gf2::BitArray< N, Word >

A fixed-size "vector" over GF(2) with N bit elements compactly stored in a standard array of primitive unsigned words whose type is given by the template parameter Word. The elements in a bit-array are initially all set to 0. More...

#include <BitArray.h>

Public Types
using	word_type = Word
	The underlying unsigned word type used to store the bits.

Public Member Functions
Required BitStore Concept Methods.
constexpr usize	size () const
	Returns the number of bit-elements in the bit-array.
constexpr usize	words () const
	Returns the number of words in the bit-array's underlying word store.
constexpr Word	word (usize i) const
	Returns word i from the bit-array's underlying word store.
constexpr void	set_word (usize i, Word word)
	Sets word i in the bit-array's underlying word store to value (masked if necessary).
constexpr const Word *	store () const
	Returns a const pointer to the underlying store of words .
constexpr Word *	store ()
	Returns a pointer to the underlying store of words.
constexpr u8	offset () const
	Returns the offset (in bits) of the first bit in the bit-array within the first word.
Constructors:
constexpr	BitArray ()
	Constructs a bit-array of length N with all the bit elements set to 0.
constexpr	BitArray (Word word)
	Constructs a bit-array with N elements by repeatedly copying all the bits from word.
Accessors for Individual Bits:
constexpr bool	get (usize i) const
	Returns true if the bit at the given index i is set, false otherwise.
constexpr bool	operator[] (usize i) const
	Returns the boolean value of the bit element i.
constexpr bool	front () const
	Returns true if the first bit element is set, false otherwise.
constexpr bool	back () const
	Returns true if the last bit element is set, false otherwise.
Bit Mutators:
constexpr auto	set (usize i, bool value=true)
	Sets the bit-element i to the specified boolean value & returns this for chaining. The default value for value is true.
constexpr auto	operator[] (usize i)
	Returns a "reference" to the bit element i.
constexpr auto	flip (usize i)
	Flips the value of the bit-element i and returns this for chaining.
constexpr auto	swap (usize i0, usize i1)
	Swaps the bits in the bit-array at indices i0 and i1 and returns this for chaining.
BitArray Queries:
constexpr bool	is_empty () const
	Returns true if the bit-array is empty, false otherwise.
constexpr bool	any () const
	Returns true if at least one bit in the bit-array is set, false otherwise.
constexpr bool	all () const
	Returns true if all bits in the bit-array are set, false otherwise.
constexpr bool	none () const
	Returns true if no bits in the bit-array are set, false otherwise.
BitArray Whole Array Mutators:
constexpr auto	set_all (bool value=true)
	Sets all the bits in the bit-array to the boolean value and returns a reference to this for chaining.
constexpr auto	flip_all ()
	Flips the value of the bits in the bit-array and returns a reference to this for chaining.
Copying into the BitArray:
template<Unsigned Src>
constexpr auto	copy (Src src)
	Copies all the bits from any unsigned integral src value to this equal-sized bit-array. Returns a reference to this for chaining.
template<typename Iter> requires std::is_unsigned_v<typename std::iterator_traits<Iter>::value_type>
constexpr void	copy (Iter src_begin, Iter src_end)
	Copies all the bits from an iteration of any unsigned integral src values to this equal-sized bit-array.
template<BitStore Src>
constexpr auto	copy (Src const &src)
	Copies all the bits from any src bit-store to this equal-sized bit-array and returns a reference to this for chaining.
constexpr auto	copy (std::bitset< N > const &src)
	Copies all the bits from a std::bitset to this equal-sized bit-array and returns a reference to this for chaining.
BitArray Fills:
constexpr auto	copy (std::invocable< usize > auto f)
	Fill the bit-array by repeatedly calling f(i) and returns a reference to this for chaining.
constexpr auto	fill_random (double p=0.5, u64 seed=0)
	Fill the bit-array with random bits and returns a reference to this for chaining.
Bit Counts:
constexpr usize	count_ones () const
	Returns the number of set bits in the bit-array.
constexpr usize	count_zeros () const
	Returns the number of unset bits in the bit-array.
constexpr usize	leading_zeros () const
	Returns the number of leading zeros in the bit-array.
constexpr usize	trailing_zeros () const
	Returns the number of trailing zeros in the bit-array.
Set-bit Indices:
constexpr std::optional< usize >	first_set () const
	Returns the index of the first set bit in the bit-array or {} if no bits are set.
constexpr std::optional< usize >	last_set () const
	Returns the index of the last set bit in the bit-array or {} if no bits are set.
constexpr std::optional< usize >	next_set (usize index) const
	Returns the index of the next set bit after index in the bit-array or {} if no more set bits exist.
constexpr std::optional< usize >	previous_set (usize index) const
	Returns the index of the previous set bit before index in the bit-array or {} if there are none.
Unset-bit Indices:
constexpr std::optional< usize >	first_unset () const
	Returns the index of the first unset bit in the bit-array or {} if no bits are unset.
constexpr std::optional< usize >	last_unset () const
	Returns the index of the last unset bit in the bit-array or {} if no bits are unset.
constexpr std::optional< usize >	next_unset (usize index) const
	Returns the index of the next unset bit after index in the bit-array or {} if no more unset bits exist.
constexpr std::optional< usize >	previous_unset (usize index) const
	Returns the index of the previous unset bit before index in the bit-array or {} if no more unset bits exist.
BitArray Iterators:
constexpr auto	bits () const
	Returns a const iterator over the bool values of the bits in the const bit-array.
constexpr auto	bits ()
	Returns a non-const iterator over the values of the bits in the mutable bit-array.
constexpr auto	set_bits () const
	Returns an iterator over the indices of any set bits in the bit-array.
constexpr auto	unset_bits () const
	Returns an iterator over the indices of any unset bits in the bit-array.
constexpr auto	store_words () const
	Returns a const iterator over all the words underlying the v.
Exports:
constexpr void	to_words (std::output_iterator< word_type > auto out)
	Returns a copy of the words underlying this bit-array and puts them into the passed output iterator.
constexpr auto	to_words () const
	Returns a copy of the words underlying this bit-array as a std::vector<word_type>.
Spans:
constexpr auto	span (usize begin, usize end) const
	Returns an immutable bit-span encompassing the bit-array's bits in the half-open range [begin, end).
constexpr auto	span (usize begin, usize end)
	Returns a mutable bit-span encompassing the bit-array's bits in the half-open range [begin, end).
Sub-vectors:
constexpr auto	sub (usize begin, usize end) const
	Returns a clone of the elements in the half-open range [begin, end) as a new bit-vector.
Splits:
constexpr void	split_at (usize at, BitVector< word_type > &left, BitVector< word_type > &right) const
	Views the bit-array as two parts containing the elements [0, at) and [at, size()) respectively.
constexpr auto	split_at (usize at) const
	Views the bit-array as two parts containing the elements [0, at) and [at, size()) respectively.
Riffling:
constexpr void	riffled (BitVector< word_type > &dst) const
	Interleaves the bits of this bit-array with zeros storing the result into the bit-vector dst.
constexpr auto	riffled () const
	Returns a new bit-vector that is the result of riffling the bits in this bit-array with zeros.
String Representations:
std::string	to_binary_string (std::string_view sep="", std::string_view pre="", std::string_view post="") const
	Returns a binary string representation of the bit-array.
std::string	to_string (std::string_view sep="", std::string_view pre="", std::string_view post="") const
	Returns a binary string representation of the bit-array.
std::string	to_pretty_string () const
	Returns a "pretty" string representation of the bit-array.
std::string	to_hex_string () const
	Returns the "hex" string representation of the bits in the bit-array.
std::string	describe () const
	Returns a multi-line string describing the bit-array in some detail.

Static Public Member Functions
Factory Constructors:
static constexpr BitArray	zeros ()
	Factory method to generate a bit-array of length N where the elements are all 0.
static constexpr BitArray	ones ()
	Factory method to generate a bit-array of length N where the elements are all 1.
static constexpr BitArray	constant (bool value)
	Factory method to generate a bit-array of length N where the elements are set to value.
static constexpr BitArray	unit (usize i)
	Factory method to generate a "unit" bit-array of length N where only element i is set.
static constexpr BitArray	alternating ()
	Factory method to generate a bit-array of length N looking like 101010....
Construct BitArrays with Random Fills:
static BitArray	random (double p=0.5, u64 seed=0)
	Factory method to generate a bit-array of size N where the elements are picked at random.
static BitArray	seeded_random (u64 seed)
	Factory method to generate a bit-array of size N where the elements are from independent fair coin flips generated from an RNG seeded with the given seed.
static BitArray	biased_random (double p)
	Factory method to generate a bit-array of size N where the elements are from independent fair coin flips and where each bit is 1 with probability p.

Static Public Attributes
static constexpr u8	bits_per_word = BITS<Word>
	The number of bits per Word.

Helper Method:
constexpr void	clean ()
	Sets any unused bits in the last occupied word to 0.
template<Unsigned Src> requires (BITS<Src> == N)
static constexpr BitArray	from (Src src)
	Factory method to construct a bit-array by copying all the bits from any Unsigned instance.
template<typename Iter> requires std::is_unsigned_v<typename std::iterator_traits<Iter>::value_type>
static constexpr BitArray	from (Iter src_begin, Iter src_end)
	Factory method to construct a bit-array by copying all the bits from an iteration of any Unsigneds.
static constexpr BitArray	from (std::bitset< N > const &src)
	Factory method to construct a bit-array from the bits of a std::bitset.
static constexpr BitArray	from (std::invocable< usize > auto f)
	Factory method to construct a bit-array by repeatedly calling f(i) for i in [0, N).

Detailed Description

template<usize N, Unsigned Word = usize>
class gf2::BitArray< N, Word >

A fixed-size "vector" over GF(2) with N bit elements compactly stored in a standard array of primitive unsigned words whose type is given by the template parameter Word. The elements in a bit-array are initially all set to 0.

BitArray<N> is similar to std::bitset<N> but has a richer set of functionality.

The BitArray class satisfies the BitStore concept.

Constructor & Destructor Documentation

BitArray() [1/2]

template<usize N, Unsigned Word = usize>

gf2::BitArray< N, Word >::BitArray ( )

inlineexplicitconstexpr

Constructs a bit-array of length N with all the bit elements set to 0.

Example

BitArray<0> u;
assert_eq(u.to_string(), "");
BitArray<10, u8> v;
assert_eq(v.to_string(), "0000000000");

BitArray() [2/2]

template<usize N, Unsigned Word = usize>

gf2::BitArray< N, Word >::BitArray ( Word word )

inlineexplicitconstexpr

Constructs a bit-array with N elements by repeatedly copying all the bits from word.

The final copy of word may be truncated and padded with zeros (unused bit slots are always set to zero).

Example

BitArray<10, u8> v{u8{0b0101'0101}};
assert_eq(v.to_string(), "1010101010");

Member Function Documentation

all()

template<usize N, Unsigned Word = usize>

bool gf2::BitArray< N, Word >::all ( ) const

inlineconstexpr

Returns true if all bits in the bit-array are set, false otherwise.

Note: Empty bit-arrays have no set bits (logical connective for all is AND with identity true).

Example

BitArray<3> v;
assert_eq(v.all(), false);
v.set(0);
v.set(1);
v.set(2);
assert_eq(v.all(), true);

alternating()

template<usize N, Unsigned Word = usize>

constexpr BitArray gf2::BitArray< N, Word >::alternating ( )

inlinestaticconstexpr

Factory method to generate a bit-array of length N looking like 101010....

Example

auto v = BitArray<10, u8>::alternating();
assert_eq(v.to_string(), "1010101010");

any()

template<usize N, Unsigned Word = usize>

bool gf2::BitArray< N, Word >::any ( ) const

inlineconstexpr

Returns true if at least one bit in the bit-array is set, false otherwise.

Note: Empty bit-arrays have no set bits (logical connective for any is OR with identity false).

Example

BitArray<10> v;
assert_eq(v.any(), false);
v.set(0);
assert_eq(v.any(), true);

back()

template<usize N, Unsigned Word = usize>

bool gf2::BitArray< N, Word >::back ( ) const

inlineconstexpr

Returns true if the last bit element is set, false otherwise.

Panics

In debug mode the method panics if the bit-array is empty.

Example

BitArray<10> v;
assert_eq(v.back(), false);
v.set_all();
assert_eq(v.back(), true);

biased_random()

template<usize N, Unsigned Word = usize>

BitArray gf2::BitArray< N, Word >::biased_random ( double p )

inlinestatic

Factory method to generate a bit-array of size N where the elements are from independent fair coin flips and where each bit is 1 with probability p.

Parameters

p	The probability of the elements being 1.

Example

auto u = BitArray<10>::biased_random(0.3);
auto v = BitArray<10>::biased_random(0.3);
assert_eq(u.size(), v.size());

bits() [1/2]

template<usize N, Unsigned Word = usize>

auto gf2::BitArray< N, Word >::bits ( )

inlineconstexpr

Returns a non-const iterator over the values of the bits in the mutable bit-array.

You can use this iterator to iterate over the bits in the store to get or set the value of each bit.

Note

For the most part, try to avoid iterating through individual bits. It is much more efficient to use methods that work on whole words of bits at a time.

Example

BitArray<10, u8> v;
for (auto&& bit : v.bits()) bit = true;
assert_eq(v.to_string(), "1111111111");

bits() [2/2]

template<usize N, Unsigned Word = usize>

auto gf2::BitArray< N, Word >::bits ( ) const

inlineconstexpr

Returns a const iterator over the bool values of the bits in the const bit-array.

You can use this iterator to iterate over the bits in the store and get the values of each bit as a bool.

Note

For the most part, try to avoid iterating through individual bits. It is much more efficient to use methods that work on whole words of bits at a time.

Example

BitArray<37, u8> v; v.set_all();
for (auto&& bit : v.bits()) assert_eq(bit, true);

clean()

template<usize N, Unsigned Word = usize>

void gf2::BitArray< N, Word >::clean ( )

inlineconstexpr

Sets any unused bits in the last occupied word to 0.

You can use this helper method to enforce the guarantee that unused bits in the store are always set to 0.

constant()

template<usize N, Unsigned Word = usize>

constexpr BitArray gf2::BitArray< N, Word >::constant ( bool value )

inlinestaticconstexpr

Factory method to generate a bit-array of length N where the elements are set to value.

Example

auto v = BitArray<10>::constant(true);
assert_eq(v.to_string(), "1111111111");
auto w = BitArray<10>::constant(false);
assert_eq(w.to_string(), "0000000000");

copy() [1/5]

template<usize N, Unsigned Word = usize>

template<typename Iter>
requires std::is_unsigned_v<typename std::iterator_traits<Iter>::value_type>

void gf2::BitArray< N, Word >::copy ( Iter src_begin, Iter src_end )

inlineconstexpr

Copies all the bits from an iteration of any unsigned integral src values to this equal-sized bit-array.

Note

We allow any unsigned integral source, e.g. copying u64 words into a BitArray<N,u8> of the correct size.

Panics

Panics if the size of this bit-array does not match the number of bits in the source iteration.

Example

BitArray<48, u8> v;
std::vector<u16> src = { 0b1010101010101010, 0b1010101010101010, 0b1111111111111111 };
v.copy(src.begin(), src.end());
assert_eq(v.to_string(), "010101010101010101010101010101011111111111111111");
BitArray<48, u32> w;
w.copy(src.begin(), src.end());
assert_eq(w.to_string(), "010101010101010101010101010101011111111111111111");

copy() [2/5]

template<usize N, Unsigned Word = usize>

template<BitStore Src>

auto gf2::BitArray< N, Word >::copy ( Src const & src )

inlineconstexpr

Copies all the bits from any src bit-store to this equal-sized bit-array and returns a reference to this for chaining.

Note

This is one of the few methods in the library that doesn't require the two stores to have the same word_type. You can use it to convert between different word_type stores (e.g., from BitArray<u32> to BitArray<u8>) as long as the sizes match.

Panics

Panics if the sizes of this bit-array and the src bit-store do not match.

Example

BitArray<10, u64> v;
assert_eq(v.to_string(), "0000000000");
v.copy(BitVector<u8>::alternating(10));
assert_eq(v.to_string(), "1010101010");

copy() [3/5]

template<usize N, Unsigned Word = usize>

template<Unsigned Src>

auto gf2::BitArray< N, Word >::copy ( Src src )

inlineconstexpr

Copies all the bits from any unsigned integral src value to this equal-sized bit-array. Returns a reference to this for chaining.

Notes:

1. We allow any unsigned integral source, e.g. copying a single u64 into a BitArray<u8> of size 64.
2. The least-significant bit of the source becomes the bit at index 0 in the bit-array.

Panics

Panics if the size of the bit-array does not match the number of bits in the source integer type.

Example

BitArray<16, u8> v;
u16 src = 0b1010101010101010;
v.copy(src);
assert_eq(v.to_string(), "0101010101010101");
BitArray<16, u32> w;
w.copy(src);
assert_eq(w.to_string(), "0101010101010101");

copy() [4/5]

template<usize N, Unsigned Word = usize>

auto gf2::BitArray< N, Word >::copy ( std::bitset< N > const & src )

inlineconstexpr

Copies all the bits from a std::bitset to this equal-sized bit-array and returns a reference to this for chaining.

Note

A std::bitset prints its bit elements in bit-order which is the reverse of our convention.

Panics

Panics if the size of the bit-array does not match the number of bits in the source std::bitset.

Example

std::bitset<10> src{0b1010101010};
BitArray<10> v;
v.copy(src);
assert_eq(v.to_string(), "0101010101");

copy() [5/5]

template<usize N, Unsigned Word = usize>

auto gf2::BitArray< N, Word >::copy ( std::invocable< usize > auto f )

inlineconstexpr

Fill the bit-array by repeatedly calling f(i) and returns a reference to this for chaining.

Example

BitArray<10> v;
v.copy([](usize i) { return i % 2 == 0; });
assert_eq(v.size(), 10);
assert_eq(v.to_string(), "1010101010");

count_ones()

template<usize N, Unsigned Word = usize>

usize gf2::BitArray< N, Word >::count_ones ( ) const

inlineconstexpr

Returns the number of set bits in the bit-array.

Example

BitArray<10> v;
assert_eq(v.count_ones(), 0);
v.set(0);
assert_eq(v.count_ones(), 1);

count_zeros()

template<usize N, Unsigned Word = usize>

usize gf2::BitArray< N, Word >::count_zeros ( ) const

inlineconstexpr

Returns the number of unset bits in the bit-array.

Example

BitArray<10> v;
assert_eq(v.count_zeros(), 10);
v.set(0);
assert_eq(v.count_zeros(), 9);

describe()

template<usize N, Unsigned Word = usize>

std::string gf2::BitArray< N, Word >::describe ( ) const

inline

Returns a multi-line string describing the bit-array in some detail.

This method is useful for debugging but you should not rely on the output format which may change.

fill_random()

template<usize N, Unsigned Word = usize>

auto gf2::BitArray< N, Word >::fill_random ( double p = 0.5, u64 seed = 0 )

inlineconstexpr

Fill the bit-array with random bits and returns a reference to this for chaining.

The default call fill_random() sets each bit to 1 with probability 0.5 (fair coin).

Parameters

p	The probability of the elements being 1 (defaults to a fair coin, i.e. 50-50).
seed	The seed to use for the random number generator (defaults to 0, which means use entropy).

If p < 0 then the fill is all zeros, if p > 1 then the fill is all ones.

Example

BitArray<10> u, v;
u64 seed = 1234567890;
u.fill_random(0.5, seed);
v.fill_random(0.5, seed);
assert(u == v);

first_set()

template<usize N, Unsigned Word = usize>

std::optional< usize > gf2::BitArray< N, Word >::first_set ( ) const

inlineconstexpr

Returns the index of the first set bit in the bit-array or {} if no bits are set.

Example

BitArray<37, u8> v;
assert(v.first_set() == std::optional<usize>{});
v.set(2);
assert(v.first_set() == std::optional<usize>{2});
v.set(2, false);
assert(v.first_set() == std::optional<usize>{});
v.set(27);
assert(v.first_set() == std::optional<usize>{27});
BitArray<0> empty;
assert(empty.first_set() == std::optional<usize>{});

first_unset()

template<usize N, Unsigned Word = usize>

std::optional< usize > gf2::BitArray< N, Word >::first_unset ( ) const

inlineconstexpr

Returns the index of the first unset bit in the bit-array or {} if no bits are unset.

Example

BitArray<37, u8> v; v.set_all();
assert(v.first_unset() == std::optional<usize>{});
v.set(2, false);
assert(v.first_unset() == std::optional<usize>{2});
v.set(2);
assert(v.first_unset() == std::optional<usize>{});
v.set(27, false);
assert(v.first_unset() == std::optional<usize>{27});
BitArray<0> empty;
assert(empty.first_unset() == std::optional<usize>{});

flip()

template<usize N, Unsigned Word = usize>

auto gf2::BitArray< N, Word >::flip ( usize i )

inlineconstexpr

Flips the value of the bit-element i and returns this for chaining.

Panics

In debug mode the index is bounds-checked.

Example

auto v = BitArray<10, u8>::ones();
v.flip(0);
assert_eq(v.to_string(), "0111111111");
v.flip(1);
assert_eq(v.to_string(), "0011111111");
v.flip(9);
assert_eq(v.to_string(), "0011111110");

flip_all()

template<usize N, Unsigned Word = usize>

auto gf2::BitArray< N, Word >::flip_all ( )

inlineconstexpr

Flips the value of the bits in the bit-array and returns a reference to this for chaining.

Example

BitArray<10> v;
v.flip_all();
assert_eq(v.to_string(), "1111111111");

from() [1/4]

template<usize N, Unsigned Word = usize>

template<typename Iter>
requires std::is_unsigned_v<typename std::iterator_traits<Iter>::value_type>

constexpr BitArray gf2::BitArray< N, Word >::from ( Iter src_begin, Iter src_end )

inlinestaticconstexpr

Factory method to construct a bit-array by copying all the bits from an iteration of any Unsigneds.

Note

We allow any unsigned integral source, e.g. copying u64 words into a BitArray<N, u8>.

Panics

Panics if the number of bits in the source iteration does not match N.

Example

std::vector<u16> src = { 0b1010101010101010, 0b1010101010101010, 0b1111111111111111 };
auto v = BitArray<48, u8>::from(src.begin(), src.end());
assert_eq(v.to_string(), "010101010101010101010101010101011111111111111111");
auto w = BitArray<48, u32>::from(src.begin(), src.end());
assert_eq(w.to_string(), "010101010101010101010101010101011111111111111111");

from() [2/4]

template<usize N, Unsigned Word = usize>

template<Unsigned Src>
requires (BITS<Src> == N)

constexpr BitArray gf2::BitArray< N, Word >::from ( Src src )

inlinestaticconstexpr

Factory method to construct a bit-array by copying all the bits from any Unsigned instance.

Note

The source type Src must have exactly N bits.

Example

u8 s8 = 0b01010101;
auto u = BitArray<8, u8>::from(s8);
assert_eq(u.to_string(), "10101010");
u16 s16 = 0b0101010101010101;
auto v = BitArray<16, u8>::from(s16);
assert_eq(v.to_string(), "1010101010101010");
auto w = BitArray<8, u32>::from(s8);
assert_eq(w.to_string(), "10101010");

from() [3/4]

template<usize N, Unsigned Word = usize>

constexpr BitArray gf2::BitArray< N, Word >::from ( std::bitset< N > const & src )

inlinestaticconstexpr

Factory method to construct a bit-array from the bits of a std::bitset.

Note

A std::bitset prints its bit elements in bit-order ...b2b1b0., we print in vector-order b0b1b2...

Example

std::bitset<10> src{0b1010101010};
auto v = BitArray<10>::from(src);
assert_eq(v.to_string(), "0101010101");

from() [4/4]

template<usize N, Unsigned Word = usize>

constexpr BitArray gf2::BitArray< N, Word >::from ( std::invocable< usize > auto f )

inlinestaticconstexpr

Factory method to construct a bit-array by repeatedly calling f(i) for i in [0, N).

Parameters

f	The function to call for each index i in [0, N).

Example

auto v = BitArray<10, u8>::from([](usize i) { return i % 2 == 0; });
assert_eq(v.to_string(), "1010101010");

front()

template<usize N, Unsigned Word = usize>

bool gf2::BitArray< N, Word >::front ( ) const

inlineconstexpr

Returns true if the first bit element is set, false otherwise.

Panics

In debug mode the method panics if the bit-array is empty.

Example

BitArray<10> v;
assert_eq(v.front(), false);
v.set_all();
assert_eq(v.front(), true);

get()

template<usize N, Unsigned Word = usize>

bool gf2::BitArray< N, Word >::get ( usize i ) const

inlineconstexpr

Returns true if the bit at the given index i is set, false otherwise.

Panics

In debug mode the index is bounds checked.

Example

BitArray<10> v;
assert_eq(v.get(0), false);
v.set(0);
assert_eq(v.get(0), true);

is_empty()

template<usize N, Unsigned Word = usize>

bool gf2::BitArray< N, Word >::is_empty ( ) const

inlineconstexpr

Returns true if the bit-array is empty, false otherwise.

Example

BitArray<0> v;
assert_eq(v.is_empty(), true);
BitArray<10> u;
assert_eq(u.is_empty(), false);

last_set()

template<usize N, Unsigned Word = usize>

std::optional< usize > gf2::BitArray< N, Word >::last_set ( ) const

inlineconstexpr

Returns the index of the last set bit in the bit-array or {} if no bits are set.

Example

BitArray<37, u8> v;
assert(v.last_set() == std::optional<usize>{});
v.set(2);
assert(v.last_set() == std::optional<usize>{2});
v.set(27);
assert(v.last_set() == std::optional<usize>{27});
BitArray<0> empty;
assert(empty.last_set() == std::optional<usize>{});

last_unset()

template<usize N, Unsigned Word = usize>

std::optional< usize > gf2::BitArray< N, Word >::last_unset ( ) const

inlineconstexpr

Returns the index of the last unset bit in the bit-array or {} if no bits are unset.

Example

BitArray<37, u8> v; v.set_all();
assert(v.last_unset() == std::optional<usize>{});
v.set(2, false);
assert(v.last_unset() == std::optional<usize>{2});
v.set(2);
assert(v.last_unset() == std::optional<usize>{});
v.set(27, false);
assert(v.last_unset() == std::optional<usize>{27});
BitArray<0> empty;
assert(empty.last_unset() == std::optional<usize>{});

leading_zeros()

template<usize N, Unsigned Word = usize>

usize gf2::BitArray< N, Word >::leading_zeros ( ) const

inlineconstexpr

Returns the number of leading zeros in the bit-array.

Example

BitArray<37, u8> v;
assert_eq(v.leading_zeros(), 37);
v.set(27);
assert_eq(v.leading_zeros(), 27);
BitArray<10, u8> w;
w.set_all();
assert_eq(w.leading_zeros(), 0);

next_set()

template<usize N, Unsigned Word = usize>

std::optional< usize > gf2::BitArray< N, Word >::next_set ( usize index ) const

inlineconstexpr

Returns the index of the next set bit after index in the bit-array or {} if no more set bits exist.

Example

BitArray<37, u8> v;
assert(v.next_set(0) == std::optional<usize>{});
v.set(2);
v.set(27);
assert(v.next_set(0) == std::optional<usize>{2});
assert(v.next_set(2) == std::optional<usize>{27});
assert(v.next_set(27) == std::optional<usize>{});

next_unset()

template<usize N, Unsigned Word = usize>

std::optional< usize > gf2::BitArray< N, Word >::next_unset ( usize index ) const

inlineconstexpr

Returns the index of the next unset bit after index in the bit-array or {} if no more unset bits exist.

Example

BitArray<37, u8> v; v.set_all();
assert(v.next_unset(0) == std::optional<usize>{});
v.set(2, false);
v.set(27, false);
assert(v.next_unset(0) == std::optional<usize>{2});
assert(v.next_unset(2) == std::optional<usize>{27});
assert(v.next_unset(27) == std::optional<usize>{});
BitArray<0> empty;
assert(empty.next_unset(0) == std::optional<usize>{});

none()

template<usize N, Unsigned Word = usize>

bool gf2::BitArray< N, Word >::none ( ) const

inlineconstexpr

Returns true if no bits in the bit-array are set, false otherwise.

Note: Empty bit-arrays have no set bits (logical connective for none is AND with identity true).

Example

BitArray<10> v;
assert_eq(v.none(), true);
v.set(0);
assert_eq(v.none(), false);

offset()

template<usize N, Unsigned Word = usize>

u8 gf2::BitArray< N, Word >::offset ( ) const

inlineconstexpr

Returns the offset (in bits) of the first bit in the bit-array within the first word.

This is always zero for BitArray.

ones()

template<usize N, Unsigned Word = usize>

constexpr BitArray gf2::BitArray< N, Word >::ones ( )

inlinestaticconstexpr

Factory method to generate a bit-array of length N where the elements are all 1.

Example

auto v = BitArray<10, u8>::ones();
assert_eq(v.to_string(), "1111111111");

operator[]() [1/2]

template<usize N, Unsigned Word = usize>

auto gf2::BitArray< N, Word >::operator[] ( usize i )

inlineconstexpr

Returns a "reference" to the bit element i.

The returned object is a BitRef reference for the bit element at index rather than a true reference.

Note

The referenced bit-array must continue to exist while the BitRef is in use.

Panics

In debug mode the index is bounds-checked.

Example

BitArray<10> v;
v[2] = true;
assert(v.to_string() == "0010000000");
BitArray<10> w;
w.set_all();
v[3] = w[3];
assert(v.to_string() == "0011000000");
v[4] |= w[4];
assert(v.to_string() == "0011100000");

operator[]() [2/2]

template<usize N, Unsigned Word = usize>

bool gf2::BitArray< N, Word >::operator[] ( usize i ) const

inlineconstexpr

Returns the boolean value of the bit element i.

Panics

In debug mode the index is bounds checked.

Example

BitArray<10> v;
assert(v[2] == false);
v[2] = true;
assert(v[2] == true);
assert(v.to_string() == "0010000000");

previous_set()

template<usize N, Unsigned Word = usize>

std::optional< usize > gf2::BitArray< N, Word >::previous_set ( usize index ) const

inlineconstexpr

Returns the index of the previous set bit before index in the bit-array or {} if there are none.

Example

BitArray<37, u8> v;
assert(v.previous_set(36) == std::optional<usize>{});
v.set(2);
v.set(27);
assert(v.previous_set(36) == std::optional<usize>{27});
assert(v.previous_set(27) == std::optional<usize>{2});
assert(v.previous_set(2)  == std::optional<usize>{});

previous_unset()

template<usize N, Unsigned Word = usize>

std::optional< usize > gf2::BitArray< N, Word >::previous_unset ( usize index ) const

inlineconstexpr

Returns the index of the previous unset bit before index in the bit-array or {} if no more unset bits exist.

Example

BitArray<37, u8> v; v.set_all();
assert(v.previous_unset(0) == std::optional<usize>{});
v.set(2, false);
v.set(27, false);
assert(v.previous_unset(36) == std::optional<usize>{27});
assert(v.previous_unset(27) == std::optional<usize>{2});
assert(v.previous_unset(2) == std::optional<usize>{});
BitArray<0> empty;
assert(empty.previous_unset(0) == std::optional<usize>{});

random()

template<usize N, Unsigned Word = usize>

BitArray gf2::BitArray< N, Word >::random ( double p = 0.5, u64 seed = 0 )

inlinestatic

Factory method to generate a bit-array of size N where the elements are picked at random.

The default call BitArray<>::random() produces a random bit-array with each bit being 1 with probability 0.5 and where the RNG is seeded from entropy.

Parameters

p	The probability of the elements being 1 (defaults to a fair coin, i.e. 50-50).
seed	The seed to use for the random number generator (defaults to 0, which means use entropy).

If p < 0 then the bit-array is all zeros, if p > 1 then the bit-array is all ones.

Example

u64 seed = 1234567890;
auto u = BitArray<10>::random(0.5, seed);
auto v = BitArray<10>::random(0.5, seed);
assert(u == v);

riffled() [1/2]

template<usize N, Unsigned Word = usize>

auto gf2::BitArray< N, Word >::riffled ( ) const

inlineconstexpr

Returns a new bit-vector that is the result of riffling the bits in this bit-array with zeros.

If the bit-array has the bits abcde then the output bit-vector will have the bits a0b0c0d0e.

Note: There is no last zero bit in dst.

Example

BitArray<10, u8> v; v.set_all();
auto dst = v.riffled();
assert_eq(dst.to_string(), "1010101010101010101");

riffled() [2/2]

template<usize N, Unsigned Word = usize>

void gf2::BitArray< N, Word >::riffled ( BitVector< word_type > & dst ) const

inlineconstexpr

Interleaves the bits of this bit-array with zeros storing the result into the bit-vector dst.

On return, dst will have the bits of this bit-array interleaved with zeros. For example, if this bit-array has the bits abcde then dst will have the bits a0b0c0d0e.

Note: There is no last zero bit in dst.

Example

BitArray<10, u8> v; v.set_all();
BitVector<u8> dst;
v.riffled(dst);
assert_eq(dst.to_string(), "1010101010101010101");

seeded_random()

template<usize N, Unsigned Word = usize>

BitArray gf2::BitArray< N, Word >::seeded_random ( u64 seed )

inlinestatic

Factory method to generate a bit-array of size N where the elements are from independent fair coin flips generated from an RNG seeded with the given seed.

This allows one to have reproducible random bit-arrays, which is useful for testing and debugging.

Parameters

seed	The seed to use for the random number generator (if you set this to 0 then entropy is used).

If p < 0 then the bit-array is all zeros, if p > 1 then the bit-array is all ones.

Example

u64 seed = 1234567890;
auto u = BitArray<10>::seeded_random(seed);
auto v = BitArray<10>::seeded_random(seed);
assert(u == v);

set()

template<usize N, Unsigned Word = usize>

auto gf2::BitArray< N, Word >::set ( usize i, bool value = true )

inlineconstexpr

Sets the bit-element i to the specified boolean value & returns this for chaining. The default value for value is true.

Panics

In debug mode the index is bounds-checked.

Example

BitArray<10> v;
assert_eq(v[0], false);
v.set(0);
assert_eq(v[0], true);

set_all()

template<usize N, Unsigned Word = usize>

auto gf2::BitArray< N, Word >::set_all ( bool value = true )

inlineconstexpr

Sets all the bits in the bit-array to the boolean value and returns a reference to this for chaining.

By default, all bits are set to true.

Example

BitArray<10> v;
v.set_all();
assert_eq(v.to_string(), "1111111111");

set_bits()

template<usize N, Unsigned Word = usize>

auto gf2::BitArray< N, Word >::set_bits ( ) const

inlineconstexpr

Returns an iterator over the indices of any set bits in the bit-array.

You can use this iterator to iterate over the set bits in the bit-array and get the index of each bit.

Example

BitArray<10, u8> v;
v.copy([](usize i) { return i % 2 == 0; });
assert_eq(v.to_string(), "1010101010");
auto indices = std::ranges::to<std::vector>(v.set_bits());
assert_eq(indices, (std::vector<usize>{0, 2, 4, 6, 8}));

set_word()

template<usize N, Unsigned Word = usize>

void gf2::BitArray< N, Word >::set_word ( usize i, Word word )

inlineconstexpr

Sets word i in the bit-array's underlying word store to value (masked if necessary).

The final word in the store may not be fully occupied but we ensure that unused bits remain set to 0.

Panics

In debug mode the index is bounds checked.

Example

BitArray<10, u8> v;
assert_eq(v.to_string(), "0000000000");
v.set_word(1, 0b1111'1111);
assert_eq(v.to_string(), "0000000011");
assert_eq(v.count_ones(), 2);

size()

template<usize N, Unsigned Word = usize>

usize gf2::BitArray< N, Word >::size ( ) const

inlineconstexpr

Returns the number of bit-elements in the bit-array.

Example

BitArray<10> v;
assert_eq(v.size(), 10);

span() [1/2]

template<usize N, Unsigned Word = usize>

auto gf2::BitArray< N, Word >::span ( usize begin, usize end )

inlineconstexpr

Returns a mutable bit-span encompassing the bit-array's bits in the half-open range [begin, end).

Mutability here is deep – the interior pointer in the returned span is to non-const words.

Panics

This method panics if the span range is not valid.

Example

BitArray<10> v;
v.copy([](usize i) { return i % 2 == 0; });
auto s = v.span(1,5);
assert_eq(s.to_string(), "0101");
s.set_all();
assert_eq(s.to_string(), "1111");
assert_eq(v.to_string(), "1111101010");

span() [2/2]

template<usize N, Unsigned Word = usize>

auto gf2::BitArray< N, Word >::span ( usize begin, usize end ) const

inlineconstexpr

Returns an immutable bit-span encompassing the bit-array's bits in the half-open range [begin, end).

Immutability here is deep – the interior pointer in the returned span is to const words.

Panics

This method panics if the span range is not valid.

Example

BitArray<10, u8> v;
v.copy([](usize i) { return i % 2 == 0; });
auto s = v.span(1,5);
assert_eq(s.to_string(), "0101");

split_at() [1/2]

template<usize N, Unsigned Word = usize>

auto gf2::BitArray< N, Word >::split_at ( usize at ) const

inlineconstexpr

Views the bit-array as two parts containing the elements [0, at) and [at, size()) respectively.

Clones of the parts are returned as a pair of bit-vectors [left, right].

On return, left is a clone of the bits from the start of the bit-array up to but not including at and right contains the bits from at to the end of the bit-array. This bit-array itself is not modified.

Panics

This method panics if the split point is beyond the end of the bit-array.

Example

BitArray<10, u8> v;
v.copy([](usize i) { return i % 2 == 0; });
auto [left, right] = v.split_at(5);
assert_eq(left.to_string(), "10101");
assert_eq(right.to_string(), "01010");
assert_eq(v.to_string(), "1010101010");

split_at() [2/2]

template<usize N, Unsigned Word = usize>

void gf2::BitArray< N, Word >::split_at ( usize at, BitVector< word_type > & left, BitVector< word_type > & right ) const

inlineconstexpr

Views the bit-array as two parts containing the elements [0, at) and [at, size()) respectively.

Clones of the parts are stored in the passed bit-vectors left and right.

On return, left contains the bits from the start of the bit-array up to but not including at and right contains the bits from at to the end of the bit-array. This bit-array itself is not modified.

This lets one reuse the left and right destinations without having to allocate new bit-vectors. This is useful when implementing iterative algorithms that need to split a bit-array into two parts repeatedly.

Panics

This method panics if the split point is beyond the end of the bit-array.

Example

BitArray<10, u8> v;
v.copy([](usize i) { return i % 2 == 0; });
BitVector<u8> left, right;
v.split_at(5, left, right);
assert_eq(left.to_string(), "10101");
assert_eq(right.to_string(), "01010");
assert_eq(v.to_string(), "1010101010");

store() [1/2]

template<usize N, Unsigned Word = usize>

Word * gf2::BitArray< N, Word >::store ( )

inlineconstexpr

Returns a pointer to the underlying store of words.

Note: The pointer is non-const but you should be careful about using it to modify the words in the store.

Example

BitArray<10, u8> v;
v.set_all();
auto ptr = v.store();
assert_eq(*ptr, 0b1111'1111);

store() [2/2]

template<usize N, Unsigned Word = usize>

const Word * gf2::BitArray< N, Word >::store ( ) const

inlineconstexpr

Returns a const pointer to the underlying store of words .

Example

BitArray<10, u8> v;
v.set_all();
auto ptr = v.store();
assert_eq(*ptr, 0b1111'1111);

store_words()

template<usize N, Unsigned Word = usize>

auto gf2::BitArray< N, Word >::store_words ( ) const

inlineconstexpr

Returns a const iterator over all the words underlying the v.

You can use this iterator to iterate over the words in the bit-array and read the Word value of each word. You cannot use this iterator to modify the words in the store.

Example

auto v = BitArray<10, u8>::ones();
assert_eq(v.to_string(), "1111111111");
auto words = std::ranges::to<std::vector>(v.store_words());
assert_eq(words, (std::vector<u8>{0b1111'1111, 0b0000'0011}));

sub()

template<usize N, Unsigned Word = usize>

auto gf2::BitArray< N, Word >::sub ( usize begin, usize end ) const

inlineconstexpr

Returns a clone of the elements in the half-open range [begin, end) as a new bit-vector.

Panics

This method panics if the range is not valid.

Example

BitArray<10> v;
v.copy([](usize i) { return i % 2 == 0; });
auto s = v.sub(1,5);
assert_eq(s.to_string(), "0101");
s.set_all();
assert_eq(s.to_string(), "1111");
assert_eq(v.to_string(), "1010101010");

swap()

template<usize N, Unsigned Word = usize>

auto gf2::BitArray< N, Word >::swap ( usize i0, usize i1 )

inlineconstexpr

Swaps the bits in the bit-array at indices i0 and i1 and returns this for chaining.

Panics

In debug mode the indices are bounds-checked.

Example

BitArray<10> v;
v.set(0);
assert_eq(v.to_string(), "1000000000");
v.swap(0, 1);
assert_eq(v.to_string(), "0100000000");
v.swap(0, 1);
assert_eq(v.to_string(), "1000000000");
v.swap(0, 9);
assert_eq(v.to_string(), "0000000001");
v.swap(0, 9);
assert_eq(v.to_string(), "1000000000");

to_binary_string()

template<usize N, Unsigned Word = usize>

std::string gf2::BitArray< N, Word >::to_binary_string ( std::string_view sep = "", std::string_view pre = "", std::string_view post = "" ) const

inline

Returns a binary string representation of the bit-array.

The string is formatted as a sequence of 0s and 1s with the least significant bit on the right.

Parameters

sep	The separator between bit elements which defaults to no separator.
pre	The prefix to add to the string which defaults to no prefix.
post	The postfix to add to the string which defaults to no postfix.

Example

BitArray<10> v;
assert_eq(v.to_binary_string(), "0000000000");
v.set(0);
assert_eq(v.to_binary_string(), "1000000000");
assert_eq(v.to_binary_string(",", "[", "]"), "[1,0,0,0,0,0,0,0,0,0]");

to_hex_string()

template<usize N, Unsigned Word = usize>

std::string gf2::BitArray< N, Word >::to_hex_string ( ) const

inline

Returns the "hex" string representation of the bits in the bit-array.

The output is a string of hex characters without any spaces, commas, or other formatting.

The string may have a two character suffix of the form ".base" where base is one of 2, 4 or 8.
All hex characters encode 4 bits: "0X0" -> 0b0000, "0X1" -> 0b0001, ..., "0XF" -> 0b1111.
The three possible ".base" suffixes allow for bit-vectors whose length is not a multiple of 4.
Empty bit-vectors are represented as the empty string.

• 0X1 is the hex representation of the bit-array 0001 => length 4.
• 0X1.8 is the hex representation of the bit-array 001 => length 3.
• 0X1.4 is the hex representation of the bit-array 01 => length 2.
• 0X1.2 is the hex representation of the bit-array 1 => length 1.

The output is in vector-order. If "h0" is the first hex digit in the output string, you can print it as four binary digits v_0v_1v_2v_3. For example, if h0 = "A" which is 1010 in binary, then v = 1010.

Example

BitArray<0> v0;
assert_eq(v0.to_hex_string(), "");
BitArray<4> v1; v1.set_all();
assert_eq(v1.to_hex_string(), "F");
BitArray<5> v2; v2.set_all();
assert_eq(v2.to_hex_string(), "F1.2");
BitArray<8> v3;
v3.copy([](usize i) { return i % 2 == 0; });
assert_eq(v3.to_binary_string(), "10101010");
assert_eq(v3.to_hex_string(), "AA");

to_pretty_string()

template<usize N, Unsigned Word = usize>

std::string gf2::BitArray< N, Word >::to_pretty_string ( ) const

inline

Returns a "pretty" string representation of the bit-array.

The output is a string of 0's and 1's with spaces between each bit, and the whole thing enclosed in square brackets.

Example

BitArray<10> v;
v.copy([](usize i) { return i % 2 == 0; });
assert_eq(v.to_pretty_string(), "[1,0,1,0,1,0,1,0,1,0]");
BitArray<0> empty;
assert_eq(empty.to_pretty_string(), "[]");

to_string()

template<usize N, Unsigned Word = usize>

std::string gf2::BitArray< N, Word >::to_string ( std::string_view sep = "", std::string_view pre = "", std::string_view post = "" ) const

inline

Returns a binary string representation of the bit-array.

The string is formatted as a sequence of 0s and 1s with the least significant bit on the right.

Parameters

sep	The separator between bit elements which defaults to no separator.
pre	The prefix to add to the string which defaults to no prefix.
post	The postfix to add to the string which defaults to no postfix.

Example

BitArray<10, u8> v;
assert_eq(v.to_string(), "0000000000");
v.set(0);
assert_eq(v.to_string(), "1000000000");
assert_eq(v.to_string(",", "[", "]"), "[1,0,0,0,0,0,0,0,0,0]");

to_words() [1/2]

template<usize N, Unsigned Word = usize>

auto gf2::BitArray< N, Word >::to_words ( ) const

inlineconstexpr

Returns a copy of the words underlying this bit-array as a std::vector<word_type>.

Note: The last word in the bit-array may not be fully occupied but unused slots will be all zeros.

Example

auto v = BitArray<10, u8>::ones();
auto words = v.to_words();
assert_eq(words, (std::vector<u8>{0b1111'1111, 0b0000'0011}));

to_words() [2/2]

template<usize N, Unsigned Word = usize>

void gf2::BitArray< N, Word >::to_words ( std::output_iterator< word_type > auto out )

inlineconstexpr

Returns a copy of the words underlying this bit-array and puts them into the passed output iterator.

Note

• The last word in the bit-array may not be fully occupied but unused slots will be all zeros.
• The output iterator must be able to accept values of the bit-arrays's word_type.
• The output iterator must have enough space to accept all the words in the bit-array.
• If there is extra space in the output iterator, those extra slots are left unchanged.

Example

auto v = BitArray<10, u8>::ones();
std::vector<u8> out8(v.words());
v.to_words(out8.begin());
assert_eq(out8, (std::vector<u8>{0b1111'1111, 0b0000'0011}));
std::vector<u16> out16(v.words());
v.to_words(out16.begin());
assert_eq(out16, (std::vector<u16>{0b1111'1111, 0b0000'0011}));

trailing_zeros()

template<usize N, Unsigned Word = usize>

usize gf2::BitArray< N, Word >::trailing_zeros ( ) const

inlineconstexpr

Returns the number of trailing zeros in the bit-array.

Example

BitArray<27, u8> v;
assert_eq(v.trailing_zeros(), 27);
v.set(0);
assert_eq(v.trailing_zeros(), 26);

unit()

template<usize N, Unsigned Word = usize>

constexpr BitArray gf2::BitArray< N, Word >::unit ( usize i )

inlinestaticconstexpr

Factory method to generate a "unit" bit-array of length N where only element i is set.

This method panics if the condition i < N is not met.

Example

assert_eq(BitArray<10>::unit(0).to_string(), "1000000000");
assert_eq(BitArray<10>::unit(9).to_string(), "0000000001");

unset_bits()

template<usize N, Unsigned Word = usize>

auto gf2::BitArray< N, Word >::unset_bits ( ) const

inlineconstexpr

Returns an iterator over the indices of any unset bits in the bit-array.

You can use this iterator to iterate over the unset bits in the bit-array and get the index of each bit.

Example

BitArray<10, u8> v;
v.copy([](usize i) { return i % 2 == 0; });
assert_eq(v.to_string(), "1010101010");
auto indices = std::ranges::to<std::vector>(v.unset_bits());
assert_eq(indices, (std::vector<usize>{1, 3, 5, 7, 9}));

word()

template<usize N, Unsigned Word = usize>

Word gf2::BitArray< N, Word >::word ( usize i ) const

inlineconstexpr

Returns word i from the bit-array's underlying word store.

The final word in the store may not be fully occupied but we guarantee that unused bits are set to 0.

Panics

In debug mode the index is bounds checked.

Example

BitArray<10, u8> v;
assert_eq(v.to_string(), "0000000000");
v.set_all();
assert_eq(v.to_string(), "1111111111");
assert_eq(v.words(), 2);
assert_eq(v.word(0), 0b1111'1111);
assert_eq(v.word(1), 0b0000'0011);

words()

template<usize N, Unsigned Word = usize>

usize gf2::BitArray< N, Word >::words ( ) const

inlineconstexpr

Returns the number of words in the bit-array's underlying word store.

The bit-elements are packed into a standard array with this number of words.

Example

BitArray<10, u8> v0;
assert_eq(v0.words(), 2);
BitArray<10, u16> v1;
assert_eq(v1.words(), 1);

zeros()

template<usize N, Unsigned Word = usize>

constexpr BitArray gf2::BitArray< N, Word >::zeros ( )

inlinestaticconstexpr

Factory method to generate a bit-array of length N where the elements are all 0.

Example

auto v = BitArray<10, u8>::zeros();
assert_eq(v.to_string(), "0000000000");