mirror of https://gitlab.com/scemama/QCaml.git
246 lines
6.7 KiB
OCaml
246 lines
6.7 KiB
OCaml
module One = struct
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type t = int
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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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module Many = struct
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type t = Z.t
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let of_int = Z.of_int
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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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type t =
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| One of int
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| Many of Z.t
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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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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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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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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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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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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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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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(** [permtutations m n] generates the list of all possible [n]-bit
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strings with [m] bits set to 1.
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Algorithm adapted from
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{{:https://graphics.stanford.edu/~seander/bithacks.html#NextBitPermutation}
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Bit twiddling hacks}.
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Example:
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{[
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bit_permtutations 2 4 = [ 0011 ; 0101 ; 0110 ; 1001 ; 1010 ; 1100 ]
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]}
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*)
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let permtutations 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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(*-----------------------------------------------------------------------------------*)
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let test_case () =
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let test_one_many () =
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let x = 8745687 in
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let z = Z.of_int 8745687 in
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let one_x = One x in
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let many_x = Many z in
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Alcotest.(check bool) "of_x" true (one_x = (of_int x));
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Alcotest.(check bool) "of_z" true (one_x = (of_z z));
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Alcotest.(check bool) "shift_left1" true (One (x lsl 3) = shift_left one_x 3);
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Alcotest.(check bool) "shift_left2" true (Many (Z.shift_left z 3) = shift_left many_x 3);
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Alcotest.(check bool) "shift_left3" true (Many (Z.shift_left z 100) = shift_left many_x 100);
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Alcotest.(check bool) "shift_right1" true (One (x lsr 3) = shift_right one_x 3);
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Alcotest.(check bool) "shift_right2" true (Many (Z.shift_right z 3) = shift_right many_x 3);
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Alcotest.(check bool) "shift_left_one1" true (One (1 lsl 3) = shift_left_one 4 3);
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Alcotest.(check bool) "shift_left_one2" true (Many (Z.shift_left Z.one 200) = shift_left_one 300 200);
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Alcotest.(check bool) "testbit1" true (testbit (One 8) 3);
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Alcotest.(check bool) "testbit2" false (testbit (One 8) 2);
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Alcotest.(check bool) "testbit3" false (testbit (One 8) 4);
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Alcotest.(check bool) "testbit4" true (testbit (Many (Z.of_int 8)) 3);
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Alcotest.(check bool) "testbit5" false (testbit (Many (Z.of_int 8)) 2);
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Alcotest.(check bool) "testbit6" false (testbit (Many (Z.of_int 8)) 4);
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Alcotest.(check bool) "logor1" true (One (1 lor 2) = logor (One 1) (One 2));
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Alcotest.(check bool) "logor2" true (Many (Z.of_int (1 lor 2)) = logor (Many Z.one) (Many (Z.of_int 2)));
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Alcotest.(check bool) "logxor1" true (One (1 lxor 2) = logxor (One 1) (One 2));
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Alcotest.(check bool) "logxor2" true (Many (Z.of_int (1 lxor 2)) = logxor (Many Z.one) (Many (Z.of_int 2)));
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Alcotest.(check bool) "logand1" true (One (1 land 2) = logand (One 1) (One 2));
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Alcotest.(check bool) "logand2" true (Many (Z.of_int (1 land 2)) = logand (Many Z.one) (Many (Z.of_int 2)));
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Alcotest.(check bool) "to_list" true ([ 1 ; 3 ; 4 ; 6 ] = (to_list (One 45)));
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in
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[
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"One-many", `Quick, test_one_many;
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]
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