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
|
dnl ******************************************************************************
dnl Copyright 2009 Paul Zimmermann and Alexander Kruppa.
dnl
dnl This file is part of the ECM Library.
dnl
dnl The ECM Library is free software; you can redistribute it and/or modify
dnl it under the terms of the GNU Lesser General Public License as published by
dnl the Free Software Foundation; either version 3 of the License, or (at your
dnl option) any later version.
dnl
dnl The ECM Library is distributed in the hope that it will be useful, but
dnl WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
dnl or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
dnl License for more details.
dnl
dnl You should have received a copy of the GNU Lesser General Public License
dnl along with the ECM Library; see the file COPYING.LIB. If not, write to
dnl the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston,
dnl MA 02110-1301, USA.
dnl ******************************************************************************
define(C, `
dnl')
C mp_limb_t mulredc12(mp_limb_t * z, const mp_limb_t * x, const mp_limb_t * y,
C const mp_limb_t *m, mp_limb_t inv_m);
C
C arguments:
C r3 = ptr to result z least significant limb
C r4 = ptr to input x least significant limb
C r5 = ptr to input y least significant limb
C r6 = ptr to modulus m least significant limb
C r7 = -1/m mod 2^64
C
C final carry returned in r3
include(`config.m4')
GLOBL GSYM_PREFIX`'mulredc12
GLOBL .GSYM_PREFIX`'mulredc12
.section ".opd", "aw"
.align 3
GSYM_PREFIX`'mulredc12:
.quad .GSYM_PREFIX`'mulredc12, .TOC.@tocbase, 0
.size GSYM_PREFIX`'mulredc12, 24
C Implements multiplication and REDC for two input numbers of 12 words
C The algorithm:
C (Notation: a:b:c == a * 2^128 + b * 2^64 + c)
C
C T1:T0 = x[i]*y[0] ;
C u = (T0*invm) % 2^64 ;
C cy:T1 = (m[0]*u + T1:T0) / 2^64 ; /* cy:T1 <= 2*2^64 - 4 (see note 1) */
C for (j = 1; j < len; j++)
C {
C cy:T1:T0 = x[i]*y[j] + m[j]*u + cy:T1 ;
C /* for all j result cy:T1 <= 2*2^64 - 3 (see note 2) */
C tmp[j-1] = T0;
C }
C tmp[len-1] = T1 ;
C tmp[len] = cy ; /* cy <= 1 (see note 2) */
C for (i = 1; i < len; i++)
C {
C cy:T1:T0 = x[i]*y[0] + tmp[1]:tmp[0] ;
C u = (T0*invm) % 2^64 ;
C cy:T1 = (m[0]*u + cy:T1:T0) / 2^64 ; /* cy:T1 <= 3*2^64 - 4 (see note 3) */
C for (j = 1; j < len; j++)
C {
C cy:T1:T0 = x[i]*y[j] + m[j]*u + (tmp[j+1] + cy):T1 ;
C /* for all j < (len-1), result cy:T1 <= 3*2^64 - 3
C for j = (len-1), result cy:T1 <= 2*2^64 - 1 (see note 4) */
C tmp[j-1] = T0;
C }
C tmp[len-1] = T1 ;
C tmp[len] = cy ; /* cy <= 1 for all i (see note 4) */
C }
C z[0 ... len-1] = tmp[0 ... len-1] ;
C return (tmp[len]) ;
C
C notes:
C
C 1: m[0]*u + T1:T0 <= 2*(2^64 - 1)^2 <= 2*2^128 - 4*2^64 + 2,
C so cy:T1 <= 2*2^64 - 4.
C 2: For j = 1, x[i]*y[j] + m[j]*u + cy:T1 <= 2*(2^64 - 1)^2 + 2*2^64 - 4
C <= 2*2^128 - 2*2^64 - 2 = 1:(2^64-3):(2^64-2),
C so cy:T1 <= 2*2^64 - 3. For j > 1,
C x[i]*y[j] + m[j]*u + cy:T1 <= 2*2^128 - 2*2^64 - 1 = 1:(2^64-3):(2^64-1),
C so cy:T1 <= 2*2^64 - 3 = 1:(2^64-3) holds for all j.
C 3: m[0]*u + cy:T1:T0 <= 2*(2^64 - 1)^2 + 2^128 - 1 = 3*2^128 - 4*2^64 + 1,
C so cy:T1 <= 3*2^64 - 4 = 2:(2^64-4)
C 4: For j = 1, x[i]*y[j] + m[j]*u + (tmp[j+1] + cy):T1
C <= 2*(2^64 - 1)^2 + (3*2^64 - 4) + (2^64-1)*2^64
C <= 3*2^128 - 2*2^64 - 2 = 2:(2^64-3):(2^64-2),
C so cy:T1 <= 3*2^64 - 3. For j > 1,
C x[i]*y[j] + m[j]*u + (tmp[j+1] + cy):T1 <= 2:(2^64-3):(2^64-1),
C so cy:T1 <= 3*2^64 - 3 = 2:(2^64-3) holds for all j < len - 1.
C For j = len - 1, we know from note 2 that tmp(len) <= 1 for i = 0.
C Assume this is true for index i-1, Then
C x[i]*y[len-1] + m[len-1]*u + (tmp[len] + cy):T1
C <= 2*(2^64 - 1)^2 + (3*2^64 - 3) + 2^64
C <= 2*2^128 - 1 = 1:(2^64-1):(2^64-1),
C so cy:T1 <= 1:(2^64-1) and tmp[len] <= 1 for all i by induction.
C
C Register vars: T0 = r13, T1 = r14, CY = r10, XI = r12, U = r11
C YP = r5, MP = r6, TP = r1 (stack ptr)
C
C local variables: tmp[0 ... 12] array, having 12+1 8-byte words
C The tmp array needs 12+1 entries, but tmp[12] is stored in
C r15, so only 12 entries are used in the stack.
TEXT
.align 5 C powerPC 32 byte alignment
.GSYM_PREFIX`'mulredc12:
C ########################################################################
C # i = 0 pass
C #########################################################################
C Pass for j = 0. We need to fetch x[i] from memory and compute the new u
ld r12, 0(r4) C XI = x[0]
ld r0, 0(r5) C y[0]
stdu r13, -8(r1) C save r13
mulld r8, r0, r12 C x[0]*y[0] low half
stdu r14, -8(r1) C save r14
mulhdu r9, r0, r12 C x[0]*y[0] high half
ld r0, 0(r6) C m[0]
mulld r11, r7, r8 C U = T0*invm mod 2^64
stdu r15, -8(r1) C save r15
mulld r13, r0, r11 C T0 = U*m[0] low
stdu r16, -8(r1) C save r16
li r16, 0 C set r16 to zero for carry propagation
subi r1, r1, 96 C set tmp stack space
mulhdu r14, r0, r11 C T1 = U*m[0] high
ld r0, 8(r5) C y[1]
addc r8, r8, r13 C
adde r13, r9, r14 C T0 = initial tmp(0)
addze r10, r16 C carry to CY
C CY:T1:T0 <= 2*(2^64-1)^2 <= 2^2*128 - 4*2^64 + 2, hence
C CY:T1 <= 2*2^64 - 4
C Pass for j = 1
mulld r8, r0, r12 C x[i]*y[j] low half
mulhdu r9, r0, r12 C x[i]*y[j] high half
ld r0, 8(r6) C m[j]
addc r13, r8, r13 C add low word to T0
adde r14, r9, r10 C add high word with carry + CY to T1
C T1:T0 <= 2^128 - 2*2^64 + 1 + 2*2^64 - 3 <= 2^128 - 2, no carry!
mulld r8, r0, r11 C U*m[j] low
mulhdu r9, r0, r11 C U*m[j] high
addc r8, r8, r13 C add T0 and low word
ld r0, 16(r5) C y[j+1]
adde r13, r9, r14 C add high word with carry to T1
addze r10, r16 C carry to CY
std r8, 0(r1) C store tmp[j-1]
C CY:T1:T0 <= 2^128 - 2 + 2^128 - 2*2^64 + 1 <=
C 2 * 2^128 - 2*2^64 - 1 ==> CY:T1 <= 2 * 2^64 - 3
C Pass for j = 2
mulld r8, r0, r12 C x[i]*y[j] low half
mulhdu r9, r0, r12 C x[i]*y[j] high half
ld r0, 16(r6) C m[j]
addc r13, r8, r13 C add low word to T0
adde r14, r9, r10 C add high word with carry + CY to T1
C T1:T0 <= 2^128 - 2*2^64 + 1 + 2*2^64 - 3 <= 2^128 - 2, no carry!
mulld r8, r0, r11 C U*m[j] low
mulhdu r9, r0, r11 C U*m[j] high
addc r8, r8, r13 C add T0 and low word
ld r0, 24(r5) C y[j+1]
adde r13, r9, r14 C add high word with carry to T1
addze r10, r16 C carry to CY
std r8, 8(r1) C store tmp[j-1]
C CY:T1:T0 <= 2^128 - 2 + 2^128 - 2*2^64 + 1 <=
C 2 * 2^128 - 2*2^64 - 1 ==> CY:T1 <= 2 * 2^64 - 3
C Pass for j = 3
mulld r8, r0, r12 C x[i]*y[j] low half
mulhdu r9, r0, r12 C x[i]*y[j] high half
ld r0, 24(r6) C m[j]
addc r13, r8, r13 C add low word to T0
adde r14, r9, r10 C add high word with carry + CY to T1
C T1:T0 <= 2^128 - 2*2^64 + 1 + 2*2^64 - 3 <= 2^128 - 2, no carry!
mulld r8, r0, r11 C U*m[j] low
mulhdu r9, r0, r11 C U*m[j] high
addc r8, r8, r13 C add T0 and low word
ld r0, 32(r5) C y[j+1]
adde r13, r9, r14 C add high word with carry to T1
addze r10, r16 C carry to CY
std r8, 16(r1) C store tmp[j-1]
C CY:T1:T0 <= 2^128 - 2 + 2^128 - 2*2^64 + 1 <=
C 2 * 2^128 - 2*2^64 - 1 ==> CY:T1 <= 2 * 2^64 - 3
C Pass for j = 4
mulld r8, r0, r12 C x[i]*y[j] low half
mulhdu r9, r0, r12 C x[i]*y[j] high half
ld r0, 32(r6) C m[j]
addc r13, r8, r13 C add low word to T0
adde r14, r9, r10 C add high word with carry + CY to T1
C T1:T0 <= 2^128 - 2*2^64 + 1 + 2*2^64 - 3 <= 2^128 - 2, no carry!
mulld r8, r0, r11 C U*m[j] low
mulhdu r9, r0, r11 C U*m[j] high
addc r8, r8, r13 C add T0 and low word
ld r0, 40(r5) C y[j+1]
adde r13, r9, r14 C add high word with carry to T1
addze r10, r16 C carry to CY
std r8, 24(r1) C store tmp[j-1]
C CY:T1:T0 <= 2^128 - 2 + 2^128 - 2*2^64 + 1 <=
C 2 * 2^128 - 2*2^64 - 1 ==> CY:T1 <= 2 * 2^64 - 3
C Pass for j = 5
mulld r8, r0, r12 C x[i]*y[j] low half
mulhdu r9, r0, r12 C x[i]*y[j] high half
ld r0, 40(r6) C m[j]
addc r13, r8, r13 C add low word to T0
adde r14, r9, r10 C add high word with carry + CY to T1
C T1:T0 <= 2^128 - 2*2^64 + 1 + 2*2^64 - 3 <= 2^128 - 2, no carry!
mulld r8, r0, r11 C U*m[j] low
mulhdu r9, r0, r11 C U*m[j] high
addc r8, r8, r13 C add T0 and low word
ld r0, 48(r5) C y[j+1]
adde r13, r9, r14 C add high word with carry to T1
addze r10, r16 C carry to CY
std r8, 32(r1) C store tmp[j-1]
C CY:T1:T0 <= 2^128 - 2 + 2^128 - 2*2^64 + 1 <=
C 2 * 2^128 - 2*2^64 - 1 ==> CY:T1 <= 2 * 2^64 - 3
C Pass for j = 6
mulld r8, r0, r12 C x[i]*y[j] low half
mulhdu r9, r0, r12 C x[i]*y[j] high half
ld r0, 48(r6) C m[j]
addc r13, r8, r13 C add low word to T0
adde r14, r9, r10 C add high word with carry + CY to T1
C T1:T0 <= 2^128 - 2*2^64 + 1 + 2*2^64 - 3 <= 2^128 - 2, no carry!
mulld r8, r0, r11 C U*m[j] low
mulhdu r9, r0, r11 C U*m[j] high
addc r8, r8, r13 C add T0 and low word
ld r0, 56(r5) C y[j+1]
adde r13, r9, r14 C add high word with carry to T1
addze r10, r16 C carry to CY
std r8, 40(r1) C store tmp[j-1]
C CY:T1:T0 <= 2^128 - 2 + 2^128 - 2*2^64 + 1 <=
C 2 * 2^128 - 2*2^64 - 1 ==> CY:T1 <= 2 * 2^64 - 3
C Pass for j = 7
mulld r8, r0, r12 C x[i]*y[j] low half
mulhdu r9, r0, r12 C x[i]*y[j] high half
ld r0, 56(r6) C m[j]
addc r13, r8, r13 C add low word to T0
adde r14, r9, r10 C add high word with carry + CY to T1
C T1:T0 <= 2^128 - 2*2^64 + 1 + 2*2^64 - 3 <= 2^128 - 2, no carry!
mulld r8, r0, r11 C U*m[j] low
mulhdu r9, r0, r11 C U*m[j] high
addc r8, r8, r13 C add T0 and low word
ld r0, 64(r5) C y[j+1]
adde r13, r9, r14 C add high word with carry to T1
addze r10, r16 C carry to CY
std r8, 48(r1) C store tmp[j-1]
C CY:T1:T0 <= 2^128 - 2 + 2^128 - 2*2^64 + 1 <=
C 2 * 2^128 - 2*2^64 - 1 ==> CY:T1 <= 2 * 2^64 - 3
C Pass for j = 8
mulld r8, r0, r12 C x[i]*y[j] low half
mulhdu r9, r0, r12 C x[i]*y[j] high half
ld r0, 64(r6) C m[j]
addc r13, r8, r13 C add low word to T0
adde r14, r9, r10 C add high word with carry + CY to T1
C T1:T0 <= 2^128 - 2*2^64 + 1 + 2*2^64 - 3 <= 2^128 - 2, no carry!
mulld r8, r0, r11 C U*m[j] low
mulhdu r9, r0, r11 C U*m[j] high
addc r8, r8, r13 C add T0 and low word
ld r0, 72(r5) C y[j+1]
adde r13, r9, r14 C add high word with carry to T1
addze r10, r16 C carry to CY
std r8, 56(r1) C store tmp[j-1]
C CY:T1:T0 <= 2^128 - 2 + 2^128 - 2*2^64 + 1 <=
C 2 * 2^128 - 2*2^64 - 1 ==> CY:T1 <= 2 * 2^64 - 3
C Pass for j = 9
mulld r8, r0, r12 C x[i]*y[j] low half
mulhdu r9, r0, r12 C x[i]*y[j] high half
ld r0, 72(r6) C m[j]
addc r13, r8, r13 C add low word to T0
adde r14, r9, r10 C add high word with carry + CY to T1
C T1:T0 <= 2^128 - 2*2^64 + 1 + 2*2^64 - 3 <= 2^128 - 2, no carry!
mulld r8, r0, r11 C U*m[j] low
mulhdu r9, r0, r11 C U*m[j] high
addc r8, r8, r13 C add T0 and low word
ld r0, 80(r5) C y[j+1]
adde r13, r9, r14 C add high word with carry to T1
addze r10, r16 C carry to CY
std r8, 64(r1) C store tmp[j-1]
C CY:T1:T0 <= 2^128 - 2 + 2^128 - 2*2^64 + 1 <=
C 2 * 2^128 - 2*2^64 - 1 ==> CY:T1 <= 2 * 2^64 - 3
C Pass for j = 10
mulld r8, r0, r12 C x[i]*y[j] low half
mulhdu r9, r0, r12 C x[i]*y[j] high half
ld r0, 80(r6) C m[j]
addc r13, r8, r13 C add low word to T0
adde r14, r9, r10 C add high word with carry + CY to T1
C T1:T0 <= 2^128 - 2*2^64 + 1 + 2*2^64 - 3 <= 2^128 - 2, no carry!
mulld r8, r0, r11 C U*m[j] low
mulhdu r9, r0, r11 C U*m[j] high
addc r8, r8, r13 C add T0 and low word
ld r0, 88(r5) C y[j+1]
adde r13, r9, r14 C add high word with carry to T1
addze r10, r16 C carry to CY
std r8, 72(r1) C store tmp[j-1]
C CY:T1:T0 <= 2^128 - 2 + 2^128 - 2*2^64 + 1 <=
C 2 * 2^128 - 2*2^64 - 1 ==> CY:T1 <= 2 * 2^64 - 3
C Pass for j = 11. Don't fetch new data from y[j+1].
mulld r8, r0, r12 C x[i]*y[j] low half
mulhdu r9, r0, r12 C x[i]*y[j] high half
ld r0, 88(r6) C m[j]
addc r13, r8, r13 C add low word to T0
adde r14, r9, r10 C add high word with carry + CY to T1
C T1:T0 <= 2^128 - 2*2^64 + 1 + 2*2^64 - 3 <= 2^128 - 2, no carry!
mulld r8, r0, r11 C U*m[j] low
mulhdu r9, r0, r11 C U*m[j] high
addc r8, r8, r13 C add T0 and low word
adde r13, r9, r14 C add high word with carry to T1
std r8, 80(r1) C store tmp[len-2]
addze r15, r16 C put carry in r15 (tmp[len] <= 1)
std r13, 88(r1) C store tmp[len-1]
C #########################################################################
C # i > 0 passes
C #########################################################################
li r9, 11 C outer loop count
mtctr r9
1:
C Pass for j = 0. We need to fetch x[i], tmp[i] and tmp[i+1] from memory
C and compute the new u
ldu r12, 8(r4) C x[i]
ld r0, 0(r5) C y[0]
ld r13, 0(r1) C tmp[0]
mulld r8, r0, r12 C x[i]*y[0] low half
ld r14, 8(r1) C tmp[1]
mulhdu r9, r0, r12 C x[i]*y[0] high half
addc r13, r8, r13 C T0
ld r0, 0(r6) C m[0]
mulld r11, r7, r13 C U = T0*invm mod 2^64
adde r14, r9, r14 C T1
mulld r8, r0, r11 C U*m[0] low
addze r10, r16 C CY
mulhdu r9, r0, r11 C U*m[0] high
ld r0, 8(r5) C y[1]
addc r8, r8, r13 C result = 0
adde r13, r9, r14 C T0, carry pending
C cy:T1:T0 <= 2*(2^64 - 1)^2 + 2^128 - 1 = 3*2^128 - 4*2^64 + 1,
C so cy:T1 <= 3*2^64 - 4
C Pass for j = 1
ld r14, 16(r1) C tmp[j+1]
mulld r8, r0, r12 C x[i]*y[j] low half
adde r14, r14, r10 C tmp[j+1] + CY + pending carry
addze r10, r16 C carry to CY
mulhdu r9, r0, r12 C x[i]*y[j] high half
ld r0, 8(r6) C m[j]
addc r13, r8, r13 C add low word to T0
mulld r8, r0, r11 C U*m[j] low
adde r14, r9, r14 C add high to T1
addze r10, r10 C add carry to CY
mulhdu r9, r0, r11 C U*m[j] high
addc r8, r8, r13 C add T0 and low word
ld r0, 16(r5) C y[j+1]
adde r13, r9, r14 C T1, carry pending
std r8, 0(r1) C store tmp[j-1]
C CY:T1:T0 <= 2*(2^64 - 1)^2 + (3*2^64 - 3) + (2^64-1)*2^64
C <= 3*2^128 - 2*2^64 - 1 ==> CY:T1 <= 3*2^64 - 3
C Pass for j = 2
ld r14, 24(r1) C tmp[j+1]
mulld r8, r0, r12 C x[i]*y[j] low half
adde r14, r14, r10 C tmp[j+1] + CY + pending carry
addze r10, r16 C carry to CY
mulhdu r9, r0, r12 C x[i]*y[j] high half
ld r0, 16(r6) C m[j]
addc r13, r8, r13 C add low word to T0
mulld r8, r0, r11 C U*m[j] low
adde r14, r9, r14 C add high to T1
addze r10, r10 C add carry to CY
mulhdu r9, r0, r11 C U*m[j] high
addc r8, r8, r13 C add T0 and low word
ld r0, 24(r5) C y[j+1]
adde r13, r9, r14 C T1, carry pending
std r8, 8(r1) C store tmp[j-1]
C CY:T1:T0 <= 2*(2^64 - 1)^2 + (3*2^64 - 3) + (2^64-1)*2^64
C <= 3*2^128 - 2*2^64 - 1 ==> CY:T1 <= 3*2^64 - 3
C Pass for j = 3
ld r14, 32(r1) C tmp[j+1]
mulld r8, r0, r12 C x[i]*y[j] low half
adde r14, r14, r10 C tmp[j+1] + CY + pending carry
addze r10, r16 C carry to CY
mulhdu r9, r0, r12 C x[i]*y[j] high half
ld r0, 24(r6) C m[j]
addc r13, r8, r13 C add low word to T0
mulld r8, r0, r11 C U*m[j] low
adde r14, r9, r14 C add high to T1
addze r10, r10 C add carry to CY
mulhdu r9, r0, r11 C U*m[j] high
addc r8, r8, r13 C add T0 and low word
ld r0, 32(r5) C y[j+1]
adde r13, r9, r14 C T1, carry pending
std r8, 16(r1) C store tmp[j-1]
C CY:T1:T0 <= 2*(2^64 - 1)^2 + (3*2^64 - 3) + (2^64-1)*2^64
C <= 3*2^128 - 2*2^64 - 1 ==> CY:T1 <= 3*2^64 - 3
C Pass for j = 4
ld r14, 40(r1) C tmp[j+1]
mulld r8, r0, r12 C x[i]*y[j] low half
adde r14, r14, r10 C tmp[j+1] + CY + pending carry
addze r10, r16 C carry to CY
mulhdu r9, r0, r12 C x[i]*y[j] high half
ld r0, 32(r6) C m[j]
addc r13, r8, r13 C add low word to T0
mulld r8, r0, r11 C U*m[j] low
adde r14, r9, r14 C add high to T1
addze r10, r10 C add carry to CY
mulhdu r9, r0, r11 C U*m[j] high
addc r8, r8, r13 C add T0 and low word
ld r0, 40(r5) C y[j+1]
adde r13, r9, r14 C T1, carry pending
std r8, 24(r1) C store tmp[j-1]
C CY:T1:T0 <= 2*(2^64 - 1)^2 + (3*2^64 - 3) + (2^64-1)*2^64
C <= 3*2^128 - 2*2^64 - 1 ==> CY:T1 <= 3*2^64 - 3
C Pass for j = 5
ld r14, 48(r1) C tmp[j+1]
mulld r8, r0, r12 C x[i]*y[j] low half
adde r14, r14, r10 C tmp[j+1] + CY + pending carry
addze r10, r16 C carry to CY
mulhdu r9, r0, r12 C x[i]*y[j] high half
ld r0, 40(r6) C m[j]
addc r13, r8, r13 C add low word to T0
mulld r8, r0, r11 C U*m[j] low
adde r14, r9, r14 C add high to T1
addze r10, r10 C add carry to CY
mulhdu r9, r0, r11 C U*m[j] high
addc r8, r8, r13 C add T0 and low word
ld r0, 48(r5) C y[j+1]
adde r13, r9, r14 C T1, carry pending
std r8, 32(r1) C store tmp[j-1]
C CY:T1:T0 <= 2*(2^64 - 1)^2 + (3*2^64 - 3) + (2^64-1)*2^64
C <= 3*2^128 - 2*2^64 - 1 ==> CY:T1 <= 3*2^64 - 3
C Pass for j = 6
ld r14, 56(r1) C tmp[j+1]
mulld r8, r0, r12 C x[i]*y[j] low half
adde r14, r14, r10 C tmp[j+1] + CY + pending carry
addze r10, r16 C carry to CY
mulhdu r9, r0, r12 C x[i]*y[j] high half
ld r0, 48(r6) C m[j]
addc r13, r8, r13 C add low word to T0
mulld r8, r0, r11 C U*m[j] low
adde r14, r9, r14 C add high to T1
addze r10, r10 C add carry to CY
mulhdu r9, r0, r11 C U*m[j] high
addc r8, r8, r13 C add T0 and low word
ld r0, 56(r5) C y[j+1]
adde r13, r9, r14 C T1, carry pending
std r8, 40(r1) C store tmp[j-1]
C CY:T1:T0 <= 2*(2^64 - 1)^2 + (3*2^64 - 3) + (2^64-1)*2^64
C <= 3*2^128 - 2*2^64 - 1 ==> CY:T1 <= 3*2^64 - 3
C Pass for j = 7
ld r14, 64(r1) C tmp[j+1]
mulld r8, r0, r12 C x[i]*y[j] low half
adde r14, r14, r10 C tmp[j+1] + CY + pending carry
addze r10, r16 C carry to CY
mulhdu r9, r0, r12 C x[i]*y[j] high half
ld r0, 56(r6) C m[j]
addc r13, r8, r13 C add low word to T0
mulld r8, r0, r11 C U*m[j] low
adde r14, r9, r14 C add high to T1
addze r10, r10 C add carry to CY
mulhdu r9, r0, r11 C U*m[j] high
addc r8, r8, r13 C add T0 and low word
ld r0, 64(r5) C y[j+1]
adde r13, r9, r14 C T1, carry pending
std r8, 48(r1) C store tmp[j-1]
C CY:T1:T0 <= 2*(2^64 - 1)^2 + (3*2^64 - 3) + (2^64-1)*2^64
C <= 3*2^128 - 2*2^64 - 1 ==> CY:T1 <= 3*2^64 - 3
C Pass for j = 8
ld r14, 72(r1) C tmp[j+1]
mulld r8, r0, r12 C x[i]*y[j] low half
adde r14, r14, r10 C tmp[j+1] + CY + pending carry
addze r10, r16 C carry to CY
mulhdu r9, r0, r12 C x[i]*y[j] high half
ld r0, 64(r6) C m[j]
addc r13, r8, r13 C add low word to T0
mulld r8, r0, r11 C U*m[j] low
adde r14, r9, r14 C add high to T1
addze r10, r10 C add carry to CY
mulhdu r9, r0, r11 C U*m[j] high
addc r8, r8, r13 C add T0 and low word
ld r0, 72(r5) C y[j+1]
adde r13, r9, r14 C T1, carry pending
std r8, 56(r1) C store tmp[j-1]
C CY:T1:T0 <= 2*(2^64 - 1)^2 + (3*2^64 - 3) + (2^64-1)*2^64
C <= 3*2^128 - 2*2^64 - 1 ==> CY:T1 <= 3*2^64 - 3
C Pass for j = 9
ld r14, 80(r1) C tmp[j+1]
mulld r8, r0, r12 C x[i]*y[j] low half
adde r14, r14, r10 C tmp[j+1] + CY + pending carry
addze r10, r16 C carry to CY
mulhdu r9, r0, r12 C x[i]*y[j] high half
ld r0, 72(r6) C m[j]
addc r13, r8, r13 C add low word to T0
mulld r8, r0, r11 C U*m[j] low
adde r14, r9, r14 C add high to T1
addze r10, r10 C add carry to CY
mulhdu r9, r0, r11 C U*m[j] high
addc r8, r8, r13 C add T0 and low word
ld r0, 80(r5) C y[j+1]
adde r13, r9, r14 C T1, carry pending
std r8, 64(r1) C store tmp[j-1]
C CY:T1:T0 <= 2*(2^64 - 1)^2 + (3*2^64 - 3) + (2^64-1)*2^64
C <= 3*2^128 - 2*2^64 - 1 ==> CY:T1 <= 3*2^64 - 3
C Pass for j = 10
ld r14, 88(r1) C tmp[j+1]
mulld r8, r0, r12 C x[i]*y[j] low half
adde r14, r14, r10 C tmp[j+1] + CY + pending carry
addze r10, r16 C carry to CY
mulhdu r9, r0, r12 C x[i]*y[j] high half
ld r0, 80(r6) C m[j]
addc r13, r8, r13 C add low word to T0
mulld r8, r0, r11 C U*m[j] low
adde r14, r9, r14 C add high to T1
addze r10, r10 C add carry to CY
mulhdu r9, r0, r11 C U*m[j] high
addc r8, r8, r13 C add T0 and low word
ld r0, 88(r5) C y[j+1]
adde r13, r9, r14 C T1, carry pending
std r8, 72(r1) C store tmp[j-1]
C CY:T1:T0 <= 2*(2^64 - 1)^2 + (3*2^64 - 3) + (2^64-1)*2^64
C <= 3*2^128 - 2*2^64 - 1 ==> CY:T1 <= 3*2^64 - 3
C Pass for j = 11. Don't fetch new data from y[j+1].
mulld r8, r0, r12 C x[i]*y[j] low half
adde r14, r15, r10 C T1 = tmp[len] + CY + pending carry
C since tmp[len] <= 1, T1 <= 3 and carry is zero
mulhdu r9, r0, r12 C x[i]*y[j] high half
ld r0, 88(r6) C m[j]
addc r13, r8, r13 C add low word to T0
mulld r8, r0, r11 C U*m[j] low
adde r14, r9, r14 C add high to T1
addze r10, r16 C CY
mulhdu r9, r0, r11 C U*m[j] high
addc r8, r8, r13 C add T0 and low word
adde r13, r9, r14 C T1, carry pending
std r8, 80(r1) C store tmp[len-2]
addze r15, r10 C store tmp[len] <= 1
std r13, 88(r1) C store tmp[len-1]
C CY:T1:T0 <= 2*(2^64 - 1)^2 + (3*2^64 - 3) + 2^64
C <= 2*2^128 - 1 ==> CY:T1 <= 2*2^64 - 1 = 1:(2^64-1)
bdnz 1b
C Copy result from tmp memory to z
ld r8, 0(r1)
ldu r9, 8(r1)
std r8, 0(r3)
stdu r9, 8(r3)
ldu r8, 8(r1)
ldu r9, 8(r1)
stdu r8, 8(r3)
stdu r9, 8(r3)
ldu r8, 8(r1)
ldu r9, 8(r1)
stdu r8, 8(r3)
stdu r9, 8(r3)
ldu r8, 8(r1)
ldu r9, 8(r1)
stdu r8, 8(r3)
stdu r9, 8(r3)
ldu r8, 8(r1)
ldu r9, 8(r1)
stdu r8, 8(r3)
stdu r9, 8(r3)
ldu r8, 8(r1)
ldu r9, 8(r1)
stdu r8, 8(r3)
stdu r9, 8(r3)
mr r3, r15 C return tmp(len)
ldu r16, 8(r1)
ldu r15, 8(r1)
ldu r14, 8(r1)
ldu r13, 8(r1)
addi r1, r1, 8
blr
.size .GSYM_PREFIX`'mulredc12, .-.GSYM_PREFIX`'mulredc12
|
