package octez-libs

  1. Overview
  2. Docs
package octez-libs
Legend:
Page
Library
Module
Module type
Parameter
Class
Class type
Source

Source file solver.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
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
(*****************************************************************************)
(*                                                                           *)
(* MIT License                                                               *)
(* Copyright (c) 2022 Nomadic Labs <contact@nomadic-labs.com>                *)
(*                                                                           *)
(* Permission is hereby granted, free of charge, to any person obtaining a   *)
(* copy of this software and associated documentation files (the "Software"),*)
(* to deal in the Software without restriction, including without limitation *)
(* the rights to use, copy, modify, merge, publish, distribute, sublicense,  *)
(* and/or sell copies of the Software, and to permit persons to whom the     *)
(* Software is furnished to do so, subject to the following conditions:      *)
(*                                                                           *)
(* The above copyright notice and this permission notice shall be included   *)
(* in all copies or substantial portions of the Software.                    *)
(*                                                                           *)
(* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR*)
(* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,  *)
(* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL   *)
(* THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER*)
(* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING   *)
(* FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER       *)
(* DEALINGS IN THE SOFTWARE.                                                 *)
(*                                                                           *)
(*****************************************************************************)

include Lang_core
module CS = Csir.CS
module VS = Linear_algebra.Make_VectorSpace (S)
module Tables = Csir.Tables

type wire = W of int [@@deriving repr] [@@ocaml.unboxed]

type row = R of int [@@deriving repr] [@@ocaml.unboxed]

type 'a tagged = Input of 'a | Output of 'a [@@deriving repr]

type arith_desc = {
  wires : row array;
  linear : S.t array;
  qm : S.t;
  qc : S.t;
  qx5a : S.t;
  qx2b : S.t;
  to_solve : wire;
}
[@@deriving repr]

type pow5_desc = {a : int; c : int} [@@deriving repr]

type wires_desc = int array [@@deriving repr]

type lookup_desc = {wires : int tagged array; table : string} [@@deriving repr]

type ws_desc = {x1 : int; y1 : int; x2 : int; y2 : int; x3 : int; y3 : int}
[@@deriving repr]

type ed_desc = {
  a : S.t;
  d : S.t;
  x1 : int;
  y1 : int;
  x2 : int;
  y2 : int;
  x3 : int;
  y3 : int;
}
[@@deriving repr]

type ed_cond_desc = {
  a : S.t;
  d : S.t;
  x1 : int;
  y1 : int;
  x2 : int;
  y2 : int;
  bit : int;
  x3 : int;
  y3 : int;
}
[@@deriving repr]

type bits_desc = {nb_bits : int; shift : Utils.Z.t; l : int; bits : int list}
[@@deriving repr]

type limbs_desc = {
  total_nb_bits : int;
  nb_bits : int;
  shift : Utils.Z.t;
  l : int;
  limbs : int list;
}
[@@deriving repr]

type pos128full_desc = {
  x0 : int;
  y0 : int;
  x1 : int;
  y1 : int;
  x2 : int;
  y2 : int;
  k : VS.t array;
  matrix : VS.matrix;
}

type swap_desc = {b : int; x : int; y : int; u : int; v : int} [@@deriving repr]

(* we define this by hand to avoid doing all linear algebra, VS.t is actually
   S.t but for some reason Repr does not see this equality. *)
let pos128full_desc_t =
  let open Repr in
  record "pos128full_desc" (fun x0 y0 x1 y1 x2 y2 k matrix ->
      {x0; y0; x1; y1; x2; y2; k; matrix})
  |+ field "x0" int (fun t -> t.x0)
  |+ field "y0" int (fun t -> t.y0)
  |+ field "x1" int (fun t -> t.x1)
  |+ field "y1" int (fun t -> t.y1)
  |+ field "x2" int (fun t -> t.x2)
  |+ field "y2" int (fun t -> t.y2)
  |+ field "k" (array S.t) (fun t -> t.k)
  |+ field "matrix" (array (array S.t)) (fun t -> t.matrix)
  |> sealr

type pos128partial_desc = {
  a : int;
  b : int;
  c : int;
  a_5 : int;
  b_5 : int;
  c_5 : int;
  x0 : int;
  y0 : int;
  x1 : int;
  y1 : int;
  x2 : int;
  y2 : int;
  (* Can we share these? *)
  k_cols : VS.matrix array;
  matrix : VS.matrix;
}

let pos128partial_desc_t =
  let open Repr in
  record
    "pos128partial_desc"
    (fun a b c a_5 b_5 c_5 x0 y0 x1 y1 x2 y2 k_cols matrix ->
      {a; b; c; a_5; b_5; c_5; x0; y0; x1; y1; x2; y2; k_cols; matrix})
  |+ field "a" int (fun t -> t.a)
  |+ field "b" int (fun t -> t.b)
  |+ field "c" int (fun t -> t.c)
  |+ field "a_5" int (fun t -> t.a_5)
  |+ field "b_5" int (fun t -> t.b_5)
  |+ field "c_5" int (fun t -> t.c_5)
  |+ field "x0" int (fun t -> t.x0)
  |+ field "y0" int (fun t -> t.y0)
  |+ field "x1" int (fun t -> t.x1)
  |+ field "y1" int (fun t -> t.y1)
  |+ field "x2" int (fun t -> t.x2)
  |+ field "y2" int (fun t -> t.y2)
  |+ field "k_cols" (array (array (array S.t))) (fun t -> t.k_cols)
  |+ field "matrix" (array (array S.t)) (fun t -> t.matrix)
  |> sealr

type anemoi_desc = {
  x0 : int;
  y0 : int;
  w : int;
  v : int;
  x1 : int;
  y1 : int;
  kx : S.t;
  ky : S.t;
}

let anemoi_desc_t =
  let open Repr in
  record "anemoi_desc" (fun x0 y0 w v x1 y1 kx ky ->
      {x0; y0; w; v; x1; y1; kx; ky})
  |+ field "x0" int (fun t -> t.x0)
  |+ field "y0" int (fun t -> t.y0)
  |+ field "w" int (fun t -> t.w)
  |+ field "v" int (fun t -> t.v)
  |+ field "x1" int (fun t -> t.x1)
  |+ field "y1" int (fun t -> t.y1)
  |+ field "kx" S.t (fun t -> t.kx)
  |+ field "ky" S.t (fun t -> t.ky)
  |> sealr

type anemoi_double_desc = {
  x0 : int;
  y0 : int;
  w0 : int;
  w1 : int;
  y1 : int;
  x2 : int;
  y2 : int;
  kx1 : S.t;
  ky1 : S.t;
  kx2 : S.t;
  ky2 : S.t;
}
[@@deriving repr]

type anemoi_custom_desc = {
  x0 : int;
  y0 : int;
  x1 : int;
  y1 : int;
  x2 : int;
  y2 : int;
  kx1 : S.t;
  ky1 : S.t;
  kx2 : S.t;
  ky2 : S.t;
}
[@@deriving repr]

let z_repr = Repr.map Repr.string Z.of_string Z.to_string

module Z = struct
  let t = z_repr

  include Z
end

type mod_arith_desc = {
  modulus : Z.t;
  base : Z.t;
  nb_limbs : int;
  moduli : Z.t list;
  qm_bound : Z.t * Z.t;
  ts_bounds : (Z.t * Z.t) list;
  inverse : bool;
  inp1 : int list;
  inp2 : int list;
  out : int list;
  qm : int;
  ts : int list;
}
[@@deriving repr]

type mod_arith_is_zero_desc = {
  modulus : Z.t;
  base : Z.t;
  nb_limbs : int;
  inp : int list;
  aux : int list;
  out : int;
}
[@@deriving repr]

type solver_desc =
  | Arith of arith_desc
  | Pow5 of pow5_desc
  | IsZero of wires_desc
  | IsNotZero of wires_desc
  | Lookup of lookup_desc
  | Ecc_Ws of ws_desc
  | Ecc_Ed of ed_desc
  | Ecc_Cond_Ed of ed_cond_desc
  | Swap of swap_desc
  | Skip
  | BitsOfS of bits_desc
  | LimbsOfS of limbs_desc
  | Poseidon128Full of pos128full_desc
  | Poseidon128Partial of pos128partial_desc
  | AnemoiRound of anemoi_desc
  | AnemoiDoubleRound of anemoi_double_desc
  | AnemoiCustom of anemoi_custom_desc
  | Mod_Add of mod_arith_desc
  | Mod_Mul of mod_arith_desc
  | Mod_IsZero of mod_arith_is_zero_desc
  | Updater of Optimizer.trace_info
[@@deriving repr]

type solvers = solver_desc list [@@deriving repr]

type t = {solvers : solvers; initial_size : int; final_size : int}
[@@deriving repr]

let empty_solver = {solvers = []; initial_size = 0; final_size = 0}

let append_solver sd t = {t with solvers = sd :: t.solvers}

let untag = function Input a -> a | Output a -> a

let from_tagged = function Input i -> Some i | Output _ -> None

let solve_one trace solver =
  (match solver with
  | Skip -> ()
  | Arith {wires; linear; qm; qc; qx5a; qx2b; to_solve} -> (
      (* A gate with degree strictly greater than 1 must be used on an input wire.
         This is to avoid having several solutions for the same equation.
      *)
      match to_solve with
      | W i ->
          assert (i <> 0 || S.is_zero qx5a) ;
          assert (i <> 1 || S.is_zero qx2b) ;
          let vs = Array.map (fun (R i) -> trace.(i)) wires in
          let qs = Array.copy linear in
          let qi = linear.(i) in
          (* We ignore the i-th term, as we are solving for it *)
          qs.(i) <- S.zero ;
          let sum = Array.map2 S.mul qs vs |> Array.fold_left S.add qc in
          let (R a_row) = wires.(0) in
          let (R b_row) = wires.(1) in
          let av = trace.(a_row) in
          let bv = trace.(b_row) in
          let m_pair = match i with 0 -> bv | 1 -> av | _ -> S.zero in
          let (R i_row) = wires.(i) in
          trace.(i_row) <-
            S.(
              (sum
              + (if i >= 2 then qm * av * bv else S.zero)
              + (qx5a * pow av (Z.of_int 5))
              + (qx2b * (bv * bv)))
              / negate (qi + (m_pair * qm))))
  | Pow5 {a; c} -> trace.(c) <- S.pow trace.(a) (Z.of_int 5)
  | Lookup {wires; table} ->
      let tbl = Tables.find table Csir.table_registry in
      let values = Array.map untag wires in
      let wires = Array.map from_tagged wires in
      let wires = Array.map (Option.map (fun i -> trace.(i))) wires in
      let entry = Option.get Csir.Table.(find wires tbl) in
      Array.iteri (fun i v -> trace.(v) <- entry.(i)) values
  | IsZero wires ->
      let av = trace.(wires.(0)) in
      trace.(wires.(2)) <- S.(if av = zero then one else zero) ;
      trace.(wires.(1)) <- S.(if av = zero then one else S.div_exn one av)
  | IsNotZero wires ->
      let av = trace.(wires.(0)) in
      trace.(wires.(2)) <- S.(if av = zero then zero else one) ;
      trace.(wires.(1)) <- S.(if av = zero then one else S.div_exn one av)
  | Ecc_Ws {x1; y1; x2; y2; x3; y3} ->
      let x1, y1 = (trace.(x1), trace.(y1)) in
      let x2, y2 = (trace.(x2), trace.(y2)) in
      let lambda = S.(sub y2 y1 / sub x2 x1) in
      let x3_v = S.(sub (lambda * lambda) (x1 + x2)) in
      trace.(x3) <- x3_v ;
      trace.(y3) <- S.(sub (lambda * sub x1 x3_v) y1)
  | Ecc_Ed {a; d; x1; y1; x2; y2; x3; y3} ->
      let x1, y1 = (trace.(x1), trace.(y1)) in
      let x2, y2 = (trace.(x2), trace.(y2)) in
      let x1x2 = S.(mul x1 x2) in
      let y1y2 = S.(mul y1 y2) in
      let denom = S.(d * x1x2 * y1y2) in
      let x_res = S.(add (x1 * y2) (x2 * y1) / add one denom) in
      let y_res = S.(sub y1y2 (a * x1x2) / sub one denom) in
      trace.(x3) <- x_res ;
      trace.(y3) <- y_res
  | Ecc_Cond_Ed {a; d; x1; y1; x2; y2; bit; x3; y3} ->
      let x1, y1 = (trace.(x1), trace.(y1)) in
      let x2, y2 = (trace.(x2), trace.(y2)) in
      let b = trace.(bit) in
      let x2' = S.(mul b x2) in
      let y2' = S.(add (mul b y2) (sub one b)) in
      let x1x2' = S.(mul x1 x2') in
      let y1y2' = S.(mul y1 y2') in
      let denom = S.(d * x1x2' * y1y2') in
      let x_res = S.(add (x1 * y2') (x2' * y1) / add one denom) in
      let y_res = S.(sub y1y2' (a * x1x2') / sub one denom) in
      trace.(x3) <- x_res ;
      trace.(y3) <- y_res
  | BitsOfS {nb_bits; shift; l; bits} ->
      let x = trace.(l) |> S.to_z in
      let x = Z.(x + shift) in
      let binary_decomposition = Utils.bool_list_of_z ~nb_bits x in
      List.iter2
        (fun b value -> trace.(b) <- (if value then S.one else S.zero))
        bits
        binary_decomposition
  | LimbsOfS {total_nb_bits; nb_bits; shift; l; limbs} ->
      let x = trace.(l) |> S.to_z in
      let x = Z.(x + shift) in
      let binary_decomposition =
        Utils.bool_list_of_z ~nb_bits:total_nb_bits x
      in
      let nb_decomposition =
        Utils.limbs_of_bool_list ~nb_bits binary_decomposition
      in
      List.iter2
        (fun b value -> trace.(b) <- S.of_int value)
        limbs
        nb_decomposition
  | Updater ti -> ignore @@ Optimizer.trace_updater ti trace
  | Swap {b; x; y; u; v} ->
      let b, x, y = (trace.(b), trace.(x), trace.(y)) in
      let x_res, y_res = if S.is_zero b then (x, y) else (y, x) in
      trace.(u) <- x_res ;
      trace.(v) <- y_res
  | Poseidon128Full {x0; y0; x1; y1; x2; y2; k; matrix} ->
      let pow5 x = S.pow trace.(x) (Z.of_int 5) in
      let x_vec = [|Array.map pow5 [|x0; x1; x2|]|] |> VS.transpose in
      let y_vec = VS.mul matrix x_vec in
      List.iteri
        (fun i yi -> trace.(yi) <- S.add k.(i) @@ y_vec.(i).(0))
        [y0; y1; y2]
  | Poseidon128Partial
      {a; b; c; a_5; b_5; c_5; x0; y0; x1; y1; x2; y2; k_cols; matrix} ->
      let pow5 x = S.pow x (Z.of_int 5) in
      let ppow5 v = [|v.(0); v.(1); [|pow5 v.(2).(0)|]|] in
      let x_vec = [|[|trace.(x0)|]; [|trace.(x1)|]; [|trace.(x2)|]|] in
      let a_vec = VS.(add (mul matrix @@ ppow5 x_vec) k_cols.(0)) in
      let b_vec = VS.(add (mul matrix @@ ppow5 a_vec) k_cols.(1)) in
      let c_vec = VS.(add (mul matrix @@ ppow5 b_vec) k_cols.(2)) in
      let y_vec = VS.(add (mul matrix @@ ppow5 c_vec) k_cols.(3)) in
      trace.(a) <- a_vec.(2).(0) ;
      trace.(b) <- b_vec.(2).(0) ;
      trace.(c) <- c_vec.(2).(0) ;
      trace.(a_5) <- pow5 trace.(a) ;
      trace.(b_5) <- pow5 trace.(b) ;
      trace.(c_5) <- pow5 trace.(c) ;
      trace.(y0) <- y_vec.(0).(0) ;
      trace.(y1) <- y_vec.(1).(0) ;
      trace.(y2) <- y_vec.(2).(0)
  | AnemoiRound {x0; y0; w; v; x1; y1; kx; ky} ->
      let _w_5', w', v', _u', x1', y1' =
        Gadget_anemoi.Anemoi128.compute_one_round trace.(x0) trace.(y0) kx ky
      in
      trace.(w) <- w' ;
      trace.(v) <- v' ;
      trace.(x1) <- x1' ;
      trace.(y1) <- y1'
  | AnemoiDoubleRound {x0; y0; w0; w1; y1; x2; y2; kx1; ky1; kx2; ky2} ->
      (* First round *)
      let _w_5', w', _v', _u', x1', y1' =
        Gadget_anemoi.Anemoi128.compute_one_round trace.(x0) trace.(y0) kx1 ky1
      in
      (* Computing w *)
      trace.(w0) <- w' ;
      trace.(y1) <- y1' ;
      (* Second round *)
      let _w_5', w', _v', _u', x2', y2' =
        Gadget_anemoi.Anemoi128.compute_one_round x1' y1' kx2 ky2
      in
      trace.(w1) <- w' ;
      trace.(x2) <- x2' ;
      trace.(y2) <- y2'
  | AnemoiCustom {x0; y0; x1; y1; x2; y2; kx1; ky1; kx2; ky2} ->
      (* First round *)
      let _w_5', _w', _v', _u', x1', y1' =
        Gadget_anemoi.Anemoi128.compute_one_round trace.(x0) trace.(y0) kx1 ky1
      in
      trace.(x1) <- x1' ;
      trace.(y1) <- y1' ;
      (* Second round *)
      let _w_5', _w', _v', _u', x2', y2' =
        Gadget_anemoi.Anemoi128.compute_one_round x1' y1' kx2 ky2
      in
      trace.(x2) <- x2' ;
      trace.(y2) <- y2'
  | Mod_Add
      {
        modulus;
        base;
        nb_limbs;
        moduli;
        qm_bound;
        ts_bounds;
        inverse;
        inp1;
        inp2;
        out;
        qm;
        ts;
      } ->
      (* See [lib_plompiler/gadget_mod_arith.ml] for explanations *)
      (* This is just a sanity check *)
      assert (List.compare_length_with inp1 nb_limbs = 0) ;
      assert (List.compare_length_with inp2 nb_limbs = 0) ;
      assert (List.compare_length_with out nb_limbs = 0) ;
      let sum = List.fold_left Z.add Z.zero in
      let ( %! ) = Z.rem in
      let xs = List.map (fun v -> trace.(v) |> S.to_z) inp1 in
      let ys = List.map (fun v -> trace.(v) |> S.to_z) inp2 in
      let zs =
        if inverse then Utils.mod_sub_limbs ~modulus ~base xs ys
        else Utils.mod_add_limbs ~modulus ~base xs ys
      in
      List.iter2 (fun v zi -> trace.(v) <- S.of_z zi) out zs ;
      (* The rest of trace values from this point onwards, i.e. qm and tj,
         are designed to enforce the equality xs + ys = zs.
         If we are doing a substraction xs - ys = zs (when inverse = true),
         we implement it as an addition zs + ys = xs. Therefore, we need to
         rename [xs <-> zs]. *)
      let xs, zs = if inverse then (zs, xs) else (xs, zs) in
      let qm_shift, qm_ubound = qm_bound in
      let bs_mod_m =
        List.init nb_limbs (fun i -> Z.pow base i %! modulus) |> List.rev
      in
      let x_plus_y_minus_z =
        List.map2 (fun (xi, yi) zi -> Z.(xi + yi - zi)) (List.combine xs ys) zs
      in
      (* \sum_i (B^i mod m) * (x_i + y_i - z_i) = (qm + qm_shift) * m *)
      let qm_value, r =
        let lhs = sum @@ List.map2 Z.mul bs_mod_m x_plus_y_minus_z in
        Z.(div_rem (lhs - (qm_shift * modulus)) modulus)
      in
      assert (Z.(equal r zero)) ;
      assert (Z.(compare qm_value zero >= 0)) ;
      assert (Z.(compare qm_value qm_ubound < 0)) ;
      trace.(qm) <- S.of_z qm_value ;
      (* For every modulo mj in moduli,
         \sum_i ((B^i mod m) mod mj) * (x_i + y_i - z_i)
         - qm * (m mod mj) - ((qm_shift * m) mod mj) = (tj + tj_shift) * mj *)
      List.iter2
        (fun mj (tj, (tj_shift, tj_ubound)) ->
          let bs_mod_m_mod_mj = List.map (fun v -> v %! mj) bs_mod_m in
          let terms = List.map2 Z.mul bs_mod_m_mod_mj x_plus_y_minus_z in
          let lhs =
            Z.(
              sum terms
              - (qm_value * (modulus %! mj))
              - (qm_shift * modulus %! mj))
          in
          let tj_value, r = Z.(div_rem (lhs - (tj_shift * mj)) mj) in
          assert (Z.(equal r zero)) ;
          assert (Z.(compare tj_value zero >= 0)) ;
          assert (Z.(compare tj_value tj_ubound < 0)) ;
          trace.(tj) <- S.of_z tj_value)
        moduli
        (List.combine ts ts_bounds)
  | Mod_Mul
      {
        modulus;
        base;
        nb_limbs;
        moduli;
        qm_bound;
        ts_bounds;
        inverse;
        inp1;
        inp2;
        out;
        qm;
        ts;
      } ->
      (* See [lib_plompiler/gadget_mod_arith.ml] for explanations *)
      (* This is just a sanity check *)
      assert (List.compare_length_with inp1 nb_limbs = 0) ;
      assert (List.compare_length_with inp2 nb_limbs = 0) ;
      assert (List.compare_length_with out nb_limbs = 0) ;
      let sum = List.fold_left Z.add Z.zero in
      let ( %! ) = Z.rem in
      let xs = List.map (fun v -> trace.(v) |> S.to_z) inp1 in
      let ys = List.map (fun v -> trace.(v) |> S.to_z) inp2 in
      let zs =
        if inverse then Utils.mod_div_limbs ~modulus ~base xs ys
        else Utils.mod_mul_limbs ~modulus ~base xs ys
      in
      List.iter2 (fun v zi -> trace.(v) <- S.of_z zi) out zs ;
      (* The rest of trace values from this point onwards, i.e. qm and tj,
         are designed to enforce the equality xs * ys = zs.
         If we are doing a division xs / ys = zs (when inverse = true),
         we implement it as a multiplication zs * ys = xs. Therefore, we need to
         rename [xs <-> zs]. *)
      let xs, zs = if inverse then (zs, xs) else (xs, zs) in
      let qm_shift, qm_ubound = qm_bound in
      let bs_mod_m =
        List.init nb_limbs (fun i -> Z.pow base i %! modulus) |> List.rev
      in
      let bij_mod_m =
        List.init nb_limbs (fun i ->
            List.init nb_limbs (fun j -> Z.pow base (i + j) %! modulus))
        |> List.concat |> List.rev
      in
      let x_times_y =
        List.concat_map (fun xi -> List.map (fun yj -> Z.(xi * yj)) ys) xs
      in
      (* \sum_i (\sum_j (B^{i+j} mod m) * x_i * y_j) - (\sum_i (B^i mod m) * z_i)
            = (qm + qm_shift) * m *)
      let qm_value, r =
        let lhs_xy = sum @@ List.map2 Z.mul bij_mod_m x_times_y in
        let lhs_z = sum @@ List.map2 Z.mul bs_mod_m zs in
        Z.(div_rem (lhs_xy - lhs_z - (qm_shift * modulus)) modulus)
      in
      assert (Z.(equal r zero)) ;
      assert (Z.(compare qm_value zero >= 0)) ;
      assert (Z.(compare qm_value qm_ubound < 0)) ;
      trace.(qm) <- S.of_z qm_value ;

      (* For every modulo mj in moduli,
         \sum_i (\sum_j ((B^{i+j} mod m) mod mj) * x_i * y_j)
            - (\sum_i ((B^i mod m) mod mj) * z_i)
            - qm * (m mod mj) - ((qm_shift * m) mod mj) = (tj + tj_shift) * mj *)
      List.iter2
        (fun mj (tj, (tj_shift, tj_ubound)) ->
          let bs_mod_m_mod_mj = List.map (fun v -> v %! mj) bs_mod_m in
          let bij_mod_m_mod_mj = List.map (fun v -> v %! mj) bij_mod_m in
          let sum_xy = sum @@ List.map2 Z.mul bij_mod_m_mod_mj x_times_y in
          let sum_z = sum @@ List.map2 Z.mul bs_mod_m_mod_mj zs in
          let lhs =
            Z.(
              sum_xy - sum_z
              - (qm_value * (modulus %! mj))
              - (qm_shift * modulus %! mj))
          in
          let tj_value, r = Z.(div_rem (lhs - (tj_shift * mj)) mj) in
          assert (Z.(equal r zero)) ;
          assert (Z.(compare tj_value zero >= 0)) ;
          assert (Z.(compare tj_value tj_ubound < 0)) ;
          trace.(tj) <- S.of_z tj_value)
        moduli
        (List.combine ts ts_bounds)
  | Mod_IsZero {modulus; base; nb_limbs; inp; aux; out} ->
      (* See [lib_plompiler/gadget_mod_arith.ml] for explanations *)
      (* This is just a sanity check *)
      assert (List.compare_length_with inp nb_limbs = 0) ;
      assert (List.compare_length_with aux nb_limbs = 0) ;
      let xs = List.map (fun v -> trace.(v) |> S.to_z) inp in
      let x = Utils.z_of_limbs ~base xs in
      if Z.(rem x modulus = zero) then (
        (* The auxiliary variable [r] must satisfy the equation [x * r = 0],
           because [x = 0], the value of [r] is irrelevant here.
           Since it must be non-zero, we set it to be 1. *)
        trace.(out) <- S.one ;
        List.iteri
          (fun i v ->
            if i < nb_limbs - 1 then trace.(v) <- S.zero else trace.(v) <- S.one)
          aux)
      else (
        (* The auxiliary variable [r] must satisfy the equation [x * r = 1],
           therefore, [r] must be the inverse of [x <> 0]. *)
        trace.(out) <- S.zero ;
        let one = Utils.z_to_limbs ~len:nb_limbs ~base Z.one in
        let x_inv = Utils.mod_div_limbs ~modulus ~base one xs in
        List.iter2 (fun v r -> trace.(v) <- S.of_z r) aux x_inv)) ;
  trace

let solve : t -> S.t array -> S.t array =
 fun {solvers; initial_size; final_size} inputs ->
  if Array.length inputs <> initial_size then
    failwith
      (Printf.sprintf
         "input size (= %d) != initial_size (= %d)"
         (Array.length inputs)
         initial_size) ;
  let dummy =
    Array.(append inputs (init (final_size - length inputs) (fun _ -> S.zero)))
  in
  List.fold_left solve_one dummy (List.rev solvers)
OCaml

Innovation. Community. Security.

GitHub Discord Twitter Peertube RSS
About
Changelog Releases Industrial Users Academic Users Why OCaml
Ecosystem
Packages Community Events OCaml Planet Jobs
Resources
Install OCaml Get Started Platform Tools Language Manual Standard Library API Books Exercises Papers OCaml Playground Logo
Policies
Carbon Footprint Governance Privacy Code of Conduct