# dynamic_bitset<Block, Allocator>

## Contents

Description
Synopsis
Definitions
Examples
Rationale
Header Files
Template Parameters
Concepts modeled
Type requirements
Public base classes
Member typedefs
Constructors
Destructor
Member functions
Non-member functions
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 implementation-defined size_type;
        enum { bits_per_block = CHAR_BIT * sizeof(Block) };

        class reference
        {
        public:
            // An automatically generated copy constructor.
            reference& operator=(bool value);
            reference& operator|=(bool value);
            reference& operator&=(bool value);
            reference& operator^=(bool value);
            reference& operator-=(bool value);
            reference& operator=(const reference& j);
            reference& operator|=(const reference& j);
            reference& operator&=(const reference& j);
            reference& operator^=(const reference& j);
            reference& operator-=(const reference& j);
            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);

        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) { return reference(*this, pos); }
        bool operator[](size_type pos) const { return test(pos); }

        unsigned long to_ulong() const;

        size_type size() const;
        size_type num_blocks() const;

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

An example of setting and reading some bits. Note that `operator[]` goes from the least-significant bit at `0` to the most significant bit at `size()-1`. The `operator<<` for `dynamic_bitset` prints the bitset from most-significant to least-significant, since that is the format most people are use to reading.

>     #include <iostream>
>     #include <boost/dynamic_bitset.hpp>
>     int main(int, char*[]) {
>       boost::dynamic_bitset<> x(5); // all 0's by default
>       x[0] = 1;
>       x[1] = 1;
>       x[4] = 1;
>       for (boost::dynamic_bitset<>::size_type i = 0; i < x.size(); ++i)
>         std::cout << x[i];
>       std::cout << "\n";
>       std::cout << x << "\n";
>       return EXIT_SUCCESS;
>     }

The output is

>     11001
>     10011

An example of creating some bitsets from integers (unsigned longs).

>     #include <iostream>
>     #include <boost/dynamic_bitset.hpp>
>     int main(int, char*[])
>     {
>       const boost::dynamic_bitset<> b0(2, 0ul);
>       std::cout << "bits(0) = " << b0 << std::endl;

>       const boost::dynamic_bitset<> b1(2, 1ul);
>       std::cout << "bits(1) = " << b1 << std::endl;

>       const boost::dynamic_bitset<> b2(2, 2ul);
>       std::cout << "bits(2) = " << b2 << std::endl;

>       const boost::dynamic_bitset<> b3(2, 3ul);
>       std::cout << "bits(3) = " << b3 << std::endl;

>       return EXIT_SUCCESS;
>     }

The output is

>     bits(0) = 00
>     bits(1) = 01
>     bits(2) = 10
>     bits(3) = 11

An example of performing some bitwise operations.

>     #include <iostream>
>     #include <boost/dynamic_bitset.hpp>
>     int main(int, char*[]) {
>       const boost::dynamic_bitset<> mask(12, 2730ul);
>       std::cout << "mask = " << mask << std::endl;

>       boost::dynamic_bitset<> x(12);

>       std::cout << "Enter a 12-bit bitset in binary: " << std::flush;
>       if (std::cin >> x) {
>         std::cout << "input number:     " << x << std::endl;
>         std::cout << "As unsigned long: " << x.to_ulong() << std::endl;
>         std::cout << "And with mask:    " << (x & mask) << std::endl;
>         std::cout << "Or with mask:     " << (x | mask) << std::endl;
>         std::cout << "Shifted left:     " << (x << 1) << std::endl;
>         std::cout << "Shifted right:    " << (x >> 1) << std::endl;
>       }
>       return EXIT_SUCCESS;
>     }

The output is

>     mask = 101010101010
>     Enter a 12-bit bitset in binary: 100110101101
>     input number =    100110101101
>     As unsigned long: 2477
>     And with mask:    100010101000
>     Or with mask:     101110101111
>     Shifted left:     001101011010
>     Shifted right:    010011010110

### Rationale

The `dynamic_bitset` does not provide iterators (and therefore is not a Container) for the following reasons:

1. `std::bitset` does not have iterators, and `dynamic_bitset` is meant to be a run-time sized version of `std::bitset`.
2. The `dynamic_bitset` is not designed to be a Container.
3. 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.

### Member typedefs

    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 for representing the size of the bit set.

    dynamic_bitset::block_type

The same type as the `Block` template parameter.

    dynamic_bitset::bits_per_block

The number of bits in a `Block`.

### 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 `val` and all other bits, if any, to zero (where `M = min(num_bits, sizeof(unsigned long) * CHAR_BIT)`). A copy of the `alloc` object will be used in subsequent bitset operations such as `resize` to allocate memory.
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+1,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: Constructs 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: The type `BlockInputIterator` must be a model of Input Iterator and its `value_type` must be 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.)

    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. Note that the expression `b << n` is equivalent to constructing a temporary copy of `b` and then using `operator<<=`.
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. Note that the expression `b >> n` is equivalent to constructing a temporary copy of `b` and then using `operator>>=`.
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 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: `true` if bit `n` is set.

    unsigned long to_ulong() const

Returns: An `unsigned long` integer whose bits corresponds to the bits in this bitset, as long as there are no bits in the bitset that are set to 1 at a position greater than `sizeof(unsigned long) * CHAR_BIT`. Throws: `std::overflow_error` if the value of the bitset can not be represented in an `unsigned long`.

    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 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`. Note that the expression `b1 & b2` is equivalent to creating a temporary copy of `b1`, using `operator&=`, and returning the temporary copy.
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`. Note that the expression `b1 & b2` is equivalent to creating a temporary copy of `b1`, using `operator&=`, and returning the temporary copy.
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`. Note that the expression `b1 & b2` is equivalent to creating a temporary copy of `b1`, using `operator&=`, and returning the temporary copy.
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`. Note that the expression `b1 - b2` is equivalent to creating a temporary copy of `b1`, using `operator-=`, and returning the temporary copy.
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>& x)

Output a `dynamic_bitset` to an output stream. This function behaves as if it converts the `dynamic_bitset` to a string and then writes that string to the output stream. That is, it is equivalent to

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

Throws: An allocation error if memory is exhausted (`std::bad_alloc` if `Allocator=std::allocator`). Also will throw `std::ios_base::failure` if there is a problem writing to the stream.

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

Effects: Extracts a `dynamic_bitset` from an input stream. This function first skips whitespace, then extracts up to `x.size()` characters from the input stream. It stops either when it has successfully extracted `x.size()` characters, or when extraction fails, or when it sees a character that is something other than `1` (in which case it does not extract that character). If extraction is successful, the function then assigns a value to the bitset in the same way as if it were initializing the bitset from a string. So, for example, if the input stream contains the characters `"1100abc"`, it will assign the value `12ul` to the bitset, and the next character read from the input stream will be `a`.
Throws: An allocation error if memory is exhausted (`std::bad_alloc` if `Allocator=std::allocator`). Also will throw `std::ios_base::failure` if there is a problem reading from the stream.

### 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 Gennaro Prota for work on increasing efficiency for many of `dynamic_bitset`'s functions.

Copyright © 2001 | Jeremy Siek, Indiana University (jsiek@osl.iu.edu) Chuck Allison, Senior Editor, C/C++ Users Journal (cda@freshsources.com)