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
|
#!/usr/bin/env perl
# ====================================================================
# Written by Andy Polyakov <appro@fy.chalmers.se> 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/.
# ====================================================================
# December 2005
#
# Pure SPARCv9/8+ and IALU-only bn_mul_mont implementation. The reasons
# for undertaken effort are multiple. First of all, UltraSPARC is not
# the whole SPARCv9 universe and other VIS-free implementations deserve
# optimized code as much. Secondly, newly introduced UltraSPARC T1,
# a.k.a. Niagara, has shared FPU and concurrent FPU-intensive paths,
# such as sparcv9a-mont, will simply sink it. Yes, T1 is equipped with
# several integrated RSA/DSA accelerator circuits accessible through
# kernel driver [only(*)], but having decent user-land software
# implementation is important too. Finally, reasons like desire to
# experiment with dedicated squaring procedure. Yes, this module
# implements one, because it was easiest to draft it in SPARCv9
# instructions...
# (*) Engine accessing the driver in question is on my TODO list.
# For reference, acceleator is estimated to give 6 to 10 times
# improvement on single-threaded RSA sign. It should be noted
# that 6-10x improvement coefficient does not actually mean
# something extraordinary in terms of absolute [single-threaded]
# performance, as SPARCv9 instruction set is by all means least
# suitable for high performance crypto among other 64 bit
# platforms. 6-10x factor simply places T1 in same performance
# domain as say AMD64 and IA-64. Improvement of RSA verify don't
# appear impressive at all, but it's the sign operation which is
# far more critical/interesting.
# You might notice that inner loops are modulo-scheduled:-) This has
# essentially negligible impact on UltraSPARC performance, it's
# Fujitsu SPARC64 V users who should notice and hopefully appreciate
# the advantage... Currently this module surpasses sparcv9a-mont.pl
# by ~20% on UltraSPARC-III and later cores, but recall that sparcv9a
# module still have hidden potential [see TODO list there], which is
# estimated to be larger than 20%...
# int bn_mul_mont(
$rp="%i0"; # BN_ULONG *rp,
$ap="%i1"; # const BN_ULONG *ap,
$bp="%i2"; # const BN_ULONG *bp,
$np="%i3"; # const BN_ULONG *np,
$n0="%i4"; # const BN_ULONG *n0,
$num="%i5"; # int num);
$bits=32;
for (@ARGV) { $bits=64 if (/\-m64/ || /\-xarch\=v9/); }
if ($bits==64) { $bias=2047; $frame=192; }
else { $bias=0; $frame=128; }
$car0="%o0";
$car1="%o1";
$car2="%o2"; # 1 bit
$acc0="%o3";
$acc1="%o4";
$mask="%g1"; # 32 bits, what a waste...
$tmp0="%g4";
$tmp1="%g5";
$i="%l0";
$j="%l1";
$mul0="%l2";
$mul1="%l3";
$tp="%l4";
$apj="%l5";
$npj="%l6";
$tpj="%l7";
$fname="bn_mul_mont_int";
$code=<<___;
.section ".text",#alloc,#execinstr
.global $fname
.align 32
$fname:
cmp %o5,4 ! 128 bits minimum
bge,pt %icc,.Lenter
sethi %hi(0xffffffff),$mask
retl
clr %o0
.align 32
.Lenter:
save %sp,-$frame,%sp
sll $num,2,$num ! num*=4
or $mask,%lo(0xffffffff),$mask
ld [$n0],$n0
cmp $ap,$bp
and $num,$mask,$num
ld [$bp],$mul0 ! bp[0]
nop
add %sp,$bias,%o7 ! real top of stack
ld [$ap],$car0 ! ap[0] ! redundant in squaring context
sub %o7,$num,%o7
ld [$ap+4],$apj ! ap[1]
and %o7,-1024,%o7
ld [$np],$car1 ! np[0]
sub %o7,$bias,%sp ! alloca
ld [$np+4],$npj ! np[1]
be,pt `$bits==32?"%icc":"%xcc"`,.Lbn_sqr_mont
mov 12,$j
mulx $car0,$mul0,$car0 ! ap[0]*bp[0]
mulx $apj,$mul0,$tmp0 !prologue! ap[1]*bp[0]
and $car0,$mask,$acc0
add %sp,$bias+$frame,$tp
ld [$ap+8],$apj !prologue!
mulx $n0,$acc0,$mul1 ! "t[0]"*n0
and $mul1,$mask,$mul1
mulx $car1,$mul1,$car1 ! np[0]*"t[0]"*n0
mulx $npj,$mul1,$acc1 !prologue! np[1]*"t[0]"*n0
srlx $car0,32,$car0
add $acc0,$car1,$car1
ld [$np+8],$npj !prologue!
srlx $car1,32,$car1
mov $tmp0,$acc0 !prologue!
.L1st:
mulx $apj,$mul0,$tmp0
mulx $npj,$mul1,$tmp1
add $acc0,$car0,$car0
ld [$ap+$j],$apj ! ap[j]
and $car0,$mask,$acc0
add $acc1,$car1,$car1
ld [$np+$j],$npj ! np[j]
srlx $car0,32,$car0
add $acc0,$car1,$car1
add $j,4,$j ! j++
mov $tmp0,$acc0
st $car1,[$tp]
cmp $j,$num
mov $tmp1,$acc1
srlx $car1,32,$car1
bl %icc,.L1st
add $tp,4,$tp ! tp++
!.L1st
mulx $apj,$mul0,$tmp0 !epilogue!
mulx $npj,$mul1,$tmp1
add $acc0,$car0,$car0
and $car0,$mask,$acc0
add $acc1,$car1,$car1
srlx $car0,32,$car0
add $acc0,$car1,$car1
st $car1,[$tp]
srlx $car1,32,$car1
add $tmp0,$car0,$car0
and $car0,$mask,$acc0
add $tmp1,$car1,$car1
srlx $car0,32,$car0
add $acc0,$car1,$car1
st $car1,[$tp+4]
srlx $car1,32,$car1
add $car0,$car1,$car1
st $car1,[$tp+8]
srlx $car1,32,$car2
mov 4,$i ! i++
ld [$bp+4],$mul0 ! bp[1]
.Louter:
add %sp,$bias+$frame,$tp
ld [$ap],$car0 ! ap[0]
ld [$ap+4],$apj ! ap[1]
ld [$np],$car1 ! np[0]
ld [$np+4],$npj ! np[1]
ld [$tp],$tmp1 ! tp[0]
ld [$tp+4],$tpj ! tp[1]
mov 12,$j
mulx $car0,$mul0,$car0
mulx $apj,$mul0,$tmp0 !prologue!
add $tmp1,$car0,$car0
ld [$ap+8],$apj !prologue!
and $car0,$mask,$acc0
mulx $n0,$acc0,$mul1
and $mul1,$mask,$mul1
mulx $car1,$mul1,$car1
mulx $npj,$mul1,$acc1 !prologue!
srlx $car0,32,$car0
add $acc0,$car1,$car1
ld [$np+8],$npj !prologue!
srlx $car1,32,$car1
mov $tmp0,$acc0 !prologue!
.Linner:
mulx $apj,$mul0,$tmp0
mulx $npj,$mul1,$tmp1
add $tpj,$car0,$car0
ld [$ap+$j],$apj ! ap[j]
add $acc0,$car0,$car0
add $acc1,$car1,$car1
ld [$np+$j],$npj ! np[j]
and $car0,$mask,$acc0
ld [$tp+8],$tpj ! tp[j]
srlx $car0,32,$car0
add $acc0,$car1,$car1
add $j,4,$j ! j++
mov $tmp0,$acc0
st $car1,[$tp] ! tp[j-1]
srlx $car1,32,$car1
mov $tmp1,$acc1
cmp $j,$num
bl %icc,.Linner
add $tp,4,$tp ! tp++
!.Linner
mulx $apj,$mul0,$tmp0 !epilogue!
mulx $npj,$mul1,$tmp1
add $tpj,$car0,$car0
add $acc0,$car0,$car0
ld [$tp+8],$tpj ! tp[j]
and $car0,$mask,$acc0
add $acc1,$car1,$car1
srlx $car0,32,$car0
add $acc0,$car1,$car1
st $car1,[$tp] ! tp[j-1]
srlx $car1,32,$car1
add $tpj,$car0,$car0
add $tmp0,$car0,$car0
and $car0,$mask,$acc0
add $tmp1,$car1,$car1
add $acc0,$car1,$car1
st $car1,[$tp+4] ! tp[j-1]
srlx $car0,32,$car0
add $i,4,$i ! i++
srlx $car1,32,$car1
add $car0,$car1,$car1
cmp $i,$num
add $car2,$car1,$car1
st $car1,[$tp+8]
srlx $car1,32,$car2
bl,a %icc,.Louter
ld [$bp+$i],$mul0 ! bp[i]
!.Louter
add $tp,12,$tp
.Ltail:
add $np,$num,$np
add $rp,$num,$rp
mov $tp,$ap
sub %g0,$num,%o7 ! k=-num
ba .Lsub
subcc %g0,%g0,%g0 ! clear %icc.c
.align 16
.Lsub:
ld [$tp+%o7],%o0
ld [$np+%o7],%o1
subccc %o0,%o1,%o1 ! tp[j]-np[j]
add $rp,%o7,$i
add %o7,4,%o7
brnz %o7,.Lsub
st %o1,[$i]
subc $car2,0,$car2 ! handle upmost overflow bit
and $tp,$car2,$ap
andn $rp,$car2,$np
or $ap,$np,$ap
sub %g0,$num,%o7
.Lcopy:
ld [$ap+%o7],%o0 ! copy or in-place refresh
st %g0,[$tp+%o7] ! zap tp
st %o0,[$rp+%o7]
add %o7,4,%o7
brnz %o7,.Lcopy
nop
mov 1,%i0
ret
restore
___
########
######## .Lbn_sqr_mont gives up to 20% *overall* improvement over
######## code without following dedicated squaring procedure.
########
$sbit="%i2"; # re-use $bp!
$code.=<<___;
.align 32
.Lbn_sqr_mont:
mulx $mul0,$mul0,$car0 ! ap[0]*ap[0]
mulx $apj,$mul0,$tmp0 !prologue!
and $car0,$mask,$acc0
add %sp,$bias+$frame,$tp
ld [$ap+8],$apj !prologue!
mulx $n0,$acc0,$mul1 ! "t[0]"*n0
srlx $car0,32,$car0
and $mul1,$mask,$mul1
mulx $car1,$mul1,$car1 ! np[0]*"t[0]"*n0
mulx $npj,$mul1,$acc1 !prologue!
and $car0,1,$sbit
ld [$np+8],$npj !prologue!
srlx $car0,1,$car0
add $acc0,$car1,$car1
srlx $car1,32,$car1
mov $tmp0,$acc0 !prologue!
.Lsqr_1st:
mulx $apj,$mul0,$tmp0
mulx $npj,$mul1,$tmp1
add $acc0,$car0,$car0 ! ap[j]*a0+c0
add $acc1,$car1,$car1
ld [$ap+$j],$apj ! ap[j]
and $car0,$mask,$acc0
ld [$np+$j],$npj ! np[j]
srlx $car0,32,$car0
add $acc0,$acc0,$acc0
or $sbit,$acc0,$acc0
mov $tmp1,$acc1
srlx $acc0,32,$sbit
add $j,4,$j ! j++
and $acc0,$mask,$acc0
cmp $j,$num
add $acc0,$car1,$car1
st $car1,[$tp]
mov $tmp0,$acc0
srlx $car1,32,$car1
bl %icc,.Lsqr_1st
add $tp,4,$tp ! tp++
!.Lsqr_1st
mulx $apj,$mul0,$tmp0 ! epilogue
mulx $npj,$mul1,$tmp1
add $acc0,$car0,$car0 ! ap[j]*a0+c0
add $acc1,$car1,$car1
and $car0,$mask,$acc0
srlx $car0,32,$car0
add $acc0,$acc0,$acc0
or $sbit,$acc0,$acc0
srlx $acc0,32,$sbit
and $acc0,$mask,$acc0
add $acc0,$car1,$car1
st $car1,[$tp]
srlx $car1,32,$car1
add $tmp0,$car0,$car0 ! ap[j]*a0+c0
add $tmp1,$car1,$car1
and $car0,$mask,$acc0
srlx $car0,32,$car0
add $acc0,$acc0,$acc0
or $sbit,$acc0,$acc0
srlx $acc0,32,$sbit
and $acc0,$mask,$acc0
add $acc0,$car1,$car1
st $car1,[$tp+4]
srlx $car1,32,$car1
add $car0,$car0,$car0
or $sbit,$car0,$car0
add $car0,$car1,$car1
st $car1,[$tp+8]
srlx $car1,32,$car2
ld [%sp+$bias+$frame],$tmp0 ! tp[0]
ld [%sp+$bias+$frame+4],$tmp1 ! tp[1]
ld [%sp+$bias+$frame+8],$tpj ! tp[2]
ld [$ap+4],$mul0 ! ap[1]
ld [$ap+8],$apj ! ap[2]
ld [$np],$car1 ! np[0]
ld [$np+4],$npj ! np[1]
mulx $n0,$tmp0,$mul1
mulx $mul0,$mul0,$car0
and $mul1,$mask,$mul1
mulx $car1,$mul1,$car1
mulx $npj,$mul1,$acc1
add $tmp0,$car1,$car1
and $car0,$mask,$acc0
ld [$np+8],$npj ! np[2]
srlx $car1,32,$car1
add $tmp1,$car1,$car1
srlx $car0,32,$car0
add $acc0,$car1,$car1
and $car0,1,$sbit
add $acc1,$car1,$car1
srlx $car0,1,$car0
mov 12,$j
st $car1,[%sp+$bias+$frame] ! tp[0]=
srlx $car1,32,$car1
add %sp,$bias+$frame+4,$tp
.Lsqr_2nd:
mulx $apj,$mul0,$acc0
mulx $npj,$mul1,$acc1
add $acc0,$car0,$car0
add $tpj,$car1,$car1
ld [$ap+$j],$apj ! ap[j]
and $car0,$mask,$acc0
ld [$np+$j],$npj ! np[j]
srlx $car0,32,$car0
add $acc1,$car1,$car1
ld [$tp+8],$tpj ! tp[j]
add $acc0,$acc0,$acc0
add $j,4,$j ! j++
or $sbit,$acc0,$acc0
srlx $acc0,32,$sbit
and $acc0,$mask,$acc0
cmp $j,$num
add $acc0,$car1,$car1
st $car1,[$tp] ! tp[j-1]
srlx $car1,32,$car1
bl %icc,.Lsqr_2nd
add $tp,4,$tp ! tp++
!.Lsqr_2nd
mulx $apj,$mul0,$acc0
mulx $npj,$mul1,$acc1
add $acc0,$car0,$car0
add $tpj,$car1,$car1
and $car0,$mask,$acc0
srlx $car0,32,$car0
add $acc1,$car1,$car1
add $acc0,$acc0,$acc0
or $sbit,$acc0,$acc0
srlx $acc0,32,$sbit
and $acc0,$mask,$acc0
add $acc0,$car1,$car1
st $car1,[$tp] ! tp[j-1]
srlx $car1,32,$car1
add $car0,$car0,$car0
or $sbit,$car0,$car0
add $car0,$car1,$car1
add $car2,$car1,$car1
st $car1,[$tp+4]
srlx $car1,32,$car2
ld [%sp+$bias+$frame],$tmp1 ! tp[0]
ld [%sp+$bias+$frame+4],$tpj ! tp[1]
ld [$ap+8],$mul0 ! ap[2]
ld [$np],$car1 ! np[0]
ld [$np+4],$npj ! np[1]
mulx $n0,$tmp1,$mul1
and $mul1,$mask,$mul1
mov 8,$i
mulx $mul0,$mul0,$car0
mulx $car1,$mul1,$car1
and $car0,$mask,$acc0
add $tmp1,$car1,$car1
srlx $car0,32,$car0
add %sp,$bias+$frame,$tp
srlx $car1,32,$car1
and $car0,1,$sbit
srlx $car0,1,$car0
mov 4,$j
.Lsqr_outer:
.Lsqr_inner1:
mulx $npj,$mul1,$acc1
add $tpj,$car1,$car1
add $j,4,$j
ld [$tp+8],$tpj
cmp $j,$i
add $acc1,$car1,$car1
ld [$np+$j],$npj
st $car1,[$tp]
srlx $car1,32,$car1
bl %icc,.Lsqr_inner1
add $tp,4,$tp
!.Lsqr_inner1
add $j,4,$j
ld [$ap+$j],$apj ! ap[j]
mulx $npj,$mul1,$acc1
add $tpj,$car1,$car1
ld [$np+$j],$npj ! np[j]
add $acc0,$car1,$car1
ld [$tp+8],$tpj ! tp[j]
add $acc1,$car1,$car1
st $car1,[$tp]
srlx $car1,32,$car1
add $j,4,$j
cmp $j,$num
be,pn %icc,.Lsqr_no_inner2
add $tp,4,$tp
.Lsqr_inner2:
mulx $apj,$mul0,$acc0
mulx $npj,$mul1,$acc1
add $tpj,$car1,$car1
add $acc0,$car0,$car0
ld [$ap+$j],$apj ! ap[j]
and $car0,$mask,$acc0
ld [$np+$j],$npj ! np[j]
srlx $car0,32,$car0
add $acc0,$acc0,$acc0
ld [$tp+8],$tpj ! tp[j]
or $sbit,$acc0,$acc0
add $j,4,$j ! j++
srlx $acc0,32,$sbit
and $acc0,$mask,$acc0
cmp $j,$num
add $acc0,$car1,$car1
add $acc1,$car1,$car1
st $car1,[$tp] ! tp[j-1]
srlx $car1,32,$car1
bl %icc,.Lsqr_inner2
add $tp,4,$tp ! tp++
.Lsqr_no_inner2:
mulx $apj,$mul0,$acc0
mulx $npj,$mul1,$acc1
add $tpj,$car1,$car1
add $acc0,$car0,$car0
and $car0,$mask,$acc0
srlx $car0,32,$car0
add $acc0,$acc0,$acc0
or $sbit,$acc0,$acc0
srlx $acc0,32,$sbit
and $acc0,$mask,$acc0
add $acc0,$car1,$car1
add $acc1,$car1,$car1
st $car1,[$tp] ! tp[j-1]
srlx $car1,32,$car1
add $car0,$car0,$car0
or $sbit,$car0,$car0
add $car0,$car1,$car1
add $car2,$car1,$car1
st $car1,[$tp+4]
srlx $car1,32,$car2
add $i,4,$i ! i++
ld [%sp+$bias+$frame],$tmp1 ! tp[0]
ld [%sp+$bias+$frame+4],$tpj ! tp[1]
ld [$ap+$i],$mul0 ! ap[j]
ld [$np],$car1 ! np[0]
ld [$np+4],$npj ! np[1]
mulx $n0,$tmp1,$mul1
and $mul1,$mask,$mul1
add $i,4,$tmp0
mulx $mul0,$mul0,$car0
mulx $car1,$mul1,$car1
and $car0,$mask,$acc0
add $tmp1,$car1,$car1
srlx $car0,32,$car0
add %sp,$bias+$frame,$tp
srlx $car1,32,$car1
and $car0,1,$sbit
srlx $car0,1,$car0
cmp $tmp0,$num ! i<num-1
bl %icc,.Lsqr_outer
mov 4,$j
.Lsqr_last:
mulx $npj,$mul1,$acc1
add $tpj,$car1,$car1
add $j,4,$j
ld [$tp+8],$tpj
cmp $j,$i
add $acc1,$car1,$car1
ld [$np+$j],$npj
st $car1,[$tp]
srlx $car1,32,$car1
bl %icc,.Lsqr_last
add $tp,4,$tp
!.Lsqr_last
mulx $npj,$mul1,$acc1
add $tpj,$car1,$car1
add $acc0,$car1,$car1
add $acc1,$car1,$car1
st $car1,[$tp]
srlx $car1,32,$car1
add $car0,$car0,$car0 ! recover $car0
or $sbit,$car0,$car0
add $car0,$car1,$car1
add $car2,$car1,$car1
st $car1,[$tp+4]
srlx $car1,32,$car2
ba .Ltail
add $tp,8,$tp
.type $fname,#function
.size $fname,(.-$fname)
.asciz "Montgomery Multipltication for SPARCv9, CRYPTOGAMS by <appro\@openssl.org>"
.align 32
___
$code =~ s/\`([^\`]*)\`/eval($1)/gem;
print $code;
close STDOUT;
|