Source file bloomer.ml

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type 'a t = {
  hash : 'a -> bytes;
      (** Cryptographically secure hash function. We must have
          [Bytes.length (hash x) >= index_bits * hashes]. *)
  hashes : int;
      (** The value returned by [hash] is split and converted in
          [hashes] indices, each [index_bits] wide. *)
  index_bits : int;
      (** [index_bits] is the width in bits of the indices into
          the [filter]. *)
  countdown_bits : int;
      (** [countdown_bits] is the width in bits of the counter cells
          stored in the [filter]. *)
  filter : bytes;
      (** [filter] stores [2^index_bits] counter cells,
          each [countdown_bits] wide. *)
  count : int array;
      (** [count] stores approximate statistics on the number of counter cells
          with a given value. [count.(i)] is the approximate number of cells
          equal to [2^countdown_bits - 1 - i].
          Note that this field is not required for Bloom filter operation. *)
}

let sf = Printf.sprintf

let check_peek_poke_args fname bytes ofs bits =
  if bits <= 0 then invalid_arg (sf "Bloomer.%s: non positive bits value" fname) ;
  if ofs < 0 then invalid_arg (sf "Bloomer.%s: negative offset" fname) ;
  if bits > Sys.int_size - 7 then
    invalid_arg (sf "Bloomer.%s: indexes out of bounds" fname) ;
  if bits + ofs > Bytes.length bytes * 8 then
    invalid_arg (sf "Bloomer.%s: indexes out of bounds" fname)

(* Read [bits] bits of [bytes] at offset [ofs] as an OCaml int in big endian order.
   The function proceeds by iteratively blitting the bytes overlapping the sought
   bit interval into [v]. The superfluous bits at the beginning and at the end
   are then removed from [v], yielding the returned value.
*)
let peek_unsafe bytes ofs bits =
  let first = ofs / 8 in
  let last = first + (((ofs mod 8) + bits + 7) / 8) in
  let v = ref 0 in
  for i = last - 1 downto first do
    v := (!v lsl 8) lor Char.code (Bytes.get bytes i)
  done ;
  v := !v lsr (ofs mod 8) ;
  v := !v land ((1 lsl bits) - 1) ;
  !v

let peek bytes ofs bits =
  check_peek_poke_args "peek" bytes ofs bits ;
  peek_unsafe bytes ofs bits

(* blits [bits] bits of [bytes] at offset [ofs] from an OCaml int in big endian order *)
let poke_unsafe bytes ofs bits v =
  let first = ofs / 8 in
  let last = first + (((ofs mod 8) + bits + 7) / 8) in
  let cur = ref 0 in
  for i = last - 1 downto first do
    cur := (!cur lsl 8) lor Char.code (Bytes.get bytes i)
  done ;
  let mask = lnot (((1 lsl bits) - 1) lsl (ofs mod 8)) in
  let v = !cur land mask lor (v lsl (ofs mod 8)) in
  for i = first to last - 1 do
    Bytes.set bytes i (Char.chr ((v lsr ((i - first) * 8)) land 0xFF))
  done

let poke bytes ofs bits v =
  if v lsr bits <> 0 then invalid_arg "Bloomer.poke: value too large" ;
  check_peek_poke_args "poke" bytes ofs bits ;
  poke_unsafe bytes ofs bits v

let%expect_test "random_read_writes" =
  let bytes_length = 45 in
  let bit_length = bytes_length * 8 in
  (* max_data_bit_width = 29 to to stay within Random.int bounds.
     int_size - 7 to stay within [check_peek_poke_args] domain. *)
  let max_data_bit_width = min 29 (Sys.int_size - 7) in
  let bytes = Bytes.make 45 '\000' in
  let poke_et_peek ofs len v =
    poke bytes ofs len v ;
    assert (peek bytes ofs len = v)
  in
  for _ = 0 to 100_000 do
    let ofs = Random.int (bit_length - max_data_bit_width) in
    let len = Random.int max_data_bit_width + 1 in
    let v = Random.int (1 lsl len) in
    poke_et_peek ofs len v
  done ;
  poke_et_peek 350 10 0x3FF ;
  poke_et_peek 355 5 0x1F ;
  poke_et_peek 350 10 0 ;
  poke_et_peek 355 5 0 ;
  try
    poke_et_peek 355 6 0 ;
    assert false
  with _ -> ()

let%expect_test "peek and poke work with bits = [1 .. Sys.int_size - 7]" =
  let fail_or_success f =
    try
      f () ;
      true
    with _ -> false
  in
  let bytes = Bytes.make 45 '\000' in
  (* we ignore len = 0, the implementation would accepts it but check_peek_poke_args is more strict. *)
  for len = 1 to Sys.int_size do
    let ints =
      List.init 400 (fun _ ->
          Int64.(to_int (Random.int64 (sub (shift_left one len) one))))
    in
    let unsafe_result =
      fail_or_success (fun () ->
          (* we want to test the property regardless of the offset, we test all possible offset (mod 8) *)
          for ofs = 8 to 16 do
            List.iter
              (fun v ->
                poke_unsafe bytes ofs len v ;
                assert (peek_unsafe bytes ofs len = v))
              ints
          done)
    in
    let check_result =
      fail_or_success (fun () ->
          (* we want to test the property regardless of the offset, we test all possible offset (mod 8) *)
          for ofs = 8 to 16 do
            List.iter
              (fun v ->
                if v lsr len <> 0 then
                  invalid_arg "Bloomer.poke: value too large" ;
                check_peek_poke_args "unti-test" bytes ofs len)
              ints
          done)
    in
    assert (unsafe_result = check_result)
  done

let%expect_test "sequential_read_writes" =
  let bytes = Bytes.make 45 '\000' in
  let bits = Bytes.length bytes * 8 in
  (* max_data_bit_width = 29 to stay within Random.int bounds.
     int_size - 7 to stay within [check_peek_poke_args] domain. *)
  let max_data_bit_width = min 29 (Sys.int_size - 7) in
  for _ = 0 to 10_000 do
    let rec init ofs acc =
      if ofs >= bits then List.rev acc
      else
        let len = min (Random.int max_data_bit_width + 1) (bits - ofs) in
        let v = Random.int (1 lsl len) in
        poke bytes ofs len v ;
        assert (peek bytes ofs len = v) ;
        init (ofs + len) ((ofs, len, v) :: acc)
    in
    List.iter (fun (ofs, len, v) -> assert (peek bytes ofs len = v)) (init 0 [])
  done

let%expect_test "read_over_write" =
  (* Check that non-overlapping writes really do not overlap. *)
  let bytes = Bytes.make 45 '\000' in
  let bits = Bytes.length bytes * 8 in
  let random_disjoint_writes () =
    let width = 1 lsl Random.int 3 in
    let indices = bits / width in
    let i1 = Random.int indices in
    let i2 = (i1 + 1 + Random.int (indices - 1)) mod indices in
    let i1 = i1 * width in
    let i2 = i2 * width in
    assert (i1 <> i2) ;
    let v1 = Random.int (1 lsl width) in
    let v2 = Random.int (1 lsl width) in
    poke bytes i1 width v1 ;
    poke bytes i2 width v2 ;
    assert (peek bytes i1 width = v1)
  in
  for _ = 0 to 10_000 do
    random_disjoint_writes ()
  done

let create ~hash ~hashes ~index_bits ~countdown_bits =
  (* We constrain [index_bits] and [countdown_bits] to a maximum of 24.  This is
     because [peek] and [poke] operate on ints with size [1 .. int_size - 7]
     and we want to stay compatible with 32bit arch (e.g. JavaScript).
       31 (int_size on 32bit) - 7 = 24
  *)
  if index_bits <= 0 || index_bits > 24 then
    invalid_arg "Bloomer.create: invalid value for index_bits" ;
  if countdown_bits <= 0 || countdown_bits > 24 then
    invalid_arg "Bloomer.create: invalid value for countdown_bits" ;
  let filter =
    Bytes.make ((((1 lsl index_bits) * countdown_bits) + 7) / 8) '\000'
  in
  let count = Array.make ((1 lsl countdown_bits) - 1) 0 in
  {hash; hashes; index_bits; countdown_bits; filter; count}

let mem {hash; hashes; index_bits; countdown_bits; filter; _} x =
  let h = hash x in
  try
    for i = 0 to hashes - 1 do
      let j = peek h (index_bits * i) index_bits in
      if peek filter (j * countdown_bits) countdown_bits = 0 then raise Exit
    done ;
    true
  with Exit -> false

let add {hash; hashes; index_bits; countdown_bits; filter; count} x =
  count.(0) <- count.(0) + 1 ;
  let h = hash x in
  for i = 0 to hashes - 1 do
    let j = peek h (index_bits * i) index_bits in
    poke filter (j * countdown_bits) countdown_bits ((1 lsl countdown_bits) - 1)
  done

let rem {hash; hashes; index_bits; countdown_bits; filter; _} x =
  let h = hash x in
  for i = 0 to hashes - 1 do
    let j = peek h (index_bits * i) index_bits in
    poke filter (j * countdown_bits) countdown_bits 0
  done

let countdown {hash = _; hashes = _; index_bits; countdown_bits; filter; count}
    =
  for i = Array.length count - 1 downto 1 do
    count.(i) <- count.(i - 1)
  done ;
  count.(0) <- 0 ;
  for j = 0 to (1 lsl index_bits) - 1 do
    let cur = peek filter (j * countdown_bits) countdown_bits in
    if cur > 0 then poke filter (j * countdown_bits) countdown_bits (cur - 1)
  done

let clear
    {hash = _; hashes = _; index_bits = _; countdown_bits = _; filter; count} =
  Array.fill count 0 (Array.length count) 0 ;
  Bytes.fill filter 0 (Bytes.length filter) '\000'

let fill_percentage
    {hash = _; hashes = _; index_bits; countdown_bits; filter; _} =
  let total = float (1 lsl index_bits) in
  let nonzero = ref 0 in
  for j = 0 to (1 lsl index_bits) - 1 do
    let cur = peek filter (j * countdown_bits) countdown_bits in
    if cur > 0 then incr nonzero
  done ;
  float !nonzero /. total

let life_expectancy_histogram
    {hash = _; hashes = _; index_bits; countdown_bits; filter; _} =
  let hist_table = Array.make (1 lsl countdown_bits) 0 in
  for j = 0 to (1 lsl index_bits) - 1 do
    let cur = peek filter (j * countdown_bits) countdown_bits in
    hist_table.(cur) <- hist_table.(cur) + 1
  done ;
  hist_table

let approx_count {count; _} = Array.fold_left ( + ) 0 count

let%expect_test "consistent_add_mem_countdown" =
  for _ = 0 to 100 do
    let index_bits = Random.int 16 + 1 in
    let hashes = Random.int 7 + 1 in
    let countdown_bits = Random.int 5 + 1 in
    let hash v =
      Bytes.init
        (((hashes * index_bits) + 7) / 8)
        (fun i -> Char.chr (Hashtbl.hash (v, i) mod 256))
    in
    let bloomer = create ~hash ~index_bits ~hashes ~countdown_bits in
    let rec init n acc =
      if n = 0 then acc
      else
        let x = Random.int (1 lsl 29) in
        add bloomer x ;
        assert (mem bloomer x) ;
        init (n - 1) (x :: acc)
    in
    let all = init 1000 [] in
    for _ = 0 to (1 lsl countdown_bits) - 2 do
      List.iter (fun x -> assert (mem bloomer x)) all ;
      countdown bloomer
    done ;
    List.iter (fun x -> assert (not (mem bloomer x))) all
  done

let%expect_test "consistent_add_countdown_count" =
  let module Set = Hashtbl.Make (struct
    include Int

    let hash = Hashtbl.hash
  end) in
  for _ = 0 to 100 do
    let index_bits = 16 in
    let hashes = Random.int 7 + 1 in
    let countdown_bits = Random.int 5 + 1 in
    let set = Set.create 100 in
    let hash v =
      Bytes.init
        (((hashes * index_bits) + 7) / 8)
        (fun i -> Char.chr (Hashtbl.hash (v, i) mod 256))
    in
    let bloomer = create ~hash ~index_bits ~hashes ~countdown_bits in
    let next_ref = ref 0 in
    let next () =
      incr next_ref ;
      !next_ref
    in
    let actual_set () =
      List.filter (mem bloomer) (List.of_seq @@ Set.to_seq_keys set)
    in
    let rec init_step n acc =
      if n = 0 then acc
      else
        let x = next () in
        add bloomer x ;
        assert (mem bloomer x) ;
        Set.add set x () ;
        init_step (n - 1) (1 + acc)
    in
    let rec init n stop counts =
      if n = stop then counts
      else
        let approx_counted = approx_count bloomer in
        let accurate_count = List.length @@ actual_set () in
        let count = Random.int 10 in
        let added = init_step count 0 in
        assert (added = count) ;
        countdown bloomer ;
        init (n + 1) stop ((approx_counted, accurate_count) :: counts)
    in
    let all = init 0 ((1 lsl countdown_bits) + 30) [] in
    List.iter (fun (approx, accurate) -> assert (approx = accurate)) all ;
    clear bloomer ;
    assert (approx_count bloomer = 0)
  done

let%test_module "false_positive_rate" =
  (module struct
    (* We acknowledge the results published in "On the false-positive
       rate of Bloom filters" (Information Processing Letters, volume
       108, issue 4, 2008, pages 210-213) stating that the model formula
       below is wrong.

       However, we still use the original approximation made by Bloom to
       check the behaviour of this implementation, as it is close enough
       for security yet much simpler to compute. *)
    let runs =
      [|
        (18, 4);
        (18, 6);
        (18, 8);
        (18, 10);
        (20, 2);
        (20, 4);
        (20, 6);
        (20, 8);
        (20, 9);
        (20, 10);
        (20, 11);
        (20, 12);
        (20, 13);
        (20, 14);
        (21, 2);
        (21, 3);
        (21, 4);
        (21, 5);
        (22, 2);
        (22, 3);
        (22, 4);
        (22, 5);
        (22, 6);
        (22, 8);
      |]

    let steps = 995

    let init_samples = 5_000

    let samples_per_step = 1_000

    let compute_data () =
      Array.map
        (fun (index_bits, hashes) ->
          let countdown_bits = 1 in
          let hash v =
            Bytes.init
              (((hashes * index_bits) + 7) / 8)
              (fun i -> Char.chr (Hashtbl.hash (v, i) mod 256))
          in
          let bloomer = create ~hash ~index_bits ~hashes ~countdown_bits in
          let add, cur =
            let cur = ref 0 in
            ( (fun n ->
                for _ = 1 to n do
                  add bloomer !cur ;
                  incr cur
                done),
              fun () -> !cur )
          in
          add init_samples ;
          ( float (Bytes.length bloomer.filter) /. 1024.,
            index_bits,
            hashes,
            Array.init steps @@ fun i ->
            add samples_per_step ;
            let n = init_samples + ((i + 1) * samples_per_step) in
            let expected_fp_proba =
              let e = 2.718281828459045 in
              (1.
              -. (e ** (-.float hashes *. float n /. float (1 lsl index_bits)))
              )
              ** float hashes
            in
            let actual_proba =
              let falses = ref 0 in
              for j = 1 to 500 do
                if mem bloomer (cur () + j) then incr falses
              done ;
              float !falses /. 500.
            in
            if abs_float (expected_fp_proba -. actual_proba) >= 0.1 then
              Printf.printf
                "wrong false positive rate for n=%d, m=%d,k=%d, expected %g, \
                 got %g\n"
                n
                (1 lsl index_bits)
                hashes
                expected_fp_proba
                actual_proba ;
            (expected_fp_proba, actual_proba) ))
        runs

    let%expect_test _ =
      ignore
        (compute_data () : (float * int * int * (float * float) array) array) ;
      [%expect {||}]

    let%test_unit _ =
      match Sys.getenv_opt "BLOOMER_TEST_GNUPLOT_PATH" with
      | Some path ->
          let data = compute_data () in
          for run = 0 to Array.length runs - 1 do
            let kb, index_bits, hashes, values = data.(run) in
            (let fp = open_out (Format.asprintf "%s/run_%02d.plot" path run) in
             Printf.fprintf
               fp
               "set title 'false positive rate (bits=%d (%g KiB), hashes=%d)'\n\
                %!"
               (1 lsl index_bits)
               kb
               hashes ;
             Printf.fprintf fp "set xlabel 'insertions'\n" ;
             Printf.fprintf fp "set ylabel 'rate'\n" ;
             Printf.fprintf fp "set yrange [0:1]\n" ;
             Printf.fprintf fp "set terminal 'png' size 800,600\n" ;
             Printf.fprintf fp "set output 'run_%02d.png'\n" run ;
             Printf.fprintf
               fp
               "plot 'run_%02d.dat' using 1:2 title 'expected', 'run_%02d.dat' \
                using 1:3 title 'obtained'\n\
                %!"
               run
               run ;
             close_out fp) ;
            let fp = open_out (Format.asprintf "%s/run_%02d.dat" path run) in
            for step = 0 to steps - 1 do
              Printf.fprintf
                fp
                "%d %f %f\n"
                (init_samples + (step * samples_per_step))
                (fst values.(step))
                (snd values.(step))
            done ;
            flush fp ;
            close_out fp
          done
      | None ->
          Format.eprintf
            "Set the BLOOMER_TEST_GNUPLOT_PATH to a directory to get some \
             human readable test results."
  end)