`.
`(bool)~b[i]` | Return the opposite of the ith bit of `b`.
`b[i].flip()` | Flip the ith bit of `b` and return `b[i]`.

    dynamic_bitset::const_reference

The type `bool`.

    dynamic_bitset::size_type

The unsigned integer type for representing the size of the bit set.

    dynamic_bitset::block_type

The same type as `Block`.

    dynamic_bitset::allocator_type;

The same type as `Allocator`.

### Public data members

    dynamic_bitset::bits_per_block

The number of bits the type `Block` uses to represent values, excluding any padding bits. Numerically equal to `std::numeric_limits<Block>::digits`.

    dynamic_bitset::npos

The maximum value of `size_type`.

### Constructors

    dynamic_bitset(const Allocator& alloc = Allocator())

Effects: Constructs a bitset of size zero. A copy of the `alloc` object will be used in subsequent bitset operations such as `resize` to allocate memory.
Postconditions: `this->size() == 0`.
Throws: An allocation error if memory is exhausted (`std::bad_alloc` if `Allocator=std::allocator`).
(Required by Default Constructible.)

    dynamic_bitset(size_type num_bits,
                   unsigned long value = 0,
                   const Allocator& alloc = Allocator())

Effects: Constructs a bitset from an integer. The first `M` bits are initialized to the corresponding bits in `value` and all other bits, if any, to zero (where `M = min(num_bits, std::numeric_limits<unsigned long>::digits)`). A copy of the `alloc` object will be used in subsequent bitset operations such as `resize` to allocate memory. Note that, e.g., the following
`dynamic_bitset b<>( 16, 7 );`
will match the constructor from an iterator range (not this one), but the underlying implementation will still "do the right thing" and construct a bitset of 16 bits, from the value 7.
Postconditions:

- `this->size() == num_bits`
- For all `i` in the range `[0,M)`, `(*this)[i] == (value >> i) & 1`.
- For all `i` in the range `[M,num_bits)`, `(*this)[i] == false`.

Throws: An allocation error if memory is exhausted (`std::bad_alloc` if `Allocator=std::allocator`).

    dynamic_bitset(const dynamic_bitset& x)

Effects: Constructs a bitset that is a copy of the bitset `x`. The allocator for this bitset is a copy of the allocator in `x`.
Postconditions: For all `i` in the range `[0,x.size())`, `(*this)[i] == x[i]`.
Throws: An allocation error if memory is exhausted (`std::bad_alloc` if `Allocator=std::allocator`).
(Required by Assignable.)

    template <typename BlockInputIterator>
    explicit
    dynamic_bitset(BlockInputIterator first, BlockInputIterator last,
                   const Allocator& alloc = Allocator());

Effects:

- If this constructor is called with a type `BlockInputIterator` which is actually an integral type, the library behaves as if the constructor from `unsigned long` were called, with arguments `static_cast<size_type>(first), last and alloc`, in that order.
  Example:

      // b is constructed as if by calling the constructor
      //
      //   dynamic_bitset(size_type num_bits,
      //                  unsigned long value = 0,
      //                  const Allocator& alloc = Allocator())
      //
      // with arguments
      //
      //   static_cast<dynamic_bitset<unsigned short>::size_type>(8),
      //   7,
      //   Allocator()
      //
      dynamic_bitset<unsigned short> b(8, 7);

  Note:
  At the time of writing (October 2008) this is aligned with the proposed resolution for library issue 438. That is a post `C++03` change, and is currently in the working paper for `C++0x`. Informally speaking, the critical changes with respect to `C++03` are the drop of a `static_cast` on the second argument, and more leeway as to when the templated constructor should have the same effect as the (size, value) one: only when `InputIterator` is an integral type, in `C++03`; when it is either an integral type or any other type that the implementation might detect as impossible to be an input iterator, with the proposed resolution. For the purposes of `dynamic_bitset` we limit ourselves to the first of these two changes.
- Otherwise (i.e. if the template argument is not an integral type), constructs—under the condition in the `requires` clause—a bitset based on a range of blocks. Let `*first` be block number 0, `*++first` block number 1, etc. Block number `b` is used to initialize the bits of the dynamic_bitset in the position range `[b*bits_per_block, (b+1)*bits_per_block)`. For each block number `b` with value `bval`, the bit `(bval >> i) & 1` corresponds to the bit at position `(b * bits_per_block + i)` in the bitset (where `i` goes through the range `[0, bits_per_block)`).

Requires: `BlockInputIterator` must be either an integral type or a model of Input Iterator whose `value_type` is the same type as `Block`.
Throws: An allocation error if memory is exhausted (`std::bad_alloc` if `Allocator=std::allocator`).

    template<typename Char, typename Traits, typename Alloc>
    explicit
    dynamic_bitset(const std::basic_string<Char,Traits,Alloc>& s,
                   typename std::basic_string<CharT, Traits, Alloc>::size_type pos = 0,
                   typename std::basic_string<CharT, Traits, Alloc>::size_type n = std::basic_string<Char,Traits,Alloc>::npos,
                   const Allocator& alloc = Allocator())

Precondition: `pos <= s.size()` and the characters used to initialize the bits must be `0` or `1`.
Effects: Constructs a bitset from a string of 0's and 1's. The first `M` bits are initialized to the corresponding characters in `s`, where `M = min(s.size() - pos, n)`. Note that the highest character position in `s`, not the lowest, corresponds to the least significant bit. That is, character position `pos + M - 1 - i` corresponds to bit `i`. So, for example, `dynamic_bitset(string("1101"))` is the same as `dynamic_bitset(13ul)`.
Throws: an allocation error if memory is exhausted (`std::bad_alloc` if `Allocator=std::allocator`).

### Destructor

    ~dynamic_bitset()

Effects: Releases the memory associated with this bitset and destroys the bitset object itself.
Throws: nothing.

### Member Functions

    void swap(dynamic_bitset& b);

Effects: The contents of this bitset and bitset `b` are exchanged.
Postconditions: This bitset is equal to the original `b`, and `b` is equal to the previous version of this bitset.
Throws: nothing.

    dynamic_bitset& operator=(const dynamic_bitset& x)

Effects: This bitset becomes a copy of the bitset `x`.
Postconditions: For all `i` in the range `[0,x.size())`, `(*this)[i] == x[i]`.
Returns: `*this`.
Throws: nothing.
(Required by Assignable.)

    allocator_type get_allocator() const;

Returns: A copy of the allocator object used to construct `*this`.

    void resize(size_type num_bits, bool value = false);

Effects: Changes the number of bits of the bitset to `num_bits`. If `num_bits > size()` then the bits in the range `[0,size())` remain the same, and the bits in `[size(),num_bits)` are all set to `value`. If `num_bits < size()` then the bits in the range `[0,num_bits)` stay the same (and the remaining bits are discarded).
Postconditions: `this->size() == num_bits`.
Throws: An allocation error if memory is exhausted (`std::bad_alloc` if `Allocator=std::allocator`).

    void clear()

Effects: The size of the bitset becomes zero.
Throws: nothing.

    void push_back(bool value);

Effects: Increases the size of the bitset by one, and sets the value of the new most-significant bit to `value`.
Throws: An allocation error if memory is exhausted (`std::bad_alloc` if `Allocator=std::allocator`).

    void append(Block value);

Effects: Appends the bits in `value` to the bitset (appends to the most-significant end). This increases the size of the bitset by `bits_per_block`. Let `s` be the old size of the bitset, then for `i` in the range `[0,bits_per_block)`, the bit at position `(s + i)` is set to `((value >> i) & 1)`.
Throws: An allocation error if memory is exhausted (`std::bad_alloc` if `Allocator=std::allocator`).

    template <typename BlockInputIterator>
    void append(BlockInputIterator first, BlockInputIterator last);

Effects: This function provides the same end result as the following code, but is typically more efficient.

    for (; first != last; ++first)
      append(*first);

Requires: The `BlockInputIterator` type must be a model of Input Iterator and the `value_type` must be the same type as `Block`.
Throws: An allocation error if memory is exhausted (`std::bad_alloc` if `Allocator=std::allocator`).

    dynamic_bitset& operator&=(const dynamic_bitset& rhs)

Requires: `this->size() == rhs.size()`.
Effects: Bitwise-AND all the bits in `rhs` with the bits in this bitset. This is equivalent to:

    for (size_type i = 0; i != this->size(); ++i)
      (*this)[i] = (*this)[i] & rhs[i];

Returns: `*this`.
Throws: nothing.

    dynamic_bitset& operator|=(const dynamic_bitset& rhs)

Requires: `this->size() == rhs.size()`.
Effects: Bitwise-OR's all the bits in `rhs` with the bits in this bitset. This is equivalent to:

    for (size_type i = 0; i != this->size(); ++i)
      (*this)[i] = (*this)[i] | rhs[i];

Returns: `*this`.
Throws: nothing.

    dynamic_bitset& operator^=(const dynamic_bitset& rhs)

Requires: `this->size() == rhs.size()`.
Effects: Bitwise-XOR's all the bits in `rhs` with the bits in this bitset. This is equivalent to:

    for (size_type i = 0; i != this->size(); ++i)
      (*this)[i] = (*this)[i] ^ rhs[i];

Returns: `*this`.
Throws: nothing.

    dynamic_bitset& operator-=(const dynamic_bitset& rhs)

Requires: `this->size() == rhs.size()`.
Effects: Computes the set difference of this bitset and the `rhs` bitset. This is equivalent to:

    for (size_type i = 0; i != this->size(); ++i)
      (*this)[i] = (*this)[i] && !rhs[i];

Returns: `*this`.
Throws: nothing.

    dynamic_bitset& operator<<=(size_type n)

Effects: Shifts the bits in this bitset to the left by `n` bits. For each bit in the bitset, the bit at position pos takes on the previous value of the bit at position `pos - n`, or zero if no such bit exists.
Returns: `*this`.
Throws: nothing.

    dynamic_bitset& operator>>=(size_type n)

Effects: Shifts the bits in this bitset to the right by `n` bits. For each bit in the bitset, the bit at position `pos` takes on the previous value of bit `pos + n`, or zero if no such bit exists.
Returns: `*this`.
Throws: nothing.

    dynamic_bitset operator<<(size_type n) const

Returns: a copy of `*this` shifted to the left by `n` bits. For each bit in the returned bitset, the bit at position pos takes on the value of the bit at position `pos - n` of this bitset, or zero if no such bit exists.
Throws: An allocation error if memory is exhausted (`std::bad_alloc` if `Allocator=std::allocator`).

    dynamic_bitset operator>>(size_type n) const

Returns: a copy of `*this` shifted to the right by `n` bits. For each bit in the returned bitset, the bit at position pos takes on the value of the bit at position `pos + n` of this bitset, or zero if no such bit exists.
Throws: An allocation error if memory is exhausted (`std::bad_alloc` if `Allocator=std::allocator`).

    dynamic_bitset& set()

Effects: Sets every bit in this bitset to 1.
Returns: `*this`
Throws: nothing.

    dynamic_bitset& flip()

Effects: Flips the value of every bit in this bitset.
Returns: `*this`
Throws: nothing.

    dynamic_bitset operator~() const

Returns: a copy of `*this` with all of its bits flipped.
Throws: An allocation error if memory is exhausted (`std::bad_alloc` if `Allocator=std::allocator`).

    dynamic_bitset& reset()

Effects: Clears every bit in this bitset.
Returns: `*this`
Throws: nothing.

    dynamic_bitset& set(size_type n, bool val = true)

Precondition: `n < this->size()`.
Effects: Sets bit `n` if `val` is `true`, and clears bit `n` if `val` is `false`.
Returns: `*this`

    dynamic_bitset& reset(size_type n)

Precondition: `n < this->size()`.
Effects: Clears bit `n`.
Returns: `*this`

    dynamic_bitset& flip(size_type n)

Precondition: `n < this->size()`.
Effects: Flips bit `n`.
Returns: `*this`

    size_type size() const

Returns: the number of bits in this bitset.
Throws: nothing.

    size_type num_blocks() const

Returns: the number of blocks in this bitset.
Throws: nothing.

    size_type max_size() const;

Returns: the maximum size of a `dynamic_bitset` object having the same type as `*this`. Note that if any `dynamic_bitset` operation causes `size()` to exceed `max_size()` then the behavior is undefined.
[The semantics of this function could change slightly when lib issue 197 will be closed]

    bool empty() const;

Returns: `true` if `this->size() == 0`, `false` otherwise. Note: not to be confused with `none()`, that has different semantics.

    size_type count() const

Returns: the number of bits in this bitset that are set.
Throws: nothing.

    bool any() const

Returns: `true` if any bits in this bitset are set, and otherwise returns `false`.
Throws: nothing.

    bool none() const

Returns: `true` if no bits are set, and otherwise returns `false`.
Throws: nothing.

    bool test(size_type n) const

Precondition: `n < this->size()`.
Returns: `true` if bit `n` is set and `false` is bit `n` is 0.

    reference operator[](size_type n)

Precondition: `n < this->size()`.
Returns: a `reference` to bit `n`. Note that `reference` is a proxy class with an assignment operator and a conversion to `bool`, which allows you to use `operator[]` for assignment. That is, you can write both `x = b[n]` and `b[n] = x`. However, in many other respects the proxy is not the same as the true reference type `bool&`.

    bool operator[](size_type n) const

Precondition: `n < this->size()`.
Returns: The same as `test(n)`.

    unsigned long to_ulong() const

Returns: The numeric value corresponding to the bits in `*this`.
Throws: `std::overflow_error` if that value is too large to be represented in an `unsigned long`, i.e. if `*this` has any non-zero bit at a position `>= std::numeric_limits<unsigned long>::digits`.

    bool is_subset_of(const dynamic_bitset& a) const

Requires: `this->size() == a.size()`
Returns: true if this bitset is a subset of bitset `a`. That is, it returns true if, for every bit that is set in this bitset, the corresponding bit in bitset `a` is also set. Otherwise this function returns false.
Throws: nothing.

    bool is_proper_subset_of(const dynamic_bitset& a) const

Requires: `this->size() == a.size()`
Returns: true if this bitset is a proper subset of bitset `a`. That is, it returns true if, for every bit that is set in this bitset, the corresponding bit in bitset `a` is also set and if `this->count() < a.count()`. Otherwise this function returns false.
Throws: nothing.

    bool intersects(const dynamic_bitset& a) const

Requires: `this->size() == a.size()`
Returns: true if this bitset and `a` intersect. That is, it returns true if, there is a bit which is set in this bitset, such that the corresponding bit in bitset `a` is also set. Otherwise this function returns false.
Throws: nothing.

    size_type find_first() const;

Returns: the lowest index `i` such as bit `i` is set, or `npos` if `*this` has no on bits.

    size_type find_next(size_type pos) const;

Returns: the lowest index `i` greater than `pos` such as bit `i` is set, or `npos` if no such index exists.

    bool operator==(const dynamic_bitset& rhs) const

Returns: `true` if `this->size() == rhs.size()` and if for all `i` in the range `[0,rhs.size())`, `(*this)[i] == rhs[i]`. Otherwise returns `false`.
Throws: nothing.
(Required by Equality Comparable.)

    bool operator!=(const dynamic_bitset& rhs) const

Returns: `!((*this) == rhs)`
Throws: nothing.
(Required by Equality Comparable.)

    bool operator<(const dynamic_bitset& rhs) const

Returns: `true` if this bitset is lexicographically less than `rhs`, and returns `false` otherwise. (See the description of lexicographical_compare for a definition of lexicographic ordering).
Throws: nothing.
(Required by Less Than Comparable.)

    bool operator>(const dynamic_bitset& rhs) const

Returns: `!((*this) < rhs || (*this) == rhs)`
Throws: nothing.
(Required by Less Than Comparable.)

    bool operator<=(const dynamic_bitset& rhs) const

Returns: `(*this) < rhs || (*this) == rhs`
Throws: nothing.
(Required by Less Than Comparable.)

    bool operator>=(const dynamic_bitset& rhs) const

Returns: `(*this) > rhs || (*this) == rhs`
Throws: nothing.
(Required by Less Than Comparable.)

### Non-Member Functions

    dynamic_bitset operator&(const dynamic_bitset& a, const dynamic_bitset& b)

Requires: `a.size() == b.size()`
Returns: A new bitset that is the bitwise-AND of the bitsets `a` and `b`.
Throws: An allocation error if memory is exhausted (`std::bad_alloc` if `Allocator=std::allocator`).

    dynamic_bitset operator|(const dynamic_bitset& a, const dynamic_bitset& b)

Requires: `a.size() == b.size()`
Returns: A new bitset that is the bitwise-OR of the bitsets `a` and `b`.
Throws: An allocation error if memory is exhausted (`std::bad_alloc` if `Allocator=std::allocator`).

    dynamic_bitset operator^(const dynamic_bitset& a, const dynamic_bitset& b)

Requires: `a.size() == b.size()`
Returns: A new bitset that is the bitwise-XOR of the bitsets `a` and `b`.
Throws: An allocation error if memory is exhausted (`std::bad_alloc` if `Allocator=std::allocator`).

    dynamic_bitset operator-(const dynamic_bitset& a, const dynamic_bitset& b)

Requires: `a.size() == b.size()`
Returns: A new bitset that is the set difference of the bitsets `a` and `b`.
Throws: An allocation error if memory is exhausted (`std::bad_alloc` if `Allocator=std::allocator`).

    template <typename CharT, typename Alloc>
    void to_string(const dynamic_bitset<Block, Allocator>& b,
                   std::basic_string<Char,Traits,Alloc>& s)

Effects: Copies a representation of `b` into the string `s`. A character in the string is `'1'` if the corresponding bit is set, and `'0'` if it is not. Character position `i` in the string corresponds to bit position `b.size() - 1 - i`.
Throws: If memory is exhausted, the string will throw an allocation error.
Rationale: This function is not a member function taking zero arguments and returning a string for a couple reasons. First, this version can be slighly more efficient because the string is not copied (due to being passed by value). Second, as a member function, to allow for flexibility with regards to the template parameters of `basic_string`, the member function would require explicit template parameters. Few C++ programmers are familiar with explicit template parameters, and some C++ compilers do not handle them properly.

    template <typename Block, typename Alloc, typename BlockOutputIterator>
    void to_block_range(const dynamic_bitset<Block, Alloc>& b, BlockOutputIterator result)

Effects: Writes the bits of the bitset into the iterator `result` a block at a time. The first block written represents the bits in the position range `[0,bits_per_block)` in the bitset, the second block written the bits in the range `[bits_pre_block,2*bits_per_block)`, and so on. For each block `bval` written, the bit `(bval >> i) & 1` corresponds to the bit at position `(b * bits_per_block + i)` in the bitset.
Requires: The type `BlockOutputIterator` must be a model of Output Iterator and its `value_type` must be the same type as `Block`. Further, the size of the output range must be greater or equal `b.num_blocks()`.

    template <typename BlockIterator, typename Block, typename Alloc>
    void from_block_range(BlockIterator first,
        BlockIterator last, const dynamic_bitset<Block, Alloc>& b)

Effects: Reads blocks from the iterator range into the bitset.
Requires: The type `BlockIterator` must be a model of Input Iterator and its `value_type` must be the same type as `Block`. The size of the iterator range must be less or equal to `b.num_blocks()`.

    template <typename Char, typename Traits, typename Block, typename Alloc>
    basic_ostream<Char, Traits>&
    operator<<(basic_ostream<Char, Traits>& os, const dynamic_bitset<Block, Alloc>& b)

Effects: Inserts a textual representation of b into the stream `os` (highest bit first). Informally, the output is the same as doing

    std::basic_string<Char, Traits> s;
    boost::to_string(x, s):
    os << s;

except that the stream inserter takes into accout the locale imbued into `os`, which `boost::to_string()` can't do. Here is a more precise specification, given in terms of "as if" rule: first, for each valid position i into the bitset `b` let's put: `character_of(b[i)]) = b[i]? os.widen('1') : os.widen('0');` Let also `s` be a `std::basic_string<Char, Traits>` object, having length `b.size()` and such as, for each `i` in `[0, b.size())`, `s[i] is character_of(b[i])` Then, the output, the effects on `os` and the exception behavior is the same as outputting the object `s` to `os` (same width, same exception mask, same padding, same setstate() logic)
Returns: os
Throws: `std::ios_base::failure` if there is a problem writing to the stream.

    template <typename Char, typename Traits, typename Block, typename Alloc>
    std::basic_istream<Char,Traits>&
    operator>>(std::basic_istream<Char,Traits>& is, dynamic_bitset<Block, Alloc>& b)

Effects: Extracts a `dynamic_bitset` from an input stream.
Definitions:
Let Tr be the traits_type of is. Then:

1. A (non-eof) character `c` extracted from `is` is a bitset digit if and only if either Tr::eq(c, is.widen('0')) or Tr::eq(c, is.widen('1')) return true.
2. If c is a bitset digit, it's corresponding bit value is 0 if Tr::eq(c, is.widen('0')) is true, 1 otherwise.

The function begins by constructing a `sentry` object `k` as if `k` were constructed by `typename std::basic_istream<Char, Traits>::sentry k(is)`. If `bool(k)` is true, it calls `b.clear()` then attempts to extract characters from `is`. For each character c that is a bitset digit the corresponding bit value is appended to the less significant end of `b` (appending may throw). If `is.width()` is greater than zero and smaller than `b.max_size()` then the maximum number `n` of bits appended is `is.width()`; otherwise `n` = `b.max_size()`. Unless the extractor is exited via an exception, characters are extracted (and corresponding bits appended) until any of the following occurs:

- `n` bits are stored into the bitset;
- end-of-file, or an error, occurs on the input sequence;
- the next available input character isn't a bitset digit

If no exception caused the function to exit then `is.width(0)` is called, regardless of how many characters were actually extracted. The sentry object k is destroyed.
If the function extracts no characters[???], it calls is.setstate(std::ios::failbit), which may throw `std::ios_base::failure`.
------
Throws: An allocation error if memory is exhausted (`std::bad_alloc` if `Allocator=std::allocator`). A `std::ios_base::failure` if there is a problem reading from the stream.

### Exception guarantees

All of `dynamic_bitset` functions offer at least the basic exception guarantee.

### Changes from previous version(s)

#### Changes in Boost 1.37.0

- The constructor from a block range implements a "do the right thing" behavior, a la standard sequences.

#### Changes from Boost 1.31.0

- The stream extractor has completely different semantics: as natural for a dynamic structure, it now expands the bitset as needed during extraction. The new behaviour mimics that of the `basic_string` extractor but there are some differences the user should be aware of; so, please, check the documentation. (One difference concerns the case where `stream.width() > bitset.max_size() > 0`. In that circumstance the extractor of `dynamic_bitset` never attempts to extract more than `max_size()` characters, whereas the extractor of `basic_string` goes on and, on conforming implementations, eventually throws a `length_error` exception. Note: That's what the standard mandates -see especially library issue 83- but not all implementations conform)
  The stream extractor is now also "exception-aware" in the sense that it works correctly when setting exception masks on the stream.
- Several member functions (`empty()`, `find_first()` , `find_next()`, `get_allocator()`, `intersects()` , `max_size()` ) have been added.
- The constructor from `basic_string` has a new parameter that was totally forgotten before.

Technicalities and minor changes

- The class `reference` has been reimplemented so that dynamic_bitset's references behave more like references to standard container elements. In particular it is now guaranteed that they cannot be invalidated from a standard library swap() function applied to their corresponding `dynamic_bitset`s.

General improvements
Several optimizations to member and non-member functions and to the nested class `reference`.

### See also

`std::bitset`, `std::vector`,

### Acknowledgements

We would like to thank the Boost community for putting in the time to review and accept this library. This library is much better than it ever would have been due to all the suggestions from Boost members. We especially thank Matt Marcus for taking on the task of review manager. Also, a special thanks goes to James Kanze for his invaluable help with the internationalization issues.

Copyright © 2001 | Jeremy Siek, Indiana University (jsiek@osl.iu.edu) Chuck Allison, Senior Editor, C/C++ Users Journal (cda@freshsources.com)
Copyright © 2003-2004, 2008 | Gennaro Prota (name.surname yahoo.com)

Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)