package bitmasks

  1. Overview
  2. Docs
Legend:
Page
Library
Module
Module type
Parameter
Class
Class type
Source

Source file BitMaskSet.ml

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
(* ********************************************************************************************** *
 * MetaStack Solutions Ltd.                                                                       *
 * ********************************************************************************************** *
 * BitMask Sets                                                                                   *
 * ********************************************************************************************** *
 * Copyright (c) 2013-17 MetaStack Solutions Ltd.                                                 *
 * ********************************************************************************************** *
 * Author: David Allsopp                                                                          *
 * 27-Dec-2013                                                                                    *
 * ********************************************************************************************** *
 * Redistribution and use in source and binary forms, with or without modification, are permitted *
 * provided that the following two conditions are met:                                            *
 *     1. Redistributions of source code must retain the above copyright notice, this list of     *
 *        conditions and the following disclaimer.                                                *
 *     2. Neither the name of MetaStack Solutions Ltd. nor the names of its contributors may be   *
 *        used to endorse or promote products derived from this software without specific prior   *
 *        written permission.                                                                     *
 *                                                                                                *
 * This software is provided by the Copyright Holder 'as is' and any express or implied           *
 * warranties, including, but not limited to, the implied warranties of merchantability and       *
 * fitness for a particular purpose are disclaimed. In no event shall the Copyright Holder be     *
 * liable for any direct, indirect, incidental, special, exemplary, or consequential damages      *
 * (including, but not limited to, procurement of substitute goods or services; loss of use,      *
 * data, or profits; or business interruption) however caused and on any theory of liability,     *
 * whether in contract, strict liability, or tort (including negligence or otherwise) arising in  *
 * any way out of the use of this software, even if advised of the possibility of such damage.    *
 * ********************************************************************************************** *)

(* ********************************************************************************************** *
 * Copied from header.                                                                            *
 * ********************************************************************************************** *)
module type S =
  sig
    include Set.S

    val map : (elt -> elt) -> t -> t
    val min_elt_opt : t -> elt option
    val max_elt_opt : t -> elt option
    val choose_opt : t -> elt option
    val find : elt -> t -> elt
    val find_opt : elt -> t -> elt option
    val find_first : (elt -> bool) -> t -> elt
    val find_first_opt : (elt -> bool) -> t -> elt option
    val find_last : (elt -> bool) -> t -> elt
    val find_last_opt : (elt -> bool) -> t -> elt option
    val of_list : elt list -> t
    val to_seq_from : elt -> t -> elt Seq.t
    val to_seq : t -> elt Seq.t
    val add_seq : elt Seq.t -> t -> t
    val of_seq : elt Seq.t -> t
    val disjoint : t -> t -> bool

    type storage

    val invalid : t -> t
  end

module type Storage =
  sig
    type storage
    val zero : storage
    val one : storage
    val logand : storage -> storage -> storage
    val logor : storage -> storage -> storage
    val lognot : storage -> storage
    val shift_left : storage -> int -> storage
    val shift_right_logical : storage -> int -> storage
    val compare : storage -> storage -> int
    val toString : storage -> string
  end

module type BitMask =
  sig
    include Storage
    type t
    val mask : storage
  end

(* ********************************************************************************************** *
 * Implementations of Storage for types int and int64.                                            *
 * ********************************************************************************************** *)
module Int =
  struct
    type storage = int
    let zero = 0
    let one = 1
    let shift_left = (lsl)
    let shift_right_logical = (lsr)
    let logand = (land)
    let logor = (lor)
    let lognot = lnot
    let compare = compare
    let toString = string_of_int
  end

module Int64 =
  struct
    type storage = int64
    let zero = 0L
    let one = 1L
    let shift_left = Int64.shift_left
    let shift_right_logical = Int64.shift_right_logical
    let logand = Int64.logand
    let logor = Int64.logor
    let lognot = Int64.lognot
    let compare = Int64.compare
    let toString = Int64.to_string
  end

(* ********************************************************************************************** *
 * Make functor.                                                                                  *
 * ********************************************************************************************** *)
module Make(Mask : BitMask) =
  struct
    type storage = Mask.storage
    type t = Mask.storage

    (* ****************************************************************************************** *
     * Convert the supplied mask in the functor into the various required values.                 *
     * ****************************************************************************************** *)
    let (storage_of_flag, shifts, shiftsInv, topbit, highest, lowest) =
      let (shifts, shiftsInv, topbit, highest, lowest) =
        let rec f shiftsInv topbit highest lowest l c i =
          let v = Mask.shift_left Mask.one i
          in
            if i > 0 && Mask.compare v Mask.one = 0
            then (List.rev shiftsInv, shiftsInv, topbit, highest, lowest)
            else if Mask.compare (Mask.logand v Mask.mask) Mask.zero <> 0
                 then let shiftsInv =
                        if l > 0
                        then (c, l)::shiftsInv
                        else shiftsInv
                      in
                        if Mask.compare lowest Mask.zero = 0
                        then f shiftsInv 0 v v 0 0 (succ i)
                        else f shiftsInv (succ topbit) v lowest 0 0 (succ i)
                 else if l > 0
                      then f shiftsInv topbit highest lowest (succ l) c (succ i)
                      else f shiftsInv topbit highest lowest 1 (succ topbit) (succ i)
        in
          f [] (-1) Mask.zero Mask.zero 0 0 0
      in
        let compute_shift shifts offset =
          let rec f a = function
            (point, amount)::shifts ->
              if offset >= point
              then f (a + amount) shifts
              else a
          | [] ->
              a
          in
            f offset shifts
        in
          let (storage_of_flag, shifts) =
            match shifts with
              [] ->
                ((fun (flag : Mask.t) -> Mask.shift_left Mask.one (Obj.magic flag : int)), [])
            | [(0, n)] ->
                ((fun (flag : Mask.t) -> Mask.shift_left Mask.one (n + (Obj.magic flag : int))), [])
            | (0, n)::shifts ->
                ((fun (flag : Mask.t) ->
                  let shift = n + compute_shift shifts (Obj.magic flag : int)
                  in
                    Mask.shift_left Mask.one shift), shifts)
            | _ ->
                ((fun (flag : Mask.t) ->
                  Mask.shift_left Mask.one (compute_shift shifts (Obj.magic flag : int))), shifts)
      in
        (storage_of_flag, shifts, shiftsInv, topbit, highest, lowest)

    (* ****************************************************************************************** *
     * create, invalid, empty and is_empty are straightforward.                                   *
     * ****************************************************************************************** *)
    let create mask =
      mask

    let invalid set =
      Mask.logand (Mask.lognot Mask.mask) set

    let empty = Mask.zero

    let is_empty set =
      (Mask.compare set Mask.zero = 0)

    (* ****************************************************************************************** *
     * Another sequence of straightforward functions.                                             *
     * ****************************************************************************************** *)
    let mem flag set =
      Mask.compare (Mask.logand set (storage_of_flag flag)) Mask.zero <> 0

    let find flag set =
      if Mask.compare (Mask.logand set (storage_of_flag flag)) Mask.zero = 0
      then raise Not_found
      else flag

    let find_opt flag set =
      if Mask.compare (Mask.logand set (storage_of_flag flag)) Mask.zero = 0
      then None
      else Some flag

    let add flag set =
      let set' = Mask.logor set (storage_of_flag flag)
      in
        if Mask.compare set set' = 0
        then set
        else set'

    let of_list l =
      List.fold_left (fun s f -> add f s) empty l

    let singleton = storage_of_flag

    let remove flag set =
      let set' = Mask.logand set (Mask.lognot (storage_of_flag flag))
      in
        if Mask.compare set set' = 0
        then set
        else set'

    let union = Mask.logor

    let inter = Mask.logand

    let disjoint a b =
      Mask.logand a b = Mask.zero

    let diff a b =
      Mask.logand b (Mask.lognot a)

    let compare = Mask.compare

    let equal a b =
      Mask.compare a b = 0

    let subset a b =
      Mask.compare (Mask.logand a b) a = 0

    (* ****************************************************************************************** *
     * deltaShift and deltaShiftInv are used to calculate bit values for the iterators.           *
     * ****************************************************************************************** *)
    let deltaShift i = function
      (point, amount)::shifts when i >= point ->
        (succ amount, shifts)
    | _ as shifts ->
        (1, shifts)

    let deltaShiftInv i = function
      (point, amount)::shifts when i < point ->
        (succ amount, shifts)
    | _ as shifts ->
        (1, shifts)

    (* ****************************************************************************************** *
     * The iterators count over the bit positions -- for the iterator itself, [i] is the          *
     * constructor number, [v] is the bit value for that constructor and [s] is the shifts.       *
     * ****************************************************************************************** *)

    let find_first g set =
      let set = Mask.logand set Mask.mask
      in
        let rec f i v s =
          let elt = (Obj.magic i : Mask.t)
          in
            if Mask.compare (Mask.logand set v) Mask.zero <> 0 && g elt
            then elt
            else if Mask.compare v highest = 0
                 then raise Not_found
                 else let i = succ i
                      in
                        let (shift, s) = deltaShift i s
                        in
                          f i (Mask.shift_left v shift) s
        in
          f 0 lowest shifts

    let find_first_opt g set =
      let set = Mask.logand set Mask.mask
      in
        let rec f i v s =
          let elt = (Obj.magic i : Mask.t)
          in
            if Mask.compare (Mask.logand set v) Mask.zero <> 0 && g elt
            then Some elt
            else if Mask.compare v highest = 0
                 then None
                 else let i = succ i
                      in
                        let (shift, s) = deltaShift i s
                        in
                          f i (Mask.shift_left v shift) s
        in
          f 0 lowest shifts

    let find_last g set =
      let set = Mask.logand set Mask.mask
      in
        let rec f i v s =
          if Mask.compare v Mask.zero <> 0
          then let elt = (Obj.magic i : Mask.t)
               in
                 if Mask.compare (Mask.logand v set) Mask.zero <> 0 && g elt
                 then elt
                 else let i = pred i
                      in
                        let (shift, s) = deltaShiftInv i s
                        in
                          f i (Mask.shift_right_logical v shift) s
          else raise Not_found
        in
          f topbit highest shiftsInv

    let find_last_opt g set =
      let set = Mask.logand set Mask.mask
      in
        let rec f i v s =
          if Mask.compare v Mask.zero <> 0
          then let elt = (Obj.magic i : Mask.t)
               in
                 if Mask.compare (Mask.logand v set) Mask.zero <> 0 && g elt
                 then Some elt
                 else let i = pred i
                      in
                        let (shift, s) = deltaShiftInv i s
                        in
                          f i (Mask.shift_right_logical v shift) s
          else None
        in
          f topbit highest shiftsInv

    let iter g set =
      let set = Mask.logand set Mask.mask
      in
        let rec f i v s =
          let _ =
            if Mask.compare (Mask.logand set v) Mask.zero <> 0
            then g (Obj.magic i : Mask.t)
          in
            if Mask.compare v highest <> 0
            then let i = succ i
                 in
                   let (shift, s) = deltaShift i s
                   in
                     f i (Mask.shift_left v shift) s
        in
          f 0 lowest shifts

    let fold g set acc =
      let set = Mask.logand set Mask.mask
      in
        let rec f a i v s =
          let a =
            if Mask.compare (Mask.logand set v) Mask.zero <> 0
            then g (Obj.magic i : Mask.t) a
            else a
          in
            if Mask.compare v highest <> 0
            then let i = succ i
                 in
                   let (shift, s) = deltaShift i s
                   in
                     f a i (Mask.shift_left v shift) s
            else a
        in
          f acc 0 lowest shifts

    let map g set' =
      let set = Mask.logand set' Mask.mask
      in
        let rec f a i v s =
          if Mask.compare v highest <> 0
          then let a =
                 if Mask.compare (Mask.logand set v) Mask.zero <> 0
                 then Mask.logor a (storage_of_flag (g (Obj.magic i : Mask.t)))
                 else a
               and i = succ i
               in
                 let (shift, s) = deltaShift i s
                 in
                   f a i (Mask.shift_left v shift) s
          else if Mask.compare a set' = 0
               then set'
               else a
        in
          f Mask.zero 0 lowest shifts

    let for_all p set =
      let set = Mask.logand set Mask.mask
      in
        let rec f i v s =
          if Mask.compare (Mask.logand set v) Mask.zero = 0 || p (Obj.magic i : Mask.t)
          then if Mask.compare v highest <> 0
               then let i = succ i
                    in
                      let (shift, s) = deltaShift i s
                      in
                        f i (Mask.shift_left v shift) s
               else true
          else false
        in
          f 0 lowest shifts

    let exists p set =
      let set = Mask.logand set Mask.mask
      in
        let rec f i v s =
          if Mask.compare (Mask.logand set v) Mask.zero = 0 || not (p (Obj.magic i : Mask.t))
          then if Mask.compare v highest <> 0
               then let i = succ i
                    in
                      let (shift, s) = deltaShift i s
                      in
                        f i (Mask.shift_left v shift) s
               else false
          else true
        in
          f 0 lowest shifts

    let filter p set =
      let set = Mask.logand set Mask.mask
      in
        let rec f a i v s =
          let a =
            if Mask.compare (Mask.logand v set) Mask.zero <> 0 && p (Obj.magic i : Mask.t)
            then Mask.logor a v
            else a
          in
            if Mask.compare v highest <> 0
            then let i = succ i
                 in
                   let (shift, s) = deltaShift i s
                   in
                     f a i (Mask.shift_left v shift) s
            else a
        in
          f Mask.zero 0 lowest shifts

    let partition p set =
      let set = Mask.logand set Mask.mask
      in
        let rec f ((l, r) as a) i v s =
          let a =
            if Mask.compare (Mask.logand v set) Mask.zero <> 0
            then if p (Obj.magic i : Mask.t)
                 then (Mask.logor l v, r)
                 else (l, Mask.logor r v)
            else a
          in
            if Mask.compare v highest <> 0
            then let i = succ i
                 in
                   let (shift, s) = deltaShift i s
                   in
                     f a i (Mask.shift_left v shift) s
            else a
        in
          f (Mask.zero, Mask.zero) 0 lowest shifts

    let cardinal set =
      let set = Mask.logand set Mask.mask
      in
        let rec f a i v =
          let a =
            if Mask.compare (Mask.logand v set) Mask.zero <> 0
            then succ a
            else a
          in
            if Mask.compare v highest = 0
            then a
            else f a (succ i) (Mask.shift_left v 1)
        in
          f 0 0 lowest

    let elements set =
      let set = Mask.logand set Mask.mask
      in
        let rec f a i v s =
          if Mask.compare v Mask.zero <> 0
          then let a =
                 if Mask.compare (Mask.logand v set) Mask.zero <> 0
                 then (Obj.magic i : Mask.t)::a
                 else a
               and i = pred i
               in
                 let (shift, s) = deltaShiftInv i s
                 in
                   f a i (Mask.shift_right_logical v shift) s
          else a
        in
          f [] topbit highest shiftsInv

    let min_elt set =
      let set = Mask.logand set Mask.mask
      in
        let rec f i v s =
          if Mask.compare (Mask.logand v set) Mask.zero <> 0
          then (Obj.magic i : Mask.t)
          else if Mask.compare v highest <> 0
               then let i = succ i
                    in
                      let (shift, s) = deltaShift i s
                      in
                        f i (Mask.shift_left v shift) s
               else raise Not_found
        in
          f 0 lowest shifts

    let min_elt_opt set =
      let set = Mask.logand set Mask.mask
      in
        let rec f i v s =
          if Mask.compare (Mask.logand v set) Mask.zero <> 0
          then Some (Obj.magic i : Mask.t)
          else if Mask.compare v highest = 0
               then let i = succ i
                    in
                      let (shift, s) = deltaShift i s
                      in
                        f i (Mask.shift_left v shift) s
               else None
        in
          f 0 lowest shifts

    let max_elt set =
      let set = Mask.logand set Mask.mask
      in
        let rec f i v s =
          if Mask.compare v Mask.zero <> 0
          then if Mask.compare (Mask.logand v set) Mask.zero <> 0
               then (Obj.magic i : Mask.t)
               else let i = pred i
                    in
                      let (shift, s) = deltaShiftInv i s
                      in
                        f i (Mask.shift_right_logical v shift) s
          else raise Not_found
        in
          f topbit highest shiftsInv

    let max_elt_opt set =
      let set = Mask.logand set Mask.mask
      in
        let rec f i v s =
          if Mask.compare v Mask.zero <> 0
          then if Mask.compare (Mask.logand v set) Mask.zero <> 0
               then Some (Obj.magic i : Mask.t)
               else let i = pred i
                    in
                      let (shift, s) = deltaShiftInv i s
                      in
                        f i (Mask.shift_right_logical v shift) s
          else None
        in
          f topbit highest shiftsInv

    let choose = min_elt

    let choose_opt = min_elt_opt

    let split (flag : Mask.t) set =
      let flag = (Obj.magic flag : int)
      and set = Mask.logand set Mask.mask
      in
        let rec f ((l, p, r) as a) i v s =
          let a =
            if Mask.compare (Mask.logand v set) Mask.zero <> 0
            then let c = Stdlib.compare i flag
                 in
                   if c = 0
                   then (l, true, r)
                   else if c < 0
                        then (Mask.logor v l, p, r)
                        else (l, p, Mask.logor v r)
            else a
          in
            if Mask.compare v highest <> 0
            then let i = succ i
                 in
                   let (shift, s) = deltaShift i s
                   in
                     f a i (Mask.shift_left v shift) s
            else a
        in
          f (Mask.zero, false, Mask.zero) 0 lowest shifts

    let to_seq_from x set =
      let set = Mask.logand set Mask.mask
      and x = (Obj.magic x : int)
      in
        let rec f i v s () =
          let tail =
            if Mask.compare v highest = 0
            then Seq.empty
            else let j = succ i
                 in
                   let (shift, s) = deltaShift j s
                   in
                     f j (Mask.shift_left v shift) s
          in
            if i >= x && Mask.compare (Mask.logand v set) Mask.zero <> 0
            then Seq.Cons((Obj.magic i : Mask.t), tail)
            else tail ()
        in
          f 0 lowest shifts

    let to_seq set = to_seq_from (Obj.magic 0 : Mask.t) set

    let add_seq s set = Seq.fold_left (fun set flag -> add flag set) set s

    let of_seq s = add_seq s empty
  end
OCaml

Innovation. Community. Security.