20 General utilities library [utilities]

20.9 Bitsets [bitset]

20.9.1 Header <bitset> synopsis [bitset.syn]

1
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The header <bitset> defines a class template and several related functions for representing and manipulating fixed-size sequences of bits.
#include <string>
#include <iosfwd>   // for istream, ostream, see [iosfwd.syn]

namespace std {
  template<size_t N> class bitset;

  // [bitset.operators], bitset operators
  template<size_t N>
    bitset<N> operator&(const bitset<N>&, const bitset<N>&) noexcept;
  template<size_t N>
    bitset<N> operator|(const bitset<N>&, const bitset<N>&) noexcept;
  template<size_t N>
    bitset<N> operator^(const bitset<N>&, const bitset<N>&) noexcept;
  template<class charT, class traits, size_t N>
    basic_istream<charT, traits>&
      operator>>(basic_istream<charT, traits>& is, bitset<N>& x);
  template<class charT, class traits, size_t N>
    basic_ostream<charT, traits>&
      operator<<(basic_ostream<charT, traits>& os, const bitset<N>& x);
}

20.9.2 Class template bitset [template.bitset]

namespace std {
  template<size_t N> class bitset {
  public:
    // bit reference
    class reference {
      friend class bitset;
      reference() noexcept;

    public:
      reference(const reference&) = default;
      ~reference();
      reference& operator=(bool x) noexcept;            // for b[i] = x;
      reference& operator=(const reference&) noexcept;  // for b[i] = b[j];
      bool operator~() const noexcept;                  // flips the bit
      operator bool() const noexcept;                   // for x = b[i];
      reference& flip() noexcept;                       // for b[i].flip();
    };

    // [bitset.cons], constructors
    constexpr bitset() noexcept;
    constexpr bitset(unsigned long long val) noexcept;
    template<class charT, class traits, class Allocator>
      explicit bitset(
        const basic_string<charT, traits, Allocator>& str,
        typename basic_string<charT, traits, Allocator>::size_type pos = 0,
        typename basic_string<charT, traits, Allocator>::size_type n
          = basic_string<charT, traits, Allocator>::npos,
        charT zero = charT('0'),
        charT one = charT('1'));
    template<class charT>
      explicit bitset(
        const charT* str,
        typename basic_string<charT>::size_type n = basic_string<charT>::npos,
        charT zero = charT('0'),
        charT one = charT('1'));

    // [bitset.members], bitset operations
    bitset<N>& operator&=(const bitset<N>& rhs) noexcept;
    bitset<N>& operator|=(const bitset<N>& rhs) noexcept;
    bitset<N>& operator^=(const bitset<N>& rhs) noexcept;
    bitset<N>& operator<<=(size_t pos) noexcept;
    bitset<N>& operator>>=(size_t pos) noexcept;
    bitset<N>& set() noexcept;
    bitset<N>& set(size_t pos, bool val = true);
    bitset<N>& reset() noexcept;
    bitset<N>& reset(size_t pos);
    bitset<N>  operator~() const noexcept;
    bitset<N>& flip() noexcept;
    bitset<N>& flip(size_t pos);

    // element access
    constexpr bool operator[](size_t pos) const;        // for b[i];
    reference operator[](size_t pos);                   // for b[i];

    unsigned long to_ulong() const;
    unsigned long long to_ullong() const;
    template<class charT = char,
             class traits = char_traits<charT>,
             class Allocator = allocator<charT>>
      basic_string<charT, traits, Allocator>
        to_string(charT zero = charT('0'), charT one = charT('1')) const;

    size_t count() const noexcept;
    constexpr size_t size() const noexcept;
    bool operator==(const bitset<N>& rhs) const noexcept;
    bool test(size_t pos) const;
    bool all() const noexcept;
    bool any() const noexcept;
    bool none() const noexcept;
    bitset<N> operator<<(size_t pos) const noexcept;
    bitset<N> operator>>(size_t pos) const noexcept;
  };

  // [bitset.hash], hash support
  template<class T> struct hash;
  template<size_t N> struct hash<bitset<N>>;
}
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The class template bitset<N> describes an object that can store a sequence consisting of a fixed number of bits, N.
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Each bit represents either the value zero (reset) or one (set).
To toggle a bit is to change the value zero to one, or the value one to zero.
Each bit has a non-negative position pos.
When converting between an object of class bitset<N> and a value of some integral type, bit position pos corresponds to the bit value 1 << pos.
The integral value corresponding to two or more bits is the sum of their bit values.
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The functions described in this subclause can report three kinds of errors, each associated with a distinct exception:

20.9.2.1 Constructors [bitset.cons]

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constexpr bitset() noexcept;
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Effects: Initializes all bits in *this to zero.
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constexpr bitset(unsigned long long val) noexcept;
2
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Effects: Initializes the first M bit positions to the corresponding bit values in val.
M is the smaller of N and the number of bits in the value representation of unsigned long long.
If M < N, the remaining bit positions are initialized to zero.
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template<class charT, class traits, class Allocator> explicit bitset( const basic_string<charT, traits, Allocator>& str, typename basic_string<charT, traits, Allocator>::size_type pos = 0, typename basic_string<charT, traits, Allocator>::size_type n = basic_string<charT, traits, Allocator>::npos, charT zero = charT('0'), charT one = charT('1'));
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Effects: Determines the effective length rlen of the initializing string as the smaller of n and str.size() - pos.
Initializes the first M bit positions to values determined from the corresponding characters in the string str.
M is the smaller of N and rlen.
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An element of the constructed object has value zero if the corresponding character in str, beginning at position pos, is zero.
Otherwise, the element has the value one.
Character position pos + M - 1 corresponds to bit position zero.
Subsequent decreasing character positions correspond to increasing bit positions.
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If M < N, remaining bit positions are initialized to zero.
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The function uses traits​::​eq to compare the character values.
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Throws: out_­of_­range if pos > str.size() or invalid_­argument if any of the rlen characters in str beginning at position pos is other than zero or one.
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template<class charT> explicit bitset( const charT* str, typename basic_string<charT>::size_type n = basic_string<charT>::npos, charT zero = charT('0'), charT one = charT('1'));
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Effects: As if by: 
bitset(n == basic_string<charT>::npos
          ? basic_string<charT>(str)
          : basic_string<charT>(str, n),
       0, n, zero, one)

20.9.2.2 Members [bitset.members]

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bitset<N>& operator&=(const bitset<N>& rhs) noexcept;
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Effects: Clears each bit in *this for which the corresponding bit in rhs is clear, and leaves all other bits unchanged.
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Returns: *this.
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bitset<N>& operator|=(const bitset<N>& rhs) noexcept;
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Effects: Sets each bit in *this for which the corresponding bit in rhs is set, and leaves all other bits unchanged.
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Returns: *this.
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bitset<N>& operator^=(const bitset<N>& rhs) noexcept;
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Effects: Toggles each bit in *this for which the corresponding bit in rhs is set, and leaves all other bits unchanged.
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Returns: *this.
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bitset<N>& operator<<=(size_t pos) noexcept;
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#
Effects: Replaces each bit at position I in *this with a value determined as follows:
  • (7.1)
    If I < pos, the new value is zero;
  • (7.2)
    If I >= pos, the new value is the previous value of the bit at position I - pos.
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Returns: *this.
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bitset<N>& operator>>=(size_t pos) noexcept;
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Effects: Replaces each bit at position I in *this with a value determined as follows:
  • (9.1)
    If pos >= N - I, the new value is zero;
  • (9.2)
    If pos < N - I, the new value is the previous value of the bit at position I + pos.
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Returns: *this.
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bitset<N>& set() noexcept;
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Effects: Sets all bits in *this.
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Returns: *this.
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bitset<N>& set(size_t pos, bool val = true);
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Effects: Stores a new value in the bit at position pos in *this.
If val is true, the stored value is one, otherwise it is zero.
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Returns: *this.
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Throws: out_­of_­range if pos does not correspond to a valid bit position.
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bitset<N>& reset() noexcept;
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Effects: Resets all bits in *this.
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Returns: *this.
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bitset<N>& reset(size_t pos);
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Effects: Resets the bit at position pos in *this.
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Returns: *this.
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Throws: out_­of_­range if pos does not correspond to a valid bit position.
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bitset<N> operator~() const noexcept;
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Effects: Constructs an object x of class bitset<N> and initializes it with *this.
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Returns: x.flip().
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bitset<N>& flip() noexcept;
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Effects: Toggles all bits in *this.
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Returns: *this.
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bitset<N>& flip(size_t pos);
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Effects: Toggles the bit at position pos in *this.
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Returns: *this.
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Throws: out_­of_­range if pos does not correspond to a valid bit position.
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unsigned long to_ulong() const;
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Returns: x.
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Throws: overflow_­error if the integral value x corresponding to the bits in *this cannot be represented as type unsigned long.
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unsigned long long to_ullong() const;
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Returns: x.
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Throws: overflow_­error if the integral value x corresponding to the bits in *this cannot be represented as type unsigned long long.
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template<class charT = char, class traits = char_traits<charT>, class Allocator = allocator<charT>> basic_string<charT, traits, Allocator> to_string(charT zero = charT('0'), charT one = charT('1')) const;
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Effects: Constructs a string object of the appropriate type and initializes it to a string of length N characters.
Each character is determined by the value of its corresponding bit position in *this.
Character position N - 1 corresponds to bit position zero.
Subsequent decreasing character positions correspond to increasing bit positions.
Bit value zero becomes the character zero, bit value one becomes the character one.
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Returns: The created object.
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size_t count() const noexcept;
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Returns: A count of the number of bits set in *this.
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constexpr size_t size() const noexcept;
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Returns: N.
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bool operator==(const bitset<N>& rhs) const noexcept;
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Returns: true if the value of each bit in *this equals the value of the corresponding bit in rhs.
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bool test(size_t pos) const;
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Returns: true if the bit at position pos in *this has the value one.
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Throws: out_­of_­range if pos does not correspond to a valid bit position.
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bool all() const noexcept;
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Returns: count() == size().
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bool any() const noexcept;
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Returns: count() != 0.
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bool none() const noexcept;
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Returns: count() == 0.
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bitset<N> operator<<(size_t pos) const noexcept;
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Returns: bitset<N>(*this) <<= pos.
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bitset<N> operator>>(size_t pos) const noexcept;
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Returns: bitset<N>(*this) >>= pos.
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constexpr bool operator[](size_t pos) const;
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Preconditions: pos is valid.
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Returns: true if the bit at position pos in *this has the value one, otherwise false.
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Throws: Nothing.
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bitset<N>::reference operator[](size_t pos);
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Preconditions: pos is valid.
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Returns: An object of type bitset<N>​::​reference such that (*this)[pos] == this->test(pos), and such that (*this)[pos] = val is equivalent to this->set(pos, val).
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Throws: Nothing.
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Remarks: For the purpose of determining the presence of a data race, any access or update through the resulting reference potentially accesses or modifies, respectively, the entire underlying bitset.

20.9.3 bitset hash support [bitset.hash]

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template<size_t N> struct hash<bitset<N>>;
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The specialization is enabled ([unord.hash]).

20.9.4 bitset operators [bitset.operators]

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bitset<N> operator&(const bitset<N>& lhs, const bitset<N>& rhs) noexcept;
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Returns: bitset<N>(lhs) &= rhs.
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bitset<N> operator|(const bitset<N>& lhs, const bitset<N>& rhs) noexcept;
2
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Returns: bitset<N>(lhs) |= rhs.
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bitset<N> operator^(const bitset<N>& lhs, const bitset<N>& rhs) noexcept;
3
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Returns: bitset<N>(lhs) ^= rhs.
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template<class charT, class traits, size_t N> basic_istream<charT, traits>& operator>>(basic_istream<charT, traits>& is, bitset<N>& x);
5
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Effects: Extracts up to N characters from is.
Stores these characters in a temporary object str of type basic_­string<charT, traits>, then evaluates the expression x = bitset<N>(str).
Characters are extracted and stored until any of the following occurs:
  • (5.1)
    N characters have been extracted and stored;
  • (5.2)
    end-of-file occurs on the input sequence;
  • (5.3)
    the next input character is neither is.widen('0') nor is.widen('1') (in which case the input character is not extracted).
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If N > 0 and no characters are stored in str, calls is.setstate(ios_­base​::​failbit) (which may throw ios_­base​::​failure ([iostate.flags])).
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Returns: is.
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template<class charT, class traits, size_t N> basic_ostream<charT, traits>& operator<<(basic_ostream<charT, traits>& os, const bitset<N>& x);
8
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Returns: 
os << x.template to_string<charT, traits, allocator<charT>>(
  use_facet<ctype<charT>>(os.getloc()).widen('0'),
  use_facet<ctype<charT>>(os.getloc()).widen('1'))
(see [ostream.formatted]).