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16 KiB
16 KiB
Bit string
We define here a data type to handle bit strings efficiently. When
the bit string contains less than 64 bits, it is stored internally
in a 63-bit integer and uses bitwise instructions. When more than
63 bits are required, the zarith
library is used to consider the
bit string as a multi-precision integer.
Type
type t
General implementation
val of_int : int -> t
val of_z : Z.t -> t
val zero : int -> t
val is_zero : t -> bool
val numbits : t -> int
val testbit : t -> int -> bool
val neg : t -> t
val shift_left : t -> int -> t
val shift_right : t -> int -> t
val shift_left_one : int -> int -> t
val logor : t -> t -> t
val logxor : t -> t -> t
val logand : t -> t -> t
val lognot : t -> t
val plus_one : t -> t
val minus_one : t -> t
val hamdist : t -> t -> int
val trailing_zeros : t -> int
val popcount : t -> int
val to_list : ?accu:(int list) -> t -> int list
val permutations : int -> int -> t list
of_int |
Creates a bit string from an int |
of_z |
Creates a bit string from an Z.t multi-precision integer |
zero |
zero n creates a zero bit string with n bits |
is_zero |
True if all the bits of the bit string are zero. |
numbits |
Returns the number of bits used to represent the bit string |
testbit |
testbit t n is true if the n -th bit of the bit string t is set to 1 |
neg |
Returns the negative of the integer interpretation of the bit string |
shift_left |
shift_left t n returns a new bit strings with all the bits shifted n positions to the left |
shift_right |
shift_right t n returns a new bit strings with all the bits shifted n positions to the right |
shift_left_one |
shift_left_one size n returns a new bit strings with the n -th bit set to one. It is equivalent as shifting 1 by n bits to the left, size is the total number of bits of the bit string |
logor |
Bitwise logical or |
logxor |
Bitwise logical exclusive or |
logand |
Bitwise logical and |
lognot |
Bitwise logical negation |
plus_one |
Takes the integer representation of the bit string and adds one |
minus_one |
Takes the integer representation of the bit string and removes one |
hamdist |
Returns the Hamming distance, i.e. the number of bits differing between two bit strings |
trailing_zeros |
Returns the number of trailing zeros in the bit string |
permutations |
permutations m n generates the list of all possible n -bit strings with m bits set to 1 . Algorithm adapted from Bit twiddling hacks |
popcount |
Returns the number of bits set to one in the bit string |
to_list |
Converts a bit string into a list of integers indicating the positions where the bits are set to 1 . The first value for the position is not 0 but 1 |
Bitstring.of_int 15;; - : Bitstring.t = ++++------------------------------------------------------------
Bitstring.(shift_left (of_int 15) 2);; - : Bitstring.t = --++++---------------------------------------------------------- Bitstring.(shift_right (of_int 15) 2);; - : Bitstring.t = ++-------------------------------------------------------------- Bitstring.shift_left_one 32 4;; - : Bitstring.t = ----+----------------------------------------------------------- Bitstring.(testbit (of_int 15) 3);; - : bool = true Bitstring.(testbit (of_int 15) 4);; - : bool = false
Bitstring.(logor (of_int 15) (of_int 73));; - : Bitstring.t = ++++--+--------------------------------------------------------- Bitstring.(logand (of_int 15) (of_int 10));; - : Bitstring.t = -+-+------------------------------------------------------------ Bitstring.(logxor (of_int 15) (of_int 73));; - : Bitstring.t = -++---+---------------------------------------------------------
Bitstring.(plus_one (of_int 15));; - : Bitstring.t = ----+----------------------------------------------------------- Bitstring.(minus_one (of_int 15));; - : Bitstring.t = -+++------------------------------------------------------------
Bitstring.(trailing_zeros (of_int 12));; - : int = 2 Bitstring.(hamdist (of_int 15) (of_int 73));; - : int = 3 Bitstring.(popcount (of_int 15));; - : int = 4
Bitstring.(to_list (of_int 45));; - : int list = [1; 3; 4; 6]
Bitstring.permutations 2 4;; - : Bitstring.t list = [++--------------------------------------------------------------; +-+-------------------------------------------------------------; -++-------------------------------------------------------------; +--+------------------------------------------------------------; -+-+------------------------------------------------------------; --++------------------------------------------------------------]
Printers
val pp : Format.formatter -> t -> unit