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| 1 #!/usr/bin/env perl |
| 2 |
| 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 # ==================================================================== |
| 9 |
| 10 # January 2007. |
| 11 |
| 12 # Montgomery multiplication for ARMv4. |
| 13 # |
| 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. |
| 21 # |
| 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. |
| 25 |
| 26 $num="r0"; # starts as num argument, but holds &tp[num-1] |
| 27 $ap="r1"; |
| 28 $bp="r2"; $bi="r2"; $rp="r2"; |
| 29 $np="r3"; |
| 30 $tp="r4"; |
| 31 $aj="r5"; |
| 32 $nj="r6"; |
| 33 $tj="r7"; |
| 34 $n0="r8"; |
| 35 ########### # r9 is reserved by ELF as platform specific, e.g. TLS pointer |
| 36 $alo="r10"; # sl, gcc uses it to keep @GOT |
| 37 $ahi="r11"; # fp |
| 38 $nlo="r12"; # ip |
| 39 ########### # r13 is stack pointer |
| 40 $nhi="r14"; # lr |
| 41 ########### # r15 is program counter |
| 42 |
| 43 #### argument block layout relative to &tp[num-1], a.k.a. $num |
| 44 $_rp="$num,#12*4"; |
| 45 # ap permanently resides in r1 |
| 46 $_bp="$num,#13*4"; |
| 47 # np permanently resides in r3 |
| 48 $_n0="$num,#14*4"; |
| 49 $_num="$num,#15*4"; $_bpend=$_num; |
| 50 |
| 51 $code=<<___; |
| 52 .text |
| 53 |
| 54 .global bn_mul_mont |
| 55 .type bn_mul_mont,%function |
| 56 |
| 57 .align 2 |
| 58 bn_mul_mont: |
| 59 stmdb sp!,{r0,r2} @ sp points at argument block |
| 60 ldr $num,[sp,#3*4] @ load num |
| 61 cmp $num,#2 |
| 62 movlt r0,#0 |
| 63 addlt sp,sp,#2*4 |
| 64 blt .Labrt |
| 65 |
| 66 stmdb sp!,{r4-r12,lr} @ save 10 registers |
| 67 |
| 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] |
| 73 |
| 74 add $num,sp,$num @ $num to point at &tp[num-1] |
| 75 ldr $n0,[$_n0] @ &n0 |
| 76 ldr $bi,[$bp] @ bp[0] |
| 77 ldr $aj,[$ap],#4 @ ap[0],ap++ |
| 78 ldr $nj,[$np],#4 @ np[0],np++ |
| 79 ldr $n0,[$n0] @ *n0 |
| 80 str $tp,[$_bpend] @ save &bp[num] |
| 81 |
| 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 |
| 85 mov $nlo,#0 |
| 86 umlal $alo,$nlo,$nj,$n0 @ np[0]*n0+"t[0]" |
| 87 mov $tp,sp |
| 88 |
| 89 .L1st: |
| 90 ldr $aj,[$ap],#4 @ ap[j],ap++ |
| 91 mov $alo,$ahi |
| 92 mov $ahi,#0 |
| 93 umlal $alo,$ahi,$aj,$bi @ ap[j]*bp[0] |
| 94 ldr $nj,[$np],#4 @ np[j],np++ |
| 95 mov $nhi,#0 |
| 96 umlal $nlo,$nhi,$nj,$n0 @ np[j]*n0 |
| 97 adds $nlo,$nlo,$alo |
| 98 str $nlo,[$tp],#4 @ tp[j-1]=,tp++ |
| 99 adc $nlo,$nhi,#0 |
| 100 cmp $tp,$num |
| 101 bne .L1st |
| 102 |
| 103 adds $nlo,$nlo,$ahi |
| 104 mov $nhi,#0 |
| 105 adc $nhi,$nhi,#0 |
| 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]= |
| 110 |
| 111 .Louter: |
| 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] |
| 120 |
| 121 mov $ahi,#0 |
| 122 umlal $alo,$ahi,$aj,$bi @ ap[0]*bp[i]+tp[0] |
| 123 str $tp,[$_bp] @ save bp |
| 124 mul $n0,$alo,$n0 |
| 125 mov $nlo,#0 |
| 126 umlal $alo,$nlo,$nj,$n0 @ np[0]*n0+"tp[0]" |
| 127 mov $tp,sp |
| 128 |
| 129 .Linner: |
| 130 ldr $aj,[$ap],#4 @ ap[j],ap++ |
| 131 adds $alo,$ahi,$tj @ +=tp[j] |
| 132 mov $ahi,#0 |
| 133 umlal $alo,$ahi,$aj,$bi @ ap[j]*bp[i] |
| 134 ldr $nj,[$np],#4 @ np[j],np++ |
| 135 mov $nhi,#0 |
| 136 umlal $nlo,$nhi,$nj,$n0 @ np[j]*n0 |
| 137 ldr $tj,[$tp,#8] @ tp[j+1] |
| 138 adc $ahi,$ahi,#0 |
| 139 adds $nlo,$nlo,$alo |
| 140 str $nlo,[$tp],#4 @ tp[j-1]=,tp++ |
| 141 adc $nlo,$nhi,#0 |
| 142 cmp $tp,$num |
| 143 bne .Linner |
| 144 |
| 145 adds $nlo,$nlo,$ahi |
| 146 mov $nhi,#0 |
| 147 adc $nhi,$nhi,#0 |
| 148 adds $nlo,$nlo,$tj |
| 149 adc $nhi,$nhi,#0 |
| 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]= |
| 155 |
| 156 cmp $tp,$tj |
| 157 bne .Louter |
| 158 |
| 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] |
| 165 |
| 166 subs $tj,$tj,$tj @ "clear" carry flag |
| 167 .Lsub: ldr $tj,[$tp],#4 |
| 168 ldr $nj,[$np],#4 |
| 169 sbcs $tj,$tj,$nj @ tp[j]-np[j] |
| 170 str $tj,[$rp],#4 @ rp[j]= |
| 171 teq $tp,$num @ preserve carry |
| 172 bne .Lsub |
| 173 sbcs $nhi,$nhi,#0 @ upmost carry |
| 174 mov $tp,sp @ "rewind" $tp |
| 175 sub $rp,$rp,$aj @ "rewind" $rp |
| 176 |
| 177 and $ap,$tp,$nhi |
| 178 bic $np,$rp,$nhi |
| 179 orr $ap,$ap,$np @ ap=borrow?tp:rp |
| 180 |
| 181 .Lcopy: ldr $tj,[$ap],#4 @ copy or in-place refresh |
| 182 str sp,[$tp],#4 @ zap tp |
| 183 str $tj,[$rp],#4 |
| 184 cmp $tp,$num |
| 185 bne .Lcopy |
| 186 |
| 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} |
| 190 mov r0,#1 |
| 191 .Labrt: tst lr,#1 |
| 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>
" |
| 196 .align 2 |
| 197 ___ |
| 198 |
| 199 $code =~ s/\bbx\s+lr\b/.word\t0xe12fff1e/gm; # make it possible to compile wi
th -march=armv4 |
| 200 print $code; |
| 201 close STDOUT; |
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