3 # ====================================================================
4 # Written by Andy Polyakov <appro@fy.chalmers.se> for the OpenSSL
5 # project. The module is, however, dual licensed under OpenSSL and
6 # CRYPTOGAMS licenses depending on where you obtain it. For further
7 # details see http://www.openssl.org/~appro/cryptogams/.
8 # ====================================================================
12 # Montgomery multiplication for ARMv4.
14 # Performance improvement naturally varies among CPU implementations
15 # and compilers. The code was observed to provide +65-35% improvement
16 # [depending on key length, less for longer keys] on ARM920T, and
17 # +115-80% on Intel IXP425. This is compared to pre-bn_mul_mont code
18 # base and compiler generated code with in-lined umull and even umlal
19 # instructions. The latter means that this code didn't really have an
20 # "advantage" of utilizing some "secret" instruction.
22 # The code is interoperable with Thumb ISA and is rather compact, less
23 # than 1/2KB. Windows CE port would be trivial, as it's exclusively
24 # about decorations, ABI and instruction syntax are identical.
26 $num="r0"; # starts as num argument, but holds &tp[num-1]
28 $bp="r2"; $bi="r2"; $rp="r2";
35 ########### # r9 is reserved by ELF as platform specific, e.g. TLS pointer
36 $alo="r10"; # sl, gcc uses it to keep @GOT
39 ########### # r13 is stack pointer
41 ########### # r15 is program counter
43 #### argument block layout relative to &tp[num-1], a.k.a. $num
45 # ap permanently resides in r1
47 # np permanently resides in r3
49 $_num="$num,#15*4"; $_bpend=$_num;
55 .type bn_mul_mont,%function
59 stmdb sp!,{r0,r2} @ sp points at argument block
60 ldr $num,[sp,#3*4] @ load num
66 stmdb sp!,{r4-r12,lr} @ save 10 registers
68 mov $num,$num,lsl#2 @ rescale $num for byte count
69 sub sp,sp,$num @ alloca(4*num)
70 sub sp,sp,#4 @ +extra dword
71 sub $num,$num,#4 @ "num=num-1"
72 add $tp,$bp,$num @ &bp[num-1]
74 add $num,sp,$num @ $num to point at &tp[num-1]
77 ldr $aj,[$ap],#4 @ ap[0],ap++
78 ldr $nj,[$np],#4 @ np[0],np++
80 str $tp,[$_bpend] @ save &bp[num]
82 umull $alo,$ahi,$aj,$bi @ ap[0]*bp[0]
83 str $n0,[$_n0] @ save n0 value
84 mul $n0,$alo,$n0 @ "tp[0]"*n0
86 umlal $alo,$nlo,$nj,$n0 @ np[0]*n0+"t[0]"
90 ldr $aj,[$ap],#4 @ ap[j],ap++
93 umlal $alo,$ahi,$aj,$bi @ ap[j]*bp[0]
94 ldr $nj,[$np],#4 @ np[j],np++
96 umlal $nlo,$nhi,$nj,$n0 @ np[j]*n0
98 str $nlo,[$tp],#4 @ tp[j-1]=,tp++
106 ldr $tp,[$_bp] @ restore bp
107 str $nlo,[$num] @ tp[num-1]=
108 ldr $n0,[$_n0] @ restore n0
109 str $nhi,[$num,#4] @ tp[num]=
112 sub $tj,$num,sp @ "original" $num-1 value
113 sub $ap,$ap,$tj @ "rewind" ap to &ap[1]
114 sub $np,$np,$tj @ "rewind" np to &np[1]
115 ldr $bi,[$tp,#4]! @ *(++bp)
116 ldr $aj,[$ap,#-4] @ ap[0]
117 ldr $nj,[$np,#-4] @ np[0]
118 ldr $alo,[sp] @ tp[0]
119 ldr $tj,[sp,#4] @ tp[1]
122 umlal $alo,$ahi,$aj,$bi @ ap[0]*bp[i]+tp[0]
123 str $tp,[$_bp] @ save bp
126 umlal $alo,$nlo,$nj,$n0 @ np[0]*n0+"tp[0]"
130 ldr $aj,[$ap],#4 @ ap[j],ap++
131 adds $alo,$ahi,$tj @ +=tp[j]
133 umlal $alo,$ahi,$aj,$bi @ ap[j]*bp[i]
134 ldr $nj,[$np],#4 @ np[j],np++
136 umlal $nlo,$nhi,$nj,$n0 @ np[j]*n0
137 ldr $tj,[$tp,#8] @ tp[j+1]
140 str $nlo,[$tp],#4 @ tp[j-1]=,tp++
150 ldr $tp,[$_bp] @ restore bp
151 ldr $tj,[$_bpend] @ restore &bp[num]
152 str $nlo,[$num] @ tp[num-1]=
153 ldr $n0,[$_n0] @ restore n0
154 str $nhi,[$num,#4] @ tp[num]=
159 ldr $rp,[$_rp] @ pull rp
160 add $num,$num,#4 @ $num to point at &tp[num]
161 sub $aj,$num,sp @ "original" num value
162 mov $tp,sp @ "rewind" $tp
163 mov $ap,$tp @ "borrow" $ap
164 sub $np,$np,$aj @ "rewind" $np to &np[0]
166 subs $tj,$tj,$tj @ "clear" carry flag
167 .Lsub: ldr $tj,[$tp],#4
169 sbcs $tj,$tj,$nj @ tp[j]-np[j]
170 str $tj,[$rp],#4 @ rp[j]=
171 teq $tp,$num @ preserve carry
173 sbcs $nhi,$nhi,#0 @ upmost carry
174 mov $tp,sp @ "rewind" $tp
175 sub $rp,$rp,$aj @ "rewind" $rp
179 orr $ap,$ap,$np @ ap=borrow?tp:rp
181 .Lcopy: ldr $tj,[$ap],#4 @ copy or in-place refresh
182 str sp,[$tp],#4 @ zap tp
187 add sp,$num,#4 @ skip over tp[num+1]
188 ldmia sp!,{r4-r12,lr} @ restore registers
189 add sp,sp,#2*4 @ skip over {r0,r2}
192 moveq pc,lr @ be binary compatible with V4, yet
193 bx lr @ interoperable with Thumb ISA:-)
194 .size bn_mul_mont,.-bn_mul_mont
195 .asciz "Montgomery multiplication for ARMv4, CRYPTOGAMS by <appro\@openssl.org>"
198 $code =~ s/\bbx\s+lr\b/.word\t0xe12fff1e/gm; # make it possible to compile with -march=armv4