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
|
#!/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/.
# ====================================================================
# March 2015
#
# "Teaser" Montgomery multiplication module for ARMv8. Needs more
# work. While it does improve RSA sign performance by 20-30% (less for
# longer keys) on most processors, for some reason RSA2048 is not
# faster and RSA4096 goes 15-20% slower on Cortex-A57. Multiplication
# instruction issue rate is limited on processor in question, meaning
# that dedicated squaring procedure is a must. Well, actually all
# contemporary AArch64 processors seem to have limited multiplication
# issue rate, i.e. they can't issue multiplication every cycle, which
# explains moderate improvement coefficients in comparison to
# compiler-generated code. Recall that compiler is instructed to use
# umulh and therefore uses same amount of multiplication instructions
# to do the job. Assembly's edge is to minimize number of "collateral"
# instructions and of course instruction scheduling.
$flavour = shift;
$output = shift;
$0 =~ m/(.*[\/\\])[^\/\\]+$/; $dir=$1;
( $xlate="${dir}arm-xlate.pl" and -f $xlate ) or
( $xlate="${dir}../../perlasm/arm-xlate.pl" and -f $xlate) or
die "can't locate arm-xlate.pl";
open OUT,"| \"$^X\" $xlate $flavour $output";
*STDOUT=*OUT;
($lo0,$hi0,$aj,$m0,$alo,$ahi,
$lo1,$hi1,$nj,$m1,$nlo,$nhi,
$ovf, $i,$j,$tp,$tj) = map("x$_",6..17,19..24);
# int bn_mul_mont(
$rp="x0"; # BN_ULONG *rp,
$ap="x1"; # const BN_ULONG *ap,
$bp="x2"; # const BN_ULONG *bp,
$np="x3"; # const BN_ULONG *np,
$n0="x4"; # const BN_ULONG *n0,
$num="x5"; # int num);
$code.=<<___;
.text
.globl bn_mul_mont
.type bn_mul_mont,%function
.align 5
bn_mul_mont:
stp x29,x30,[sp,#-64]!
add x29,sp,#0
stp x19,x20,[sp,#16]
stp x21,x22,[sp,#32]
stp x23,x24,[sp,#48]
ldr $m0,[$bp],#8 // bp[0]
sub $tp,sp,$num,lsl#3
ldp $hi0,$aj,[$ap],#16 // ap[0..1]
lsl $num,$num,#3
ldr $n0,[$n0] // *n0
and $tp,$tp,#-16 // ABI says so
ldp $hi1,$nj,[$np],#16 // np[0..1]
mul $lo0,$hi0,$m0 // ap[0]*bp[0]
sub $j,$num,#16 // j=num-2
umulh $hi0,$hi0,$m0
mul $alo,$aj,$m0 // ap[1]*bp[0]
umulh $ahi,$aj,$m0
mul $m1,$lo0,$n0 // "tp[0]"*n0
mov sp,$tp // alloca
mul $lo1,$hi1,$m1 // np[0]*m1
umulh $hi1,$hi1,$m1
mul $nlo,$nj,$m1 // np[1]*m1
adds $lo1,$lo1,$lo0 // discarded
umulh $nhi,$nj,$m1
adc $hi1,$hi1,xzr
cbz $j,.L1st_skip
.L1st:
ldr $aj,[$ap],#8
adds $lo0,$alo,$hi0
sub $j,$j,#8 // j--
adc $hi0,$ahi,xzr
ldr $nj,[$np],#8
adds $lo1,$nlo,$hi1
mul $alo,$aj,$m0 // ap[j]*bp[0]
adc $hi1,$nhi,xzr
umulh $ahi,$aj,$m0
adds $lo1,$lo1,$lo0
mul $nlo,$nj,$m1 // np[j]*m1
adc $hi1,$hi1,xzr
umulh $nhi,$nj,$m1
str $lo1,[$tp],#8 // tp[j-1]
cbnz $j,.L1st
.L1st_skip:
adds $lo0,$alo,$hi0
sub $ap,$ap,$num // rewind $ap
adc $hi0,$ahi,xzr
adds $lo1,$nlo,$hi1
sub $np,$np,$num // rewind $np
adc $hi1,$nhi,xzr
adds $lo1,$lo1,$lo0
sub $i,$num,#8 // i=num-1
adcs $hi1,$hi1,$hi0
adc $ovf,xzr,xzr // upmost overflow bit
stp $lo1,$hi1,[$tp]
.Louter:
ldr $m0,[$bp],#8 // bp[i]
ldp $hi0,$aj,[$ap],#16
ldr $tj,[sp] // tp[0]
add $tp,sp,#8
mul $lo0,$hi0,$m0 // ap[0]*bp[i]
sub $j,$num,#16 // j=num-2
umulh $hi0,$hi0,$m0
ldp $hi1,$nj,[$np],#16
mul $alo,$aj,$m0 // ap[1]*bp[i]
adds $lo0,$lo0,$tj
umulh $ahi,$aj,$m0
adc $hi0,$hi0,xzr
mul $m1,$lo0,$n0
sub $i,$i,#8 // i--
mul $lo1,$hi1,$m1 // np[0]*m1
umulh $hi1,$hi1,$m1
mul $nlo,$nj,$m1 // np[1]*m1
adds $lo1,$lo1,$lo0
umulh $nhi,$nj,$m1
cbz $j,.Linner_skip
.Linner:
ldr $aj,[$ap],#8
adc $hi1,$hi1,xzr
ldr $tj,[$tp],#8 // tp[j]
adds $lo0,$alo,$hi0
sub $j,$j,#8 // j--
adc $hi0,$ahi,xzr
adds $lo1,$nlo,$hi1
ldr $nj,[$np],#8
adc $hi1,$nhi,xzr
mul $alo,$aj,$m0 // ap[j]*bp[i]
adds $lo0,$lo0,$tj
umulh $ahi,$aj,$m0
adc $hi0,$hi0,xzr
mul $nlo,$nj,$m1 // np[j]*m1
adds $lo1,$lo1,$lo0
umulh $nhi,$nj,$m1
str $lo1,[$tp,#-16] // tp[j-1]
cbnz $j,.Linner
.Linner_skip:
ldr $tj,[$tp],#8 // tp[j]
adc $hi1,$hi1,xzr
adds $lo0,$alo,$hi0
sub $ap,$ap,$num // rewind $ap
adc $hi0,$ahi,xzr
adds $lo1,$nlo,$hi1
sub $np,$np,$num // rewind $np
adc $hi1,$nhi,$ovf
adds $lo0,$lo0,$tj
adc $hi0,$hi0,xzr
adds $lo1,$lo1,$lo0
adcs $hi1,$hi1,$hi0
adc $ovf,xzr,xzr // upmost overflow bit
stp $lo1,$hi1,[$tp,#-16]
cbnz $i,.Louter
// Final step. We see if result is larger than modulus, and
// if it is, subtract the modulus. But comparison implies
// subtraction. So we subtract modulus, see if it borrowed,
// and conditionally copy original value.
ldr $tj,[sp] // tp[0]
add $tp,sp,#8
ldr $nj,[$np],#8 // np[0]
subs $j,$num,#8 // j=num-1 and clear borrow
mov $ap,$rp
.Lsub:
sbcs $aj,$tj,$nj // tp[j]-np[j]
ldr $tj,[$tp],#8
sub $j,$j,#8 // j--
ldr $nj,[$np],#8
str $aj,[$ap],#8 // rp[j]=tp[j]-np[j]
cbnz $j,.Lsub
sbcs $aj,$tj,$nj
sbcs $ovf,$ovf,xzr // did it borrow?
str $aj,[$ap],#8 // rp[num-1]
ldr $tj,[sp] // tp[0]
add $tp,sp,#8
ldr $aj,[$rp],#8 // rp[0]
sub $num,$num,#8 // num--
nop
.Lcond_copy:
sub $num,$num,#8 // num--
csel $nj,$aj,$tj,cs // did it borrow?
ldr $tj,[$tp],#8
ldr $aj,[$rp],#8
str xzr,[$tp,#-16] // wipe tp
str $nj,[$rp,#-16]
cbnz $num,.Lcond_copy
csel $nj,$aj,$tj,cs
str xzr,[$tp,#-8] // wipe tp
str $nj,[$rp,#-8]
ldp x19,x20,[x29,#16]
mov sp,x29
ldp x21,x22,[x29,#32]
ldp x23,x24,[x29,#48]
ldr x29,[sp],#64
ret
.size bn_mul_mont,.-bn_mul_mont
.asciz "Montgomery Multiplication for ARMv8, CRYPTOGAMS by <appro\@openssl.org>"
.align 4
___
print $code;
close STDOUT;
|