/
element_exp.go
695 lines (541 loc) · 16.3 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
// 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, 1fffffffffffffffffffffffffffffffd755db9cd5e9140777fa4bd19a06c82)
//
// 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
// _111 = _10 + _101
// _1001 = _10 + _111
// _1011 = _10 + _1001
// _1101 = _10 + _1011
// _1111 = _10 + _1101
// _1111000 = _1111 << 3
// _1111111 = _111 + _1111000
// _11111110 = 2*_1111111
// _11111111 = 1 + _11111110
// i21 = _11111111 << 7
// x15 = _1111111 + i21
// i30 = i21 << 8
// x23 = x15 + i30
// x31 = i30 << 8 + x23
// x32 = 2*x31 + 1
// x64 = x32 << 32 + x32
// x96 = x64 << 32 + x32
// x127 = x96 << 31 + x31
// i154 = ((x127 << 5 + _1011) << 3 + _101) << 4
// i166 = ((_101 + i154) << 4 + _111) << 5 + _1101
// i181 = ((i166 << 2 + _11) << 5 + _111) << 6
// i193 = ((_1101 + i181) << 5 + _1011) << 4 + _1101
// i214 = ((i193 << 3 + 1) << 6 + _101) << 10
// i230 = ((_111 + i214) << 4 + _111) << 9 + _11111111
// i247 = ((i230 << 5 + _1001) << 6 + _1011) << 4
// i261 = ((_1101 + i247) << 5 + _11) << 6 + _1101
// i283 = ((i261 << 10 + _1101) << 4 + _1001) << 6
// return 2*(1 + i283)
//
// Operations: 246 squares 39 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)
)
// var t0,t1,t2,t3,t4,t5,t6,t7,t8 Element
// Step 1: t3 = x^0x2
t3.Square(&x)
// Step 2: t1 = x^0x3
t1.Mul(&x, t3)
// Step 3: t5 = x^0x5
t5.Mul(t3, t1)
// Step 4: t4 = x^0x7
t4.Mul(t3, t5)
// Step 5: z = x^0x9
z.Mul(t3, t4)
// Step 6: t2 = x^0xb
t2.Mul(t3, z)
// Step 7: t0 = x^0xd
t0.Mul(t3, t2)
// Step 8: t3 = x^0xf
t3.Mul(t3, t0)
// Step 11: t3 = x^0x78
for s := 0; s < 3; s++ {
t3.Square(t3)
}
// Step 12: t6 = x^0x7f
t6.Mul(t4, t3)
// Step 13: t3 = x^0xfe
t3.Square(t6)
// Step 14: t3 = x^0xff
t3.Mul(&x, t3)
// Step 21: t7 = x^0x7f80
t7.Square(t3)
for s := 1; s < 7; s++ {
t7.Square(t7)
}
// Step 22: t6 = x^0x7fff
t6.Mul(t6, t7)
// Step 30: t7 = x^0x7f8000
for s := 0; s < 8; s++ {
t7.Square(t7)
}
// Step 31: t6 = x^0x7fffff
t6.Mul(t6, t7)
// Step 39: t7 = x^0x7f800000
for s := 0; s < 8; s++ {
t7.Square(t7)
}
// Step 40: t6 = x^0x7fffffff
t6.Mul(t6, t7)
// Step 41: t7 = x^0xfffffffe
t7.Square(t6)
// Step 42: t7 = x^0xffffffff
t7.Mul(&x, t7)
// Step 74: t8 = x^0xffffffff00000000
t8.Square(t7)
for s := 1; s < 32; s++ {
t8.Square(t8)
}
// Step 75: t8 = x^0xffffffffffffffff
t8.Mul(t7, t8)
// Step 107: t8 = x^0xffffffffffffffff00000000
for s := 0; s < 32; s++ {
t8.Square(t8)
}
// Step 108: t7 = x^0xffffffffffffffffffffffff
t7.Mul(t7, t8)
// Step 139: t7 = x^0x7fffffffffffffffffffffff80000000
for s := 0; s < 31; s++ {
t7.Square(t7)
}
// Step 140: t6 = x^0x7fffffffffffffffffffffffffffffff
t6.Mul(t6, t7)
// Step 145: t6 = x^0xfffffffffffffffffffffffffffffffe0
for s := 0; s < 5; s++ {
t6.Square(t6)
}
// Step 146: t6 = x^0xfffffffffffffffffffffffffffffffeb
t6.Mul(t2, t6)
// Step 149: t6 = x^0x7fffffffffffffffffffffffffffffff58
for s := 0; s < 3; s++ {
t6.Square(t6)
}
// Step 150: t6 = x^0x7fffffffffffffffffffffffffffffff5d
t6.Mul(t5, t6)
// Step 154: t6 = x^0x7fffffffffffffffffffffffffffffff5d0
for s := 0; s < 4; s++ {
t6.Square(t6)
}
// Step 155: t6 = x^0x7fffffffffffffffffffffffffffffff5d5
t6.Mul(t5, t6)
// Step 159: t6 = x^0x7fffffffffffffffffffffffffffffff5d50
for s := 0; s < 4; s++ {
t6.Square(t6)
}
// Step 160: t6 = x^0x7fffffffffffffffffffffffffffffff5d57
t6.Mul(t4, t6)
// Step 165: t6 = x^0xfffffffffffffffffffffffffffffffebaae0
for s := 0; s < 5; s++ {
t6.Square(t6)
}
// Step 166: t6 = x^0xfffffffffffffffffffffffffffffffebaaed
t6.Mul(t0, t6)
// Step 168: t6 = x^0x3fffffffffffffffffffffffffffffffaeabb4
for s := 0; s < 2; s++ {
t6.Square(t6)
}
// Step 169: t6 = x^0x3fffffffffffffffffffffffffffffffaeabb7
t6.Mul(t1, t6)
// Step 174: t6 = x^0x7fffffffffffffffffffffffffffffff5d576e0
for s := 0; s < 5; s++ {
t6.Square(t6)
}
// Step 175: t6 = x^0x7fffffffffffffffffffffffffffffff5d576e7
t6.Mul(t4, t6)
// Step 181: t6 = x^0x1fffffffffffffffffffffffffffffffd755db9c0
for s := 0; s < 6; s++ {
t6.Square(t6)
}
// Step 182: t6 = x^0x1fffffffffffffffffffffffffffffffd755db9cd
t6.Mul(t0, t6)
// Step 187: t6 = x^0x3fffffffffffffffffffffffffffffffaeabb739a0
for s := 0; s < 5; s++ {
t6.Square(t6)
}
// Step 188: t6 = x^0x3fffffffffffffffffffffffffffffffaeabb739ab
t6.Mul(t2, t6)
// Step 192: t6 = x^0x3fffffffffffffffffffffffffffffffaeabb739ab0
for s := 0; s < 4; s++ {
t6.Square(t6)
}
// Step 193: t6 = x^0x3fffffffffffffffffffffffffffffffaeabb739abd
t6.Mul(t0, t6)
// Step 196: t6 = x^0x1fffffffffffffffffffffffffffffffd755db9cd5e8
for s := 0; s < 3; s++ {
t6.Square(t6)
}
// Step 197: t6 = x^0x1fffffffffffffffffffffffffffffffd755db9cd5e9
t6.Mul(&x, t6)
// Step 203: t6 = x^0x7fffffffffffffffffffffffffffffff5d576e7357a40
for s := 0; s < 6; s++ {
t6.Square(t6)
}
// Step 204: t5 = x^0x7fffffffffffffffffffffffffffffff5d576e7357a45
t5.Mul(t5, t6)
// Step 214: t5 = x^0x1fffffffffffffffffffffffffffffffd755db9cd5e91400
for s := 0; s < 10; s++ {
t5.Square(t5)
}
// Step 215: t5 = x^0x1fffffffffffffffffffffffffffffffd755db9cd5e91407
t5.Mul(t4, t5)
// Step 219: t5 = x^0x1fffffffffffffffffffffffffffffffd755db9cd5e914070
for s := 0; s < 4; s++ {
t5.Square(t5)
}
// Step 220: t4 = x^0x1fffffffffffffffffffffffffffffffd755db9cd5e914077
t4.Mul(t4, t5)
// Step 229: t4 = x^0x3fffffffffffffffffffffffffffffffaeabb739abd2280ee00
for s := 0; s < 9; s++ {
t4.Square(t4)
}
// Step 230: t3 = x^0x3fffffffffffffffffffffffffffffffaeabb739abd2280eeff
t3.Mul(t3, t4)
// Step 235: t3 = x^0x7fffffffffffffffffffffffffffffff5d576e7357a4501ddfe0
for s := 0; s < 5; s++ {
t3.Square(t3)
}
// Step 236: t3 = x^0x7fffffffffffffffffffffffffffffff5d576e7357a4501ddfe9
t3.Mul(z, t3)
// Step 242: t3 = x^0x1fffffffffffffffffffffffffffffffd755db9cd5e9140777fa40
for s := 0; s < 6; s++ {
t3.Square(t3)
}
// Step 243: t2 = x^0x1fffffffffffffffffffffffffffffffd755db9cd5e9140777fa4b
t2.Mul(t2, t3)
// Step 247: t2 = x^0x1fffffffffffffffffffffffffffffffd755db9cd5e9140777fa4b0
for s := 0; s < 4; s++ {
t2.Square(t2)
}
// Step 248: t2 = x^0x1fffffffffffffffffffffffffffffffd755db9cd5e9140777fa4bd
t2.Mul(t0, t2)
// Step 253: t2 = x^0x3fffffffffffffffffffffffffffffffaeabb739abd2280eeff497a0
for s := 0; s < 5; s++ {
t2.Square(t2)
}
// Step 254: t1 = x^0x3fffffffffffffffffffffffffffffffaeabb739abd2280eeff497a3
t1.Mul(t1, t2)
// Step 260: t1 = x^0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8c0
for s := 0; s < 6; s++ {
t1.Square(t1)
}
// Step 261: t1 = x^0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd
t1.Mul(t0, t1)
// Step 271: t1 = x^0x3fffffffffffffffffffffffffffffffaeabb739abd2280eeff497a33400
for s := 0; s < 10; s++ {
t1.Square(t1)
}
// Step 272: t0 = x^0x3fffffffffffffffffffffffffffffffaeabb739abd2280eeff497a3340d
t0.Mul(t0, t1)
// Step 276: t0 = x^0x3fffffffffffffffffffffffffffffffaeabb739abd2280eeff497a3340d0
for s := 0; s < 4; s++ {
t0.Square(t0)
}
// Step 277: z = x^0x3fffffffffffffffffffffffffffffffaeabb739abd2280eeff497a3340d9
z.Mul(z, t0)
// Step 283: z = x^0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd03640
for s := 0; s < 6; s++ {
z.Square(z)
}
// Step 284: z = x^0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd03641
z.Mul(&x, z)
// Step 285: z = x^0x1fffffffffffffffffffffffffffffffd755db9cd5e9140777fa4bd19a06c82
z.Square(z)
return z
}
// expByLegendreExp is equivalent to z.Exp(x, 7fffffffffffffffffffffffffffffff5d576e7357a4501ddfe92f46681b20a0)
//
// 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
// _111 = _10 + _101
// _1001 = _10 + _111
// _1011 = _10 + _1001
// _1101 = _10 + _1011
// _1111 = _10 + _1101
// _1111000 = _1111 << 3
// _1111111 = _111 + _1111000
// _11111110 = 2*_1111111
// _11111111 = 1 + _11111110
// i21 = _11111111 << 7
// x15 = _1111111 + i21
// i30 = i21 << 8
// x23 = x15 + i30
// x31 = i30 << 8 + x23
// x32 = 2*x31 + 1
// x64 = x32 << 32 + x32
// x96 = x64 << 32 + x32
// x127 = x96 << 31 + x31
// i154 = ((x127 << 5 + _1011) << 3 + _101) << 4
// i166 = ((_101 + i154) << 4 + _111) << 5 + _1101
// i181 = ((i166 << 2 + _11) << 5 + _111) << 6
// i193 = ((_1101 + i181) << 5 + _1011) << 4 + _1101
// i214 = ((i193 << 3 + 1) << 6 + _101) << 10
// i230 = ((_111 + i214) << 4 + _111) << 9 + _11111111
// i247 = ((i230 << 5 + _1001) << 6 + _1011) << 4
// i261 = ((_1101 + i247) << 5 + _11) << 6 + _1101
// i285 = ((i261 << 10 + _1101) << 4 + _1001) << 8
// return (_101 + i285) << 5
//
// Operations: 252 squares 39 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)
)
// var t0,t1,t2,t3,t4,t5,t6,t7,t8 Element
// Step 1: t4 = x^0x2
t4.Square(&x)
// Step 2: t2 = x^0x3
t2.Mul(&x, t4)
// Step 3: z = x^0x5
z.Mul(t4, t2)
// Step 4: t5 = x^0x7
t5.Mul(t4, z)
// Step 5: t0 = x^0x9
t0.Mul(t4, t5)
// Step 6: t3 = x^0xb
t3.Mul(t4, t0)
// Step 7: t1 = x^0xd
t1.Mul(t4, t3)
// Step 8: t4 = x^0xf
t4.Mul(t4, t1)
// Step 11: t4 = x^0x78
for s := 0; s < 3; s++ {
t4.Square(t4)
}
// Step 12: t6 = x^0x7f
t6.Mul(t5, t4)
// Step 13: t4 = x^0xfe
t4.Square(t6)
// Step 14: t4 = x^0xff
t4.Mul(&x, t4)
// Step 21: t7 = x^0x7f80
t7.Square(t4)
for s := 1; s < 7; s++ {
t7.Square(t7)
}
// Step 22: t6 = x^0x7fff
t6.Mul(t6, t7)
// Step 30: t7 = x^0x7f8000
for s := 0; s < 8; s++ {
t7.Square(t7)
}
// Step 31: t6 = x^0x7fffff
t6.Mul(t6, t7)
// Step 39: t7 = x^0x7f800000
for s := 0; s < 8; s++ {
t7.Square(t7)
}
// Step 40: t6 = x^0x7fffffff
t6.Mul(t6, t7)
// Step 41: t7 = x^0xfffffffe
t7.Square(t6)
// Step 42: t7 = x^0xffffffff
t7.Mul(&x, t7)
// Step 74: t8 = x^0xffffffff00000000
t8.Square(t7)
for s := 1; s < 32; s++ {
t8.Square(t8)
}
// Step 75: t8 = x^0xffffffffffffffff
t8.Mul(t7, t8)
// Step 107: t8 = x^0xffffffffffffffff00000000
for s := 0; s < 32; s++ {
t8.Square(t8)
}
// Step 108: t7 = x^0xffffffffffffffffffffffff
t7.Mul(t7, t8)
// Step 139: t7 = x^0x7fffffffffffffffffffffff80000000
for s := 0; s < 31; s++ {
t7.Square(t7)
}
// Step 140: t6 = x^0x7fffffffffffffffffffffffffffffff
t6.Mul(t6, t7)
// Step 145: t6 = x^0xfffffffffffffffffffffffffffffffe0
for s := 0; s < 5; s++ {
t6.Square(t6)
}
// Step 146: t6 = x^0xfffffffffffffffffffffffffffffffeb
t6.Mul(t3, t6)
// Step 149: t6 = x^0x7fffffffffffffffffffffffffffffff58
for s := 0; s < 3; s++ {
t6.Square(t6)
}
// Step 150: t6 = x^0x7fffffffffffffffffffffffffffffff5d
t6.Mul(z, t6)
// Step 154: t6 = x^0x7fffffffffffffffffffffffffffffff5d0
for s := 0; s < 4; s++ {
t6.Square(t6)
}
// Step 155: t6 = x^0x7fffffffffffffffffffffffffffffff5d5
t6.Mul(z, t6)
// Step 159: t6 = x^0x7fffffffffffffffffffffffffffffff5d50
for s := 0; s < 4; s++ {
t6.Square(t6)
}
// Step 160: t6 = x^0x7fffffffffffffffffffffffffffffff5d57
t6.Mul(t5, t6)
// Step 165: t6 = x^0xfffffffffffffffffffffffffffffffebaae0
for s := 0; s < 5; s++ {
t6.Square(t6)
}
// Step 166: t6 = x^0xfffffffffffffffffffffffffffffffebaaed
t6.Mul(t1, t6)
// Step 168: t6 = x^0x3fffffffffffffffffffffffffffffffaeabb4
for s := 0; s < 2; s++ {
t6.Square(t6)
}
// Step 169: t6 = x^0x3fffffffffffffffffffffffffffffffaeabb7
t6.Mul(t2, t6)
// Step 174: t6 = x^0x7fffffffffffffffffffffffffffffff5d576e0
for s := 0; s < 5; s++ {
t6.Square(t6)
}
// Step 175: t6 = x^0x7fffffffffffffffffffffffffffffff5d576e7
t6.Mul(t5, t6)
// Step 181: t6 = x^0x1fffffffffffffffffffffffffffffffd755db9c0
for s := 0; s < 6; s++ {
t6.Square(t6)
}
// Step 182: t6 = x^0x1fffffffffffffffffffffffffffffffd755db9cd
t6.Mul(t1, t6)
// Step 187: t6 = x^0x3fffffffffffffffffffffffffffffffaeabb739a0
for s := 0; s < 5; s++ {
t6.Square(t6)
}
// Step 188: t6 = x^0x3fffffffffffffffffffffffffffffffaeabb739ab
t6.Mul(t3, t6)
// Step 192: t6 = x^0x3fffffffffffffffffffffffffffffffaeabb739ab0
for s := 0; s < 4; s++ {
t6.Square(t6)
}
// Step 193: t6 = x^0x3fffffffffffffffffffffffffffffffaeabb739abd
t6.Mul(t1, t6)
// Step 196: t6 = x^0x1fffffffffffffffffffffffffffffffd755db9cd5e8
for s := 0; s < 3; s++ {
t6.Square(t6)
}
// Step 197: t6 = x^0x1fffffffffffffffffffffffffffffffd755db9cd5e9
t6.Mul(&x, t6)
// Step 203: t6 = x^0x7fffffffffffffffffffffffffffffff5d576e7357a40
for s := 0; s < 6; s++ {
t6.Square(t6)
}
// Step 204: t6 = x^0x7fffffffffffffffffffffffffffffff5d576e7357a45
t6.Mul(z, t6)
// Step 214: t6 = x^0x1fffffffffffffffffffffffffffffffd755db9cd5e91400
for s := 0; s < 10; s++ {
t6.Square(t6)
}
// Step 215: t6 = x^0x1fffffffffffffffffffffffffffffffd755db9cd5e91407
t6.Mul(t5, t6)
// Step 219: t6 = x^0x1fffffffffffffffffffffffffffffffd755db9cd5e914070
for s := 0; s < 4; s++ {
t6.Square(t6)
}
// Step 220: t5 = x^0x1fffffffffffffffffffffffffffffffd755db9cd5e914077
t5.Mul(t5, t6)
// Step 229: t5 = x^0x3fffffffffffffffffffffffffffffffaeabb739abd2280ee00
for s := 0; s < 9; s++ {
t5.Square(t5)
}
// Step 230: t4 = x^0x3fffffffffffffffffffffffffffffffaeabb739abd2280eeff
t4.Mul(t4, t5)
// Step 235: t4 = x^0x7fffffffffffffffffffffffffffffff5d576e7357a4501ddfe0
for s := 0; s < 5; s++ {
t4.Square(t4)
}
// Step 236: t4 = x^0x7fffffffffffffffffffffffffffffff5d576e7357a4501ddfe9
t4.Mul(t0, t4)
// Step 242: t4 = x^0x1fffffffffffffffffffffffffffffffd755db9cd5e9140777fa40
for s := 0; s < 6; s++ {
t4.Square(t4)
}
// Step 243: t3 = x^0x1fffffffffffffffffffffffffffffffd755db9cd5e9140777fa4b
t3.Mul(t3, t4)
// Step 247: t3 = x^0x1fffffffffffffffffffffffffffffffd755db9cd5e9140777fa4b0
for s := 0; s < 4; s++ {
t3.Square(t3)
}
// Step 248: t3 = x^0x1fffffffffffffffffffffffffffffffd755db9cd5e9140777fa4bd
t3.Mul(t1, t3)
// Step 253: t3 = x^0x3fffffffffffffffffffffffffffffffaeabb739abd2280eeff497a0
for s := 0; s < 5; s++ {
t3.Square(t3)
}
// Step 254: t2 = x^0x3fffffffffffffffffffffffffffffffaeabb739abd2280eeff497a3
t2.Mul(t2, t3)
// Step 260: t2 = x^0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8c0
for s := 0; s < 6; s++ {
t2.Square(t2)
}
// Step 261: t2 = x^0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd
t2.Mul(t1, t2)
// Step 271: t2 = x^0x3fffffffffffffffffffffffffffffffaeabb739abd2280eeff497a33400
for s := 0; s < 10; s++ {
t2.Square(t2)
}
// Step 272: t1 = x^0x3fffffffffffffffffffffffffffffffaeabb739abd2280eeff497a3340d
t1.Mul(t1, t2)
// Step 276: t1 = x^0x3fffffffffffffffffffffffffffffffaeabb739abd2280eeff497a3340d0
for s := 0; s < 4; s++ {
t1.Square(t1)
}
// Step 277: t0 = x^0x3fffffffffffffffffffffffffffffffaeabb739abd2280eeff497a3340d9
t0.Mul(t0, t1)
// Step 285: t0 = x^0x3fffffffffffffffffffffffffffffffaeabb739abd2280eeff497a3340d900
for s := 0; s < 8; s++ {
t0.Square(t0)
}
// Step 286: z = x^0x3fffffffffffffffffffffffffffffffaeabb739abd2280eeff497a3340d905
z.Mul(z, t0)
// Step 291: z = x^0x7fffffffffffffffffffffffffffffff5d576e7357a4501ddfe92f46681b20a0
for s := 0; s < 5; s++ {
z.Square(z)
}
return z
}