-
Notifications
You must be signed in to change notification settings - Fork 162
/
element_exp.go
1040 lines (804 loc) · 25.3 KB
/
element_exp.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
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
// 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 fr
// expBySqrtExp is equivalent to z.Exp(x, fbac1059a1346414f2d74903b441e8a10167ad91c408c9a60370d83429275ff3a5fddaa08b0000265228)
//
// uses github.com/mmcloughlin/addchain v0.4.0 to generate a shorter addition chain
func (z *Element) expBySqrtExp(x Element) *Element {
// addition chain:
//
// _10 = 2*1
// _11 = 1 + _10
// _101 = _10 + _11
// _110 = 1 + _101
// _1001 = _11 + _110
// _1011 = _10 + _1001
// _1100 = 1 + _1011
// _1101 = 1 + _1100
// _10001 = _101 + _1100
// _10011 = _10 + _10001
// _10101 = _10 + _10011
// _11011 = _110 + _10101
// _11101 = _10 + _11011
// _100011 = _110 + _11101
// _100111 = _1100 + _11011
// _101001 = _10 + _100111
// _110101 = _1100 + _101001
// _110111 = _10 + _110101
// _111001 = _10 + _110111
// _111011 = _10 + _111001
// _111101 = _10 + _111011
// _111111 = _10 + _111101
// _1111100 = _111101 + _111111
// _1111111 = _11 + _1111100
// i39 = ((_1111100 << 4 + _11101) << 3 + _11) << 6
// i57 = ((1 + i39) << 9 + _1011) << 6 + _1101
// i78 = ((i57 << 9 + _10011) << 7 + _100011) << 3
// i98 = ((1 + i78) << 11 + _101001) << 6 + _111001
// i117 = ((i98 << 7 + _110101) << 4 + _1101) << 6
// i138 = ((_1001 + i117) << 12 + _111011) << 6 + _10001
// i162 = ((i138 << 11 + _111101) << 6 + _101) << 5
// i184 = ((1 + i162) << 11 + _1011) << 8 + _111101
// i205 = ((i184 << 6 + _11011) << 8 + _100011) << 5
// i227 = ((_10001 + i205) << 12 + _100011) << 7 + _10011
// i257 = ((i227 << 6 + _10011) << 13 + _110111) << 9
// i279 = ((_11011 + i257) << 9 + _1101) << 10 + _101001
// i299 = ((i279 << 8 + _100111) << 2 + 1) << 8
// i311 = ((_1111111 + i299) << 2 + _11) << 7 + _11101
// i331 = ((i311 << 3 + 1) << 8 + _1111111) << 7
// i350 = ((_111011 + i331) << 6 + _10101) << 10 + _10001
// i386 = ((i350 << 3 + _11) << 23 + _10011) << 8
// return ((_101001 + i386) << 6 + _101) << 3
//
// Operations: 330 squares 67 multiplies
// Allocate Temporaries.
var (
t0 = new(Element)
t1 = new(Element)
t2 = new(Element)
t3 = new(Element)
t4 = new(Element)
t5 = new(Element)
t6 = new(Element)
t7 = new(Element)
t8 = new(Element)
t9 = new(Element)
t10 = new(Element)
t11 = new(Element)
t12 = new(Element)
t13 = new(Element)
t14 = new(Element)
t15 = new(Element)
t16 = new(Element)
t17 = new(Element)
t18 = new(Element)
)
// var t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18 Element
// Step 1: t6 = x^0x2
t6.Square(&x)
// Step 2: t2 = x^0x3
t2.Mul(&x, t6)
// Step 3: z = x^0x5
z.Mul(t6, t2)
// Step 4: t0 = x^0x6
t0.Mul(&x, z)
// Step 5: t15 = x^0x9
t15.Mul(t2, t0)
// Step 6: t14 = x^0xb
t14.Mul(t6, t15)
// Step 7: t5 = x^0xc
t5.Mul(&x, t14)
// Step 8: t9 = x^0xd
t9.Mul(&x, t5)
// Step 9: t3 = x^0x11
t3.Mul(z, t5)
// Step 10: t1 = x^0x13
t1.Mul(t6, t3)
// Step 11: t4 = x^0x15
t4.Mul(t6, t1)
// Step 12: t10 = x^0x1b
t10.Mul(t0, t4)
// Step 13: t7 = x^0x1d
t7.Mul(t6, t10)
// Step 14: t12 = x^0x23
t12.Mul(t0, t7)
// Step 15: t8 = x^0x27
t8.Mul(t5, t10)
// Step 16: t0 = x^0x29
t0.Mul(t6, t8)
// Step 17: t16 = x^0x35
t16.Mul(t5, t0)
// Step 18: t11 = x^0x37
t11.Mul(t6, t16)
// Step 19: t17 = x^0x39
t17.Mul(t6, t11)
// Step 20: t5 = x^0x3b
t5.Mul(t6, t17)
// Step 21: t13 = x^0x3d
t13.Mul(t6, t5)
// Step 22: t6 = x^0x3f
t6.Mul(t6, t13)
// Step 23: t18 = x^0x7c
t18.Mul(t13, t6)
// Step 24: t6 = x^0x7f
t6.Mul(t2, t18)
// Step 28: t18 = x^0x7c0
for s := 0; s < 4; s++ {
t18.Square(t18)
}
// Step 29: t18 = x^0x7dd
t18.Mul(t7, t18)
// Step 32: t18 = x^0x3ee8
for s := 0; s < 3; s++ {
t18.Square(t18)
}
// Step 33: t18 = x^0x3eeb
t18.Mul(t2, t18)
// Step 39: t18 = x^0xfbac0
for s := 0; s < 6; s++ {
t18.Square(t18)
}
// Step 40: t18 = x^0xfbac1
t18.Mul(&x, t18)
// Step 49: t18 = x^0x1f758200
for s := 0; s < 9; s++ {
t18.Square(t18)
}
// Step 50: t18 = x^0x1f75820b
t18.Mul(t14, t18)
// Step 56: t18 = x^0x7dd6082c0
for s := 0; s < 6; s++ {
t18.Square(t18)
}
// Step 57: t18 = x^0x7dd6082cd
t18.Mul(t9, t18)
// Step 66: t18 = x^0xfbac1059a00
for s := 0; s < 9; s++ {
t18.Square(t18)
}
// Step 67: t18 = x^0xfbac1059a13
t18.Mul(t1, t18)
// Step 74: t18 = x^0x7dd6082cd0980
for s := 0; s < 7; s++ {
t18.Square(t18)
}
// Step 75: t18 = x^0x7dd6082cd09a3
t18.Mul(t12, t18)
// Step 78: t18 = x^0x3eeb0416684d18
for s := 0; s < 3; s++ {
t18.Square(t18)
}
// Step 79: t18 = x^0x3eeb0416684d19
t18.Mul(&x, t18)
// Step 90: t18 = x^0x1f75820b34268c800
for s := 0; s < 11; s++ {
t18.Square(t18)
}
// Step 91: t18 = x^0x1f75820b34268c829
t18.Mul(t0, t18)
// Step 97: t18 = x^0x7dd6082cd09a320a40
for s := 0; s < 6; s++ {
t18.Square(t18)
}
// Step 98: t17 = x^0x7dd6082cd09a320a79
t17.Mul(t17, t18)
// Step 105: t17 = x^0x3eeb0416684d19053c80
for s := 0; s < 7; s++ {
t17.Square(t17)
}
// Step 106: t16 = x^0x3eeb0416684d19053cb5
t16.Mul(t16, t17)
// Step 110: t16 = x^0x3eeb0416684d19053cb50
for s := 0; s < 4; s++ {
t16.Square(t16)
}
// Step 111: t16 = x^0x3eeb0416684d19053cb5d
t16.Mul(t9, t16)
// Step 117: t16 = x^0xfbac1059a1346414f2d740
for s := 0; s < 6; s++ {
t16.Square(t16)
}
// Step 118: t15 = x^0xfbac1059a1346414f2d749
t15.Mul(t15, t16)
// Step 130: t15 = x^0xfbac1059a1346414f2d749000
for s := 0; s < 12; s++ {
t15.Square(t15)
}
// Step 131: t15 = x^0xfbac1059a1346414f2d74903b
t15.Mul(t5, t15)
// Step 137: t15 = x^0x3eeb0416684d19053cb5d240ec0
for s := 0; s < 6; s++ {
t15.Square(t15)
}
// Step 138: t15 = x^0x3eeb0416684d19053cb5d240ed1
t15.Mul(t3, t15)
// Step 149: t15 = x^0x1f75820b34268c829e5ae920768800
for s := 0; s < 11; s++ {
t15.Square(t15)
}
// Step 150: t15 = x^0x1f75820b34268c829e5ae92076883d
t15.Mul(t13, t15)
// Step 156: t15 = x^0x7dd6082cd09a320a796ba481da20f40
for s := 0; s < 6; s++ {
t15.Square(t15)
}
// Step 157: t15 = x^0x7dd6082cd09a320a796ba481da20f45
t15.Mul(z, t15)
// Step 162: t15 = x^0xfbac1059a1346414f2d74903b441e8a0
for s := 0; s < 5; s++ {
t15.Square(t15)
}
// Step 163: t15 = x^0xfbac1059a1346414f2d74903b441e8a1
t15.Mul(&x, t15)
// Step 174: t15 = x^0x7dd6082cd09a320a796ba481da20f450800
for s := 0; s < 11; s++ {
t15.Square(t15)
}
// Step 175: t14 = x^0x7dd6082cd09a320a796ba481da20f45080b
t14.Mul(t14, t15)
// Step 183: t14 = x^0x7dd6082cd09a320a796ba481da20f45080b00
for s := 0; s < 8; s++ {
t14.Square(t14)
}
// Step 184: t13 = x^0x7dd6082cd09a320a796ba481da20f45080b3d
t13.Mul(t13, t14)
// Step 190: t13 = x^0x1f75820b34268c829e5ae92076883d14202cf40
for s := 0; s < 6; s++ {
t13.Square(t13)
}
// Step 191: t13 = x^0x1f75820b34268c829e5ae92076883d14202cf5b
t13.Mul(t10, t13)
// Step 199: t13 = x^0x1f75820b34268c829e5ae92076883d14202cf5b00
for s := 0; s < 8; s++ {
t13.Square(t13)
}
// Step 200: t13 = x^0x1f75820b34268c829e5ae92076883d14202cf5b23
t13.Mul(t12, t13)
// Step 205: t13 = x^0x3eeb0416684d19053cb5d240ed107a284059eb6460
for s := 0; s < 5; s++ {
t13.Square(t13)
}
// Step 206: t13 = x^0x3eeb0416684d19053cb5d240ed107a284059eb6471
t13.Mul(t3, t13)
// Step 218: t13 = x^0x3eeb0416684d19053cb5d240ed107a284059eb6471000
for s := 0; s < 12; s++ {
t13.Square(t13)
}
// Step 219: t12 = x^0x3eeb0416684d19053cb5d240ed107a284059eb6471023
t12.Mul(t12, t13)
// Step 226: t12 = x^0x1f75820b34268c829e5ae92076883d14202cf5b23881180
for s := 0; s < 7; s++ {
t12.Square(t12)
}
// Step 227: t12 = x^0x1f75820b34268c829e5ae92076883d14202cf5b23881193
t12.Mul(t1, t12)
// Step 233: t12 = x^0x7dd6082cd09a320a796ba481da20f45080b3d6c8e20464c0
for s := 0; s < 6; s++ {
t12.Square(t12)
}
// Step 234: t12 = x^0x7dd6082cd09a320a796ba481da20f45080b3d6c8e20464d3
t12.Mul(t1, t12)
// Step 247: t12 = x^0xfbac1059a1346414f2d74903b441e8a10167ad91c408c9a6000
for s := 0; s < 13; s++ {
t12.Square(t12)
}
// Step 248: t11 = x^0xfbac1059a1346414f2d74903b441e8a10167ad91c408c9a6037
t11.Mul(t11, t12)
// Step 257: t11 = x^0x1f75820b34268c829e5ae92076883d14202cf5b238811934c06e00
for s := 0; s < 9; s++ {
t11.Square(t11)
}
// Step 258: t10 = x^0x1f75820b34268c829e5ae92076883d14202cf5b238811934c06e1b
t10.Mul(t10, t11)
// Step 267: t10 = x^0x3eeb0416684d19053cb5d240ed107a284059eb647102326980dc3600
for s := 0; s < 9; s++ {
t10.Square(t10)
}
// Step 268: t9 = x^0x3eeb0416684d19053cb5d240ed107a284059eb647102326980dc360d
t9.Mul(t9, t10)
// Step 278: t9 = x^0xfbac1059a1346414f2d74903b441e8a10167ad91c408c9a60370d83400
for s := 0; s < 10; s++ {
t9.Square(t9)
}
// Step 279: t9 = x^0xfbac1059a1346414f2d74903b441e8a10167ad91c408c9a60370d83429
t9.Mul(t0, t9)
// Step 287: t9 = x^0xfbac1059a1346414f2d74903b441e8a10167ad91c408c9a60370d8342900
for s := 0; s < 8; s++ {
t9.Square(t9)
}
// Step 288: t8 = x^0xfbac1059a1346414f2d74903b441e8a10167ad91c408c9a60370d8342927
t8.Mul(t8, t9)
// Step 290: t8 = x^0x3eeb0416684d19053cb5d240ed107a284059eb647102326980dc360d0a49c
for s := 0; s < 2; s++ {
t8.Square(t8)
}
// Step 291: t8 = x^0x3eeb0416684d19053cb5d240ed107a284059eb647102326980dc360d0a49d
t8.Mul(&x, t8)
// Step 299: t8 = x^0x3eeb0416684d19053cb5d240ed107a284059eb647102326980dc360d0a49d00
for s := 0; s < 8; s++ {
t8.Square(t8)
}
// Step 300: t8 = x^0x3eeb0416684d19053cb5d240ed107a284059eb647102326980dc360d0a49d7f
t8.Mul(t6, t8)
// Step 302: t8 = x^0xfbac1059a1346414f2d74903b441e8a10167ad91c408c9a60370d83429275fc
for s := 0; s < 2; s++ {
t8.Square(t8)
}
// Step 303: t8 = x^0xfbac1059a1346414f2d74903b441e8a10167ad91c408c9a60370d83429275ff
t8.Mul(t2, t8)
// Step 310: t8 = x^0x7dd6082cd09a320a796ba481da20f45080b3d6c8e20464d301b86c1a1493aff80
for s := 0; s < 7; s++ {
t8.Square(t8)
}
// Step 311: t7 = x^0x7dd6082cd09a320a796ba481da20f45080b3d6c8e20464d301b86c1a1493aff9d
t7.Mul(t7, t8)
// Step 314: t7 = x^0x3eeb0416684d19053cb5d240ed107a284059eb647102326980dc360d0a49d7fce8
for s := 0; s < 3; s++ {
t7.Square(t7)
}
// Step 315: t7 = x^0x3eeb0416684d19053cb5d240ed107a284059eb647102326980dc360d0a49d7fce9
t7.Mul(&x, t7)
// Step 323: t7 = x^0x3eeb0416684d19053cb5d240ed107a284059eb647102326980dc360d0a49d7fce900
for s := 0; s < 8; s++ {
t7.Square(t7)
}
// Step 324: t6 = x^0x3eeb0416684d19053cb5d240ed107a284059eb647102326980dc360d0a49d7fce97f
t6.Mul(t6, t7)
// Step 331: t6 = x^0x1f75820b34268c829e5ae92076883d14202cf5b238811934c06e1b068524ebfe74bf80
for s := 0; s < 7; s++ {
t6.Square(t6)
}
// Step 332: t5 = x^0x1f75820b34268c829e5ae92076883d14202cf5b238811934c06e1b068524ebfe74bfbb
t5.Mul(t5, t6)
// Step 338: t5 = x^0x7dd6082cd09a320a796ba481da20f45080b3d6c8e20464d301b86c1a1493aff9d2feec0
for s := 0; s < 6; s++ {
t5.Square(t5)
}
// Step 339: t4 = x^0x7dd6082cd09a320a796ba481da20f45080b3d6c8e20464d301b86c1a1493aff9d2feed5
t4.Mul(t4, t5)
// Step 349: t4 = x^0x1f75820b34268c829e5ae92076883d14202cf5b238811934c06e1b068524ebfe74bfbb5400
for s := 0; s < 10; s++ {
t4.Square(t4)
}
// Step 350: t3 = x^0x1f75820b34268c829e5ae92076883d14202cf5b238811934c06e1b068524ebfe74bfbb5411
t3.Mul(t3, t4)
// Step 353: t3 = x^0xfbac1059a1346414f2d74903b441e8a10167ad91c408c9a60370d83429275ff3a5fddaa088
for s := 0; s < 3; s++ {
t3.Square(t3)
}
// Step 354: t2 = x^0xfbac1059a1346414f2d74903b441e8a10167ad91c408c9a60370d83429275ff3a5fddaa08b
t2.Mul(t2, t3)
// Step 377: t2 = x^0x7dd6082cd09a320a796ba481da20f45080b3d6c8e20464d301b86c1a1493aff9d2feed5045800000
for s := 0; s < 23; s++ {
t2.Square(t2)
}
// Step 378: t1 = x^0x7dd6082cd09a320a796ba481da20f45080b3d6c8e20464d301b86c1a1493aff9d2feed5045800013
t1.Mul(t1, t2)
// Step 386: t1 = x^0x7dd6082cd09a320a796ba481da20f45080b3d6c8e20464d301b86c1a1493aff9d2feed504580001300
for s := 0; s < 8; s++ {
t1.Square(t1)
}
// Step 387: t0 = x^0x7dd6082cd09a320a796ba481da20f45080b3d6c8e20464d301b86c1a1493aff9d2feed504580001329
t0.Mul(t0, t1)
// Step 393: t0 = x^0x1f75820b34268c829e5ae92076883d14202cf5b238811934c06e1b068524ebfe74bfbb5411600004ca40
for s := 0; s < 6; s++ {
t0.Square(t0)
}
// Step 394: z = x^0x1f75820b34268c829e5ae92076883d14202cf5b238811934c06e1b068524ebfe74bfbb5411600004ca45
z.Mul(z, t0)
// Step 397: z = x^0xfbac1059a1346414f2d74903b441e8a10167ad91c408c9a60370d83429275ff3a5fddaa08b0000265228
for s := 0; s < 3; s++ {
z.Square(z)
}
return z
}
// expByLegendreExp is equivalent to z.Exp(x, 1f75820b34268c829e5ae92076883d14202cf5b238811934c06e1b068524ebfe74bfbb5411600004ca4510000000000)
//
// uses github.com/mmcloughlin/addchain v0.4.0 to generate a shorter addition chain
func (z *Element) expByLegendreExp(x Element) *Element {
// addition chain:
//
// _10 = 2*1
// _11 = 1 + _10
// _101 = _10 + _11
// _110 = 1 + _101
// _1001 = _11 + _110
// _1011 = _10 + _1001
// _1100 = 1 + _1011
// _1101 = 1 + _1100
// _10001 = _101 + _1100
// _10011 = _10 + _10001
// _10101 = _10 + _10011
// _11011 = _110 + _10101
// _11101 = _10 + _11011
// _100011 = _110 + _11101
// _100111 = _1100 + _11011
// _101001 = _10 + _100111
// _110101 = _1100 + _101001
// _110111 = _10 + _110101
// _111001 = _10 + _110111
// _111011 = _10 + _111001
// _111101 = _10 + _111011
// _111111 = _10 + _111101
// _1111100 = _111101 + _111111
// _1111111 = _11 + _1111100
// i39 = ((_1111100 << 4 + _11101) << 3 + _11) << 6
// i57 = ((1 + i39) << 9 + _1011) << 6 + _1101
// i78 = ((i57 << 9 + _10011) << 7 + _100011) << 3
// i98 = ((1 + i78) << 11 + _101001) << 6 + _111001
// i117 = ((i98 << 7 + _110101) << 4 + _1101) << 6
// i138 = ((_1001 + i117) << 12 + _111011) << 6 + _10001
// i162 = ((i138 << 11 + _111101) << 6 + _101) << 5
// i184 = ((1 + i162) << 11 + _1011) << 8 + _111101
// i205 = ((i184 << 6 + _11011) << 8 + _100011) << 5
// i227 = ((_10001 + i205) << 12 + _100011) << 7 + _10011
// i257 = ((i227 << 6 + _10011) << 13 + _110111) << 9
// i279 = ((_11011 + i257) << 9 + _1101) << 10 + _101001
// i299 = ((i279 << 8 + _100111) << 2 + 1) << 8
// i311 = ((_1111111 + i299) << 2 + _11) << 7 + _11101
// i331 = ((i311 << 3 + 1) << 8 + _1111111) << 7
// i350 = ((_111011 + i331) << 6 + _10101) << 10 + _10001
// i386 = ((i350 << 3 + _11) << 23 + _10011) << 8
// i399 = ((_101001 + i386) << 6 + _101) << 4 + 1
// return i399 << 40
//
// Operations: 371 squares 68 multiplies
// Allocate Temporaries.
var (
t0 = new(Element)
t1 = new(Element)
t2 = new(Element)
t3 = new(Element)
t4 = new(Element)
t5 = new(Element)
t6 = new(Element)
t7 = new(Element)
t8 = new(Element)
t9 = new(Element)
t10 = new(Element)
t11 = new(Element)
t12 = new(Element)
t13 = new(Element)
t14 = new(Element)
t15 = new(Element)
t16 = new(Element)
t17 = new(Element)
t18 = new(Element)
)
// var t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18 Element
// Step 1: t6 = x^0x2
t6.Square(&x)
// Step 2: t2 = x^0x3
t2.Mul(&x, t6)
// Step 3: z = x^0x5
z.Mul(t6, t2)
// Step 4: t0 = x^0x6
t0.Mul(&x, z)
// Step 5: t15 = x^0x9
t15.Mul(t2, t0)
// Step 6: t14 = x^0xb
t14.Mul(t6, t15)
// Step 7: t5 = x^0xc
t5.Mul(&x, t14)
// Step 8: t9 = x^0xd
t9.Mul(&x, t5)
// Step 9: t3 = x^0x11
t3.Mul(z, t5)
// Step 10: t1 = x^0x13
t1.Mul(t6, t3)
// Step 11: t4 = x^0x15
t4.Mul(t6, t1)
// Step 12: t10 = x^0x1b
t10.Mul(t0, t4)
// Step 13: t7 = x^0x1d
t7.Mul(t6, t10)
// Step 14: t12 = x^0x23
t12.Mul(t0, t7)
// Step 15: t8 = x^0x27
t8.Mul(t5, t10)
// Step 16: t0 = x^0x29
t0.Mul(t6, t8)
// Step 17: t16 = x^0x35
t16.Mul(t5, t0)
// Step 18: t11 = x^0x37
t11.Mul(t6, t16)
// Step 19: t17 = x^0x39
t17.Mul(t6, t11)
// Step 20: t5 = x^0x3b
t5.Mul(t6, t17)
// Step 21: t13 = x^0x3d
t13.Mul(t6, t5)
// Step 22: t6 = x^0x3f
t6.Mul(t6, t13)
// Step 23: t18 = x^0x7c
t18.Mul(t13, t6)
// Step 24: t6 = x^0x7f
t6.Mul(t2, t18)
// Step 28: t18 = x^0x7c0
for s := 0; s < 4; s++ {
t18.Square(t18)
}
// Step 29: t18 = x^0x7dd
t18.Mul(t7, t18)
// Step 32: t18 = x^0x3ee8
for s := 0; s < 3; s++ {
t18.Square(t18)
}
// Step 33: t18 = x^0x3eeb
t18.Mul(t2, t18)
// Step 39: t18 = x^0xfbac0
for s := 0; s < 6; s++ {
t18.Square(t18)
}
// Step 40: t18 = x^0xfbac1
t18.Mul(&x, t18)
// Step 49: t18 = x^0x1f758200
for s := 0; s < 9; s++ {
t18.Square(t18)
}
// Step 50: t18 = x^0x1f75820b
t18.Mul(t14, t18)
// Step 56: t18 = x^0x7dd6082c0
for s := 0; s < 6; s++ {
t18.Square(t18)
}
// Step 57: t18 = x^0x7dd6082cd
t18.Mul(t9, t18)
// Step 66: t18 = x^0xfbac1059a00
for s := 0; s < 9; s++ {
t18.Square(t18)
}
// Step 67: t18 = x^0xfbac1059a13
t18.Mul(t1, t18)
// Step 74: t18 = x^0x7dd6082cd0980
for s := 0; s < 7; s++ {
t18.Square(t18)
}
// Step 75: t18 = x^0x7dd6082cd09a3
t18.Mul(t12, t18)
// Step 78: t18 = x^0x3eeb0416684d18
for s := 0; s < 3; s++ {
t18.Square(t18)
}
// Step 79: t18 = x^0x3eeb0416684d19
t18.Mul(&x, t18)
// Step 90: t18 = x^0x1f75820b34268c800
for s := 0; s < 11; s++ {
t18.Square(t18)
}
// Step 91: t18 = x^0x1f75820b34268c829
t18.Mul(t0, t18)
// Step 97: t18 = x^0x7dd6082cd09a320a40
for s := 0; s < 6; s++ {
t18.Square(t18)
}
// Step 98: t17 = x^0x7dd6082cd09a320a79
t17.Mul(t17, t18)
// Step 105: t17 = x^0x3eeb0416684d19053c80
for s := 0; s < 7; s++ {
t17.Square(t17)
}
// Step 106: t16 = x^0x3eeb0416684d19053cb5
t16.Mul(t16, t17)
// Step 110: t16 = x^0x3eeb0416684d19053cb50
for s := 0; s < 4; s++ {
t16.Square(t16)
}
// Step 111: t16 = x^0x3eeb0416684d19053cb5d
t16.Mul(t9, t16)
// Step 117: t16 = x^0xfbac1059a1346414f2d740
for s := 0; s < 6; s++ {
t16.Square(t16)
}
// Step 118: t15 = x^0xfbac1059a1346414f2d749
t15.Mul(t15, t16)
// Step 130: t15 = x^0xfbac1059a1346414f2d749000
for s := 0; s < 12; s++ {
t15.Square(t15)
}
// Step 131: t15 = x^0xfbac1059a1346414f2d74903b
t15.Mul(t5, t15)
// Step 137: t15 = x^0x3eeb0416684d19053cb5d240ec0
for s := 0; s < 6; s++ {
t15.Square(t15)
}
// Step 138: t15 = x^0x3eeb0416684d19053cb5d240ed1
t15.Mul(t3, t15)
// Step 149: t15 = x^0x1f75820b34268c829e5ae920768800
for s := 0; s < 11; s++ {
t15.Square(t15)
}
// Step 150: t15 = x^0x1f75820b34268c829e5ae92076883d
t15.Mul(t13, t15)
// Step 156: t15 = x^0x7dd6082cd09a320a796ba481da20f40
for s := 0; s < 6; s++ {
t15.Square(t15)
}
// Step 157: t15 = x^0x7dd6082cd09a320a796ba481da20f45
t15.Mul(z, t15)
// Step 162: t15 = x^0xfbac1059a1346414f2d74903b441e8a0
for s := 0; s < 5; s++ {
t15.Square(t15)
}
// Step 163: t15 = x^0xfbac1059a1346414f2d74903b441e8a1
t15.Mul(&x, t15)
// Step 174: t15 = x^0x7dd6082cd09a320a796ba481da20f450800
for s := 0; s < 11; s++ {
t15.Square(t15)
}
// Step 175: t14 = x^0x7dd6082cd09a320a796ba481da20f45080b
t14.Mul(t14, t15)
// Step 183: t14 = x^0x7dd6082cd09a320a796ba481da20f45080b00
for s := 0; s < 8; s++ {
t14.Square(t14)
}
// Step 184: t13 = x^0x7dd6082cd09a320a796ba481da20f45080b3d
t13.Mul(t13, t14)
// Step 190: t13 = x^0x1f75820b34268c829e5ae92076883d14202cf40
for s := 0; s < 6; s++ {
t13.Square(t13)
}
// Step 191: t13 = x^0x1f75820b34268c829e5ae92076883d14202cf5b
t13.Mul(t10, t13)
// Step 199: t13 = x^0x1f75820b34268c829e5ae92076883d14202cf5b00
for s := 0; s < 8; s++ {
t13.Square(t13)
}
// Step 200: t13 = x^0x1f75820b34268c829e5ae92076883d14202cf5b23
t13.Mul(t12, t13)
// Step 205: t13 = x^0x3eeb0416684d19053cb5d240ed107a284059eb6460
for s := 0; s < 5; s++ {
t13.Square(t13)
}
// Step 206: t13 = x^0x3eeb0416684d19053cb5d240ed107a284059eb6471
t13.Mul(t3, t13)
// Step 218: t13 = x^0x3eeb0416684d19053cb5d240ed107a284059eb6471000
for s := 0; s < 12; s++ {
t13.Square(t13)
}
// Step 219: t12 = x^0x3eeb0416684d19053cb5d240ed107a284059eb6471023
t12.Mul(t12, t13)
// Step 226: t12 = x^0x1f75820b34268c829e5ae92076883d14202cf5b23881180
for s := 0; s < 7; s++ {
t12.Square(t12)
}
// Step 227: t12 = x^0x1f75820b34268c829e5ae92076883d14202cf5b23881193
t12.Mul(t1, t12)
// Step 233: t12 = x^0x7dd6082cd09a320a796ba481da20f45080b3d6c8e20464c0
for s := 0; s < 6; s++ {
t12.Square(t12)
}
// Step 234: t12 = x^0x7dd6082cd09a320a796ba481da20f45080b3d6c8e20464d3
t12.Mul(t1, t12)
// Step 247: t12 = x^0xfbac1059a1346414f2d74903b441e8a10167ad91c408c9a6000
for s := 0; s < 13; s++ {
t12.Square(t12)
}
// Step 248: t11 = x^0xfbac1059a1346414f2d74903b441e8a10167ad91c408c9a6037
t11.Mul(t11, t12)
// Step 257: t11 = x^0x1f75820b34268c829e5ae92076883d14202cf5b238811934c06e00
for s := 0; s < 9; s++ {
t11.Square(t11)
}
// Step 258: t10 = x^0x1f75820b34268c829e5ae92076883d14202cf5b238811934c06e1b
t10.Mul(t10, t11)
// Step 267: t10 = x^0x3eeb0416684d19053cb5d240ed107a284059eb647102326980dc3600
for s := 0; s < 9; s++ {
t10.Square(t10)
}
// Step 268: t9 = x^0x3eeb0416684d19053cb5d240ed107a284059eb647102326980dc360d
t9.Mul(t9, t10)
// Step 278: t9 = x^0xfbac1059a1346414f2d74903b441e8a10167ad91c408c9a60370d83400
for s := 0; s < 10; s++ {
t9.Square(t9)
}
// Step 279: t9 = x^0xfbac1059a1346414f2d74903b441e8a10167ad91c408c9a60370d83429
t9.Mul(t0, t9)
// Step 287: t9 = x^0xfbac1059a1346414f2d74903b441e8a10167ad91c408c9a60370d8342900
for s := 0; s < 8; s++ {
t9.Square(t9)
}
// Step 288: t8 = x^0xfbac1059a1346414f2d74903b441e8a10167ad91c408c9a60370d8342927
t8.Mul(t8, t9)
// Step 290: t8 = x^0x3eeb0416684d19053cb5d240ed107a284059eb647102326980dc360d0a49c
for s := 0; s < 2; s++ {
t8.Square(t8)
}
// Step 291: t8 = x^0x3eeb0416684d19053cb5d240ed107a284059eb647102326980dc360d0a49d
t8.Mul(&x, t8)
// Step 299: t8 = x^0x3eeb0416684d19053cb5d240ed107a284059eb647102326980dc360d0a49d00
for s := 0; s < 8; s++ {
t8.Square(t8)
}
// Step 300: t8 = x^0x3eeb0416684d19053cb5d240ed107a284059eb647102326980dc360d0a49d7f
t8.Mul(t6, t8)
// Step 302: t8 = x^0xfbac1059a1346414f2d74903b441e8a10167ad91c408c9a60370d83429275fc
for s := 0; s < 2; s++ {
t8.Square(t8)
}
// Step 303: t8 = x^0xfbac1059a1346414f2d74903b441e8a10167ad91c408c9a60370d83429275ff
t8.Mul(t2, t8)
// Step 310: t8 = x^0x7dd6082cd09a320a796ba481da20f45080b3d6c8e20464d301b86c1a1493aff80
for s := 0; s < 7; s++ {
t8.Square(t8)
}
// Step 311: t7 = x^0x7dd6082cd09a320a796ba481da20f45080b3d6c8e20464d301b86c1a1493aff9d
t7.Mul(t7, t8)
// Step 314: t7 = x^0x3eeb0416684d19053cb5d240ed107a284059eb647102326980dc360d0a49d7fce8
for s := 0; s < 3; s++ {
t7.Square(t7)
}
// Step 315: t7 = x^0x3eeb0416684d19053cb5d240ed107a284059eb647102326980dc360d0a49d7fce9
t7.Mul(&x, t7)
// Step 323: t7 = x^0x3eeb0416684d19053cb5d240ed107a284059eb647102326980dc360d0a49d7fce900
for s := 0; s < 8; s++ {
t7.Square(t7)
}
// Step 324: t6 = x^0x3eeb0416684d19053cb5d240ed107a284059eb647102326980dc360d0a49d7fce97f
t6.Mul(t6, t7)
// Step 331: t6 = x^0x1f75820b34268c829e5ae92076883d14202cf5b238811934c06e1b068524ebfe74bf80
for s := 0; s < 7; s++ {
t6.Square(t6)
}
// Step 332: t5 = x^0x1f75820b34268c829e5ae92076883d14202cf5b238811934c06e1b068524ebfe74bfbb
t5.Mul(t5, t6)
// Step 338: t5 = x^0x7dd6082cd09a320a796ba481da20f45080b3d6c8e20464d301b86c1a1493aff9d2feec0
for s := 0; s < 6; s++ {
t5.Square(t5)
}
// Step 339: t4 = x^0x7dd6082cd09a320a796ba481da20f45080b3d6c8e20464d301b86c1a1493aff9d2feed5
t4.Mul(t4, t5)
// Step 349: t4 = x^0x1f75820b34268c829e5ae92076883d14202cf5b238811934c06e1b068524ebfe74bfbb5400
for s := 0; s < 10; s++ {
t4.Square(t4)
}
// Step 350: t3 = x^0x1f75820b34268c829e5ae92076883d14202cf5b238811934c06e1b068524ebfe74bfbb5411
t3.Mul(t3, t4)
// Step 353: t3 = x^0xfbac1059a1346414f2d74903b441e8a10167ad91c408c9a60370d83429275ff3a5fddaa088
for s := 0; s < 3; s++ {
t3.Square(t3)
}
// Step 354: t2 = x^0xfbac1059a1346414f2d74903b441e8a10167ad91c408c9a60370d83429275ff3a5fddaa08b
t2.Mul(t2, t3)