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291 lines
11 KiB
OCaml
291 lines
11 KiB
OCaml
(* Single-integer implementation :noexport: *)
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(* [[file:~/QCaml/common/bitstring.org::*Single-integer%20implementation][Single-integer implementation:1]] *)
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module One = struct
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let of_int x =
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assert (x > 0); x
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let numbits _ = 63
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let zero = 0
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let is_zero x = x = 0
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let shift_left x i = x lsl i
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let shift_right x i = x lsr i
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let shift_left_one i = 1 lsl i
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let testbit x i = ( (x lsr i) land 1 ) = 1
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let logor a b = a lor b
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let neg a = - a
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let logxor a b = a lxor b
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let logand a b = a land b
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let lognot a = lnot a
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let minus_one a = a - 1
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let plus_one a = a + 1
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let popcount = function
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| 0 -> 0
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| r -> Util.popcnt (Int64.of_int r)
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let trailing_zeros r =
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Util.trailz (Int64.of_int r)
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let hamdist a b =
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a lxor b
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|> popcount
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let pp ppf s =
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Format.fprintf ppf "@[@[%a@]@]" (Util.pp_bitstring 64)
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(Z.of_int s)
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end
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(* Single-integer implementation:1 ends here *)
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(* Zarith implementation :noexport: *)
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(* [[file:~/QCaml/common/bitstring.org::*Zarith%20implementation][Zarith implementation:1]] *)
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module Many = struct
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let of_z x = x
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let zero = Z.zero
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let is_zero x = x = Z.zero
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let shift_left = Z.shift_left
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let shift_right = Z.shift_right
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let shift_left_one i = Z.shift_left Z.one i
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let testbit = Z.testbit
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let logor = Z.logor
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let logxor = Z.logxor
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let logand = Z.logand
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let lognot = Z.lognot
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let neg = Z.neg
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let minus_one = Z.pred
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let plus_one = Z.succ
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let trailing_zeros = Z.trailing_zeros
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let hamdist = Z.hamdist
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let numbits i = max (Z.numbits i) 64
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let popcount z =
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if z = Z.zero then 0 else Z.popcount z
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let pp ppf s =
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Format.fprintf ppf "@[@[%a@]@]" (Util.pp_bitstring (Z.numbits s)) s
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end
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(* Zarith implementation:1 ends here *)
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(* [[file:~/QCaml/common/bitstring.org::*Type][Type:2]] *)
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type t =
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| One of int
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| Many of Z.t
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(* Type:2 ends here *)
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(* | ~of_int~ | Creates a bit string from an ~int~ |
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* | ~of_z~ | Creates a bit string from an ~Z.t~ multi-precision integer |
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* | ~zero~ | ~zero n~ creates a zero bit string with ~n~ bits |
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* | ~is_zero~ | True if all the bits of the bit string are zero. |
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* | ~numbits~ | Returns the number of bits used to represent the bit string |
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* | ~testbit~ | ~testbit t n~ is true if the ~n~-th bit of the bit string ~t~ is set to ~1~ |
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* | ~neg~ | Returns the negative of the integer interpretation of the bit string |
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* | ~shift_left~ | ~shift_left t n~ returns a new bit strings with all the bits shifted ~n~ positions to the left |
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* | ~shift_right~ | ~shift_right t n~ returns a new bit strings with all the bits shifted ~n~ positions to the right |
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* | ~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 |
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* | ~logor~ | Bitwise logical or |
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* | ~logxor~ | Bitwise logical exclusive or |
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* | ~logand~ | Bitwise logical and |
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* | ~lognot~ | Bitwise logical negation |
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* | ~plus_one~ | Takes the integer representation of the bit string and adds one |
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* | ~minus_one~ | Takes the integer representation of the bit string and removes one |
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* | ~hamdist~ | Returns the Hamming distance, i.e. the number of bits differing between two bit strings |
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* | ~trailing_zeros~ | Returns the number of trailing zeros in the bit string |
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* | ~permutations~ | ~permutations m n~ generates the list of all possible ~n~-bit strings with ~m~ bits set to ~1~. Algorithm adapted from [[https://graphics.stanford.edu/~seander/bithacks.html#NextBitPermutation][Bit twiddling hacks]] |
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* | ~popcount~ | Returns the number of bits set to one in the bit string |
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* | ~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~ | *)
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(* [[file:~/QCaml/common/bitstring.org::*General%20implementation][General implementation:2]] *)
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let of_int x =
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One (One.of_int x)
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let of_z x =
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if Z.numbits x < 64 then One (Z.to_int x) else Many (Many.of_z x)
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(* General implementation:2 ends here *)
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(* #+begin_example
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* Bitstring.of_int 15;;
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* - : Bitstring.t =
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* ++++------------------------------------------------------------
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* #+end_example *)
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(* [[file:~/QCaml/common/bitstring.org::*General%20implementation][General implementation:4]] *)
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let zero = function
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| n when n < 64 -> One (One.zero)
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| _ -> Many (Many.zero)
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let numbits = function
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| One x -> One.numbits x
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| Many x -> Many.numbits x
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let is_zero = function
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| One x -> One.is_zero x
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| Many x -> Many.is_zero x
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let neg = function
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| One x -> One (One.neg x)
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| Many x -> Many (Many.neg x)
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let shift_left x i = match x with
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| One x -> One (One.shift_left x i)
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| Many x -> Many (Many.shift_left x i)
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let shift_right x i = match x with
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| One x -> One (One.shift_right x i)
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| Many x -> Many (Many.shift_right x i)
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let shift_left_one = function
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| n when n < 64 -> fun i -> One (One.shift_left_one i)
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| _ -> fun i -> Many (Many.shift_left_one i)
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let testbit = function
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| One x -> One.testbit x
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| Many x -> Many.testbit x
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(* General implementation:4 ends here *)
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(* [[file:~/QCaml/common/bitstring.org::*General%20implementation][General implementation:6]] *)
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let logor a b =
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match a,b with
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| One a, One b -> One (One.logor a b)
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| Many a, Many b -> Many (Many.logor a b)
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| _ -> invalid_arg "Bitstring.logor"
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let logxor a b =
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match a,b with
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| One a, One b -> One (One.logxor a b)
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| Many a, Many b -> Many (Many.logxor a b)
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| _ -> invalid_arg "Bitstring.logxor"
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let logand a b =
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match a,b with
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| One a, One b -> One (One.logand a b)
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| Many a, Many b -> Many (Many.logand a b)
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| _ -> invalid_arg "Bitstring.logand"
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let lognot = function
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| One x -> One (One.lognot x)
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| Many x -> Many (Many.lognot x)
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(* General implementation:6 ends here *)
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(* [[file:~/QCaml/common/bitstring.org::*General%20implementation][General implementation:8]] *)
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let minus_one = function
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| One x -> One (One.minus_one x)
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| Many x -> Many (Many.minus_one x)
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let plus_one = function
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| One x -> One (One.plus_one x)
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| Many x -> Many (Many.plus_one x)
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(* General implementation:8 ends here *)
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(* #+begin_example
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* Bitstring.(plus_one (of_int 15));;
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* - : Bitstring.t =
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* ----+-----------------------------------------------------------
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*
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* Bitstring.(minus_one (of_int 15));;
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* - : Bitstring.t =
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* -+++------------------------------------------------------------
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* #+end_example *)
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(* [[file:~/QCaml/common/bitstring.org::*General%20implementation][General implementation:9]] *)
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let trailing_zeros = function
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| One x -> One.trailing_zeros x
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| Many x -> Many.trailing_zeros x
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let hamdist a b = match a, b with
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| One a, One b -> One.hamdist a b
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| Many a, Many b -> Many.hamdist a b
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| _ -> invalid_arg "Bitstring.hamdist"
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let popcount = function
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| One x -> One.popcount x
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| Many x -> Many.popcount x
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(* General implementation:9 ends here *)
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(* #+begin_example
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* Bitstring.(trailing_zeros (of_int 12));;
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* - : int = 2
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*
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* Bitstring.(hamdist (of_int 15) (of_int 73));;
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* - : int = 3
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*
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* Bitstring.(popcount (of_int 15));;
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* - : int = 4
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* #+end_example *)
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(* [[file:~/QCaml/common/bitstring.org::*General%20implementation][General implementation:10]] *)
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let rec to_list ?(accu=[]) = function
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| t when (is_zero t) -> List.rev accu
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| t -> let newlist =
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(trailing_zeros t + 1)::accu
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in
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logand t @@ minus_one t
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|> (to_list [@tailcall]) ~accu:newlist
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(* General implementation:10 ends here *)
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(* #+begin_example
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* Bitstring.(to_list (of_int 45));;
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* - : int list = [1; 3; 4; 6]
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* #+end_example *)
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(* [[file:~/QCaml/common/bitstring.org::*General%20implementation][General implementation:12]] *)
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let permutations m n =
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let rec aux k u rest =
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if k=1 then
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List.rev (u :: rest)
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else
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let t = logor u @@ minus_one u in
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let t' = plus_one t in
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let not_t = lognot t in
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let neg_not_t = neg not_t in
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let t'' = shift_right (minus_one @@ logand not_t neg_not_t) (trailing_zeros u + 1) in
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(*
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let t'' = shift_right (minus_one (logand (lognot t) t')) (trailing_zeros u + 1) in
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*)
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(aux [@tailcall]) (k-1) (logor t' t'') (u :: rest)
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in
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aux (Util.binom n m) (minus_one (shift_left_one n m)) []
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(* General implementation:12 ends here *)
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(* [[file:~/QCaml/common/bitstring.org::*Printers][Printers:2]] *)
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let pp ppf = function
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| One x -> One.pp ppf x
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| Many x -> Many.pp ppf x
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(* Printers:2 ends here *)
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