Newer
Older
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
#!/usr/bin/env perl
# ====================================================================
# Written by Andy Polyakov <appro@openssl.org> for the OpenSSL
# project. The module is, however, dual licensed under OpenSSL and
# CRYPTOGAMS licenses depending on where you obtain it. For further
# details see http://www.openssl.org/~appro/cryptogams/.
# ====================================================================
# August 2011.
#
# Companion to x86_64-mont.pl that optimizes cache-timing attack
# countermeasures. The subroutines are produced by replacing bp[i]
# references in their x86_64-mont.pl counterparts with cache-neutral
# references to powers table computed in BN_mod_exp_mont_consttime.
# In addition subroutine that scatters elements of the powers table
# is implemented, so that scatter-/gathering can be tuned without
# bn_exp.c modifications.
$flavour = shift;
$output = shift;
if ($flavour =~ /\./) { $output = $flavour; undef $flavour; }
$win64=0; $win64=1 if ($flavour =~ /[nm]asm|mingw64/ || $output =~ /\.asm$/);
$0 =~ m/(.*[\/\\])[^\/\\]+$/; $dir=$1;
( $xlate="${dir}x86_64-xlate.pl" and -f $xlate ) or
( $xlate="${dir}../../perlasm/x86_64-xlate.pl" and -f $xlate) or
die "can't locate x86_64-xlate.pl";
open STDOUT,"| $^X $xlate $flavour $output";
# int bn_mul_mont_gather5(
$rp="%rdi"; # BN_ULONG *rp,
$ap="%rsi"; # const BN_ULONG *ap,
$bp="%rdx"; # const BN_ULONG *bp,
$np="%rcx"; # const BN_ULONG *np,
$n0="%r8"; # const BN_ULONG *n0,
$num="%r9"; # int num,
# int idx); # 0 to 2^5-1, "index" in $bp holding
# pre-computed powers of a', interlaced
# in such manner that b[0] is $bp[idx],
# b[1] is [2^5+idx], etc.
$lo0="%r10";
$hi0="%r11";
$hi1="%r13";
$i="%r14";
$j="%r15";
$m0="%rbx";
$m1="%rbp";
$code=<<___;
.text
.globl bn_mul_mont_gather5
.type bn_mul_mont_gather5,\@function,6
.align 64
bn_mul_mont_gather5:
test \$3,${num}d
jnz .Lmul_enter
cmp \$8,${num}d
jb .Lmul_enter
jmp .Lmul4x_enter
.align 16
.Lmul_enter:
mov `($win64?56:8)`(%rsp),%r10d # load 7th argument
push %rbx
push %rbp
push %r12
push %r13
push %r14
push %r15
___
$code.=<<___ if ($win64);
lea -0x28(%rsp),%rsp
movaps %xmm6,(%rsp)
movaps %xmm7,0x10(%rsp)
.Lmul_alloca:
___
$code.=<<___;
mov %rsp,%rax
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
neg %r11
lea (%rsp,%r11,8),%rsp # tp=alloca(8*(num+2))
and \$-1024,%rsp # minimize TLB usage
mov %rax,8(%rsp,$num,8) # tp[num+1]=%rsp
.Lmul_body:
mov $bp,%r12 # reassign $bp
___
$bp="%r12";
$STRIDE=2**5*8; # 5 is "window size"
$N=$STRIDE/4; # should match cache line size
$code.=<<___;
mov %r10,%r11
shr \$`log($N/8)/log(2)`,%r10
and \$`$N/8-1`,%r11
not %r10
lea .Lmagic_masks(%rip),%rax
and \$`2**5/($N/8)-1`,%r10 # 5 is "window size"
lea 96($bp,%r11,8),$bp # pointer within 1st cache line
movq 0(%rax,%r10,8),%xmm4 # set of masks denoting which
movq 8(%rax,%r10,8),%xmm5 # cache line contains element
movq 16(%rax,%r10,8),%xmm6 # denoted by 7th argument
movq 24(%rax,%r10,8),%xmm7
movq `0*$STRIDE/4-96`($bp),%xmm0
movq `1*$STRIDE/4-96`($bp),%xmm1
pand %xmm4,%xmm0
movq `2*$STRIDE/4-96`($bp),%xmm2
pand %xmm5,%xmm1
movq `3*$STRIDE/4-96`($bp),%xmm3
pand %xmm6,%xmm2
por %xmm1,%xmm0
pand %xmm7,%xmm3
por %xmm2,%xmm0
lea $STRIDE($bp),$bp
por %xmm3,%xmm0
movq %xmm0,$m0 # m0=bp[0]
mov ($n0),$n0 # pull n0[0] value
mov ($ap),%rax
xor $i,$i # i=0
xor $j,$j # j=0
movq `0*$STRIDE/4-96`($bp),%xmm0
movq `1*$STRIDE/4-96`($bp),%xmm1
pand %xmm4,%xmm0
movq `2*$STRIDE/4-96`($bp),%xmm2
pand %xmm5,%xmm1
mov $n0,$m1
mulq $m0 # ap[0]*bp[0]
mov %rax,$lo0
mov ($np),%rax
movq `3*$STRIDE/4-96`($bp),%xmm3
pand %xmm6,%xmm2
por %xmm1,%xmm0
pand %xmm7,%xmm3
imulq $lo0,$m1 # "tp[0]"*n0
mov %rdx,$hi0
por %xmm2,%xmm0
lea $STRIDE($bp),$bp
por %xmm3,%xmm0
mulq $m1 # np[0]*m1
add %rax,$lo0 # discarded
mov 8($ap),%rax
adc \$0,%rdx
mov %rdx,$hi1
lea 1($j),$j # j++
jmp .L1st_enter
.align 16
.L1st:
add %rax,$hi1
mov ($ap,$j,8),%rax
adc \$0,%rdx
add $hi0,$hi1 # np[j]*m1+ap[j]*bp[0]
mov $lo0,$hi0
adc \$0,%rdx
mov $hi1,-16(%rsp,$j,8) # tp[j-1]
mov %rdx,$hi1
.L1st_enter:
mulq $m0 # ap[j]*bp[0]
add %rax,$hi0
mov ($np,$j,8),%rax
adc \$0,%rdx
lea 1($j),$j # j++
mov %rdx,$lo0
mulq $m1 # np[j]*m1
cmp $num,$j
jne .L1st
movq %xmm0,$m0 # bp[1]
add %rax,$hi1
mov ($ap),%rax # ap[0]
adc \$0,%rdx
add $hi0,$hi1 # np[j]*m1+ap[j]*bp[0]
adc \$0,%rdx
mov $hi1,-16(%rsp,$j,8) # tp[j-1]
mov %rdx,$hi1
mov $lo0,$hi0
xor %rdx,%rdx
add $hi0,$hi1
adc \$0,%rdx
mov $hi1,-8(%rsp,$num,8)
mov %rdx,(%rsp,$num,8) # store upmost overflow bit
lea 1($i),$i # i++
jmp .Louter
.align 16
.Louter:
xor $j,$j # j=0
mov $n0,$m1
mov (%rsp),$lo0
movq `0*$STRIDE/4-96`($bp),%xmm0
movq `1*$STRIDE/4-96`($bp),%xmm1
pand %xmm4,%xmm0
movq `2*$STRIDE/4-96`($bp),%xmm2
pand %xmm5,%xmm1
mulq $m0 # ap[0]*bp[i]
add %rax,$lo0 # ap[0]*bp[i]+tp[0]
mov ($np),%rax
adc \$0,%rdx
movq `3*$STRIDE/4-96`($bp),%xmm3
pand %xmm6,%xmm2
por %xmm1,%xmm0
pand %xmm7,%xmm3
imulq $lo0,$m1 # tp[0]*n0
mov %rdx,$hi0
por %xmm2,%xmm0
lea $STRIDE($bp),$bp
por %xmm3,%xmm0
mulq $m1 # np[0]*m1
add %rax,$lo0 # discarded
mov 8($ap),%rax
adc \$0,%rdx
mov 8(%rsp),$lo0 # tp[1]
mov %rdx,$hi1
lea 1($j),$j # j++
jmp .Linner_enter
.align 16
.Linner:
add %rax,$hi1
mov ($ap,$j,8),%rax
adc \$0,%rdx
add $lo0,$hi1 # np[j]*m1+ap[j]*bp[i]+tp[j]
mov (%rsp,$j,8),$lo0
adc \$0,%rdx
mov $hi1,-16(%rsp,$j,8) # tp[j-1]
mov %rdx,$hi1
.Linner_enter:
mulq $m0 # ap[j]*bp[i]
add %rax,$hi0
mov ($np,$j,8),%rax
adc \$0,%rdx
add $hi0,$lo0 # ap[j]*bp[i]+tp[j]
mov %rdx,$hi0
adc \$0,$hi0
lea 1($j),$j # j++
mulq $m1 # np[j]*m1
cmp $num,$j
jne .Linner
movq %xmm0,$m0 # bp[i+1]
add %rax,$hi1
mov ($ap),%rax # ap[0]
adc \$0,%rdx
add $lo0,$hi1 # np[j]*m1+ap[j]*bp[i]+tp[j]
mov (%rsp,$j,8),$lo0
adc \$0,%rdx
mov $hi1,-16(%rsp,$j,8) # tp[j-1]
mov %rdx,$hi1
xor %rdx,%rdx
add $hi0,$hi1
adc \$0,%rdx
add $lo0,$hi1 # pull upmost overflow bit
adc \$0,%rdx
mov $hi1,-8(%rsp,$num,8)
mov %rdx,(%rsp,$num,8) # store upmost overflow bit
lea 1($i),$i # i++
cmp $num,$i
jl .Louter
xor $i,$i # i=0 and clear CF!
mov (%rsp),%rax # tp[0]
lea (%rsp),$ap # borrow ap for tp
mov $num,$j # j=num
jmp .Lsub
.align 16
.Lsub: sbb ($np,$i,8),%rax
mov %rax,($rp,$i,8) # rp[i]=tp[i]-np[i]
mov 8($ap,$i,8),%rax # tp[i+1]
lea 1($i),$i # i++
dec $j # doesnn't affect CF!
jnz .Lsub
sbb \$0,%rax # handle upmost overflow bit
xor $i,$i
and %rax,$ap
not %rax
mov $rp,$np
and %rax,$np
mov $num,$j # j=num
or $np,$ap # ap=borrow?tp:rp
.align 16
.Lcopy: # copy or in-place refresh
mov ($ap,$i,8),%rax
mov $i,(%rsp,$i,8) # zap temporary vector
mov %rax,($rp,$i,8) # rp[i]=tp[i]
lea 1($i),$i
sub \$1,$j
jnz .Lcopy
mov 8(%rsp,$num,8),%rsi # restore %rsp
mov \$1,%rax
___
$code.=<<___ if ($win64);
movaps (%rsi),%xmm6
movaps 0x10(%rsi),%xmm7
lea 0x28(%rsi),%rsi
___
$code.=<<___;
mov (%rsi),%r15
mov 8(%rsi),%r14
mov 16(%rsi),%r13
mov 24(%rsi),%r12
mov 32(%rsi),%rbp
mov 40(%rsi),%rbx
lea 48(%rsi),%rsp
.Lmul_epilogue:
ret
.size bn_mul_mont_gather5,.-bn_mul_mont_gather5
___
{{{
my @A=("%r10","%r11");
my @N=("%r13","%rdi");
$code.=<<___;
.type bn_mul4x_mont_gather5,\@function,6
.align 16
bn_mul4x_mont_gather5:
.Lmul4x_enter:
mov `($win64?56:8)`(%rsp),%r10d # load 7th argument
push %rbx
push %rbp
push %r12
push %r13
push %r14
push %r15
___
$code.=<<___ if ($win64);
lea -0x28(%rsp),%rsp
movaps %xmm6,(%rsp)
movaps %xmm7,0x10(%rsp)
.Lmul4x_alloca:
___
$code.=<<___;
mov %rsp,%rax
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
lea 4($num),%r11
neg %r11
lea (%rsp,%r11,8),%rsp # tp=alloca(8*(num+4))
and \$-1024,%rsp # minimize TLB usage
mov %rax,8(%rsp,$num,8) # tp[num+1]=%rsp
.Lmul4x_body:
mov $rp,16(%rsp,$num,8) # tp[num+2]=$rp
mov %rdx,%r12 # reassign $bp
___
$bp="%r12";
$STRIDE=2**5*8; # 5 is "window size"
$N=$STRIDE/4; # should match cache line size
$code.=<<___;
mov %r10,%r11
shr \$`log($N/8)/log(2)`,%r10
and \$`$N/8-1`,%r11
not %r10
lea .Lmagic_masks(%rip),%rax
and \$`2**5/($N/8)-1`,%r10 # 5 is "window size"
lea 96($bp,%r11,8),$bp # pointer within 1st cache line
movq 0(%rax,%r10,8),%xmm4 # set of masks denoting which
movq 8(%rax,%r10,8),%xmm5 # cache line contains element
movq 16(%rax,%r10,8),%xmm6 # denoted by 7th argument
movq 24(%rax,%r10,8),%xmm7
movq `0*$STRIDE/4-96`($bp),%xmm0
movq `1*$STRIDE/4-96`($bp),%xmm1
pand %xmm4,%xmm0
movq `2*$STRIDE/4-96`($bp),%xmm2
pand %xmm5,%xmm1
movq `3*$STRIDE/4-96`($bp),%xmm3
pand %xmm6,%xmm2
por %xmm1,%xmm0
pand %xmm7,%xmm3
por %xmm2,%xmm0
lea $STRIDE($bp),$bp
por %xmm3,%xmm0
movq %xmm0,$m0 # m0=bp[0]
mov ($n0),$n0 # pull n0[0] value
mov ($ap),%rax
xor $i,$i # i=0
xor $j,$j # j=0
movq `0*$STRIDE/4-96`($bp),%xmm0
movq `1*$STRIDE/4-96`($bp),%xmm1
pand %xmm4,%xmm0
movq `2*$STRIDE/4-96`($bp),%xmm2
pand %xmm5,%xmm1
mov $n0,$m1
mulq $m0 # ap[0]*bp[0]
mov %rax,$A[0]
mov ($np),%rax
movq `3*$STRIDE/4-96`($bp),%xmm3
pand %xmm6,%xmm2
por %xmm1,%xmm0
pand %xmm7,%xmm3
imulq $A[0],$m1 # "tp[0]"*n0
mov %rdx,$A[1]
por %xmm2,%xmm0
lea $STRIDE($bp),$bp
por %xmm3,%xmm0
mulq $m1 # np[0]*m1
add %rax,$A[0] # discarded
mov 8($ap),%rax
adc \$0,%rdx
mov %rdx,$N[1]
mulq $m0
add %rax,$A[1]
mov 8($np),%rax
adc \$0,%rdx
mov %rdx,$A[0]
mulq $m1
add %rax,$N[1]
mov 16($ap),%rax
adc \$0,%rdx
add $A[1],$N[1]
lea 4($j),$j # j++
adc \$0,%rdx
mov $N[1],(%rsp)
mov %rdx,$N[0]
jmp .L1st4x
.align 16
.L1st4x:
mulq $m0 # ap[j]*bp[0]
add %rax,$A[0]
mov -16($np,$j,8),%rax
adc \$0,%rdx
mov %rdx,$A[1]
mulq $m1 # np[j]*m1
add %rax,$N[0]
mov -8($ap,$j,8),%rax
adc \$0,%rdx
add $A[0],$N[0] # np[j]*m1+ap[j]*bp[0]
adc \$0,%rdx
mov $N[0],-24(%rsp,$j,8) # tp[j-1]
mov %rdx,$N[1]
mulq $m0 # ap[j]*bp[0]
add %rax,$A[1]
mov -8($np,$j,8),%rax
adc \$0,%rdx
mov %rdx,$A[0]
mulq $m1 # np[j]*m1
add %rax,$N[1]
mov ($ap,$j,8),%rax
adc \$0,%rdx
add $A[1],$N[1] # np[j]*m1+ap[j]*bp[0]
adc \$0,%rdx
mov $N[1],-16(%rsp,$j,8) # tp[j-1]
mov %rdx,$N[0]
mulq $m0 # ap[j]*bp[0]
add %rax,$A[0]
mov ($np,$j,8),%rax
adc \$0,%rdx
mov %rdx,$A[1]
mulq $m1 # np[j]*m1
add %rax,$N[0]
mov 8($ap,$j,8),%rax
adc \$0,%rdx
add $A[0],$N[0] # np[j]*m1+ap[j]*bp[0]
adc \$0,%rdx
mov $N[0],-8(%rsp,$j,8) # tp[j-1]
mov %rdx,$N[1]
mulq $m0 # ap[j]*bp[0]
add %rax,$A[1]
mov 8($np,$j,8),%rax
adc \$0,%rdx
lea 4($j),$j # j++
mov %rdx,$A[0]
mulq $m1 # np[j]*m1
add %rax,$N[1]
mov -16($ap,$j,8),%rax
adc \$0,%rdx
add $A[1],$N[1] # np[j]*m1+ap[j]*bp[0]
adc \$0,%rdx
mov $N[1],-32(%rsp,$j,8) # tp[j-1]
mov %rdx,$N[0]
cmp $num,$j
jl .L1st4x
mulq $m0 # ap[j]*bp[0]
add %rax,$A[0]
mov -16($np,$j,8),%rax
adc \$0,%rdx
mov %rdx,$A[1]
mulq $m1 # np[j]*m1
add %rax,$N[0]
mov -8($ap,$j,8),%rax
adc \$0,%rdx
add $A[0],$N[0] # np[j]*m1+ap[j]*bp[0]
adc \$0,%rdx
mov $N[0],-24(%rsp,$j,8) # tp[j-1]
mov %rdx,$N[1]
mulq $m0 # ap[j]*bp[0]
add %rax,$A[1]
mov -8($np,$j,8),%rax
adc \$0,%rdx
mov %rdx,$A[0]
mulq $m1 # np[j]*m1
add %rax,$N[1]
mov ($ap),%rax # ap[0]
adc \$0,%rdx
add $A[1],$N[1] # np[j]*m1+ap[j]*bp[0]
adc \$0,%rdx
mov $N[1],-16(%rsp,$j,8) # tp[j-1]
mov %rdx,$N[0]
movq %xmm0,$m0 # bp[1]
xor $N[1],$N[1]
add $A[0],$N[0]
adc \$0,$N[1]
mov $N[0],-8(%rsp,$j,8)
mov $N[1],(%rsp,$j,8) # store upmost overflow bit
lea 1($i),$i # i++
.align 4
.Louter4x:
xor $j,$j # j=0
movq `0*$STRIDE/4-96`($bp),%xmm0
movq `1*$STRIDE/4-96`($bp),%xmm1
pand %xmm4,%xmm0
movq `2*$STRIDE/4-96`($bp),%xmm2
pand %xmm5,%xmm1
mov (%rsp),$A[0]
mov $n0,$m1
mulq $m0 # ap[0]*bp[i]
add %rax,$A[0] # ap[0]*bp[i]+tp[0]
mov ($np),%rax
adc \$0,%rdx
movq `3*$STRIDE/4-96`($bp),%xmm3
pand %xmm6,%xmm2
por %xmm1,%xmm0
pand %xmm7,%xmm3
imulq $A[0],$m1 # tp[0]*n0
mov %rdx,$A[1]
por %xmm2,%xmm0
lea $STRIDE($bp),$bp
por %xmm3,%xmm0
mulq $m1 # np[0]*m1
add %rax,$A[0] # "$N[0]", discarded
mov 8($ap),%rax
adc \$0,%rdx
mov %rdx,$N[1]
mulq $m0 # ap[j]*bp[i]
add %rax,$A[1]
mov 8($np),%rax
adc \$0,%rdx
add 8(%rsp),$A[1] # +tp[1]
adc \$0,%rdx
mov %rdx,$A[0]
mulq $m1 # np[j]*m1
add %rax,$N[1]
mov 16($ap),%rax
adc \$0,%rdx
add $A[1],$N[1] # np[j]*m1+ap[j]*bp[i]+tp[j]
lea 4($j),$j # j+=2
adc \$0,%rdx
mov $N[1],(%rsp) # tp[j-1]
mov %rdx,$N[0]
jmp .Linner4x
.align 16
.Linner4x:
mulq $m0 # ap[j]*bp[i]
add %rax,$A[0]
mov -16($np,$j,8),%rax
adc \$0,%rdx
add -16(%rsp,$j,8),$A[0] # ap[j]*bp[i]+tp[j]
adc \$0,%rdx
mov %rdx,$A[1]
mulq $m1 # np[j]*m1
add %rax,$N[0]
mov -8($ap,$j,8),%rax
adc \$0,%rdx
add $A[0],$N[0]
adc \$0,%rdx
mov $N[0],-24(%rsp,$j,8) # tp[j-1]
mov %rdx,$N[1]
mulq $m0 # ap[j]*bp[i]
add %rax,$A[1]
mov -8($np,$j,8),%rax
adc \$0,%rdx
add -8(%rsp,$j,8),$A[1]
adc \$0,%rdx
mov %rdx,$A[0]
mulq $m1 # np[j]*m1
add %rax,$N[1]
mov ($ap,$j,8),%rax
adc \$0,%rdx
add $A[1],$N[1]
adc \$0,%rdx
mov $N[1],-16(%rsp,$j,8) # tp[j-1]
mov %rdx,$N[0]
mulq $m0 # ap[j]*bp[i]
add %rax,$A[0]
mov ($np,$j,8),%rax
adc \$0,%rdx
add (%rsp,$j,8),$A[0] # ap[j]*bp[i]+tp[j]
adc \$0,%rdx
mov %rdx,$A[1]
mulq $m1 # np[j]*m1
add %rax,$N[0]
mov 8($ap,$j,8),%rax
adc \$0,%rdx
add $A[0],$N[0]
adc \$0,%rdx
mov $N[0],-8(%rsp,$j,8) # tp[j-1]
mov %rdx,$N[1]
mulq $m0 # ap[j]*bp[i]
add %rax,$A[1]
mov 8($np,$j,8),%rax
adc \$0,%rdx
add 8(%rsp,$j,8),$A[1]
adc \$0,%rdx
lea 4($j),$j # j++
mov %rdx,$A[0]
mulq $m1 # np[j]*m1
add %rax,$N[1]
mov -16($ap,$j,8),%rax
adc \$0,%rdx
add $A[1],$N[1]
adc \$0,%rdx
mov $N[1],-32(%rsp,$j,8) # tp[j-1]
mov %rdx,$N[0]
cmp $num,$j
jl .Linner4x
mulq $m0 # ap[j]*bp[i]
add %rax,$A[0]
mov -16($np,$j,8),%rax
adc \$0,%rdx
add -16(%rsp,$j,8),$A[0] # ap[j]*bp[i]+tp[j]
adc \$0,%rdx
mov %rdx,$A[1]
mulq $m1 # np[j]*m1
add %rax,$N[0]
mov -8($ap,$j,8),%rax
adc \$0,%rdx
add $A[0],$N[0]
adc \$0,%rdx
mov $N[0],-24(%rsp,$j,8) # tp[j-1]
mov %rdx,$N[1]
mulq $m0 # ap[j]*bp[i]
add %rax,$A[1]
mov -8($np,$j,8),%rax
adc \$0,%rdx
add -8(%rsp,$j,8),$A[1]
adc \$0,%rdx
lea 1($i),$i # i++
mov %rdx,$A[0]
mulq $m1 # np[j]*m1
add %rax,$N[1]
mov ($ap),%rax # ap[0]
adc \$0,%rdx
add $A[1],$N[1]
adc \$0,%rdx
mov $N[1],-16(%rsp,$j,8) # tp[j-1]
mov %rdx,$N[0]
movq %xmm0,$m0 # bp[i+1]
xor $N[1],$N[1]
add $A[0],$N[0]
adc \$0,$N[1]
add (%rsp,$num,8),$N[0] # pull upmost overflow bit
adc \$0,$N[1]
mov $N[0],-8(%rsp,$j,8)
mov $N[1],(%rsp,$j,8) # store upmost overflow bit
cmp $num,$i
jl .Louter4x
___
{
my @ri=("%rax","%rdx",$m0,$m1);
$code.=<<___;
mov 16(%rsp,$num,8),$rp # restore $rp
mov 0(%rsp),@ri[0] # tp[0]
pxor %xmm0,%xmm0
mov 8(%rsp),@ri[1] # tp[1]
shr \$2,$num # num/=4
lea (%rsp),$ap # borrow ap for tp
xor $i,$i # i=0 and clear CF!
sub 0($np),@ri[0]
mov 16($ap),@ri[2] # tp[2]
mov 24($ap),@ri[3] # tp[3]
sbb 8($np),@ri[1]
lea -1($num),$j # j=num/4-1
jmp .Lsub4x
.align 16
.Lsub4x:
mov @ri[0],0($rp,$i,8) # rp[i]=tp[i]-np[i]
mov @ri[1],8($rp,$i,8) # rp[i]=tp[i]-np[i]
sbb 16($np,$i,8),@ri[2]
mov 32($ap,$i,8),@ri[0] # tp[i+1]
mov 40($ap,$i,8),@ri[1]
sbb 24($np,$i,8),@ri[3]
mov @ri[2],16($rp,$i,8) # rp[i]=tp[i]-np[i]
mov @ri[3],24($rp,$i,8) # rp[i]=tp[i]-np[i]
sbb 32($np,$i,8),@ri[0]
mov 48($ap,$i,8),@ri[2]
mov 56($ap,$i,8),@ri[3]
sbb 40($np,$i,8),@ri[1]
lea 4($i),$i # i++
dec $j # doesnn't affect CF!
jnz .Lsub4x
mov @ri[0],0($rp,$i,8) # rp[i]=tp[i]-np[i]
mov 32($ap,$i,8),@ri[0] # load overflow bit
sbb 16($np,$i,8),@ri[2]
mov @ri[1],8($rp,$i,8) # rp[i]=tp[i]-np[i]
sbb 24($np,$i,8),@ri[3]
mov @ri[2],16($rp,$i,8) # rp[i]=tp[i]-np[i]
sbb \$0,@ri[0] # handle upmost overflow bit
mov @ri[3],24($rp,$i,8) # rp[i]=tp[i]-np[i]
xor $i,$i # i=0
and @ri[0],$ap
not @ri[0]
mov $rp,$np
and @ri[0],$np
lea -1($num),$j
or $np,$ap # ap=borrow?tp:rp
movdqu ($ap),%xmm1
movdqa %xmm0,(%rsp)
movdqu %xmm1,($rp)
jmp .Lcopy4x
.align 16
.Lcopy4x: # copy or in-place refresh
movdqu 16($ap,$i),%xmm2
movdqu 32($ap,$i),%xmm1
movdqa %xmm0,16(%rsp,$i)
movdqu %xmm2,16($rp,$i)
movdqa %xmm0,32(%rsp,$i)
movdqu %xmm1,32($rp,$i)
lea 32($i),$i
dec $j
jnz .Lcopy4x
shl \$2,$num
movdqu 16($ap,$i),%xmm2
movdqa %xmm0,16(%rsp,$i)
movdqu %xmm2,16($rp,$i)
___
}
$code.=<<___;
mov 8(%rsp,$num,8),%rsi # restore %rsp
mov \$1,%rax
___
$code.=<<___ if ($win64);
movaps (%rsi),%xmm6
movaps 0x10(%rsi),%xmm7
lea 0x28(%rsi),%rsi
___
$code.=<<___;
mov (%rsi),%r15
mov 8(%rsi),%r14
mov 16(%rsi),%r13
mov 24(%rsi),%r12
mov 32(%rsi),%rbp
mov 40(%rsi),%rbx
lea 48(%rsi),%rsp
.Lmul4x_epilogue:
ret
.size bn_mul4x_mont_gather5,.-bn_mul4x_mont_gather5
___
}}}
{
my ($inp,$num,$tbl,$idx)=$win64?("%rcx","%rdx","%r8", "%r9") : # Win64 order
("%rdi","%rsi","%rdx","%rcx"); # Unix order
$code.=<<___;
.globl bn_scatter5
.type bn_scatter5,\@abi-omnipotent
.align 16
bn_scatter5:
cmp \$0, $num
jz .Lscatter_epilogue
lea ($tbl,$idx,8),$tbl
.Lscatter:
mov ($inp),%rax
lea 8($inp),$inp
mov %rax,($tbl)
lea 32*8($tbl),$tbl
sub \$1,$num
jnz .Lscatter
.Lscatter_epilogue:
ret
.size bn_scatter5,.-bn_scatter5
___
}
$code.=<<___;
.align 64
.Lmagic_masks:
.long 0,0, 0,0, 0,0, -1,-1
.long 0,0, 0,0, 0,0, 0,0
.asciz "Montgomery Multiplication with scatter/gather for x86_64, CRYPTOGAMS by <appro\@openssl.org>"
___
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
# EXCEPTION_DISPOSITION handler (EXCEPTION_RECORD *rec,ULONG64 frame,
# CONTEXT *context,DISPATCHER_CONTEXT *disp)
if ($win64) {
$rec="%rcx";
$frame="%rdx";
$context="%r8";
$disp="%r9";
$code.=<<___;
.extern __imp_RtlVirtualUnwind
.type mul_handler,\@abi-omnipotent
.align 16
mul_handler:
push %rsi
push %rdi
push %rbx
push %rbp
push %r12
push %r13
push %r14
push %r15
pushfq
sub \$64,%rsp
mov 120($context),%rax # pull context->Rax
mov 248($context),%rbx # pull context->Rip
mov 8($disp),%rsi # disp->ImageBase
mov 56($disp),%r11 # disp->HandlerData
mov 0(%r11),%r10d # HandlerData[0]
lea (%rsi,%r10),%r10 # end of prologue label
cmp %r10,%rbx # context->Rip<end of prologue label
jb .Lcommon_seh_tail
lea `40+48`(%rax),%rax
mov 4(%r11),%r10d # HandlerData[1]
lea (%rsi,%r10),%r10 # end of alloca label
cmp %r10,%rbx # context->Rip<end of alloca label
jb .Lcommon_seh_tail
mov 152($context),%rax # pull context->Rsp
mov 8(%r11),%r10d # HandlerData[2]
lea (%rsi,%r10),%r10 # epilogue label
cmp %r10,%rbx # context->Rip>=epilogue label
jae .Lcommon_seh_tail
mov 192($context),%r10 # pull $num
mov 8(%rax,%r10,8),%rax # pull saved stack pointer
movaps (%rax),%xmm0
movaps 16(%rax),%xmm1
lea `40+48`(%rax),%rax
mov -8(%rax),%rbx
mov -16(%rax),%rbp
mov -24(%rax),%r12
mov -32(%rax),%r13
mov -40(%rax),%r14
mov -48(%rax),%r15
mov %rbx,144($context) # restore context->Rbx
mov %rbp,160($context) # restore context->Rbp
mov %r12,216($context) # restore context->R12
mov %r13,224($context) # restore context->R13
mov %r14,232($context) # restore context->R14
mov %r15,240($context) # restore context->R15
movups %xmm0,512($context) # restore context->Xmm6
movups %xmm1,528($context) # restore context->Xmm7
.Lcommon_seh_tail:
mov 8(%rax),%rdi
mov 16(%rax),%rsi
mov %rax,152($context) # restore context->Rsp
mov %rsi,168($context) # restore context->Rsi
mov %rdi,176($context) # restore context->Rdi
mov 40($disp),%rdi # disp->ContextRecord
mov $context,%rsi # context
mov \$154,%ecx # sizeof(CONTEXT)
.long 0xa548f3fc # cld; rep movsq
mov $disp,%rsi
xor %rcx,%rcx # arg1, UNW_FLAG_NHANDLER
mov 8(%rsi),%rdx # arg2, disp->ImageBase
mov 0(%rsi),%r8 # arg3, disp->ControlPc
mov 16(%rsi),%r9 # arg4, disp->FunctionEntry
mov 40(%rsi),%r10 # disp->ContextRecord
lea 56(%rsi),%r11 # &disp->HandlerData
lea 24(%rsi),%r12 # &disp->EstablisherFrame
mov %r10,32(%rsp) # arg5
mov %r11,40(%rsp) # arg6
mov %r12,48(%rsp) # arg7
mov %rcx,56(%rsp) # arg8, (NULL)
call *__imp_RtlVirtualUnwind(%rip)
mov \$1,%eax # ExceptionContinueSearch
add \$64,%rsp
popfq
pop %r15
pop %r14
pop %r13
pop %r12
pop %rbp
pop %rbx
pop %rdi
pop %rsi
ret
.size mul_handler,.-mul_handler
.section .pdata
.align 4
.rva .LSEH_begin_bn_mul_mont_gather5
.rva .LSEH_end_bn_mul_mont_gather5
.rva .LSEH_info_bn_mul_mont_gather5
.rva .LSEH_begin_bn_mul4x_mont_gather5
.rva .LSEH_end_bn_mul4x_mont_gather5
.rva .LSEH_info_bn_mul4x_mont_gather5
.section .xdata
.align 8
.LSEH_info_bn_mul_mont_gather5:
.byte 9,0,0,0
.rva mul_handler
.rva .Lmul_alloca,.Lmul_body,.Lmul_epilogue # HandlerData[]
.align 8
.LSEH_info_bn_mul4x_mont_gather5:
.byte 9,0,0,0
.rva mul_handler
.rva .Lmul4x_alloca,.Lmul4x_body,.Lmul4x_epilogue # HandlerData[]
.align 8
___
}
$code =~ s/\`([^\`]*)\`/eval($1)/gem;
print $code;