-
Notifications
You must be signed in to change notification settings - Fork 160
/
multiexp.go
813 lines (726 loc) · 30.4 KB
/
multiexp.go
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
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
// Copyright 2020 Consensys Software Inc.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
// Code generated by consensys/gnark-crypto DO NOT EDIT
package bls12377
import (
"errors"
"github.com/consensys/gnark-crypto/ecc"
"github.com/consensys/gnark-crypto/ecc/bls12-377/fr"
"github.com/consensys/gnark-crypto/internal/parallel"
"math"
"runtime"
)
// MultiExp implements section 4 of https://eprint.iacr.org/2012/549.pdf
//
// This call return an error if len(scalars) != len(points) or if provided config is invalid.
func (p *G1Affine) MultiExp(points []G1Affine, scalars []fr.Element, config ecc.MultiExpConfig) (*G1Affine, error) {
var _p G1Jac
if _, err := _p.MultiExp(points, scalars, config); err != nil {
return nil, err
}
p.FromJacobian(&_p)
return p, nil
}
// MultiExp implements section 4 of https://eprint.iacr.org/2012/549.pdf
//
// This call return an error if len(scalars) != len(points) or if provided config is invalid.
func (p *G1Jac) MultiExp(points []G1Affine, scalars []fr.Element, config ecc.MultiExpConfig) (*G1Jac, error) {
// TODO @gbotrel replace the ecc.MultiExpConfig by a Option pattern for maintainability.
// note:
// each of the msmCX method is the same, except for the c constant it declares
// duplicating (through template generation) these methods allows to declare the buckets on the stack
// the choice of c needs to be improved:
// there is a theoretical value that gives optimal asymptotics
// but in practice, other factors come into play, including:
// * if c doesn't divide 64, the word size, then we're bound to select bits over 2 words of our scalars, instead of 1
// * number of CPUs
// * cache friendliness (which depends on the host, G1 or G2... )
// --> for example, on BN254, a G1 point fits into one cache line of 64bytes, but a G2 point don't.
// for each msmCX
// step 1
// we compute, for each scalars over c-bit wide windows, nbChunk digits
// if the digit is larger than 2^{c-1}, then, we borrow 2^c from the next window and subtract
// 2^{c} to the current digit, making it negative.
// negative digits will be processed in the next step as adding -G into the bucket instead of G
// (computing -G is cheap, and this saves us half of the buckets)
// step 2
// buckets are declared on the stack
// notice that we have 2^{c-1} buckets instead of 2^{c} (see step1)
// we use jacobian extended formulas here as they are faster than mixed addition
// msmProcessChunk places points into buckets base on their selector and return the weighted bucket sum in given channel
// step 3
// reduce the buckets weighed sums into our result (msmReduceChunk)
// ensure len(points) == len(scalars)
nbPoints := len(points)
if nbPoints != len(scalars) {
return nil, errors.New("len(points) != len(scalars)")
}
// if nbTasks is not set, use all available CPUs
if config.NbTasks <= 0 {
config.NbTasks = runtime.NumCPU() * 2
} else if config.NbTasks > 1024 {
return nil, errors.New("invalid config: config.NbTasks > 1024")
}
// here, we compute the best C for nbPoints
// we split recursively until nbChunks(c) >= nbTasks,
bestC := func(nbPoints int) uint64 {
// implemented msmC methods (the c we use must be in this slice)
implementedCs := []uint64{4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16}
var C uint64
// approximate cost (in group operations)
// cost = bits/c * (nbPoints + 2^{c})
// this needs to be verified empirically.
// for example, on a MBP 2016, for G2 MultiExp > 8M points, hand picking c gives better results
min := math.MaxFloat64
for _, c := range implementedCs {
cc := (fr.Bits + 1) * (nbPoints + (1 << c))
cost := float64(cc) / float64(c)
if cost < min {
min = cost
C = c
}
}
return C
}
C := bestC(nbPoints)
nbChunks := int(computeNbChunks(C))
// should we recursively split the msm in half? (see below)
// we want to minimize the execution time of the algorithm;
// splitting the msm will **add** operations, but if it allows to use more CPU, it might be worth it.
// costFunction returns a metric that represent the "wall time" of the algorithm
costFunction := func(nbTasks, nbCpus, costPerTask int) int {
// cost for the reduction of all tasks (msmReduceChunk)
totalCost := nbTasks
// cost for the computation of each task (msmProcessChunk)
for nbTasks >= nbCpus {
nbTasks -= nbCpus
totalCost += costPerTask
}
if nbTasks > 0 {
totalCost += costPerTask
}
return totalCost
}
// costPerTask is the approximate number of group ops per task
costPerTask := func(c uint64, nbPoints int) int { return (nbPoints + int((1 << c))) }
costPreSplit := costFunction(nbChunks, config.NbTasks, costPerTask(C, nbPoints))
cPostSplit := bestC(nbPoints / 2)
nbChunksPostSplit := int(computeNbChunks(cPostSplit))
costPostSplit := costFunction(nbChunksPostSplit*2, config.NbTasks, costPerTask(cPostSplit, nbPoints/2))
// if the cost of the split msm is lower than the cost of the non split msm, we split
if costPostSplit < costPreSplit {
config.NbTasks = int(math.Ceil(float64(config.NbTasks) / 2.0))
var _p G1Jac
chDone := make(chan struct{}, 1)
go func() {
_p.MultiExp(points[:nbPoints/2], scalars[:nbPoints/2], config)
close(chDone)
}()
p.MultiExp(points[nbPoints/2:], scalars[nbPoints/2:], config)
<-chDone
p.AddAssign(&_p)
return p, nil
}
// if we don't split, we use the best C we found
_innerMsmG1(p, C, points, scalars, config)
return p, nil
}
func _innerMsmG1(p *G1Jac, c uint64, points []G1Affine, scalars []fr.Element, config ecc.MultiExpConfig) *G1Jac {
// partition the scalars
digits, chunkStats := partitionScalars(scalars, c, config.NbTasks)
nbChunks := computeNbChunks(c)
// for each chunk, spawn one go routine that'll loop through all the scalars in the
// corresponding bit-window
// note that buckets is an array allocated on the stack and this is critical for performance
// each go routine sends its result in chChunks[i] channel
chChunks := make([]chan g1JacExtended, nbChunks)
for i := 0; i < len(chChunks); i++ {
chChunks[i] = make(chan g1JacExtended, 1)
}
// we use a semaphore to limit the number of go routines running concurrently
// (only if nbTasks < nbCPU)
var sem chan struct{}
if config.NbTasks < runtime.NumCPU() {
// we add nbChunks because if chunk is overweight we split it in two
sem = make(chan struct{}, config.NbTasks+int(nbChunks))
for i := 0; i < config.NbTasks; i++ {
sem <- struct{}{}
}
defer func() {
close(sem)
}()
}
// the last chunk may be processed with a different method than the rest, as it could be smaller.
n := len(points)
for j := int(nbChunks - 1); j >= 0; j-- {
processChunk := getChunkProcessorG1(c, chunkStats[j])
if j == int(nbChunks-1) {
processChunk = getChunkProcessorG1(lastC(c), chunkStats[j])
}
if chunkStats[j].weight >= 115 {
// we split this in more go routines since this chunk has more work to do than the others.
// else what would happen is this go routine would finish much later than the others.
chSplit := make(chan g1JacExtended, 2)
split := n / 2
if sem != nil {
sem <- struct{}{} // add another token to the semaphore, since we split in two.
}
go processChunk(uint64(j), chSplit, c, points[:split], digits[j*n:(j*n)+split], sem)
go processChunk(uint64(j), chSplit, c, points[split:], digits[(j*n)+split:(j+1)*n], sem)
go func(chunkID int) {
s1 := <-chSplit
s2 := <-chSplit
close(chSplit)
s1.add(&s2)
chChunks[chunkID] <- s1
}(j)
continue
}
go processChunk(uint64(j), chChunks[j], c, points, digits[j*n:(j+1)*n], sem)
}
return msmReduceChunkG1Affine(p, int(c), chChunks[:])
}
// getChunkProcessorG1 decides, depending on c window size and statistics for the chunk
// to return the best algorithm to process the chunk.
func getChunkProcessorG1(c uint64, stat chunkStat) func(chunkID uint64, chRes chan<- g1JacExtended, c uint64, points []G1Affine, digits []uint16, sem chan struct{}) {
switch c {
case 2:
return processChunkG1Jacobian[bucketg1JacExtendedC2]
case 4:
return processChunkG1Jacobian[bucketg1JacExtendedC4]
case 5:
return processChunkG1Jacobian[bucketg1JacExtendedC5]
case 6:
return processChunkG1Jacobian[bucketg1JacExtendedC6]
case 7:
return processChunkG1Jacobian[bucketg1JacExtendedC7]
case 8:
return processChunkG1Jacobian[bucketg1JacExtendedC8]
case 9:
return processChunkG1Jacobian[bucketg1JacExtendedC9]
case 10:
const batchSize = 80
// here we could check some chunk statistic (deviation, ...) to determine if calling
// the batch affine version is worth it.
if stat.nbBucketFilled < batchSize {
// clear indicator that batch affine method is not appropriate here.
return processChunkG1Jacobian[bucketg1JacExtendedC10]
}
return processChunkG1BatchAffine[bucketg1JacExtendedC10, bucketG1AffineC10, bitSetC10, pG1AffineC10, ppG1AffineC10, qG1AffineC10, cG1AffineC10]
case 11:
const batchSize = 150
// here we could check some chunk statistic (deviation, ...) to determine if calling
// the batch affine version is worth it.
if stat.nbBucketFilled < batchSize {
// clear indicator that batch affine method is not appropriate here.
return processChunkG1Jacobian[bucketg1JacExtendedC11]
}
return processChunkG1BatchAffine[bucketg1JacExtendedC11, bucketG1AffineC11, bitSetC11, pG1AffineC11, ppG1AffineC11, qG1AffineC11, cG1AffineC11]
case 12:
const batchSize = 200
// here we could check some chunk statistic (deviation, ...) to determine if calling
// the batch affine version is worth it.
if stat.nbBucketFilled < batchSize {
// clear indicator that batch affine method is not appropriate here.
return processChunkG1Jacobian[bucketg1JacExtendedC12]
}
return processChunkG1BatchAffine[bucketg1JacExtendedC12, bucketG1AffineC12, bitSetC12, pG1AffineC12, ppG1AffineC12, qG1AffineC12, cG1AffineC12]
case 13:
const batchSize = 350
// here we could check some chunk statistic (deviation, ...) to determine if calling
// the batch affine version is worth it.
if stat.nbBucketFilled < batchSize {
// clear indicator that batch affine method is not appropriate here.
return processChunkG1Jacobian[bucketg1JacExtendedC13]
}
return processChunkG1BatchAffine[bucketg1JacExtendedC13, bucketG1AffineC13, bitSetC13, pG1AffineC13, ppG1AffineC13, qG1AffineC13, cG1AffineC13]
case 14:
const batchSize = 400
// here we could check some chunk statistic (deviation, ...) to determine if calling
// the batch affine version is worth it.
if stat.nbBucketFilled < batchSize {
// clear indicator that batch affine method is not appropriate here.
return processChunkG1Jacobian[bucketg1JacExtendedC14]
}
return processChunkG1BatchAffine[bucketg1JacExtendedC14, bucketG1AffineC14, bitSetC14, pG1AffineC14, ppG1AffineC14, qG1AffineC14, cG1AffineC14]
case 15:
const batchSize = 500
// here we could check some chunk statistic (deviation, ...) to determine if calling
// the batch affine version is worth it.
if stat.nbBucketFilled < batchSize {
// clear indicator that batch affine method is not appropriate here.
return processChunkG1Jacobian[bucketg1JacExtendedC15]
}
return processChunkG1BatchAffine[bucketg1JacExtendedC15, bucketG1AffineC15, bitSetC15, pG1AffineC15, ppG1AffineC15, qG1AffineC15, cG1AffineC15]
case 16:
const batchSize = 640
// here we could check some chunk statistic (deviation, ...) to determine if calling
// the batch affine version is worth it.
if stat.nbBucketFilled < batchSize {
// clear indicator that batch affine method is not appropriate here.
return processChunkG1Jacobian[bucketg1JacExtendedC16]
}
return processChunkG1BatchAffine[bucketg1JacExtendedC16, bucketG1AffineC16, bitSetC16, pG1AffineC16, ppG1AffineC16, qG1AffineC16, cG1AffineC16]
default:
// panic("will not happen c != previous values is not generated by templates")
return processChunkG1Jacobian[bucketg1JacExtendedC16]
}
}
// msmReduceChunkG1Affine reduces the weighted sum of the buckets into the result of the multiExp
func msmReduceChunkG1Affine(p *G1Jac, c int, chChunks []chan g1JacExtended) *G1Jac {
var _p g1JacExtended
totalj := <-chChunks[len(chChunks)-1]
_p.Set(&totalj)
for j := len(chChunks) - 2; j >= 0; j-- {
for l := 0; l < c; l++ {
_p.double(&_p)
}
totalj := <-chChunks[j]
_p.add(&totalj)
}
return p.unsafeFromJacExtended(&_p)
}
// MultiExp implements section 4 of https://eprint.iacr.org/2012/549.pdf
//
// This call return an error if len(scalars) != len(points) or if provided config is invalid.
func (p *G2Affine) MultiExp(points []G2Affine, scalars []fr.Element, config ecc.MultiExpConfig) (*G2Affine, error) {
var _p G2Jac
if _, err := _p.MultiExp(points, scalars, config); err != nil {
return nil, err
}
p.FromJacobian(&_p)
return p, nil
}
// MultiExp implements section 4 of https://eprint.iacr.org/2012/549.pdf
//
// This call return an error if len(scalars) != len(points) or if provided config is invalid.
func (p *G2Jac) MultiExp(points []G2Affine, scalars []fr.Element, config ecc.MultiExpConfig) (*G2Jac, error) {
// TODO @gbotrel replace the ecc.MultiExpConfig by a Option pattern for maintainability.
// note:
// each of the msmCX method is the same, except for the c constant it declares
// duplicating (through template generation) these methods allows to declare the buckets on the stack
// the choice of c needs to be improved:
// there is a theoretical value that gives optimal asymptotics
// but in practice, other factors come into play, including:
// * if c doesn't divide 64, the word size, then we're bound to select bits over 2 words of our scalars, instead of 1
// * number of CPUs
// * cache friendliness (which depends on the host, G1 or G2... )
// --> for example, on BN254, a G1 point fits into one cache line of 64bytes, but a G2 point don't.
// for each msmCX
// step 1
// we compute, for each scalars over c-bit wide windows, nbChunk digits
// if the digit is larger than 2^{c-1}, then, we borrow 2^c from the next window and subtract
// 2^{c} to the current digit, making it negative.
// negative digits will be processed in the next step as adding -G into the bucket instead of G
// (computing -G is cheap, and this saves us half of the buckets)
// step 2
// buckets are declared on the stack
// notice that we have 2^{c-1} buckets instead of 2^{c} (see step1)
// we use jacobian extended formulas here as they are faster than mixed addition
// msmProcessChunk places points into buckets base on their selector and return the weighted bucket sum in given channel
// step 3
// reduce the buckets weighed sums into our result (msmReduceChunk)
// ensure len(points) == len(scalars)
nbPoints := len(points)
if nbPoints != len(scalars) {
return nil, errors.New("len(points) != len(scalars)")
}
// if nbTasks is not set, use all available CPUs
if config.NbTasks <= 0 {
config.NbTasks = runtime.NumCPU() * 2
} else if config.NbTasks > 1024 {
return nil, errors.New("invalid config: config.NbTasks > 1024")
}
// here, we compute the best C for nbPoints
// we split recursively until nbChunks(c) >= nbTasks,
bestC := func(nbPoints int) uint64 {
// implemented msmC methods (the c we use must be in this slice)
implementedCs := []uint64{4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16}
var C uint64
// approximate cost (in group operations)
// cost = bits/c * (nbPoints + 2^{c})
// this needs to be verified empirically.
// for example, on a MBP 2016, for G2 MultiExp > 8M points, hand picking c gives better results
min := math.MaxFloat64
for _, c := range implementedCs {
cc := (fr.Bits + 1) * (nbPoints + (1 << c))
cost := float64(cc) / float64(c)
if cost < min {
min = cost
C = c
}
}
return C
}
C := bestC(nbPoints)
nbChunks := int(computeNbChunks(C))
// should we recursively split the msm in half? (see below)
// we want to minimize the execution time of the algorithm;
// splitting the msm will **add** operations, but if it allows to use more CPU, it might be worth it.
// costFunction returns a metric that represent the "wall time" of the algorithm
costFunction := func(nbTasks, nbCpus, costPerTask int) int {
// cost for the reduction of all tasks (msmReduceChunk)
totalCost := nbTasks
// cost for the computation of each task (msmProcessChunk)
for nbTasks >= nbCpus {
nbTasks -= nbCpus
totalCost += costPerTask
}
if nbTasks > 0 {
totalCost += costPerTask
}
return totalCost
}
// costPerTask is the approximate number of group ops per task
costPerTask := func(c uint64, nbPoints int) int { return (nbPoints + int((1 << c))) }
costPreSplit := costFunction(nbChunks, config.NbTasks, costPerTask(C, nbPoints))
cPostSplit := bestC(nbPoints / 2)
nbChunksPostSplit := int(computeNbChunks(cPostSplit))
costPostSplit := costFunction(nbChunksPostSplit*2, config.NbTasks, costPerTask(cPostSplit, nbPoints/2))
// if the cost of the split msm is lower than the cost of the non split msm, we split
if costPostSplit < costPreSplit {
config.NbTasks = int(math.Ceil(float64(config.NbTasks) / 2.0))
var _p G2Jac
chDone := make(chan struct{}, 1)
go func() {
_p.MultiExp(points[:nbPoints/2], scalars[:nbPoints/2], config)
close(chDone)
}()
p.MultiExp(points[nbPoints/2:], scalars[nbPoints/2:], config)
<-chDone
p.AddAssign(&_p)
return p, nil
}
// if we don't split, we use the best C we found
_innerMsmG2(p, C, points, scalars, config)
return p, nil
}
func _innerMsmG2(p *G2Jac, c uint64, points []G2Affine, scalars []fr.Element, config ecc.MultiExpConfig) *G2Jac {
// partition the scalars
digits, chunkStats := partitionScalars(scalars, c, config.NbTasks)
nbChunks := computeNbChunks(c)
// for each chunk, spawn one go routine that'll loop through all the scalars in the
// corresponding bit-window
// note that buckets is an array allocated on the stack and this is critical for performance
// each go routine sends its result in chChunks[i] channel
chChunks := make([]chan g2JacExtended, nbChunks)
for i := 0; i < len(chChunks); i++ {
chChunks[i] = make(chan g2JacExtended, 1)
}
// we use a semaphore to limit the number of go routines running concurrently
// (only if nbTasks < nbCPU)
var sem chan struct{}
if config.NbTasks < runtime.NumCPU() {
// we add nbChunks because if chunk is overweight we split it in two
sem = make(chan struct{}, config.NbTasks+int(nbChunks))
for i := 0; i < config.NbTasks; i++ {
sem <- struct{}{}
}
defer func() {
close(sem)
}()
}
// the last chunk may be processed with a different method than the rest, as it could be smaller.
n := len(points)
for j := int(nbChunks - 1); j >= 0; j-- {
processChunk := getChunkProcessorG2(c, chunkStats[j])
if j == int(nbChunks-1) {
processChunk = getChunkProcessorG2(lastC(c), chunkStats[j])
}
if chunkStats[j].weight >= 115 {
// we split this in more go routines since this chunk has more work to do than the others.
// else what would happen is this go routine would finish much later than the others.
chSplit := make(chan g2JacExtended, 2)
split := n / 2
if sem != nil {
sem <- struct{}{} // add another token to the semaphore, since we split in two.
}
go processChunk(uint64(j), chSplit, c, points[:split], digits[j*n:(j*n)+split], sem)
go processChunk(uint64(j), chSplit, c, points[split:], digits[(j*n)+split:(j+1)*n], sem)
go func(chunkID int) {
s1 := <-chSplit
s2 := <-chSplit
close(chSplit)
s1.add(&s2)
chChunks[chunkID] <- s1
}(j)
continue
}
go processChunk(uint64(j), chChunks[j], c, points, digits[j*n:(j+1)*n], sem)
}
return msmReduceChunkG2Affine(p, int(c), chChunks[:])
}
// getChunkProcessorG2 decides, depending on c window size and statistics for the chunk
// to return the best algorithm to process the chunk.
func getChunkProcessorG2(c uint64, stat chunkStat) func(chunkID uint64, chRes chan<- g2JacExtended, c uint64, points []G2Affine, digits []uint16, sem chan struct{}) {
switch c {
case 2:
return processChunkG2Jacobian[bucketg2JacExtendedC2]
case 4:
return processChunkG2Jacobian[bucketg2JacExtendedC4]
case 5:
return processChunkG2Jacobian[bucketg2JacExtendedC5]
case 6:
return processChunkG2Jacobian[bucketg2JacExtendedC6]
case 7:
return processChunkG2Jacobian[bucketg2JacExtendedC7]
case 8:
return processChunkG2Jacobian[bucketg2JacExtendedC8]
case 9:
return processChunkG2Jacobian[bucketg2JacExtendedC9]
case 10:
const batchSize = 80
// here we could check some chunk statistic (deviation, ...) to determine if calling
// the batch affine version is worth it.
if stat.nbBucketFilled < batchSize {
// clear indicator that batch affine method is not appropriate here.
return processChunkG2Jacobian[bucketg2JacExtendedC10]
}
return processChunkG2BatchAffine[bucketg2JacExtendedC10, bucketG2AffineC10, bitSetC10, pG2AffineC10, ppG2AffineC10, qG2AffineC10, cG2AffineC10]
case 11:
const batchSize = 150
// here we could check some chunk statistic (deviation, ...) to determine if calling
// the batch affine version is worth it.
if stat.nbBucketFilled < batchSize {
// clear indicator that batch affine method is not appropriate here.
return processChunkG2Jacobian[bucketg2JacExtendedC11]
}
return processChunkG2BatchAffine[bucketg2JacExtendedC11, bucketG2AffineC11, bitSetC11, pG2AffineC11, ppG2AffineC11, qG2AffineC11, cG2AffineC11]
case 12:
const batchSize = 200
// here we could check some chunk statistic (deviation, ...) to determine if calling
// the batch affine version is worth it.
if stat.nbBucketFilled < batchSize {
// clear indicator that batch affine method is not appropriate here.
return processChunkG2Jacobian[bucketg2JacExtendedC12]
}
return processChunkG2BatchAffine[bucketg2JacExtendedC12, bucketG2AffineC12, bitSetC12, pG2AffineC12, ppG2AffineC12, qG2AffineC12, cG2AffineC12]
case 13:
const batchSize = 350
// here we could check some chunk statistic (deviation, ...) to determine if calling
// the batch affine version is worth it.
if stat.nbBucketFilled < batchSize {
// clear indicator that batch affine method is not appropriate here.
return processChunkG2Jacobian[bucketg2JacExtendedC13]
}
return processChunkG2BatchAffine[bucketg2JacExtendedC13, bucketG2AffineC13, bitSetC13, pG2AffineC13, ppG2AffineC13, qG2AffineC13, cG2AffineC13]
case 14:
const batchSize = 400
// here we could check some chunk statistic (deviation, ...) to determine if calling
// the batch affine version is worth it.
if stat.nbBucketFilled < batchSize {
// clear indicator that batch affine method is not appropriate here.
return processChunkG2Jacobian[bucketg2JacExtendedC14]
}
return processChunkG2BatchAffine[bucketg2JacExtendedC14, bucketG2AffineC14, bitSetC14, pG2AffineC14, ppG2AffineC14, qG2AffineC14, cG2AffineC14]
case 15:
const batchSize = 500
// here we could check some chunk statistic (deviation, ...) to determine if calling
// the batch affine version is worth it.
if stat.nbBucketFilled < batchSize {
// clear indicator that batch affine method is not appropriate here.
return processChunkG2Jacobian[bucketg2JacExtendedC15]
}
return processChunkG2BatchAffine[bucketg2JacExtendedC15, bucketG2AffineC15, bitSetC15, pG2AffineC15, ppG2AffineC15, qG2AffineC15, cG2AffineC15]
case 16:
const batchSize = 640
// here we could check some chunk statistic (deviation, ...) to determine if calling
// the batch affine version is worth it.
if stat.nbBucketFilled < batchSize {
// clear indicator that batch affine method is not appropriate here.
return processChunkG2Jacobian[bucketg2JacExtendedC16]
}
return processChunkG2BatchAffine[bucketg2JacExtendedC16, bucketG2AffineC16, bitSetC16, pG2AffineC16, ppG2AffineC16, qG2AffineC16, cG2AffineC16]
default:
// panic("will not happen c != previous values is not generated by templates")
return processChunkG2Jacobian[bucketg2JacExtendedC16]
}
}
// msmReduceChunkG2Affine reduces the weighted sum of the buckets into the result of the multiExp
func msmReduceChunkG2Affine(p *G2Jac, c int, chChunks []chan g2JacExtended) *G2Jac {
var _p g2JacExtended
totalj := <-chChunks[len(chChunks)-1]
_p.Set(&totalj)
for j := len(chChunks) - 2; j >= 0; j-- {
for l := 0; l < c; l++ {
_p.double(&_p)
}
totalj := <-chChunks[j]
_p.add(&totalj)
}
return p.unsafeFromJacExtended(&_p)
}
// selector stores the index, mask and shifts needed to select bits from a scalar
// it is used during the multiExp algorithm or the batch scalar multiplication
type selector struct {
index uint64 // index in the multi-word scalar to select bits from
mask uint64 // mask (c-bit wide)
shift uint64 // shift needed to get our bits on low positions
multiWordSelect bool // set to true if we need to select bits from 2 words (case where c doesn't divide 64)
maskHigh uint64 // same than mask, for index+1
shiftHigh uint64 // same than shift, for index+1
}
// return number of chunks for a given window size c
// the last chunk may be bigger to accommodate a potential carry from the NAF decomposition
func computeNbChunks(c uint64) uint64 {
return (fr.Bits + c - 1) / c
}
// return the last window size for a scalar;
// this last window should accommodate a carry (from the NAF decomposition)
// it can be == c if we have 1 available bit
// it can be > c if we have 0 available bit
// it can be < c if we have 2+ available bits
func lastC(c uint64) uint64 {
nbAvailableBits := (computeNbChunks(c) * c) - fr.Bits
return c + 1 - nbAvailableBits
}
type chunkStat struct {
// relative weight of work compared to other chunks. 100.0 -> nominal weight.
weight float32
// percentage of bucket filled in the window;
ppBucketFilled float32
nbBucketFilled int
}
// partitionScalars compute, for each scalars over c-bit wide windows, nbChunk digits
// if the digit is larger than 2^{c-1}, then, we borrow 2^c from the next window and subtract
// 2^{c} to the current digit, making it negative.
// negative digits can be processed in a later step as adding -G into the bucket instead of G
// (computing -G is cheap, and this saves us half of the buckets in the MultiExp or BatchScalarMultiplication)
func partitionScalars(scalars []fr.Element, c uint64, nbTasks int) ([]uint16, []chunkStat) {
// no benefit here to have more tasks than CPUs
if nbTasks > runtime.NumCPU() {
nbTasks = runtime.NumCPU()
}
// number of c-bit radixes in a scalar
nbChunks := computeNbChunks(c)
digits := make([]uint16, len(scalars)*int(nbChunks))
mask := uint64((1 << c) - 1) // low c bits are 1
max := int(1<<(c-1)) - 1 // max value (inclusive) we want for our digits
cDivides64 := (64 % c) == 0 // if c doesn't divide 64, we may need to select over multiple words
// compute offset and word selector / shift to select the right bits of our windows
selectors := make([]selector, nbChunks)
for chunk := uint64(0); chunk < nbChunks; chunk++ {
jc := uint64(chunk * c)
d := selector{}
d.index = jc / 64
d.shift = jc - (d.index * 64)
d.mask = mask << d.shift
d.multiWordSelect = !cDivides64 && d.shift > (64-c) && d.index < (fr.Limbs-1)
if d.multiWordSelect {
nbBitsHigh := d.shift - uint64(64-c)
d.maskHigh = (1 << nbBitsHigh) - 1
d.shiftHigh = (c - nbBitsHigh)
}
selectors[chunk] = d
}
parallel.Execute(len(scalars), func(start, end int) {
for i := start; i < end; i++ {
if scalars[i].IsZero() {
// everything is 0, no need to process this scalar
continue
}
scalar := scalars[i].Bits()
var carry int
// for each chunk in the scalar, compute the current digit, and an eventual carry
for chunk := uint64(0); chunk < nbChunks-1; chunk++ {
s := selectors[chunk]
// init with carry if any
digit := carry
carry = 0
// digit = value of the c-bit window
digit += int((scalar[s.index] & s.mask) >> s.shift)
if s.multiWordSelect {
// we are selecting bits over 2 words
digit += int(scalar[s.index+1]&s.maskHigh) << s.shiftHigh
}
// if the digit is larger than 2^{c-1}, then, we borrow 2^c from the next window and subtract
// 2^{c} to the current digit, making it negative.
if digit > max {
digit -= (1 << c)
carry = 1
}
// if digit is zero, no impact on result
if digit == 0 {
continue
}
var bits uint16
if digit > 0 {
bits = uint16(digit) << 1
} else {
bits = (uint16(-digit-1) << 1) + 1
}
digits[int(chunk)*len(scalars)+i] = bits
}
// for the last chunk, we don't want to borrow from a next window
// (but may have a larger max value)
chunk := nbChunks - 1
s := selectors[chunk]
// init with carry if any
digit := carry
// digit = value of the c-bit window
digit += int((scalar[s.index] & s.mask) >> s.shift)
if s.multiWordSelect {
// we are selecting bits over 2 words
digit += int(scalar[s.index+1]&s.maskHigh) << s.shiftHigh
}
digits[int(chunk)*len(scalars)+i] = uint16(digit) << 1
}
}, nbTasks)
// aggregate chunk stats
chunkStats := make([]chunkStat, nbChunks)
if c <= 9 {
// no need to compute stats for small window sizes
return digits, chunkStats
}
parallel.Execute(len(chunkStats), func(start, end int) {
// for each chunk compute the statistics
for chunkID := start; chunkID < end; chunkID++ {
// indicates if a bucket is hit.
var b bitSetC16
// digits for the chunk
chunkDigits := digits[chunkID*len(scalars) : (chunkID+1)*len(scalars)]
totalOps := 0
nz := 0 // non zero buckets count
for _, digit := range chunkDigits {
if digit == 0 {
continue
}
totalOps++
bucketID := digit >> 1
if digit&1 == 0 {
bucketID -= 1
}
if !b[bucketID] {
nz++
b[bucketID] = true
}
}
chunkStats[chunkID].weight = float32(totalOps) // count number of ops for now, we will compute the weight after
chunkStats[chunkID].ppBucketFilled = (float32(nz) * 100.0) / float32(int(1<<(c-1)))
chunkStats[chunkID].nbBucketFilled = nz
}
}, nbTasks)
totalOps := float32(0.0)
for _, stat := range chunkStats {
totalOps += stat.weight
}
target := totalOps / float32(nbChunks)
if target != 0.0 {
// if target == 0, it means all the scalars are 0 everywhere, there is no work to be done.
for i := 0; i < len(chunkStats); i++ {
chunkStats[i].weight = (chunkStats[i].weight * 100.0) / target
}
}
return digits, chunkStats
}