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>

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 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 *	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 store within the first word.
Constructors:
constexpr	BitSet ()
	Constructs a bit-set of length N with all the bit elements set to 0.
constexpr	BitSet (Word word)
	Constructs a bit-set with N elements by repeatedly copying all the bits from word.
Bit Accessors:
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:
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.
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-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.
Copying Bits into the Store:
template<Unsigned Src>
auto	copy (Src src)
	Copies the bits from an unsigned integral src value and returns a reference to this for chaining.
template<BitStore Src>
auto	copy (Src const &src)
	Copies the bits from an equal-sized src store and returns a reference to this for chaining.
auto	copy (std::bitset< N > const &src)
	Copies the bits of an equal-sized std::bitset and returns a reference to this for chaining.
Store Fills:
auto	copy (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:
constexpr std::optional< usize >	first_set () const
	Returns the index of the first set bit in the bit-store or {} if no bits are set.
constexpr std::optional< usize >	last_set () const
	Returns the index of the last set bit in the bit-store 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 store 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 store 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-store or {} if no bits are unset.
constexpr std::optional< usize >	last_unset () const
	Returns the index of the last unset bit in the bit-store 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 store 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 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	bits ()
	Returns a non-const iterator over the values of the bits in the mutable bit-store.
constexpr auto	set_bits () const
	Returns an iterator over the indices of any set bits in the bit-store.
constexpr auto	unset_bits () 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 store's bits in the half-open range [begin, end).
constexpr auto	span (usize begin, usize end)
	Returns a mutable 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-set.
Splits:
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.
constexpr auto	split_at (usize at) const
	Views a bit-store as two parts containing the elements [0, at) and [at, size()) respectively.
Riffling:
constexpr void	riffled (BitVec< word_type > &dst) const
	Interleaves the bits of this bit-store with zeros storing the result into the bit-set dst.
constexpr auto	riffled () const
	Returns a new bit-set that is the result of riffling the bits in this bit-store 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 store.
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_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-store in some detail.

Static Public Member Functions
Factory Constructors:
static constexpr BitSet	zeros ()
	Factory method to generate a bit-set of length N where the elements are all 0.
static constexpr BitSet	ones ()
	Factory method to generate a bit-set of length N where the elements are all 1.
static constexpr BitSet	constant (bool value)
	Factory method to generate a bit-set of length N where the elements are set to value.
static constexpr BitSet	unit (usize i)
	Factory method to generate a "unit" bit-set of length N where only element i is set.
static constexpr BitSet	alternating ()
	Factory method to generate a bit-set of length N looking like 101010....
Random BitSet Constructors:
static BitSet	random (double p=0.5, u64 seed=0)
	Factory method to generate a bit-set of size N where the elements are picked at random.
static BitSet	seeded_random (u64 seed)
	Factory method to generate a bit-set of size N where the elements are from independent fair coin flips generated from an RNG seeded with the given seed.
static BitSet	biased_random (double p)
	Factory method to generate a bit-set 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.
static constexpr BitSet	from (std::bitset< N > const &src)
	Factory method to construct a bit-set from the bits of a std::bitset.
static constexpr BitSet	from (std::invocable< usize > auto f)
	Factory method to construct a bit-set by repeatedly calling f(i) for i in [0, N).

Detailed Description

template<usize N, Unsigned 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 richer set of functionality.

The BitSet class satisfies the BitStore concept.

Constructor & Destructor Documentation

BitSet() [1/2]

template<usize N, Unsigned Word = usize>

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

inlineexplicitconstexpr

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

Example

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

BitSet() [2/2]

template<usize N, Unsigned Word = usize>

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

inlineexplicitconstexpr

Constructs a bit-set 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

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

Member Function Documentation

all()

template<usize N, Unsigned Word = usize>

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

inlineconstexpr

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

BitSet<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 BitSet gf2::BitSet< N, Word >::alternating ( )

inlinestaticconstexpr

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

Example

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

any()

template<usize N, Unsigned Word = usize>

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

inlineconstexpr

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

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

back()

template<usize N, Unsigned Word = usize>

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

inlineconstexpr

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

Note

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

Example

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

biased_random()

template<usize N, Unsigned Word = usize>

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

inlinestatic

Factory method to generate a bit-set 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 = BitSet<10>::biased_random(0.3);
auto v = BitSet<10>::biased_random(0.3);
assert_eq(u.size(), v.size());

bits() [1/2]

template<usize N, Unsigned Word = usize>

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

inlineconstexpr

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

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

BitSet<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::BitSet< N, Word >::bits ( ) const

inlineconstexpr

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

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

clean()

template<usize N, Unsigned Word = usize>

void gf2::BitSet< 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 BitSet gf2::BitSet< N, Word >::constant ( bool value )

inlinestaticconstexpr

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

Example

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

copy() [1/4]

template<usize N, Unsigned Word = usize>

template<BitStore Src>

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

inline

Copies the bits from an equal-sized src store 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 BitSet<u32> to BitSet<u8>) as long as the sizes match.

Example

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

copy() [2/4]

template<usize N, Unsigned Word = usize>

template<Unsigned Src>

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

inline

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 BitSet<u8> of size 64.
3. The least-significant bit of the source becomes the bit at index 0 in the store.

Example

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

copy() [3/4]

template<usize N, Unsigned Word = usize>

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

inline

Copies the bits of an equal-sized std::bitset and returns a reference to this for chaining.

Note

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

Example

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

copy() [4/4]

template<usize N, Unsigned Word = usize>

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

inline

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

Example

BitSet<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::BitSet< N, Word >::count_ones ( ) const

inlineconstexpr

Returns the number of set bits in the store.

Example

BitSet<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::BitSet< N, Word >::count_zeros ( ) const

inlineconstexpr

Returns the number of unset bits in the store.

Example

BitSet<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::BitSet< N, Word >::describe ( ) const

inline

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

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

first_set()

template<usize N, Unsigned Word = usize>

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

inlineconstexpr

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

Example

BitSet<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});
BitSet<0> empty;
assert(empty.first_set() == std::optional<usize>{});

first_unset()

template<usize N, Unsigned Word = usize>

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

inlineconstexpr

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

Example

BitSet<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});
BitSet<0> empty;
assert(empty.first_unset() == std::optional<usize>{});

flip()

template<usize N, Unsigned Word = usize>

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

inline

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

Note

In debug mode the index is bounds-checked.

Example

auto v = BitSet<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::BitSet< N, Word >::flip_all ( )

inline

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

Example

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

from() [1/2]

template<usize N, Unsigned Word = usize>

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

inlinestaticconstexpr

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

Note

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

Example

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

from() [2/2]

template<usize N, Unsigned Word = usize>

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

inlinestaticconstexpr

Factory method to construct a bit-set 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 = BitSet<10, u8>::from([](usize i) { return i % 2 == 0; });
assert_eq(v.to_string(), "1010101010");

front()

template<usize N, Unsigned Word = usize>

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

inlineconstexpr

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

Note

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

Example

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

get()

template<usize N, Unsigned Word = usize>

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

inlineconstexpr

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

BitSet<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::BitSet< N, Word >::is_empty ( ) const

inlineconstexpr

Returns true if the store is empty, false otherwise.

Example

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

last_set()

template<usize N, Unsigned Word = usize>

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

inlineconstexpr

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

Example

BitSet<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});
BitSet<0> empty;
assert(empty.last_set() == std::optional<usize>{});

last_unset()

template<usize N, Unsigned Word = usize>

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

inlineconstexpr

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

Example

BitSet<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});
BitSet<0> empty;
assert(empty.last_unset() == std::optional<usize>{});

leading_zeros()

template<usize N, Unsigned Word = usize>

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

inlineconstexpr

Returns the number of leading zeros in the store.

Example

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

next_set()

template<usize N, Unsigned Word = usize>

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

inlineconstexpr

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

Example

BitSet<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::BitSet< N, Word >::next_unset ( usize index ) const

inlineconstexpr

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

Example

BitSet<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>{});
BitSet<0> empty;
assert(empty.next_unset(0) == std::optional<usize>{});

none()

template<usize N, Unsigned Word = usize>

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

inlineconstexpr

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

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

offset()

template<usize N, Unsigned 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.

ones()

template<usize N, Unsigned Word = usize>

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

inlinestaticconstexpr

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

Example

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

operator[]() [1/2]

template<usize N, Unsigned Word = usize>

auto gf2::BitSet< 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-store must continue to exist while the BitRef is in use.

In debug mode the index i is bounds-checked.

Example

BitSet<10> v;
v[2] = true;
assert(v.to_string() == "0010000000");
BitSet<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::BitSet< N, Word >::operator[] ( usize i ) const

inlineconstexpr

Returns the boolean value of the bit element i.

Note

In debug mode the index is bounds-checked.

Example

BitSet<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::BitSet< N, Word >::previous_set ( usize index ) const

inlineconstexpr

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

Example

BitSet<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::BitSet< N, Word >::previous_unset ( usize index ) const

inlineconstexpr

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

Example

BitSet<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>{});
BitSet<0> empty;
assert(empty.previous_unset(0) == std::optional<usize>{});

random()

template<usize N, Unsigned Word = usize>

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

inlinestatic

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

The default call BitSet<>::random() produces a random bit-set 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).

Note

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

Example

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

random_fill()

template<usize N, Unsigned Word = usize>

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

inline

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

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

riffled() [1/2]

template<usize N, Unsigned Word = usize>

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

inlineconstexpr

Returns a new bit-set 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-set will have the bits a0b0c0d0e.

Note

There is no last zero bit in dst.

Example

BitSet<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::BitSet< N, Word >::riffled ( BitVec< word_type > & dst ) const

inlineconstexpr

Interleaves the bits of this bit-store with zeros storing the result into the bit-set 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

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

seeded_random()

template<usize N, Unsigned Word = usize>

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

inlinestatic

Factory method to generate a bit-set 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-vectors, 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).

Note

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

Example

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

set()

template<usize N, Unsigned Word = usize>

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

inline

Sets the bit-element i 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

BitSet<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::BitSet< N, Word >::set_all ( bool value = true )

inline

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

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

set_bits()

template<usize N, Unsigned Word = usize>

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

inlineconstexpr

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

BitSet<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::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);

size()

template<usize N, Unsigned 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() [1/2]

template<usize N, Unsigned Word = usize>

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

inlineconstexpr

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

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

Note

This method panics if the span range is not valid.

Example

BitSet<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::BitSet< N, Word >::span ( usize begin, usize end ) const

inlineconstexpr

Returns an immutable bit-span encompassing the store's 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 span range is not valid.

Example

BitSet<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::BitSet< N, Word >::split_at ( usize at ) const

inlineconstexpr

Views a bit-store 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-set up to but not including at and right contains the bits from at to the end of the bit-set. This bit-set itself is not modified.

Note

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

Example

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

inlineconstexpr

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

Note

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

Example

BitSet<10, u8> v;
v.copy([](usize i) { return i % 2 == 0; });
BitVec<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::BitSet< 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

BitSet<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::BitSet< N, Word >::store ( ) const

inlineconstexpr

Returns a const pointer to the underlying store of words .

Example

BitSet<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::BitSet< N, Word >::store_words ( ) const

inlineconstexpr

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. 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-set words. Nevertheless, almost all the methods in BitStore are implemented efficiently by operating on those words.

Example

BitSet<10, u8> v; v.set_all();
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::BitSet< 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-set.

Note

This method panics if the range is not valid.

Example

BitSet<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::BitSet< N, Word >::swap ( usize i0, usize i1 )

inlineconstexpr

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

BitSet<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::BitSet< 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 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

BitSet<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::BitSet< N, Word >::to_hex_string ( ) const

inline

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

BitSet<0> v0;
assert_eq(v0.to_hex_string(), "");
BitSet<4> v1; v1.set_all();
assert_eq(v1.to_hex_string(), "F");
BitSet<5> v2; v2.set_all();
assert_eq(v2.to_hex_string(), "F1.2");
BitSet<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::BitSet< N, Word >::to_pretty_string ( ) const

inline

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

BitSet<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]");
BitSet<0> empty;
assert_eq(empty.to_pretty_string(), "[]");

to_string()

template<usize N, Unsigned Word = usize>

std::string gf2::BitSet< 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 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

BitSet<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()

template<usize N, Unsigned Word = usize>

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

inlineconstexpr

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

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

trailing_zeros()

template<usize N, Unsigned Word = usize>

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

inlineconstexpr

Returns the number of trailing zeros in the store.

Example

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

inlinestaticconstexpr

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

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

Example

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

unset_bits()

template<usize N, Unsigned Word = usize>

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

inlineconstexpr

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

BitSet<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::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 = 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);

zeros()

template<usize N, Unsigned Word = usize>

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

inlinestaticconstexpr

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

Example

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