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
| #! /usr/bin/env perl
| # Copyright 2006-2020 The OpenSSL Project Authors. All Rights Reserved.
| #
| # Licensed under the OpenSSL license (the "License"). You may not use
| # this file except in compliance with the License. You can obtain a copy
| # in the file LICENSE in the source distribution or at
| # https://www.openssl.org/source/license.html
|
| #
| # ====================================================================
| # 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/.
| # ====================================================================
| #
| # On 21264 RSA sign performance improves by 70/35/20/15 percent for
| # 512/1024/2048/4096 bit key lengths. This is against vendor compiler
| # instructed to '-tune host' code with in-line assembler. Other
| # benchmarks improve by 15-20%. To anchor it to something else, the
| # code provides approximately the same performance per GHz as AMD64.
| # I.e. if you compare 1GHz 21264 and 2GHz Opteron, you'll observe ~2x
| # difference.
|
| $output=pop;
| open STDOUT,">$output";
|
| # int bn_mul_mont(
| $rp="a0"; # BN_ULONG *rp,
| $ap="a1"; # const BN_ULONG *ap,
| $bp="a2"; # const BN_ULONG *bp,
| $np="a3"; # const BN_ULONG *np,
| $n0="a4"; # const BN_ULONG *n0,
| $num="a5"; # int num);
|
| $lo0="t0";
| $hi0="t1";
| $lo1="t2";
| $hi1="t3";
| $aj="t4";
| $bi="t5";
| $nj="t6";
| $tp="t7";
| $alo="t8";
| $ahi="t9";
| $nlo="t10";
| $nhi="t11";
| $tj="t12";
| $i="s3";
| $j="s4";
| $m1="s5";
|
| $code=<<___;
| #ifdef __linux__
| #include <asm/regdef.h>
| #else
| #include <asm.h>
| #include <regdef.h>
| #endif
|
| .text
|
| .set noat
| .set noreorder
|
| .globl bn_mul_mont
| .align 5
| .ent bn_mul_mont
| bn_mul_mont:
| lda sp,-48(sp)
| stq ra,0(sp)
| stq s3,8(sp)
| stq s4,16(sp)
| stq s5,24(sp)
| stq fp,32(sp)
| mov sp,fp
| .mask 0x0400f000,-48
| .frame fp,48,ra
| .prologue 0
|
| .align 4
| .set reorder
| sextl $num,$num
| mov 0,v0
| cmplt $num,4,AT
| bne AT,.Lexit
|
| ldq $hi0,0($ap) # ap[0]
| s8addq $num,16,AT
| ldq $aj,8($ap)
| subq sp,AT,sp
| ldq $bi,0($bp) # bp[0]
| lda AT,-4096(zero) # mov -4096,AT
| ldq $n0,0($n0)
| and sp,AT,sp
|
| mulq $hi0,$bi,$lo0
| ldq $hi1,0($np) # np[0]
| umulh $hi0,$bi,$hi0
| ldq $nj,8($np)
|
| mulq $lo0,$n0,$m1
|
| mulq $hi1,$m1,$lo1
| umulh $hi1,$m1,$hi1
|
| addq $lo1,$lo0,$lo1
| cmpult $lo1,$lo0,AT
| addq $hi1,AT,$hi1
|
| mulq $aj,$bi,$alo
| mov 2,$j
| umulh $aj,$bi,$ahi
| mov sp,$tp
|
| mulq $nj,$m1,$nlo
| s8addq $j,$ap,$aj
| umulh $nj,$m1,$nhi
| s8addq $j,$np,$nj
| .align 4
| .L1st:
| .set noreorder
| ldq $aj,0($aj)
| addl $j,1,$j
| ldq $nj,0($nj)
| lda $tp,8($tp)
|
| addq $alo,$hi0,$lo0
| mulq $aj,$bi,$alo
| cmpult $lo0,$hi0,AT
| addq $nlo,$hi1,$lo1
|
| mulq $nj,$m1,$nlo
| addq $ahi,AT,$hi0
| cmpult $lo1,$hi1,v0
| cmplt $j,$num,$tj
|
| umulh $aj,$bi,$ahi
| addq $nhi,v0,$hi1
| addq $lo1,$lo0,$lo1
| s8addq $j,$ap,$aj
|
| umulh $nj,$m1,$nhi
| cmpult $lo1,$lo0,v0
| addq $hi1,v0,$hi1
| s8addq $j,$np,$nj
|
| stq $lo1,-8($tp)
| nop
| unop
| bne $tj,.L1st
| .set reorder
|
| addq $alo,$hi0,$lo0
| addq $nlo,$hi1,$lo1
| cmpult $lo0,$hi0,AT
| cmpult $lo1,$hi1,v0
| addq $ahi,AT,$hi0
| addq $nhi,v0,$hi1
|
| addq $lo1,$lo0,$lo1
| cmpult $lo1,$lo0,v0
| addq $hi1,v0,$hi1
|
| stq $lo1,0($tp)
|
| addq $hi1,$hi0,$hi1
| cmpult $hi1,$hi0,AT
| stq $hi1,8($tp)
| stq AT,16($tp)
|
| mov 1,$i
| .align 4
| .Louter:
| s8addq $i,$bp,$bi
| ldq $hi0,0($ap)
| ldq $aj,8($ap)
| ldq $bi,0($bi)
| ldq $hi1,0($np)
| ldq $nj,8($np)
| ldq $tj,0(sp)
|
| mulq $hi0,$bi,$lo0
| umulh $hi0,$bi,$hi0
|
| addq $lo0,$tj,$lo0
| cmpult $lo0,$tj,AT
| addq $hi0,AT,$hi0
|
| mulq $lo0,$n0,$m1
|
| mulq $hi1,$m1,$lo1
| umulh $hi1,$m1,$hi1
|
| addq $lo1,$lo0,$lo1
| cmpult $lo1,$lo0,AT
| mov 2,$j
| addq $hi1,AT,$hi1
|
| mulq $aj,$bi,$alo
| mov sp,$tp
| umulh $aj,$bi,$ahi
|
| mulq $nj,$m1,$nlo
| s8addq $j,$ap,$aj
| umulh $nj,$m1,$nhi
| .align 4
| .Linner:
| .set noreorder
| ldq $tj,8($tp) #L0
| nop #U1
| ldq $aj,0($aj) #L1
| s8addq $j,$np,$nj #U0
|
| ldq $nj,0($nj) #L0
| nop #U1
| addq $alo,$hi0,$lo0 #L1
| lda $tp,8($tp)
|
| mulq $aj,$bi,$alo #U1
| cmpult $lo0,$hi0,AT #L0
| addq $nlo,$hi1,$lo1 #L1
| addl $j,1,$j
|
| mulq $nj,$m1,$nlo #U1
| addq $ahi,AT,$hi0 #L0
| addq $lo0,$tj,$lo0 #L1
| cmpult $lo1,$hi1,v0 #U0
|
| umulh $aj,$bi,$ahi #U1
| cmpult $lo0,$tj,AT #L0
| addq $lo1,$lo0,$lo1 #L1
| addq $nhi,v0,$hi1 #U0
|
| umulh $nj,$m1,$nhi #U1
| s8addq $j,$ap,$aj #L0
| cmpult $lo1,$lo0,v0 #L1
| cmplt $j,$num,$tj #U0 # borrow $tj
|
| addq $hi0,AT,$hi0 #L0
| addq $hi1,v0,$hi1 #U1
| stq $lo1,-8($tp) #L1
| bne $tj,.Linner #U0
| .set reorder
|
| ldq $tj,8($tp)
| addq $alo,$hi0,$lo0
| addq $nlo,$hi1,$lo1
| cmpult $lo0,$hi0,AT
| cmpult $lo1,$hi1,v0
| addq $ahi,AT,$hi0
| addq $nhi,v0,$hi1
|
| addq $lo0,$tj,$lo0
| cmpult $lo0,$tj,AT
| addq $hi0,AT,$hi0
|
| ldq $tj,16($tp)
| addq $lo1,$lo0,$j
| cmpult $j,$lo0,v0
| addq $hi1,v0,$hi1
|
| addq $hi1,$hi0,$lo1
| stq $j,0($tp)
| cmpult $lo1,$hi0,$hi1
| addq $lo1,$tj,$lo1
| cmpult $lo1,$tj,AT
| addl $i,1,$i
| addq $hi1,AT,$hi1
| stq $lo1,8($tp)
| cmplt $i,$num,$tj # borrow $tj
| stq $hi1,16($tp)
| bne $tj,.Louter
|
| s8addq $num,sp,$tj # &tp[num]
| mov $rp,$bp # put rp aside
| mov sp,$tp
| mov sp,$ap
| mov 0,$hi0 # clear borrow bit
|
| .align 4
| .Lsub: ldq $lo0,0($tp)
| ldq $lo1,0($np)
| lda $tp,8($tp)
| lda $np,8($np)
| subq $lo0,$lo1,$lo1 # tp[i]-np[i]
| cmpult $lo0,$lo1,AT
| subq $lo1,$hi0,$lo0
| cmpult $lo1,$lo0,$hi0
| or $hi0,AT,$hi0
| stq $lo0,0($rp)
| cmpult $tp,$tj,v0
| lda $rp,8($rp)
| bne v0,.Lsub
|
| subq $hi1,$hi0,$hi0 # handle upmost overflow bit
| mov sp,$tp
| mov $bp,$rp # restore rp
|
| .align 4
| .Lcopy: ldq $aj,0($tp) # conditional copy
| ldq $nj,0($rp)
| lda $tp,8($tp)
| lda $rp,8($rp)
| cmoveq $hi0,$nj,$aj
| stq zero,-8($tp) # zap tp
| cmpult $tp,$tj,AT
| stq $aj,-8($rp)
| bne AT,.Lcopy
| mov 1,v0
|
| .Lexit:
| .set noreorder
| mov fp,sp
| /*ldq ra,0(sp)*/
| ldq s3,8(sp)
| ldq s4,16(sp)
| ldq s5,24(sp)
| ldq fp,32(sp)
| lda sp,48(sp)
| ret (ra)
| .end bn_mul_mont
| .ascii "Montgomery Multiplication for Alpha, CRYPTOGAMS by <appro\@openssl.org>"
| .align 2
| ___
|
| print $code;
| close STDOUT or die "error closing STDOUT: $!";
|
|
