gf2::BitSet< N, Word >

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

#include <BitSet.h>

Inheritance diagram for gf2::BitSet< N, Word >:

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

Public Member Functions
BitStore Required Methods.
constexpr usize	size () const
	Returns the number of bit-elements in the bitset.
constexpr usize	words () const
	Returns the number of words in the bitset's underlying word store.
constexpr Word	word (usize i) const
	Returns word i from the bitset's underlying word store.
constexpr void	set_word (usize i, Word word)
	Sets word i in the bitset's underlying word store to value (masked if necessary).
constexpr const Word *	data () const
	Returns a const pointer to the underlying store of words .
constexpr Word *	data ()
	Returns a pointer to the underlying store of words.
constexpr u8	offset () const
	Returns the offset (in bits) of the first bit in the store within the first word.
Helper Methods:
constexpr void	clean ()
	Sets any unused bits in the last occupied word to 0.
Required methods:
The BitStore subclasses implement the following methods ...
constexpr void	set_word (usize i, word_type value)
	This method sets "word" at index i to the specified value.
Individual bit reads:
constexpr bool	get (usize i) const
	Returns true if the bit at the given index i is set, false otherwise.
constexpr bool	operator[] (usize index) const
	Returns the boolean value of the bit element at index.
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.
Individual bit mutators:
auto	set (usize index, bool value=true)
	Sets the bit-element at the given index to the specified boolean value & returns this for chaining. The default value for value is true.
auto	flip (usize index)
	Flips the value of the bit-element at the given index and returns this for chaining/.
constexpr auto	swap (usize i0, usize i1)
	Swaps the bits in the bit-store at indices i0 and i1 and returns this for chaining.
Store queries:
constexpr bool	is_empty () const
	Returns true if the store is empty, false otherwise.
constexpr bool	any () const
	Returns true if at least one bit in the store is set, false otherwise.
constexpr bool	all () const
	Returns true if all bits in the store are set, false otherwise.
constexpr bool	none () const
	Returns true if no bits in the store are set, false otherwise.
Store mutators:
auto	set_all (bool value=true)
	Sets the bits in the store to the boolean value and returns a reference to this for chaining.
auto	flip_all ()
	Flips the value of the bits in the store and returns a reference to this for chaining.
Store fills:
auto	copy (Src src)
	Copies the bits from an unsigned integral src value and returns a reference to this for chaining.
auto	fill (std::invocable< usize > auto f)
	Fill the store by repeatedly calling f(i) and returns a reference to this for chaining.
auto	random_fill (double p=0.5, u64 seed=0)
	Fill the store 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 store.
constexpr usize	count_zeros () const
	Returns the number of unset bits in the store.
constexpr usize	leading_zeros () const
	Returns the number of leading zeros in the store.
constexpr usize	trailing_zeros () const
	Returns the number of trailing zeros in the store.
Set bit indices:
std::optional< usize >	first_set () const
	Returns the index of the first set bit in the bit-store or {} if no bits are set.
std::optional< usize >	last_set () const
	Returns the index of the last set bit in the bit-store or {} if no bits are set.
std::optional< usize >	next_set (usize index) const
	Returns the index of the next set bit after index in the store or {} if no more set bits exist.
std::optional< usize >	previous_set (usize index) const
	Returns the index of the previous set bit before index in the store or {} if there are none.
Unset bit indices:
std::optional< usize >	first_unset () const
	Returns the index of the first unset bit in the bit-store or {} if no bits are unset.
std::optional< usize >	last_unset () const
	Returns the index of the last unset bit in the bit-store or {} if no bits are unset.
std::optional< usize >	next_unset (usize index) const
	Returns the index of the next unset bit after index in the store or {} if no more unset bits exist.
std::optional< usize >	previous_unset (usize index) const
	Returns the index of the previous unset bit before index in the store or {} if no more unset bits exist.
Iterators:
constexpr auto	bits () const
	Returns a const iterator over the bool values of the bits in the const bit-store.
constexpr auto	set_bit_indices () const
	Returns an iterator over the indices of any set bits in the bit-store.
constexpr auto	unset_bit_indices () const
	Returns an iterator over the indices of any unset bits in the bit-store.
constexpr auto	store_words () const
	Returns a const iterator over all the words underlying the bit-store.
constexpr auto	to_words () const
	Returns a copy of the words underlying this bit-store.
Spans:
constexpr auto	span (usize begin, usize end) const
	Returns an immutable bit-span encompassing the 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.
constexpr void	split_at (usize at, BitVec< word_type > &left, BitVec< word_type > &right) const
	Views a bit-store as two parts containing the elements [0, at) and [at, size()) respectively.
Riffling:
constexpr void	riffle_into (BitVec< word_type > &dst) const
	Interleaves the bits of this bit-store 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-store with zeros.
Bit shifts:
constexpr void	operator<<= (usize shift)
	In-place left shift of the bit-store by shift bits.
constexpr void	operator>>= (usize shift)
	In-place right shift of the bit-store by shift bits.
constexpr auto	operator<< (usize shift) const
	Returns a new bit-vector that is lhs shifted left by shift bits.
constexpr auto	operator>> (usize shift) const
	Returns a new bit-vector that is lhs shifted right by shift bits.
Bit-wise operations:
void	operator^= (const BitStore< Rhs > &rhs)
	In-place XOR with another equal-sized bit-store.
void	operator&= (const BitStore< Rhs > &rhs)
	In-place AND with another equal-sized bit-store.
void	operator|= (const BitStore< Rhs > &rhs)
	In-place OR with another equal-sized bit-store.
auto	operator~ () const
	Returns a new bit-vector that has the same bits as the current bit-store but with all the bits flipped.
auto	operator^ (const BitStore< Rhs > &rhs) const
	Returns a new bit-vector that is the XOR of the current bit-store and another equal-sized bit-store.
auto	operator& (const BitStore< Rhs > &rhs) const
	Returns a new bit-vector that is the AND of the current bit-store and another equal-sized bit-store.
auto	operator| (const BitStore< Rhs > &rhs) const
	Returns a new bit-vector that is the OR of the current bit-store and another equal-sized bit-store.
Arithmetic operations:
void	operator+= (const BitStore< Rhs > &rhs)
	In-place addition of this bit-store with the an equal-sized rhs bit-store.
void	operator-= (const BitStore< Rhs > &rhs)
	In-place subtraction of this bit-store with the an equal-sized rhs bit-store.
auto	operator+ (const BitStore< Rhs > &rhs) const
	Returns a new bit-vector that is the + of this store with the passed (equal-sized) rhs bit-store.
auto	operator- (const BitStore< Rhs > &rhs) const
	Returns a new bit-vector that is the - of this store with the passed (equal-sized) rhs bit-store.
String representations:
std::string	to_string (std::string_view sep="", std::string_view pre="", std::string_view post="") const
	Returns a binary string representation of the store.
std::string	to_pretty_string () const
	Returns a "pretty" string representation of the store.
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 store.
std::string	to_hex_string () const
	Returns the "hex" string representation of the bits in the bit-store.
std::string	describe () const
	Returns a multi-line string describing the bit-vector in some detail.

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

Detailed Description

template<usize N, unsigned_word Word = usize>
class gf2::BitSet< N, Word >

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

BitSet<N> is similar to std::bitset<N> but has a different interface and a richer set of functionality.

The BitSet class inherits from the base gf2::BitStore class. We implement a small number of required methods and then inherit the majority of our functionality from that base.

Note

Inheritance is done using the CRTP to avoid all runtime virtual method dispatch overhad..

Member Function Documentation

all()

bool gf2::BitStore< BitSet< N, usize > >::all ( ) const

inlineconstexprinherited

Returns true if all bits in the store are set, false otherwise.

Note

Empty stores have no set bits (logical connective for all is AND with identity true).

Example

BitVec v{3};
assert_eq(v.all(), false);
v.set(0);
v.set(1);
v.set(2);
assert_eq(v.all(), true);

any()

bool gf2::BitStore< BitSet< N, usize > >::any ( ) const

inlineconstexprinherited

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

Note

Empty stores have no set bits (logical connective for any is OR with identity false).

Example

BitVec v{10};
assert_eq(v.any(), false);
v.set(0);
assert_eq(v.any(), true);

back()

bool gf2::BitStore< BitSet< N, usize > >::back ( ) const

inlineconstexprinherited

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

Note

In debug mode the method panics of the store is empty.

Example

auto v = BitVec<>::ones(10);
assert_eq(v.back(), true);
v.set_all(false);
assert_eq(v.back(), false);

bits()

auto gf2::BitStore< BitSet< N, usize > >::bits ( ) const

inlineconstexprinherited

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

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

auto u = BitVec<u8>::ones(10);
for (auto&& bit : u.bits()) assert_eq(bit, true);

clean()

template<usize N, unsigned_word Word = usize>

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

inlineconstexpr

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

This is used to enforce the guarantee that unused bits in the store are always set to 0.

copy()

auto gf2::BitStore< BitSet< N, usize > >::copy ( Src src )

inlineinherited

Copies the bits from an unsigned integral src value and returns a reference to this for chaining.

Notes:

1. The size of the store must match the number of bits in the source type.
2. We allow any unsigned integral source, e.g. copying a single u64 into a BitVec<u8> of size 64.
3. The least-significant bit of the source becomes the bit at index 0 in the store.

Example

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

count_ones()

usize gf2::BitStore< BitSet< N, usize > >::count_ones ( ) const

inlineconstexprinherited

Returns the number of set bits in the store.

Example

BitVec v{10};
assert_eq(v.count_ones(), 0);
v.set(0);
assert_eq(v.count_ones(), 1);

count_zeros()

usize gf2::BitStore< BitSet< N, usize > >::count_zeros ( ) const

inlineconstexprinherited

Returns the number of unset bits in the store.

Example

BitVec v{10};
assert_eq(v.count_zeros(), 10);
v.set(0);
assert_eq(v.count_zeros(), 9);

data() [1/2]

template<usize N, unsigned_word Word = usize>

Word * gf2::BitSet< N, Word >::data ( )

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

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

data() [2/2]

template<usize N, unsigned_word Word = usize>

const Word * gf2::BitSet< N, Word >::data ( ) const

inlineconstexpr

Returns a const pointer to the underlying store of words .

Example

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

describe()

std::string gf2::BitStore< BitSet< N, usize > >::describe ( ) const

inlineinherited

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

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

fill()

auto gf2::BitStore< BitSet< N, usize > >::fill ( std::invocable< usize > auto f )

inlineinherited

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

Example

BitVec v{10};
v.fill([](usize i) { return i % 2 == 0; });
assert_eq(v.size(), 10);
assert_eq(v.to_string(), "1010101010");

first_set()

std::optional< usize > gf2::BitStore< BitSet< N, usize > >::first_set ( ) const

inlineinherited

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

Example

auto v = BitVec<u8>::zeros(37);
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});
BitVec empty;
assert(empty.first_set() == std::optional<usize>{});

first_unset()

std::optional< usize > gf2::BitStore< BitSet< N, usize > >::first_unset ( ) const

inlineinherited

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

Example

auto v = BitVec<u8>::ones(37);
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});
BitVec empty;
assert(empty.first_unset() == std::optional<usize>{});

flip()

auto gf2::BitStore< BitSet< N, usize > >::flip ( usize index )

inlineinherited

Flips the value of the bit-element at the given index and returns this for chaining/.

Note

In debug mode the index is bounds-checked.

Example

auto v = BitVec<u8>::ones(10);
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()

auto gf2::BitStore< BitSet< N, usize > >::flip_all ( )

inlineinherited

Flips the value of the bits in the store and returns a reference to this for chaining.

Example

auto v = BitVec<u8>::zeros(10);
v.flip_all();
assert_eq(v.to_string(), "1111111111");

front()

bool gf2::BitStore< BitSet< N, usize > >::front ( ) const

inlineconstexprinherited

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

Note

In debug mode the method panics of the store is empty.

Example

auto v = BitVec<>::ones(10);
assert_eq(v.front(), true);
v.set_all(false);
assert_eq(v.front(), false);

get()

bool gf2::BitStore< BitSet< N, usize > >::get ( usize i ) const

inlineconstexprinherited

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

Note

In debug mode the index i is bounds-checked.

Example

BitVec v{10};
assert_eq(v.get(0), false);
v.set(0);
assert_eq(v.get(0), true);

is_empty()

bool gf2::BitStore< BitSet< N, usize > >::is_empty ( ) const

inlineconstexprinherited

Returns true if the store is empty, false otherwise.

Example

BitVec v;
assert_eq(v.is_empty(), true);
BitVec u{10};
assert_eq(u.is_empty(), false);

last_set()

std::optional< usize > gf2::BitStore< BitSet< N, usize > >::last_set ( ) const

inlineinherited

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

Example

auto v = BitVec<u8>::zeros(37);
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});
BitVec empty;
assert(empty.last_set() == std::optional<usize>{});

last_unset()

std::optional< usize > gf2::BitStore< BitSet< N, usize > >::last_unset ( ) const

inlineinherited

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

Example

auto v = BitVec<u8>::ones(37);
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});
BitVec empty;
assert(empty.last_unset() == std::optional<usize>{});

leading_zeros()

usize gf2::BitStore< BitSet< N, usize > >::leading_zeros ( ) const

inlineconstexprinherited

Returns the number of leading zeros in the store.

Example

BitVec v{37};
assert_eq(v.leading_zeros(), 37);
v.set(27);
assert_eq(v.leading_zeros(), 27);
auto w = BitVec<u8>::ones(10);
assert_eq(w.leading_zeros(), 0);

next_set()

std::optional< usize > gf2::BitStore< BitSet< N, usize > >::next_set ( usize index ) const

inlineinherited

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

Example

auto v = BitVec<u8>::zeros(37);
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()

std::optional< usize > gf2::BitStore< BitSet< N, usize > >::next_unset ( usize index ) const

inlineinherited

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

Example

auto v = BitVec<u8>::ones(37);
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>{});
BitVec empty;
assert(empty.next_unset(0) == std::optional<usize>{});

none()

bool gf2::BitStore< BitSet< N, usize > >::none ( ) const

inlineconstexprinherited

Returns true if no bits in the store are set, false otherwise.

Note

Empty store have no set bits (logical connective for none is AND with identity true).

Example

BitVec v{10};
assert_eq(v.none(), true);
v.set(0);
assert_eq(v.none(), false);

offset()

template<usize N, unsigned_word Word = usize>

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

inlineconstexpr

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

This is always zero for BitSet.

operator&()

auto gf2::BitStore< BitSet< N, usize > >::operator& ( const BitStore< Rhs > & rhs ) const

inlineinherited

Returns a new bit-vector that is the AND of the current bit-store and another equal-sized bit-store.

Note

In debug mode, this method panics if the lengths of the two bit-stores do not match.

Example

auto v1 = BitVec<u8>::alternating(10);
auto v2 = ~v1;
auto v3 = v1 & v2;
assert_eq(v3.to_string(), "0000000000");

operator&=()

void gf2::BitStore< BitSet< N, usize > >::operator&= ( const BitStore< Rhs > & rhs )

inlineinherited

In-place AND with another equal-sized bit-store.

Note

In debug mode, this method panics if the lengths of the two bit-stores do not match.

Example

auto v1 = BitVec<u8>::alternating(10);
v1 &= ~v1;
assert_eq(v1.to_string(), "0000000000");

operator+()

auto gf2::BitStore< BitSet< N, usize > >::operator+ ( const BitStore< Rhs > & rhs ) const

inlineinherited

Returns a new bit-vector that is the + of this store with the passed (equal-sized) rhs bit-store.

In GF(2) subtraction is the same as XOR.

Note

In debug mode, this methods panics if the lengths of lhs and rhs do not match.

Example

auto v1 = BitVec<u8>::alternating(10);
auto v2 = ~v1;
auto v3 = v1 + v2;
assert_eq(v3.to_string(), "1111111111");

operator+=()

void gf2::BitStore< BitSet< N, usize > >::operator+= ( const BitStore< Rhs > & rhs )

inlineinherited

In-place addition of this bit-store with the an equal-sized rhs bit-store.

In GF(2) addition is the same as XOR.

Note

In debug mode, this methods panics if the lengths of lhs and rhs do not match.

Example

auto v1 = BitVec<u8>::alternating(10);
v1 += ~v1;
assert_eq(v1.to_string(), "1111111111");

operator-()

auto gf2::BitStore< BitSet< N, usize > >::operator- ( const BitStore< Rhs > & rhs ) const

inlineinherited

Returns a new bit-vector that is the - of this store with the passed (equal-sized) rhs bit-store.

In GF(2) subtraction is the same as XOR.

Note

In debug mode, this methods panics if the lengths of lhs and rhs do not match.

Example

auto v1 = BitVec<u8>::alternating(10);
auto v2 = ~v1;
auto v3 = v1 - v2;
assert_eq(v3.to_string(), "1111111111");

operator-=()

void gf2::BitStore< BitSet< N, usize > >::operator-= ( const BitStore< Rhs > & rhs )

inlineinherited

In-place subtraction of this bit-store with the an equal-sized rhs bit-store.

In GF(2) subtraction is the same as XOR.

Note

In debug mode, this methods panics if the lengths of lhs and rhs do not match.

Example

auto v1 = BitVec<u8>::alternating(10);
v1 -= ~v1;
assert_eq(v1.to_string(), "1111111111");

operator<<()

auto gf2::BitStore< BitSet< N, usize > >::operator<< ( usize shift ) const

inlineconstexprinherited

Returns a new bit-vector that is lhs shifted left by shift bits.

Shifting is in vector-order so if v = [v0,v1,v2,v3] then v << 1 is [v1,v2,v3,0] with zeros added to the right. Left shifting in vector-order is the same as right shifting in bit-order.

Note

Only accessible bits are affected by the shift.

Example

auto v = BitVec<u8>::ones(20);
auto w = v << 8;
assert_eq(w.to_string(), "11111111111100000000");

operator<<=()

void gf2::BitStore< BitSet< N, usize > >::operator<<= ( usize shift )

inlineconstexprinherited

In-place left shift of the bit-store by shift bits.

Shifting is in vector-order so if v = [v0,v1,v2,v3] then v <<= 1 is [v1,v2,v3,0] with zeros added to the right. Left shifting in vector-order is the same as right shifting in bit-order.

Note

Only accessible bits are affected by the shift.

Example

auto v = BitVec<u8>::ones(20);
v <<= 8;
assert_eq(v.to_string(), "11111111111100000000");

operator>>()

auto gf2::BitStore< BitSet< N, usize > >::operator>> ( usize shift ) const

inlineconstexprinherited

Returns a new bit-vector that is lhs shifted right by shift bits.

Shifting is in vector-order so if v = [v0,v1,v2,v3] then v >>= 1 is [0,v0,v1,v2] with zeros added to the left. Right shifting in vector-order is the same as left shifting in bit-order.

Note

Only accessible bits are affected by the shift.

Example

auto v = BitVec<u8>::ones(20);
auto w = v >> 8;
assert_eq(w.to_string(), "00000000111111111111");

operator>>=()

void gf2::BitStore< BitSet< N, usize > >::operator>>= ( usize shift )

inlineconstexprinherited

In-place right shift of the bit-store by shift bits.

Shifting is in vector-order so if v = [v0,v1,v2,v3] then v >>= 1 is [0,v0,v1,v2] with zeros added to the left. Right shifting in vector-order is the same as left shifting in bit-order.

Note

Only accessible bits are affected by the shift.

Example

auto v = BitVec<u8>::ones(20);
v >>= 8;
assert_eq(v.to_string(), "00000000111111111111");

operator[]()

bool gf2::BitStore< BitSet< N, usize > >::operator[] ( usize index ) const

inlineconstexprinherited

Returns the boolean value of the bit element at index.

Note

In debug mode the index is bounds-checked.

Example

BitVec v{10};
assert(v[2] == false);
v[2] = true;
assert(v[2] == true);
assert(v.to_string() == "0010000000");

operator^()

auto gf2::BitStore< BitSet< N, usize > >::operator^ ( const BitStore< Rhs > & rhs ) const

inlineinherited

Returns a new bit-vector that is the XOR of the current bit-store and another equal-sized bit-store.

Note

In debug mode, this method panics if the lengths of the two bit-stores do not match.

Example

auto v1 = BitVec<u8>::alternating(10);
auto v2 = ~v1;
auto v3 = v1 ^ v2;
assert_eq(v3.to_string(), "1111111111");

operator^=()

void gf2::BitStore< BitSet< N, usize > >::operator^= ( const BitStore< Rhs > & rhs )

inlineinherited

In-place XOR with another equal-sized bit-store.

Note

In debug mode, this method panics if the lengths of the two bit-stores do not match.

Example

auto v1 = BitVec<u8>::alternating(10);
v1 ^= ~v1;
assert_eq(v1.to_string(), "1111111111");

operator|()

auto gf2::BitStore< BitSet< N, usize > >::operator| ( const BitStore< Rhs > & rhs ) const

inlineinherited

Returns a new bit-vector that is the OR of the current bit-store and another equal-sized bit-store.

Note

In debug mode, this methods panics if the lengths of lhs and rhs do not match.

Example

auto v1 = BitVec<u8>::alternating(10);
auto v2 = ~v1;
auto v3 = v1 | v2;
assert_eq(v3.to_string(), "1111111111");

operator|=()

void gf2::BitStore< BitSet< N, usize > >::operator|= ( const BitStore< Rhs > & rhs )

inlineinherited

In-place OR with another equal-sized bit-store.

Note

In debug mode, this method panics if the lengths of the two bit-stores do not match.

Example

auto v1 = BitVec<u8>::alternating(10);
v1 |= ~v1;
assert_eq(v1.to_string(), "1111111111");

operator~()

auto gf2::BitStore< BitSet< N, usize > >::operator~ ( ) const

inlineinherited

Returns a new bit-vector that has the same bits as the current bit-store but with all the bits flipped.

Example

auto v = BitVec<u8>::alternating(10);
assert_eq(v.to_string(), "1010101010");
auto w = ~v;
assert_eq(w.to_string(), "0101010101");

previous_set()

std::optional< usize > gf2::BitStore< BitSet< N, usize > >::previous_set ( usize index ) const

inlineinherited

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

Example

auto v = BitVec<u8>::zeros(37);
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()

std::optional< usize > gf2::BitStore< BitSet< N, usize > >::previous_unset ( usize index ) const

inlineinherited

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

Example

auto v = BitVec<u8>::ones(37);
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>{});
BitVec empty;
assert(empty.previous_unset(0) == std::optional<usize>{});

random_fill()

auto gf2::BitStore< BitSet< N, usize > >::random_fill ( double p = 0.5, u64 seed = 0 )

inlineinherited

Fill the store with random bits and returns a reference to this for chaining.

The default call random_fill() 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).

Note

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

Example

BitVec u{10}, v{10};
u64 seed = 1234567890;
u.random_fill(0.5, seed);
v.random_fill(0.5, seed);
assert(u == v);

riffle_into()

void gf2::BitStore< BitSet< N, usize > >::riffle_into ( BitVec< word_type > & dst ) const

inlineconstexprinherited

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

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

Note

There is no last zero bit in dst.

Example

auto v = BitVec<u8>::ones(10);
BitVec<u8> dst;
v.riffle_into(dst);
assert_eq(dst.to_string(), "1010101010101010101");

riffled()

auto gf2::BitStore< BitSet< N, usize > >::riffled ( ) const

inlineconstexprinherited

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

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

Note

There is no last zero bit in dst.

Example

auto v = BitVec<u8>::ones(10);
auto dst = v.riffled();
assert_eq(dst.to_string(), "1010101010101010101");

set()

auto gf2::BitStore< BitSet< N, usize > >::set ( usize index, bool value = true )

inlineinherited

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

Note

In debug mode the index is bounds-checked.

Example

BitVec v{10};
assert_eq(v.get(0), false);
v.set(0);
assert_eq(v.get(0), true);

set_all()

auto gf2::BitStore< BitSet< N, usize > >::set_all ( bool value = true )

inlineinherited

Sets the bits in the store to the boolean value and returns a reference to this for chaining.

By default, all bits are set to true.

Example

auto v = BitVec<u8>::zeros(10);
v.set_all();
assert_eq(v.to_string(), "1111111111");

set_bit_indices()

auto gf2::BitStore< BitSet< N, usize > >::set_bit_indices ( ) const

inlineconstexprinherited

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

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

Example

auto v = BitVec<u8>::alternating(10);
assert_eq(v.to_string(), "1010101010");
auto indices = std::ranges::to<std::vector>(v.set_bit_indices());
assert_eq(indices, (std::vector<usize>{0, 2, 4, 6, 8}));

set_word() [1/2]

template<usize N, unsigned_word Word = usize>

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

inlineconstexpr

Sets word i in the bitset'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.

Note

In debug mode the index is bounds checked.

Example

BitSet<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);

set_word() [2/2]

void gf2::BitStore< BitSet< N, usize > >::set_word ( usize i, word_type value )

inlineconstexprinherited

This method sets "word" at index i to the specified value.

For example, if the store has 18 bit elements, then setting the first word changes bit elements 0 through 7, the second word changes bit elements 8 through 15, and the third word changes bit elements 16 and 17.

This method is trivially implemented by the BitVec class. However, the bits in a BitSpan may not be aligned to word boundaries but that class synthesises words as if they were by combining adjacent words as needed.

Note

The method must ensure that inaccessible bits in the underlying store are not changed by this call.

size()

template<usize N, unsigned_word Word = usize>

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

inlineconstexpr

Returns the number of bit-elements in the bitset.

Example

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

span()

auto gf2::BitStore< BitSet< N, usize > >::span ( usize begin, usize end ) const

inlineconstexprinherited

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

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

Note

This method panics if the bit-store is empty or if the range is not valid.

Example

auto v = BitVec<>::alternating(10);
auto s = v.span(1,5);
assert_eq(s.to_string(), "0101");

split_at()

void gf2::BitStore< BitSet< N, usize > >::split_at ( usize at, BitVec< word_type > & left, BitVec< word_type > & right ) const

inlineconstexprinherited

Views a bit-store 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-vector up to but not including at and right contains the bits from at to the end of the bit-vector. This bit-vector 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-vector into two parts repeatedly.

Note

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

Example

auto v = BitVec<>::alternating(10);
BitVec 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_words()

auto gf2::BitStore< BitSet< N, usize > >::store_words ( ) const

inlineconstexprinherited

Returns a const iterator over all the words underlying the bit-store.

You can use this iterator to iterate over the words in the store and read the Word value of each word. Note that you cannot use this iterator to modify the words in the store.

Note

The words here may be a synthetic construct. The expectation is that the bit 0 in the store is located at the bit-location 0 of word(0). That is always the case for bit-vectors but bit-slices typically synthesise "words" on the fly from adjacent pairs of bit-vector words. Nevertheless, almost all the methods in BitStore are implemented efficiently by operating on those words.

Example

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

sub()

auto gf2::BitStore< BitSet< N, usize > >::sub ( usize begin, usize end ) const

inlineconstexprinherited

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

Note

This method panics if the bit-vector is empty or if the range is not valid.

Example

auto v = BitVec<>::alternating(10);
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()

auto gf2::BitStore< BitSet< N, usize > >::swap ( usize i0, usize i1 )

inlineconstexprinherited

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

Note

In debug mode, panics if either of the indices is out of bounds.

Example

auto v = BitVec<>::zeros(10);
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()

std::string gf2::BitStore< BitSet< N, usize > >::to_binary_string ( std::string_view sep = "", std::string_view pre = "", std::string_view post = "" ) const

inlineinherited

Returns a binary string representation of the store.

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

BitVec v{10};
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()

std::string gf2::BitStore< BitSet< N, usize > >::to_hex_string ( ) const

inlineinherited

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

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

BitVec v0;
assert_eq(v0.to_hex_string(), "");
auto v1 = BitVec<>::ones(4);
assert_eq(v1.to_hex_string(), "F");
auto v2 = BitVec<>::ones(5);
assert_eq(v2.to_hex_string(), "F1.2");
auto v3 = BitVec<>::alternating(8);
assert_eq(v3.to_binary_string(), "10101010");
assert_eq(v3.to_hex_string(), "AA");

to_pretty_string()

std::string gf2::BitStore< BitSet< N, usize > >::to_pretty_string ( ) const

inlineinherited

Returns a "pretty" string representation of the store.

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

auto v = BitVec<>::alternating(10);
assert_eq(v.to_pretty_string(), "[1,0,1,0,1,0,1,0,1,0]");
BitVec empty;
assert_eq(empty.to_pretty_string(), "[]");

to_string()

std::string gf2::BitStore< BitSet< N, usize > >::to_string ( std::string_view sep = "", std::string_view pre = "", std::string_view post = "" ) const

inlineinherited

Returns a binary string representation of the store.

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

BitVec v{10};
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()

auto gf2::BitStore< BitSet< N, usize > >::to_words ( ) const

inlineconstexprinherited

Returns a copy of the words underlying this bit-store.

Note

The last word in the vector may not be fully occupied but unused slots will be all zeros.

Example

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

trailing_zeros()

usize gf2::BitStore< BitSet< N, usize > >::trailing_zeros ( ) const

inlineconstexprinherited

Returns the number of trailing zeros in the store.

Example

auto v = BitVec<u8>::zeros(27);
assert_eq(v.trailing_zeros(), 27);
v.set(0);
assert_eq(v.trailing_zeros(), 26);

unset_bit_indices()

auto gf2::BitStore< BitSet< N, usize > >::unset_bit_indices ( ) const

inlineconstexprinherited

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

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

Example

auto v = BitVec<u8>::alternating(10);
assert_eq(v.to_string(), "1010101010");
auto indices = std::ranges::to<std::vector>(v.unset_bit_indices());
assert_eq(indices, (std::vector<usize>{1, 3, 5, 7, 9}));

word()

template<usize N, unsigned_word Word = usize>

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

inlineconstexpr

Returns word i from the bitset'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.

Note

In debug mode the index is bounds checked.

Example

BitSet<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 Word = usize>

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

inlineconstexpr

Returns the number of words in the bitset's underlying word store.

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

Example

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