Document number: | N3542 |
Date: | 2013-03-18 |
Revises: | N3417=12-0107 |
Project: | Programming Language C++ |
Reference: | ISO/IEC IS 14882:2011(E) |
Reply to: | Pete Becker |
Roundhouse Consulting, Ltd. | |
pete@versatilecoding.com |
unsigned_integer
and integer
;unsigned_integer
;integer_data_proxy
for manipulating the internal
representation of an integer
object to provide advanced users
with hooks for extended operations;unsigned_integer
to bits
and gave it
the same interface as std::bitset
.
Programmers sometimes need to manipulate integer values that are too large to repesent with C++’s standard integer types. Doing a Google search for terms that describe large integers produces many hits for libraries that handle large integers. These libraries vary in quality, from hacks by beginners to sophisticated, professional implementations. Also, Java has unbounded precision integers as part of its standard class library.
One important use for unbounded-precision integers is cryptography. Cryptographic applications typically manipulate integer values of several hundred digits. If the C++ standard library provides facilities for such values it will make cryptographic applications easier to write and to port.
There have been two Committee papers proposing unbounded-precision integer libraries for C++: N1718 (2004) and N2143 (2007), both by M.J. Kronenburg. Nothing was done with these papers, in part because there was too much else going on in the Library Working Group at the time. Now that the Committee is looking to greatly expand the scope of the standard library, it’s time to reconsider unbounded-precision integers.
An unbounded-precision integer type is an integer type that does not impose pre-defined limits on the precision of the values that it can represent. Of course, in practice, unbounded precision can’t be achieved; sooner or later the system runs out of resources. So unbounded in this context means bounded only by the availability of system resources; there is no hard-coded limit to the number of digits in the value that an unbounded-precision integer type an represent.
Unbounded-precision integer types should interoperate with C++’s built-in integer types. Applying arithmetic operations to a mix of standard integer types and unbounded-precision integer types should just work. And to the extent possible, operations that can be applied to standard integer types should also be applicable, using the same syntax, to unbounded-precision integer types.
Unbounded-precision integer types should also provide operations that facilitate their use in areas that demand such types. Since there is a potentially unbounded list of operations that could be useful in applications that need unbounded-precision integer types, it is not practical to provide every useful operation. This proposal presents a small set of required operations and provides a facility for users to write their own extensions.
This paper proposes two unbounded-precision integer types.
The type
integer
represents signed integer values.
The type
bits
represents an unbounded set of bit values.
To support interoperability, objects of either type can be constructed from values of any of the standard integer types. So code like this just works:
integer i = 30000;
integer j = 1000 * i;
bits b = 0xFF;
bits c = b & 0xAA;
Converting a negative number to an object of type
bits
sets the number to the complement of
this initializer, so this code just works:
bits b = -3; // sets b
to ...11111100
This is easily implemented by storing a finite set of 1 bits (in this case, 0x03) and using a flag to indicate whether the actual value is represented by that set of bits or by its complement.
As currently specified, neither integer
nor
bits
provides overloaded operators that take standard integer
types. When an operation is applied to a standard integer type and an
integer
object or a bits
object, the standard integer
operand is converted to the appropriate unbounded-precision integer type and the
operation is applied to the result. It is assumed that implementations will make
this kind of mixed operation efficient by implementing a small-integer
optimization, storing small values directly in the integer
or bits
object, and using heap storage when needed for larger
values. This greatly simplifies the interface specification.
Objects of these types can be constructed from string representations (with the usual range of possible bases) and from an initializer list that holds unsigned 32-bit values.
Objects of type integer
can also be constructed from values of floating-point
types.
Values of type integer
and of type bits
can be
freely inter-converted.
Bit manipulations on bits
objects treat the value as
having an unbounded number of bits above the highest bit stored in the
object. As a result, the usual bit operations, &, |, and ^, can be applied to
values of different sizes. Further, std::seminumeric::bits
can be used as
a replacement for std::bitset
when limiting the object
to a fixed number of bits is undesirable.
bits
value from a smaller value doesn’t have any specified semantics in
this paper. This should probably throw an exception. Resolution: removed arithmetic operations
on bits
objects.bits
object from a negative value doesn’t have
any specified semantics in this paper. This should probably throw an
exception. Resolution: negative values produce complemented bit sets.bits
or integer
object to an integral type
that cannot represent its value doesn’t have any specified semantics in
this paper. Should this throw an exception?integer operator+(integer&& lhs, const integer& rhs) {
return std::move(lsh += rhs);
}
std::string
, many operations can be made faster by pre-allocating enough
memory to hold the expected result. In some cases the desired capacity is best expressed in bits and
in some cases in decimal digits, so the suggestion is to offer both:
size_t capacity_in_bits() const; // The number of bits the object can hold without reallocation.
size_t capacity_in_digits() const; // The largest number n such that the object can hold n decimal
// digits without reallocation.
void reserve_bits(size_t n); // Postcondition: capacity_in_bits() >= n.
void reserve_digits(size_t n); // Postcondition: capacity_in_digits() >= n.
void shrink_to_fit()(); // A non-binding request to reduce memory usage.
constexpr
, which they cannot, in general, be, because they need
to allocate memory.noexcept
specifications as appropriate
(Alisdair Meredith) -- there are several that are obvious. In addition, if we require the
small-object optimization, some or all of the constructors that take integral types can be
noexcept
.constexpr
specifications as appropriate
(Alisdair Meredith) -- although most functions can allocate memory, there are a few that
could be marked constexpr
. It’s not clear how useful this would be.int
argument?
(Alisdiar Meredith, Marc Glisse) -- this may be limiting, for example, on a 64-bit OS with a 32-bit
int
type. size_t
or ptrdiff_t
may be a better choice.basic_string
typedefs. Resolution: string operations are now fully
templated.template<class charT, class Traits, class Alloc>
void bits::load(basic_string<charT, Traits, Alloc>&);
unsigned_integer
to bits
with same interface as std::bitset
.powmod
should be specified to run in constant time with identical cache access patterns
for arguments of the same size (Jack Lloyd) -- this is important for cryptographic
purposes, to avoid side-channel attacks. Resolution: removed powmod
and provided a do-it-yourself solution.integer_data_proxy
.unsigned_integer
type necessary? (Marc Glisse) -- if this is there
to support bit manipulation, why not just specify those operations as undefined for
negative numbers. Resolution: removed unsigned_integer
and added
bits
, whose sole purpose is bit manipulation.mod
return negative values?string
should be explicit. (Marc Glisse) Resolution: done.to_string()
a non-member function. (Daniel Krügler)
-- this would be a good match with the existing to_string
functions.
Resolution: done for integer
; bits
has it as a
member to match std::bitset
.explicit operator std::string() const
. (Daniel Krügler,
Jens Maurer) -- to_string()
is sufficient. Resolution: done.<seminumeric>
synopsisnamespace std {
namespace seminumeric {
/* class integer */
class integer;
class integer_data_proxy;
void swap(integer& lhs, integer& rhs);
// comparisons
bool operator==(const integer& lhs, const integer& rhs);
bool operator!=(const integer& lhs, const integer& rhs);
bool operator<(const integer& lhs, const integer& rhs);
bool operator<=(const integer& lhs, const integer& rhs);
bool operator>(const integer& lhs, const integer& rhs);
bool operator>=(const integer& lhs, const integer& rhs);
// arithmetic operations
integer operator+(const integer& lhs, const integer& rhs);
integer operator-(const integer& lhs, const integer& rhs);
integer operator*(const integer& lhs, const integer& rhs);
integer operator/(const integer& lhs, const integer& rhs);
integer operator%(const integer& lhs, const integer& rhs);
std::pair<integer, integer> div(const integer& lhs, const integer& rhs);
integer abs(const integer& val);
integer operator<<(const integer& lhs, int shift);
integer operator>>(const integer& lhs, int shift);
// numeric operations
integer sqr(const integer& val);
integer sqrt(const integer& val);
integer pow(const integer& val, const integer& exp);
// conversions
std::string to_string(const integer& val, int radix = 16);
// I/O operations
template <class CharT, class Traits>
std::basic_ostream<CharT, Traits>& operator<<(
std::basic_ostream<CharT, Traits>& str, const integer& val);
template <class CharT, class Traits>
std::basic_istream<CharT, Traits>& operator>>(
std::basic_istream<CharT, Traits>& str, integer& val);
/* class bits */
class bits;
void swap(bits& lhs, bits& rhs);
// logical operations
bits operator&(const bits& lhs, const bits& rhs);
bits operator|(const bits& lhs, const bits& rhs);
bits operator^(const bits& lhs, const bits& rhs);
// I/O operations
template <class CharT, class Traits>
std::basic_ostream<CharT, Traits>& operator<<(
std::basic_ostream<CharT, Traits>& str, const bits& val);
template <class CharT, class Traits>
std::basic_istream<CharT, Traits>& operator>>(
std::basic_istream<CharT, Traits>& str, bits& val);
} /* namespace seminumeric */
template <> class numeric_limits<seminumeric::integer>;
} /* namespace std */
integer
class integer {
public:
// constructors
integer();
integer(char val);
integer(signed char val);
integer(unsigned char val);
integer(short val);
integer(unsigned short val);
integer(int val);
integer(unsigned val);
integer(long val);
integer(unsigned long val);
integer(long long val);
integer(unsigned long long val);
integer(float val);
integer(double val);
integer(long double val);
integer(std::initializer_list<uint_least32_t> init);
template <class CharT, class Traits, class Alloc>
explicit integer(const std::basic_string<CharT, Traits, Alloc>& str);
integer(const integer& other);
integer(integer&& other);
explicit integer(const bits& val);
explicit integer(bits&& val);
// assignment and swap
integer& operator=(const integer& rhs);
integer& operator=(integer&& rhs);
integer& operator=(const bits& rhs);
integer& operator=(bits&& rhs);
void swap(integer& other);
// conversions
explicit operator long long() const;
explicit operator unsigned long long() const;
explicit operator long double() const;
explicit operator bool() const;
// comparisons
int compare(const integer& rhs) const;
// arithmetic operations
integer& operator+=(const integer& rhs);
integer& operator-=(const integer& rhs);
integer& operator*=(const integer& rhs);
integer& operator/=(const integer& rhs);
integer& operator%=(const integer& rhs);
integer& operator++();
integer operator++(int);
integer& operator--();
integer operator--(int);
integer div(const integer& rhs);
integer& abs();
integer& negate();
integer operator+() const;
integer operator-() const;
integer& operator<<=(int shift);
integer& operator>>=(int shift);
// numeric operations
integer& sqr();
integer& sqrt();
integer& pow(const integer& exp);
// observers
bool is_odd() const;
// accessors
integer_data_proxy get_data_proxy();
};
The class describes an object that manages an unbounded-precision signed integral type
that can be used in most contexts where an int
could be used.
integer abs(const integer& other);
integer& integer::abs();
The first function returns an object that holds the absolute value lf
other. The second function sets the stored value of
*this
to its absolute value and returns a reference to
*this
.
int integer::compare(const integer& right) const;
The member function returns a value less than 0 if *this
is less than
rhs
, 0 if *this
is equal to rhs
, and greater than 0
if *this
is greater than rhs
.
std::pair<integer, integer> div(const integer& left, const integer& right);
std::pair<integer, integer> integer::div(const integer& right) const;
The functions return an object that is an instantiation of
std::pair
; its first
field holds the quotient,
left / right
or *this / right
, and its
second
field holds the remainder, left % right
or
*this % right
.
integer_data_proxy integer::get_data_proxy();
The member function returns an object of type
integer_data_proxy
that can be used to examine and modify the internal storage of
*this
. If an object of type integer_data_proxy
that refers
to *this
exists at the time of a call to this function, the function
throws an exception object of type std::runtime_error
.
integer::integer();
integer::integer(char val);
integer::integer(signed char val);
integer::integer(unsigned char val);
integer::integer(short val);
integer::integer(unsigned short val);
integer::integer(int val);
integer::integer(unsigned int val);
integer::integer(long val);
integer::integer(unsigned long val);
integer::integer(long long val);
integer::integer(unsigned long long val);
integer::integer(float val);
integer::integer(double val);
integer::integer(long double val);
integer::integer(std::initializer_list<unspecified> list);
template<class CharT, class Traits, class Alloc>
explicit integer::integer(const std::basic_string<CharT, Traits, Alloc>& str);
integer::integer(const integer& other);
integer::integer(integer&& other);
integer::integer(const bits& other);
integer::integer(bits&& other);
The default constructor constructs an object whose value is
0
.
The constructors that take integral arguments construct objects whose value
is val
.
The constructors that take floating-point arguments construct objects whose
value is an approximation to val
, accurate to at least
std::numeric_limits
.
The constructor that takes a string
constructs an object whose
value is the value represented by the string object. The string object shall
have the form required for the string argument to the function
std::strtol
with a radix of base
, and shall be
interpreted as if by std::strtol(str.c_str(), 0, base)
, except that
the resulting value can never be outside the range of representable values.
The constructor that takes an initializer_list constructs an object whose
stored value is equal to the elements of the initializer_list treated as a
series of unsigned 32-bit digits with the leftmost digit being most significant.
For example, the initializer list { 0xFE, 0xF0, 0xAA, 0x31 }
represents the value 0xFE * 323 + 0xF0 * 322 + 0xAA
* 321 + 0x31 * 320
.
The copy and move constructors construct objects with the same value as
other
.
bool integer::is_odd() const;
The member function returns true
only if the stored value
represents an odd number.
integer& integer::negate();
The member function sets the stored value of *this
to the
negation of its previous vaue and returns a reference to *this
.
integer& integer::operator=(const integer& right);
integer& integer::operator=(integer&& right);
integer& integer::operator=(const bits& right);
integer& integer::operator=(bits&& right);
The operators store the value of right
into
*this
.
integer operator+(const integer& left, const integer& right);
integer integer::operator+() const;
The first operator returns an object whose value is the sum of the values of
left
and right
. The second operator returns a copy of
*this
.
integer& integer::operator+=(const integer& right);
The member operator sets the stored value of *this
to the sum of
the values of *this
and right
and returns a reference
to *this
.
integer& integer::operator++();
integer integer::operator++(int);
The member operators set the value stored in *this
to
*this + 1
. The first operator returns *this
. The
second operator returns an object whose value is the value stored in
*this
prior to the increment.
integer operator-(const integer& left, const integer& right)
integer integer::operator-();
The first operator returns an object whose value is the difference between the
values of left
and right
. The second operator returns
an object whose value is the negation of the value of *this
.
integer& integer::operator-=(const integer&);
The member operator sets the stored value of *this
to the
difference between the values of *this
and right
and
returns a reference to *this
.
integer& integer::operator--();
integer integer::operator--(int);
The member operators set the value stored in *this
to
*this - 1
. The first operator returns *this
. The
second operator returns an object whose value is the value stored in
*this
prior to the decrement.
integer operator*(const integer& left, const integer& right);
The operator returns an object whose value is the product of the values of
left
and right
.
integer& integer::operator*=(const integer& right);
The member operator sets the stored value of *this
to the
product of the values of *this
and right
and returns a
reference to *this
.
integer operator/(const integer& left, const integer& right);
The operator returns an object whose value is the quotient of the value of
left
divided by the value of right
, discarding any
fractional part.
integer& integer::operator/=(const integer& right);
The member operator sets the stored value of *this
to the
quotient of the value of *this
divided by the value of
right
, discarding any fractional part, and returns a reference to
*this
.
integer operator%(const integer&, const integer&);
The operator returns an object whose value is the remainder of the value of
left
divided by the value of right
. The remainder is
the value such that (left / right) * right + left % right
is equal
to left
.
integer& integer::operator%=(const integer&);
The member operator sets the stored value of *this
to the
remainder of *this
divided by the value of right
and
returns a reference to *this
.
integer operator>>(const integer& val, int shift);
If the value of shift
is negative, the operator
returns operator<<(val, -shift)
. Otherwise,
the operator returns a new object whose value is
val / 2shift
.
integer& integer::operator>>=(int);
If the value of shift
is negative, the operator has the
effect of *this <<= -shift
. Otherwise, the operator
sets the value of *this
to *this / 2shift
.
The operator returns a reference to *this
.
template <class Elem, class Traits>
std::basic_istream<Elem, Traits>& operator>>(std::basic_istream<Elem, Traits>& strm, integer& val);
The operator has the effect of { std::string temp; strm >>
temp; val = temp; }
. It returns a reference to strm
.
integer operator<<(const integer& val, int shift);
If the value of shift
is negative, the operator returns
operator>>(val, -shift)
. Otherwise, the operator returns a new
object whose value is val * 2shift
.
integer& integer::operator<<=(int shift);
If the value of shift
is negative, the operator has the effect
of *this >>= -shift
. Otherwise, the operator sets the value
of *this
to *this * 2shift
. The operator
returns a reference to *this
.
template <class Elem, class Traits>
std::basic_ostream<Elem, Traits>& operator<<(std::basic_ostream<Elem, Traits>& strm, const integer& val);
The operator has the effect of strm << val.to_string()
.
It returns a reference to strm
.
explicit integer::operator bool() const;
The operator returns false
only if *this
is equal to
0
.
explicit integer::operator long double() const;
The operator returns a value equal to the stored value of
*this
.
explicit bits::operator long long() const;
The operator returns a value equal to the stored value of
*this
.
explicit bits::operator unsigned long long() const;
The operator returns a value equal to the stored value of
*this
.
bool operator==(const integer& left, const integer& right);
The operator returns true
only if the value stored
in left
is equal to the value stored in right
.
bool operator!=(const integer& left, const integer& right);
The operator returns !(left == right)
.
bool operator>(const integer& left, const integer& right);
The operator returns right < left
.
bool operator>=(const integer& left, const integer& right);
The operator returns !(left < right)
.
bool operator<(const integer& left, const integer& right);
The operator return true
only if left.compare(right)
returns -1.
bool operator<=(const integer& left, const integer& right);
The operator returns !(right < left)
.
integer pow(const integer& val, const integer& exp);
integer& integer::pow(const integer& exp);
The non-member function returns an object whose value is
valexp
. The member function sets the value of
*this
to *thisexp
and returns
*this
. Requires: 0 <= exp
.
integer sqr(const integer& val);
integer& integer::sqr();
The non-member function returns an object whose value is
val * val
. The member function sets the value
of *this
to *this * *this
and returns
a reference to *this
.
integer sqrt(const integer&);
integer& integer::sqrt();
The non-member function returns an object whose value is the square root of
the value held by val
, discarding any fractional part. The member
function sets the value of *this
to the square root of the value
held by *this
, discarding any fractional part, and returns a
reference to *this
. Requires: 0 <= exp
.
void swap(integer& left, integer& right);
void integer::swap(integer& right);
The non-member function swaps the stored values of
left
and right
. The member function
swaps the stored values of *this
and right
.
std::string integer::to_string(int radix = 16) const;
The member function returns a string representation of the value stored in
*this
, using radix
as the radix.
integer_data_proxy
class integer_data_proxy {
// type names
typedef unspecified data_type;
typedef unspecified arithmetic_type;
typedef unspecified uarithmetic_type;
typedef unspecified size_type;
typedef unspecified iterator;
typedef unspecified const_iterator;
typedef unspecified reverse_iterator;
typedef unspecified const_reverse_iterator;
// constructors
integer_data_proxy(const integer_data_proxy& other) = delete;
integer_data_proxy(integer_data_proxy&& other) = default;
// assignment
integer_data_proxy& operator=(const integer_data_proxy& rhs) = delete;
integer_data_proxy& operator=(integer_data_proxy&& rhs) = default;
// iterators
iterator begin();
const_iterator begin() const;
iterator end();
const_iterator end() const;
reverse_iterator rbegin();
const_reverse_iterator rbegin() const;
reverse_iterator rend();
const_reverse_iterator rend() const;
const_iterator cbegin() const;
const_iterator cend() const;
const_reverse_iterator crbegin() const;
const_reverse_iterator crend() const;
// capacity
size_type size() const;
void resize(size_type sz);
// element access
data_type operator[](size_type n) const;
data_type& operator[](size_type n);
};
The class describes an object that can be used to examine and
modify the internal representation of an object of type
integer
. This allows advanced users to portably implement
algorithms that are not provided natively.
There can be only one integer_data_proxy
object
associated with a particular integer
object at any given
time; that object is obtained by calling the get_data_proxy
member
function on the integer
object. The resulting object can
be moved but not copied.
typedef unspecified integer_data:proxy::arithmetic_type;
The typedef defines a synonym for a signed arithmetic type with at least twice as many bits as the internal storage type.
beginiterator integer_data_proxy::begin();
The member function returns an iterator object such that the iterators [begin(), end())
point to the internal data elements of the integer
object.
const_iterator integer_data_proxy::cbegin() const;
The member function returns an iterator object such that the iterators [cbegin(), cend())
point to the internal data elements of the integer
object.
const_iterator integer_data_proxy::cend() const;
The member function returns an iterator object such that the iterators [cbegin(), cend())
point to the internal data elements of the integer
object.
typedef unspecified integer_data_proxy::const_iterator;
The typedef defines a synonym for an iterator that can be used to access but not
modify internal data elements of the integer
object.
typedef unspecified integer_data_proxy::const_reverse_iterator;
The typedef defines a synonym for a reverse iterator that can be used to access but not
modify internal data elements of the integer
object.
const_reverse_iterator integer_data_proxy::crbegin() const;
The member function returns a reverse iterator object such that the iterators [crbegin(), crend())
point to the internal data elements of the integer
object.
const_reverse_iterator integer_data_proxy::crend() const;
The member function returns a reverse iterator object such that the iterators [crbegin(), crend())
point to the internal data elements of the integer
object.
typedef unspecified integer_data_proxy::data_type;
The typedef defines a synonym for the type of the integer
object's internal data elements.
iterator integer_data_proxy::end();
The member function returns an iterator object such that the iterators [begin(), end())
point to the internal data elements of the integer
object.
integer_data_proxy::integer_data_proxy(const integer_data_proxy&) = delete;
integer_data_proxy::integer_data_proxy(integer_data_proxy&&) = delete;
The copy constructor and move constructor are deleted.
iteratortypedef unspecified integer_data_proxy::iterator;
The typedef defines a synonym for an iterator that can be used to access
internal data elements of the integer
object.
integer& integer_data_proxy::operator=(const integer_data_proxy&) = delete;
integer& integer_data_proxy::operator=(integer_data_proxy&&) = delete;
The copy assignment and move assignment operators are deleted.
operator[]data_type integer_data_proxy::operator[](size_type n) const;
data_type& integer_data_proxy::operator[](size_type n);
The first member function returns the value of the internal data element at
index n
. The second member function returns a reference to the
value of the internal data element at index n
.
const_reverse_iterator integer_data_proxy::rbegin() const;
reverse_iterator integer_data_proxy::rbegin();
The member functions return a reverse iterator object such that the iterators [crbegin(), crend())
point to the internal data elements of the integer
object.
const_reverse_iterator integer_data_proxy::rend() const;
reverse_iterator integer_data_proxy::rend();
The member functions return a reverse iterator object such that the iterators [crbegin(), crend())
point to the internal data elements of the integer
object.
void integer_data_proxy::resize(size_type sz);
The member function ensures that the integer
object holds
at least sz
internal data elements.
typedef unspecified integer_data_proxy::reverse_iterator;
The typedef defines a synonym for a reverse iterator that can be used to access
internal data elements of the integer
object.
size_type integer_data_proxy::size() const;
The member function returns the number of internal data elements in the
integer
object.
typedef unspecified integer_data_proxy::size_type;
The typedef defines a synonym for an unsigned arithmetic type that can hold a
count of the number of internal data elements in the integer
object.
typedef unspecified integer_data:proxy::uarithmetic_type;
The typedef defines a synonym for an unsigned arithmetic type with at least twice as many bits as the internal storage type.
bits
class bits {
public:
class reference;
// constructors
bits();
bits(char val);
bits(signed char val);
bits(unsigned char val);
bits(short val);
bits(unsigned short val);
bits(int val);
bits(unsigned val);
bits(long val);
bits(unsigned long val);
bits(long long val);
bits(unsigned long long val);
bits(const char *str);
template <class CharT, class Traits, class Alloc>
explicit bits(const basic_string<CharT, Traits, Alloc>& str,
typename basic_string<CharT, Traits, Alloc>::size_type pos = 0,
typename basic_string<CharT, Traits, Alloc>::size_type count = std::basic_string<CharT>::npos,
CharT digit0 = CharT('0'),
CharT digit1 = CharT('1'));
template <class CharT>
explicit bits(const CharT *ptr,
typename basic_string<CharT>::size_type count = std::basic_string<CharT>::npos,
CharT digit0 = CharT('0'),
CharT digit1 = CharT('1'));
bits(std::initializer_list<uint_least32_t> list);
bits(const bits& other);
bits(bits&& other);
bits(const integer& val);
bits(integer&& val);
// assignment and swap
bits& operator=(const bits& rhs);
bits& operator=(bits&& rhs);
bits& operator=(const integer& rhs);
bits& operator=(integer&& rhs);
void swap(bits& rhs);
// conversions
unsigned long to_ulong() const;
unsigned long long to_ullong() const;
template <class CharT = char, class Traits = std::char_traits<CharT>, class Alloc = std::allocator<CharT> >
std::basic_string<CharT, Traits, Alloc> to_string(CharT zero = CharT('0'), CharT one = CharT('1'));
// logical operations
bits& operator&=(const bits& rhs);
bits& operator|=(const bits& rhs);
bits& operator^=(const bits& rhs);
bits operator~() const;
bits& operator<<=(size_type shift);
bits& operator>>=(size_type shift);
bits& operator<<(size_type shift) const;
bits& operator>>(size_type shift) const;
// element access and modification
bits& set();
bits& set(size_type pos, bool val = true);
bits& reset();
bits& reset(size_type pos);
bits& flip();
bits& flip(size_type pos);
bool operator[](size_type pos) const;
reference operator[](size_type pos);
bool test(size_type pos) const;
bool all() const;
bool any() const;
bool none() const;
size_type lowest_bit() const;
size_type highest_bit() const;
size_type count() const;
// capacity
size_type size() const;
void resize(size_type sz);
};
The class describes an object that represents an unbounded set of bits.
allbool all() const
The member function returns true only if all the bits in
*this
are set.
bool any() const
The member function returns true if at least one of the
bits in *this
is set.
bits::bits();
bits::bits(char val);
bits::bits(signed char val);
bits::bits(unsigned char val);
bits::bits(short val);
bits::bits(unsigned short val);
bits::bits(int val);
bits::bits(unsigned int val);
bits::bits(long val);
bits::bits(unsigned long val);
bits::bits(long long val);
bits::bits(unsigned long long val);
bits::bits(const char *str);
template <class CharT, class Traits, class Alloc>
explicit bits::bits(const basic_string<CharT, Traits, Alloc>& str,
typename basic_string<CharT, Traits, Alloc>::size_type pos = 0,
typename basic_string<CharT, Traits, Alloc>::size_type count = std::basic_string<CharT>::npos,
CharT digit0 = CharT('0'),
CharT digit1 = CharT('1'));
template <class CharT>
explicit bits::bits(const CharT *ptr,
typename basic_string<CharT>::size_type count = std::basic_string<CharT>::npos,
CharT digit0 = CharT('0'),
CharT digit1 = CharT('1'));
bits::bits(std::initializer_list<uint_least32_t> list);
bits::bits(const bits& other);
bits::bits(bits&& other);
explicit bits::bits(const integer& other);
explicit bits::bits(integer&& other);
The default constructor constructs an object whose value is
0
.
The constructors that take integral arguments
construct objects whose value is val
; negative values
construct an object whose value is the complement of bits(abs(val))
.
The constructors that take string
and const char*
objects construct an object whose value is the value represented by their argument,
treating zero
as 0 and one
as 1.
The constructor that takes an initializer_list constructs an object whose
stored value is equal to the elements of the initializer_list treated as a
series of unsigned 32-bit digits with the leftmost digit being most significant.
For example, the initializer list { 0xFE, 0xF0, 0xAA, 0x31 }
represents the value 0xFE * 323 + 0xF0 * 322 + 0xAA
* 321 + 0x31 * 320
.
The copy and move constructors construct objects with the same value as
other
; the move constructors leave other
in an unspecified
valid state. Construction from a negative integer
value constructs
an object whose value is the complement of bits(abs(val))
.
size_type count() const;
The member function returns the number of bits in *this
that are set.
void bits::flip(size_t pos);
The member function toggles the bit at position pos
in the
stored value.
int bits::highest_bit() const;
The member function returns the zero-based position of the highest non-zero bit in the stored value, or -1 if there are no non-zero bits.
lowest_bitint bits::lowest_bit() const;
The member function returns the zero-based position of the lowest non-zero bit in the stored value, or -1 if there are no non-zero bits.
nonebool none() const;
The member function returns true only if none of the bits in *this
is set.
bits& bits::operator=(const bits& right);
bits& bits::operator=(bits&& right);
bits& bits::operator=(const unsigned_bits& right);
bits& bits::operator=(unsigned_bits&& right);
The operators store the value of right
into
*this
.
bits operator&(const bits& left, const bits& right);
The operator returns an object whose value is the bitwise AND of the values
of left
and right
.
bits& bits::operator&=(const bits& right);
The member operator sets the value of *this
to the bitwise AND
of the values of *this
and right
and returns a
reference to *this
.
bits operator|(const bits& left, const bits& right);
The operator returns an object whose value is the bitwise inclusive OR of the
values of left
and right
.
bits& bits::operator|=(const bits& right);
The member operator sets the value of *this
to the bitwise
inclusive OR of the values of *this
and right
and
returns a reference to *this
.
bits operator^(const bits& left, const bits& right);
The operator returns an object whose value is the bitwise exclusive OR of
the values of left
and right
.
bits& bits::operator^=(const bits& right);
The member operator sets the value of *this
to the bitwise
exclusive OR of the values of *this
and right
and
returns a reference to *this
.
bits operator~() const;
The member function returns an object that holds the complement
of the set of bits held by *this
.
bits operator>>(const bits& val, int shift);
If the value of shift
is negative, the operator
returns operator<<(val, -shift)
. Otherwise,
the operator returns a new object whose stored value is the value of
the bits in *this
shifted right shift
positions.
bits& bits::operator>>=(int shift);
If the value of shift
is negative, the operator
returns val << -shift
. Otherwise,
the operator sets the stored value in *this
to the value of
the bits in *this
shifted right shift
positions.
template <class CharT, class Traits>
std::basic_istream<CharT, Traits>& operator>>(
std::basic_istream<CharT, Traits>& str, bits& val);
The operator has the effect of { std::string temp; strm >>
temp; val = temp; }
and returns a reference to strm
.
bits operator<<(const bits& val, int shift);
If the value of shift
is negative, the operator
returns operator>>(val, -shift)
. Otherwise,
the operator returns a new object whose stored value is the value of
the bits in *this
shifted left shift
positions.
bits& bits::operator<<=(int shift);
If the value of shift
is negative, the operator
returns val >> -shift
. Otherwise,
the operator sets the stored value in *this
to the value of
the bits in *this
shifted left shift
positions.
template <class CharT, class Traits>
std::basic_ostream<CharT, Traits>& operator<<(
std::basic_ostream<CharT, Traits>& str, const bits& val);
The operator has the effect of strm << val.to_string()
and returns a reference to strm
.
bool operator[](size_type pos) const;
reference operator[](size_type pos);
The first member function returns the value of the bit at position pos
.
The second member function returns an object of type bits::reference
that refers to the bit at position pos
.
bits& reset();
bits& reset(size_type pos);
The first member function clears all the bits of *this
.
The second member function clears the bit as position pos
.
void resize(size_type sz);
The member function adjusts the storage capacity of*this
so that it can hold at least sz
bits without reallocating.
void bits::set();
void bits::set(size_t pos, bool val = true);
The first member function sets all the bits of *this
.
The second member function sets the bit at position pos
in the stored
value to val
.
size_type size() const;
The member function returns the maximum number of bits that can be held in
*this
without reallocating.
void swap(bits& left, bits& right);
void bits::swap(bits& right);
The non-member function swaps the stored values of
left
and right
. The member function
swaps the stored values of *this
and right
.
bool bits::test(size_t pos) const;
The member function returns true
only if the bit
at position pos
in the stored value is non-zero.
template <class CharT = char, class Traits = std::char_traits<CharT>, class Alloc = std::allocator<CharT> >
std::basic_string<CharT, Traits, Alloc> bits::to_string(
CharT zero = CharT('0'), CharT one = CharT('1'));
The member function returns a string representation of the value stored in
*this
, using zero
to represent 0 and one
to represent 1.
unsigned long long bits::to_ullong() const;
The member function returns a value equal to the stored value of
*this
.
unsigned long bits::to_ulong() const;
The member function returns a value equal to the stored value of
*this
.
bits::reference
class bits {
class reference {
public:
reference& operator=(bool val);
reference& operator=(const reference& rhs);
bool operator~() const;
operator bool() const;
reference& flip();
};
};
The nested class bits::reference
describes an object that
can be used to manage a particular bit in an object of type bits
.
reference& bits::reference::flip();
The member function toggles the bit that the object manages.
operator=reference& bits::reference::operator=(bool right);
reference& bits::reference::operator=(const reference& right);
The first member operator sets the bit that the object manages to the
value of right
. The second member operator sets the bit that
the object manages to the value managed by right
.
bool bits::reference::operator~() const;
The member operator returns true
if the bit managed by the
object is set, otherwise false
.
bits::reference::operator bool() const;
The member operator returns true if the bit that the object manages is set.