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
// generated source. do not edit.
#![allow(non_upper_case_globals, unused_macros, unused_imports)]
use crate::low::macros::*;
// Copyright Amazon.com, Inc. or its affiliates. All Rights Reserved.
// SPDX-License-Identifier: Apache-2.0 OR ISC OR MIT-0
// ----------------------------------------------------------------------------
// Test bignums for coprimality, gcd(x,y) = 1
// Inputs x[m], y[n]; output function return; temporary buffer t[>=2*max(m,n)]
//
// extern uint64_t bignum_coprime(uint64_t m, const uint64_t *x, uint64_t n,
// const uint64_t *y, uint64_t *t);
//
// Test for whether two bignums are coprime (no common factor besides 1).
// This is equivalent to testing if their gcd is 1, but a bit faster than
// doing those two computations separately.
//
// Here bignum x is m digits long, y is n digits long and the temporary
// buffer t needs to be 2 * max(m,n) digits long. The return value is
// 1 if coprime(x,y) and 0 otherwise.
//
// Standard x86-64 ABI: RDI = m, RSI = x, RDX = n, RCX = y, R8 = t, returns RAX
// Microsoft x64 ABI: RCX = m, RDX = x, R8 = n, R9 = y, [RSP+40] = t, returns RAX
// ----------------------------------------------------------------------------
// We get CHUNKSIZE bits per outer iteration, 64 minus a bit for proxy errors
macro_rules! CHUNKSIZE {
() => {
"58"
};
}
// These variables are so fundamental we keep them consistently in registers.
// m is in fact the temporary buffer argument w so use the same register
macro_rules! m {
() => {
"r8"
};
}
macro_rules! n {
() => {
"r15"
};
}
macro_rules! k {
() => {
"r14"
};
}
macro_rules! l {
() => {
"r13"
};
}
// These are kept on the stack since there aren't enough registers
macro_rules! mat_mm {
() => {
"QWORD PTR [rsp]"
};
}
macro_rules! mat_mn {
() => {
"QWORD PTR [rsp + 8]"
};
}
macro_rules! mat_nm {
() => {
"QWORD PTR [rsp + 16]"
};
}
macro_rules! mat_nn {
() => {
"QWORD PTR [rsp + 24]"
};
}
macro_rules! t {
() => {
"QWORD PTR [rsp + 32]"
};
}
macro_rules! evenor {
() => {
"QWORD PTR [rsp + 40]"
};
}
macro_rules! STACKVARSIZE {
() => {
"48"
};
}
// These are shorthands for common temporary register
macro_rules! a {
() => {
"rax"
};
}
macro_rules! b {
() => {
"rbx"
};
}
macro_rules! c {
() => {
"rcx"
};
}
macro_rules! d {
() => {
"rdx"
};
}
macro_rules! i {
() => {
"r9"
};
}
// Temporaries for the top proxy selection part
macro_rules! c1 {
() => {
"r10"
};
}
macro_rules! c2 {
() => {
"r11"
};
}
macro_rules! h1 {
() => {
"r12"
};
}
macro_rules! h2 {
() => {
"rbp"
};
}
macro_rules! l1 {
() => {
"rdi"
};
}
macro_rules! l2 {
() => {
"rsi"
};
}
// Re-use for the actual proxies; m_hi = h1 and n_hi = h2 are assumed
macro_rules! m_hi {
() => {
"r12"
};
}
macro_rules! n_hi {
() => {
"rbp"
};
}
macro_rules! m_lo {
() => {
"rdi"
};
}
macro_rules! n_lo {
() => {
"rsi"
};
}
// Re-use for the matrix entries in the inner loop, though they
// get spilled to the corresponding memory locations mat_...
macro_rules! m_m {
() => {
"r10"
};
}
macro_rules! m_n {
() => {
"r11"
};
}
macro_rules! n_m {
() => {
"rcx"
};
}
macro_rules! n_n {
() => {
"rdx"
};
}
macro_rules! ishort {
() => {
"r9d"
};
}
macro_rules! m_mshort {
() => {
"r10d"
};
}
macro_rules! m_nshort {
() => {
"r11d"
};
}
macro_rules! n_mshort {
() => {
"ecx"
};
}
macro_rules! n_nshort {
() => {
"edx"
};
}
// Because they are so unmemorable
macro_rules! arg1 {
() => {
"rdi"
};
}
macro_rules! arg2 {
() => {
"rsi"
};
}
macro_rules! arg3 {
() => {
"rdx"
};
}
macro_rules! arg4 {
() => {
"rcx"
};
}
/// Test bignums for coprimality, gcd(x,y) = 1
///
/// Inputs x[m], y[n]; output function return; temporary buffer t[>=2*max(m,n)]
///
/// Test for whether two bignums are coprime (no common factor besides 1).
/// This is equivalent to testing if their gcd is 1, but a bit faster than
/// doing those two computations separately.
///
/// Here bignum x is m digits long, y is n digits long and the temporary
/// buffer t needs to be 2 * max(m,n) digits long. The return value is
/// 1 if coprime(x,y) and 0 otherwise.
pub(crate) fn bignum_coprime(x: &[u64], y: &[u64], t: &mut [u64]) -> bool {
let ret: u64;
debug_assert!(t.len() >= 2 * core::cmp::max(x.len(), y.len()));
// SAFETY: inline assembly. see [crate::low::inline_assembly_safety] for safety info.
unsafe {
core::arch::asm!(
Q!(" endbr64 " ),
// Save all required registers and make room on stack for all the above vars
Q!(" push " "rbp"),
Q!(" push " "rbx"),
Q!(" push " "r12"),
Q!(" push " "r13"),
Q!(" push " "r14"),
Q!(" push " "r15"),
Q!(" sub " "rsp, " STACKVARSIZE!()),
// Compute k = max(m,n), and if this is zero skip to the end. Note that
// in this case k is also in rax so serves as the right answer of "false"
Q!(" mov " "rax, " arg1!()),
Q!(" cmp " "rax, " arg3!()),
Q!(" cmovc " "rax, " arg3!()),
Q!(" mov " k!() ", rax"),
Q!(" test " "rax, rax"),
Q!(" jz " Label!("bignum_coprime_end", 2, After)),
// Set up inside w two size-k buffers m and n
Q!(" lea " n!() ", [" m!() "+ 8 * " k!() "]"),
// Copy the input x into the buffer m, padding with zeros as needed
Q!(" xor " i!() ", " i!()),
Q!(" test " arg1!() ", " arg1!()),
Q!(" jz " Label!("bignum_coprime_xpadloop", 3, After)),
Q!(Label!("bignum_coprime_xloop", 4) ":"),
Q!(" mov " a!() ", [" arg2!() "+ 8 * " i!() "]"),
Q!(" mov " "[" m!() "+ 8 * " i!() "], " a!()),
Q!(" inc " i!()),
Q!(" cmp " i!() ", " arg1!()),
Q!(" jc " Label!("bignum_coprime_xloop", 4, Before)),
Q!(" cmp " i!() ", " k!()),
Q!(" jnc " Label!("bignum_coprime_xskip", 5, After)),
Q!(Label!("bignum_coprime_xpadloop", 3) ":"),
Q!(" mov " "QWORD PTR [" m!() "+ 8 * " i!() "], 0"),
Q!(" inc " i!()),
Q!(" cmp " i!() ", " k!()),
Q!(" jc " Label!("bignum_coprime_xpadloop", 3, Before)),
Q!(Label!("bignum_coprime_xskip", 5) ":"),
// Copy the input y into the buffer n, padding with zeros as needed
Q!(" xor " i!() ", " i!()),
Q!(" test " arg3!() ", " arg3!()),
Q!(" jz " Label!("bignum_coprime_ypadloop", 6, After)),
Q!(Label!("bignum_coprime_yloop", 7) ":"),
Q!(" mov " a!() ", [" arg4!() "+ 8 * " i!() "]"),
Q!(" mov " "[" n!() "+ 8 * " i!() "], " a!()),
Q!(" inc " i!()),
Q!(" cmp " i!() ", " arg3!()),
Q!(" jc " Label!("bignum_coprime_yloop", 7, Before)),
Q!(" cmp " i!() ", " k!()),
Q!(" jnc " Label!("bignum_coprime_yskip", 8, After)),
Q!(Label!("bignum_coprime_ypadloop", 6) ":"),
Q!(" mov " "QWORD PTR [" n!() "+ 8 * " i!() "], 0"),
Q!(" inc " i!()),
Q!(" cmp " i!() ", " k!()),
Q!(" jc " Label!("bignum_coprime_ypadloop", 6, Before)),
Q!(Label!("bignum_coprime_yskip", 8) ":"),
// Set up the outer loop count of 64 * sum of input sizes.
// The invariant is that m * n < 2^t at all times.
Q!(" lea " a!() ", [" arg1!() "+ " arg3!() "]"),
Q!(" shl " a!() ", 6"),
Q!(" mov " t!() ", " a!()),
// Record for the very end the OR of the lowest words.
// If the bottom bit is zero we know both are even so the answer is false.
// But since this is constant-time code we still execute all the main part.
Q!(" mov " a!() ", [" m!() "]"),
Q!(" mov " b!() ", [" n!() "]"),
Q!(" or " a!() ", " b!()),
Q!(" mov " evenor!() ", " a!()),
// Now if n is even trigger a swap of m and n. This ensures that if
// one or other of m and n is odd then we make sure now that n is,
// as expected by our invariant later on.
Q!(" and " b!() ", 1"),
Q!(" sub " b!() ", 1"),
Q!(" xor " i!() ", " i!()),
Q!(Label!("bignum_coprime_swaploop", 9) ":"),
Q!(" mov " a!() ", [" m!() "+ 8 * " i!() "]"),
Q!(" mov " c!() ", [" n!() "+ 8 * " i!() "]"),
Q!(" mov " d!() ", " a!()),
Q!(" xor " d!() ", " c!()),
Q!(" and " d!() ", " b!()),
Q!(" xor " a!() ", " d!()),
Q!(" xor " c!() ", " d!()),
Q!(" mov " "[" m!() "+ 8 * " i!() "], " a!()),
Q!(" mov " "[" n!() "+ 8 * " i!() "], " c!()),
Q!(" inc " i!()),
Q!(" cmp " i!() ", " k!()),
Q!(" jnz " Label!("bignum_coprime_swaploop", 9, Before)),
// Start of the main outer loop iterated t / CHUNKSIZE times
Q!(Label!("bignum_coprime_outerloop", 12) ":"),
// We need only bother with sharper l = min k (ceil(t/64)) digits
// Either both m and n fit in l digits, or m has become zero and so
// nothing happens in the loop anyway and this makes no difference.
Q!(" mov " l!() ", " t!()),
Q!(" add " l!() ", 63"),
Q!(" shr " l!() ", 6"),
Q!(" cmp " l!() ", " k!()),
Q!(" cmovnc " l!() ", " k!()),
// Select upper and lower proxies for both m and n to drive the inner
// loop. The lower proxies are simply the lowest digits themselves,
// m_lo = m[0] and n_lo = n[0], while the upper proxies are bitfields
// of the two inputs selected so their top bit (63) aligns with the
// most significant bit of *either* of the two inputs.
Q!(" xor " h1!() ", " h1!()),
Q!(" xor " l1!() ", " l1!()),
Q!(" xor " h2!() ", " h2!()),
Q!(" xor " l2!() ", " l2!()),
Q!(" xor " c2!() ", " c2!()),
// and in this case h1 and h2 are those words
Q!(" xor " i!() ", " i!()),
Q!(Label!("bignum_coprime_toploop", 13) ":"),
Q!(" mov " b!() ", [" m!() "+ 8 * " i!() "]"),
Q!(" mov " c!() ", [" n!() "+ 8 * " i!() "]"),
Q!(" mov " c1!() ", " c2!()),
Q!(" and " c1!() ", " h1!()),
Q!(" and " c2!() ", " h2!()),
Q!(" mov " a!() ", " b!()),
Q!(" or " a!() ", " c!()),
Q!(" neg " a!()),
Q!(" cmovc " l1!() ", " c1!()),
Q!(" cmovc " l2!() ", " c2!()),
Q!(" cmovc " h1!() ", " b!()),
Q!(" cmovc " h2!() ", " c!()),
Q!(" sbb " c2!() ", " c2!()),
Q!(" inc " i!()),
Q!(" cmp " i!() ", " l!()),
Q!(" jc " Label!("bignum_coprime_toploop", 13, Before)),
Q!(" mov " a!() ", " h1!()),
Q!(" or " a!() ", " h2!()),
Q!(" bsr " c!() ", " a!()),
Q!(" xor " c!() ", 63"),
Q!(" shld " h1!() ", " l1!() ", cl"),
Q!(" shld " h2!() ", " l2!() ", cl"),
// m_lo = m[0], n_lo = n[0];
Q!(" mov " "rax, [" m!() "]"),
Q!(" mov " m_lo!() ", rax"),
Q!(" mov " "rax, [" n!() "]"),
Q!(" mov " n_lo!() ", rax"),
// Now the inner loop, with i as loop counter from CHUNKSIZE down.
// This records a matrix of updates to apply to the initial
// values of m and n with, at stage j:
//
// sgn * m' = (m_m * m - m_n * n) / 2^j
// -sgn * n' = (n_m * m - n_n * n) / 2^j
//
// where "sgn" is either +1 or -1, and we lose track of which except
// that both instance above are the same. This throwing away the sign
// costs nothing (since we have to correct in general anyway because
// of the proxied comparison) and makes things a bit simpler. But it
// is simply the parity of the number of times the first condition,
// used as the swapping criterion, fires in this loop.
Q!(" mov " m_mshort!() ", 1"),
Q!(" mov " m_nshort!() ", 0"),
Q!(" mov " n_mshort!() ", 0"),
Q!(" mov " n_nshort!() ", 1"),
Q!(" mov " ishort!() ", " CHUNKSIZE!()),
// Stash more variables over the inner loop to free up regs
Q!(" mov " mat_mn!() ", " k!()),
Q!(" mov " mat_nm!() ", " l!()),
Q!(" mov " mat_mm!() ", " m!()),
Q!(" mov " mat_nn!() ", " n!()),
// Conceptually in the inner loop we follow these steps:
//
// * If m_lo is odd and m_hi < n_hi, then swap the four pairs
// (m_hi,n_hi); (m_lo,n_lo); (m_m,n_m); (m_n,n_n)
//
// * Now, if m_lo is odd (old or new, doesn't matter as initial n_lo is odd)
// m_hi := m_hi - n_hi, m_lo := m_lo - n_lo
// m_m := m_m + n_m, m_n := m_n + n_n
//
// * Halve and double them
// m_hi := m_hi / 2, m_lo := m_lo / 2
// n_m := n_m * 2, n_n := n_n * 2
//
// The actual computation computes updates before actually swapping and
// then corrects as needed.
Q!(Label!("bignum_coprime_innerloop", 14) ":"),
Q!(" xor " "eax, eax"),
Q!(" xor " "ebx, ebx"),
Q!(" xor " m!() ", " m!()),
Q!(" xor " n!() ", " n!()),
Q!(" bt " m_lo!() ", 0"),
Q!(" cmovc " "rax, " n_hi!()),
Q!(" cmovc " "rbx, " n_lo!()),
Q!(" cmovc " m!() ", " n_m!()),
Q!(" cmovc " n!() ", " n_n!()),
Q!(" mov " l!() ", " m_lo!()),
Q!(" sub " m_lo!() ", rbx"),
Q!(" sub " "rbx, " l!()),
Q!(" mov " k!() ", " m_hi!()),
Q!(" sub " k!() ", rax"),
Q!(" cmovc " n_hi!() ", " m_hi!()),
Q!(" lea " m_hi!() ", [" k!() "-1]"),
Q!(" cmovc " m_lo!() ", rbx"),
Q!(" cmovc " n_lo!() ", " l!()),
Q!(" not " m_hi!()),
Q!(" cmovc " n_m!() ", " m_m!()),
Q!(" cmovc " n_n!() ", " m_n!()),
Q!(" cmovnc " m_hi!() ", " k!()),
Q!(" shr " m_lo!() ", 1"),
Q!(" add " m_m!() ", " m!()),
Q!(" add " m_n!() ", " n!()),
Q!(" shr " m_hi!() ", 1"),
Q!(" add " n_m!() ", " n_m!()),
Q!(" add " n_n!() ", " n_n!()),
// End of the inner for-loop
Q!(" dec " i!()),
Q!(" jnz " Label!("bignum_coprime_innerloop", 14, Before)),
// Unstash the temporary variables
Q!(" mov " k!() ", " mat_mn!()),
Q!(" mov " l!() ", " mat_nm!()),
Q!(" mov " m!() ", " mat_mm!()),
Q!(" mov " n!() ", " mat_nn!()),
// Put the matrix entries in memory since we're out of registers
// We pull them out repeatedly in the next loop
Q!(" mov " mat_mm!() ", " m_m!()),
Q!(" mov " mat_mn!() ", " m_n!()),
Q!(" mov " mat_nm!() ", " n_m!()),
Q!(" mov " mat_nn!() ", " n_n!()),
// Now actually compute the updates to m and n corresponding to that matrix,
// and correct the signs if they have gone negative. First we compute the
// (k+1)-sized updates with the following invariant (here h1 and h2 are in
// fact carry bitmasks, either 0 or -1):
//
// h1::l1::m = m_m * m - m_n * n
// h2::l2::n = n_m * m - n_n * n
Q!(" xor " i!() ", " i!()),
Q!(" xor " h1!() ", " h1!()),
Q!(" xor " l1!() ", " l1!()),
Q!(" xor " h2!() ", " h2!()),
Q!(" xor " l2!() ", " l2!()),
Q!(Label!("bignum_coprime_crossloop", 15) ":"),
Q!(" mov " c!() ", [" m!() "+ 8 * " i!() "]"),
Q!(" mov " a!() ", " mat_mm!()),
Q!(" mul " c!()),
Q!(" add " l1!() ", " a!()),
Q!(" adc " d!() ", 0"),
Q!(" mov " c1!() ", " d!()),
Q!(" mov " a!() ", " mat_nm!()),
Q!(" mul " c!()),
Q!(" add " l2!() ", " a!()),
Q!(" adc " d!() ", 0"),
Q!(" mov " c2!() ", " d!()),
Q!(" mov " c!() ", [" n!() "+ 8 * " i!() "]"),
Q!(" mov " a!() ", " mat_mn!()),
Q!(" mul " c!()),
Q!(" sub " d!() ", " h1!()),
Q!(" sub " l1!() ", " a!()),
Q!(" sbb " c1!() ", " d!()),
Q!(" sbb " h1!() ", " h1!()),
Q!(" mov " "[" m!() "+ 8 * " i!() "], " l1!()),
Q!(" mov " l1!() ", " c1!()),
Q!(" mov " a!() ", " mat_nn!()),
Q!(" mul " c!()),
Q!(" sub " d!() ", " h2!()),
Q!(" sub " l2!() ", " a!()),
Q!(" sbb " c2!() ", " d!()),
Q!(" sbb " h2!() ", " h2!()),
Q!(" mov " "[" n!() "+ 8 * " i!() "], " l2!()),
Q!(" mov " l2!() ", " c2!()),
Q!(" inc " i!()),
Q!(" cmp " i!() ", " l!()),
Q!(" jc " Label!("bignum_coprime_crossloop", 15, Before)),
// Now fix the signs of m and n if they have gone negative
Q!(" xor " i!() ", " i!()),
Q!(" mov " c1!() ", " h1!()),
Q!(" mov " c2!() ", " h2!()),
Q!(" xor " l1!() ", " h1!()),
Q!(" xor " l2!() ", " h2!()),
Q!(Label!("bignum_coprime_optnegloop", 16) ":"),
Q!(" mov " a!() ", [" m!() "+ 8 * " i!() "]"),
Q!(" xor " a!() ", " h1!()),
Q!(" neg " c1!()),
Q!(" adc " a!() ", 0"),
Q!(" sbb " c1!() ", " c1!()),
Q!(" mov " "[" m!() "+ 8 * " i!() "], " a!()),
Q!(" mov " a!() ", [" n!() "+ 8 * " i!() "]"),
Q!(" xor " a!() ", " h2!()),
Q!(" neg " c2!()),
Q!(" adc " a!() ", 0"),
Q!(" sbb " c2!() ", " c2!()),
Q!(" mov " "[" n!() "+ 8 * " i!() "], " a!()),
Q!(" inc " i!()),
Q!(" cmp " i!() ", " l!()),
Q!(" jc " Label!("bignum_coprime_optnegloop", 16, Before)),
Q!(" sub " l1!() ", " c1!()),
Q!(" sub " l2!() ", " c2!()),
// Now shift them right CHUNKSIZE bits
Q!(" mov " i!() ", " l!()),
Q!(Label!("bignum_coprime_shiftloop", 17) ":"),
Q!(" mov " a!() ", [" m!() "+ 8 * " i!() "-8]"),
Q!(" mov " h1!() ", " a!()),
Q!(" shrd " a!() ", " l1!() ", " CHUNKSIZE!()),
Q!(" mov " "[" m!() "+ 8 * " i!() "-8], " a!()),
Q!(" mov " l1!() ", " h1!()),
Q!(" mov " a!() ", [" n!() "+ 8 * " i!() "-8]"),
Q!(" mov " h2!() ", " a!()),
Q!(" shrd " a!() ", " l2!() ", " CHUNKSIZE!()),
Q!(" mov " "[" n!() "+ 8 * " i!() "-8], " a!()),
Q!(" mov " l2!() ", " h2!()),
Q!(" dec " i!()),
Q!(" jnz " Label!("bignum_coprime_shiftloop", 17, Before)),
// End of main loop. We can stop if t' <= 0 since then m * n < 2^0, which
// since n is odd (in the main cases where we had one or other input odd)
// means that m = 0 and n is the final gcd. Moreover we do in fact need to
// maintain strictly t > 0 in the main loop, or the computation of the
// optimized digit bound l could collapse to 0.
Q!(" sub " t!() ", " CHUNKSIZE!()),
Q!(" jnbe " Label!("bignum_coprime_outerloop", 12, Before)),
// Now compare n with 1 (OR of the XORs in a)
Q!(" mov " a!() ", [" n!() "]"),
Q!(" xor " a!() ", 1"),
Q!(" cmp " k!() ", 1"),
Q!(" jz " Label!("bignum_coprime_finalcomb", 18, After)),
Q!(" mov " ishort!() ", 1"),
Q!(Label!("bignum_coprime_compareloop", 19) ":"),
Q!(" or " a!() ", [" n!() "+ 8 * " i!() "]"),
Q!(" inc " i!()),
Q!(" cmp " i!() ", " k!()),
Q!(" jc " Label!("bignum_coprime_compareloop", 19, Before)),
// Now combine that with original "evenor" oddness flag
// The final condition is lsb(evenor) = 1 AND a = 0
Q!(Label!("bignum_coprime_finalcomb", 18) ":"),
Q!(" neg " a!()),
Q!(" sbb " a!() ", " a!()),
Q!(" inc " a!()),
Q!(" and " a!() ", " evenor!()),
// The end
Q!(Label!("bignum_coprime_end", 2) ":"),
Q!(" add " "rsp, " STACKVARSIZE!()),
Q!(" pop " "r15"),
Q!(" pop " "r14"),
Q!(" pop " "r13"),
Q!(" pop " "r12"),
Q!(" pop " "rbx"),
Q!(" pop " "rbp"),
inout("rdi") x.len() => _,
inout("rsi") x.as_ptr() => _,
inout("rdx") y.len() => _,
inout("rcx") y.as_ptr() => _,
inout("r8") t.as_mut_ptr() => _,
out("rax") ret,
// clobbers
out("r10") _,
out("r11") _,
out("r12") _,
out("r13") _,
out("r14") _,
out("r15") _,
out("r9") _,
)
};
ret > 0
}