Unsigned.h

Utility functions that work on primitive unsigned word types.
See the Unsigned page for more details. More...

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Namespaces
namespace	gf2
	The namespace for the gf2 library.

Concepts
concept	gf2::Unsigned
	The Unsigned concept is the same as std::unsigned_integral. It is satisfied by all primitive unsigned integer types.

Typedefs
Shorthand Type Aliases.
using	gf2::u8 = std::uint8_t
	Word type alias for an 8-bit unsigned integer.
using	gf2::u16 = std::uint16_t
	Word type alias for a 16-bit unsigned integer.
using	gf2::u32 = std::uint32_t
	Word type alias for a 32-bit unsigned integer.
using	gf2::u64 = std::uint64_t
	Word type alias for a 64-bit unsigned integer.
using	gf2::usize = std::size_t
	Word type alias for the platform's "native"-sized unsigned integer.

Functions
Constructors:
template<Unsigned Word>
constexpr Word	gf2::with_set_bits (u8 begin, u8 end)
	Returns an Unsigned with the bits in the half-open range [begin, end) set to 1 and the others set to 0.
template<Unsigned Word>
constexpr Word	gf2::with_unset_bits (u8 begin, u8 end)
	Returns an Unsigned with the bits in the half-open range [begin, end) set to 0 and the others set to 1.
Bit mutators:
template<Unsigned Word>
constexpr void	gf2::set_bits (Word &word, u8 begin, u8 end)
	Sets the bits in the half-open range [begin, end) of word to one, leaving the others unchanged.
template<Unsigned Word>
constexpr void	gf2::reset_bits (Word &word, u8 begin, u8 end)
	Resets the bits in the half-open range [begin, end) of word to zero, leaving the others unchanged.
template<Unsigned Word>
constexpr void	gf2::set_except_bits (Word &word, u8 begin, u8 end)
	Sets the bits of word to 1 except for those in the half-open range [begin, end) which are unchanged.
template<Unsigned Word>
constexpr void	gf2::reset_except_bits (Word &word, u8 begin, u8 end)
	Sets the bits of word to 0 except for those in the half-open range [begin, end) which are unchanged.
template<Unsigned Word>
constexpr Word	gf2::reverse_bits (Word word)
	Returns a copy of word with all its bits reversed.
template<Unsigned Word, typename Other> requires std::convertible_to<Other, Word>
constexpr void	gf2::replace_bits (Word &word, u8 begin, u8 end, Other other)
	Replace the bits of word in the range [begin, end) with the bits from other leaving the rest unchanged.
Bit Riffling:
template<Unsigned Word>
constexpr std::pair< Word, Word >	gf2::riffle (Word word)
	Riffles an Unsigned into a pair of others containing the bits in the original word interleaved with zeros.
Bit Counts:
template<Unsigned Word>
constexpr u8	gf2::count_ones (Word word)
	Returns the number of set bits in an Unsigned.
template<Unsigned Word>
constexpr u8	gf2::count_zeros (Word word)
	Returns the number of unset bits in an Unsigned.
template<Unsigned Word>
constexpr u8	gf2::trailing_zeros (Word word)
	Returns the number of trailing zeros in an Unsigned.
template<Unsigned Word>
constexpr u8	gf2::leading_zeros (Word word)
	Returns the number of leading zeros in an Unsigned.
template<Unsigned Word>
constexpr u8	gf2::trailing_ones (Word word)
	Returns the number of trailing ones in an Unsigned.
template<Unsigned Word>
constexpr u8	gf2::leading_ones (Word word)
	Returns the number of leading ones in an Unsigned.
template<Unsigned Word>
constexpr std::optional< u8 >	gf2::lowest_set_bit (Word word)
	Returns the index of the lowest set bit in an Unsigned or std::nullopt if no bits are set.
Searches:
template<Unsigned Word>
constexpr std::optional< u8 >	gf2::highest_set_bit (Word word)
	Returns the index of the highest set bit in an Unsigned or std::nullopt if no bits are set.
template<Unsigned Word>
constexpr std::optional< u8 >	gf2::lowest_unset_bit (Word word)
	Returns the index of the lowest unset bit in an Unsigned or std::nullopt if there are no unset bits.
template<Unsigned Word>
constexpr std::optional< u8 >	gf2::highest_unset_bit (Word word)
	Returns the index of the highest unset bit in an Unsigned or std::nullopt if there are none.
Stringification:
template<Unsigned Word>
static std::string	gf2::to_binary_string (Word word)
	Returns the binary string representation of an Unsigned showing all the bits.
template<Unsigned Word>
static std::string	gf2::to_hex_string (Word word)
	Returns the hex string representation of an Unsigned showing all the bits.
Bit Locations:
template<Unsigned Word>
constexpr usize	gf2::words_needed (usize n_bits)
	Returns the number of Unsigneds needed to store n_bits bits.
template<Unsigned Word>
constexpr usize	gf2::word_index (usize i)
	Returns the index of the Unsigned word holding bit element i.
template<Unsigned Word>
constexpr u8	gf2::bit_offset (usize i)
	Returns the bit position within the containing word for bit element i.
template<Unsigned Word>
constexpr std::pair< usize, u8 >	gf2::index_and_offset (usize i)
	Returns a pair of the index of the word and the bit position within the word for bit element i.
template<Unsigned Word>
constexpr std::pair< usize, Word >	gf2::index_and_mask (usize i)
	Returns a pair of the index of the word and a mask isolating bit element i.

Variables
Variables:
template<Unsigned Word>
constexpr u8	gf2::BITS = std::numeric_limits<Word>::digits
	The number of bits in an Unsigned returned as a u8.
template<Unsigned Word>
constexpr Word	gf2::ZERO = Word{0}
	The zero value for an Unsigned type.
template<Unsigned Word>
constexpr Word	gf2::ONE = Word{1}
	The one value for an Unsigned type.
template<Unsigned Word>
constexpr Word	gf2::MAX = std::numeric_limits<Word>::max()
	The Unsigned instance with all its bits set to 1.
template<Unsigned Word>
constexpr Word	gf2::ALTERNATING = MAX<Word> / 3
	The Unsigned instance with alternating bits set to 0 and 1.

Detailed Description

Utility functions that work on primitive unsigned word types.
See the Unsigned page for more details.